VIBRONIC	COHERENCE	IN	KETOCAROTENOIDS	AND	SEMICONDUCTOR	QUANTUM	DOTS	

By	

Nila	Mohan	Thazhe	Mecheri	

A	DISSERTATION	

Submitted	to	
Michigan	State	University	
in	partial	fulfillment	of	the	requirements	
for	the	degree	of	

Chemistry	–	Doctor	of	Philosophy	

2023	

	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
ABSTRACT	

Electronic-vibrational	coupling	drives	the	relaxation	of	optically	prepared	excitations	in	

both	carotenoids	and	semiconductor	quantum	dots	(QDs).	As	a	result	of	this	electronic-

vibrational	(vibronic)	coupling,	coherent	wavepacket	motions	are	observed	during	the	

excitation	relaxation	processes.	The	first	part	of	the	dissertation	describes	the	relaxation	of	

the	optically	prepared	bright	S2	state	to	dark	S1	state	via	bridging	intermediate,	Sx.	The	

spectroscopic	signature	and	the	vibrational	coherences	of	the	intermediate	state	Sx	

involved	in	the	nonradiative	decay	were	characterized	using	broadband	multidimensional	

spectroscopic	techniques.	Analysis	of	vibrational	coherences	shows	that	Sx	undergoes	

displacements	along	out-of-plane	coordinates	as	it	passes	to	the	S1	state.	The	second	part	of	

the	dissertation	discusses	the	nonradiative	relaxation	in	oleate-capped	QDs.	This	process	

involves	excited-state	coherent	wavepacket	motions	through	a	cascade	of	conical	

intersections	between	exciton	potential-energy	surfaces.	Excited	state	wavepacket	motions	

are	observed	at	frequencies	matching	the	vibrational	modes	of	the	organic	ligands.	These	

observations	indicate	that	the	ligand	vibrations	are	quantum	coherently	mixed	with	the	

core	electronic	states	of	the	QDs.	The	third	part	of	the	dissertation	presents	the	role	

vibronic	coupling	in	photoinduced	charge	transfer	from	the	QD	core	to	a	surface	ligand	

electron	acceptor	molecule,	methyl	viologen	dication	(MV2+).	The	observation	of	coherent	

wavepacket	motions	is	consistent	with	presence	of	a	charge	transfer	intermediate	with	a	

mixed	QD-MV	character,	and	this	intermediate	initiate	photoinduced	charge	transfer	from	

the	core	of	the	QD	to	the	surface	acceptor	molecule.	These	results	raise	new	opportunities	

for	the	engineering	light-harvesting	properties	of	materials	through	the	control	of	

electronic-vibrational	coupling	and	quantum	coherences.			

	
	
	
Copyright	by	
NILA	MOHAN	THAZHE	MECHERI	
2023

	
To	my	parents	and	Louis	

iv	

	
	
ACKNOWLEDGEMENTS	

I	would	like	to	thank	my	advisor,	Professor	Warren	F.	Beck,	for	the	opportunity	to	learn	

and	grow	under	his	guidance.	You	guided	and	supported	my	journey,	ensuring	my	success	

as	a	researcher.	I	have	enjoyed	every	opportunity	to	discuss	new	possibilities	and	new	

science	with	you.	Our	engaging	conversations	have	been	a	source	of	motivation,	

consistently	igniting	my	enthusiasm	to	experiment	with	novel	ideas	after	each	meeting.	

You	have	also	granted	me	intellectual	freedom	to	pursue	new	and	innovative	ideas,	

allowing	me	to	follow	my	interests	and	passion	for	research.	Thank	you.	I	would	like	to	

thank	our	collaborators,	Professor	P.	Gregory	Van	Patten	at	Middle	Tennessee	State	

University	for	providing	us	the	quantum	dot	samples	and	Professor	Benjamin	Levine	at	

Stony	Brook	University	for	the	contributions	on	the	theory	calculations.	

I	would	like	to	thank	Ryan	Tilluck	for	training,	mentoring,	and	helping	me	solve	

problems	in	the	laser	lab	as	well	as	guiding	me	in	getting	started	with	the	quantum	dot	

project.	I	thank	Jessica	Gurchiek	for	mentoring	me	during	the	initial	days	of	my	PhD.	I	

would	like	to	thank	my	cohorts,	Sourav,	and	Justin	for	helping	me	with	the	experiments,	for	

their	friendship	and	support	throughout	my	time	in	the	Beck	lab.	Chase,	thank	you	for	

helping	me	with	the	data	analysis	and	all	the	best	for	your	future	endeavors.	Thank	you	

Kunwei	for	being	a	very	supportive	friend	and	all	the	best	for	your	future.	Despite	our	

limited	time	together	in	the	lab,	Shanu,	thank	you	for	being	understanding	and	supporting	

friend.	I	am	excited	to	see	the	progress	and	success	of	your	research	projects	in	the	future.	I	

am	thankful	to	my	committee	members,	Professors	Benjamin	Levine,	Marcos	Dantus,	and	

Thomas	Hamann	for	asking	insightful	questions	and	providing	me	support	during	my	PhD.	

v	

	
	
I	also	thank	Kevin	Cavey	at	MTSU	for	accommodating	our	requests	and	sending	us	

quantum	dot	samples	to	carry	out	the	femtosecond	experiments.		

I	have	made	some	great	friends	at	my	time	at	the	MSU.	We’ve	cherished	many	fun	

moments,	camping	adventures,	and	good	food	with	each	other	that	reminded	me	of	home.	

Thank	you,	Arnab,	Atanu,	Saro,	Manoj,	Akhil,	Anand	and	Amal.	I	received	a	great	deal	of	

support	from	my	IISER	friends	throughout	this	journey.	I	thank	Vinaya,	Elizabeth,	Aparna,	

Neha,	Abhin,	Ajmal,	Sreya	and	Mirsana	for	their	friendship.	Thank	you,	Manasa,	for	all	love,	

care,	and	support	over	the	past	several	years.	

I	am	incredibly	grateful	to	for	my	loving	and	supportive	family.	Thank	you,	Amma	and	

Pappa,	for	everything	you	have	provided	me	till	today.	Without	your	love	and	support,	I	

would	never	be	able	to	achieve	my	goals.	Thank	you	for	always	believing	in	me.	I	am	

thankful	to	my	brother	for	his	care	and	support	throughout	my	life.	Most	importantly,	I	

thank	my	partner,	Louis	for	his	tremendous	patience,	support,	love,	and	care	during	the	ups	

and	downs	of	this	journey.		

The	work	featured	in	this	dissertation	was	supported	by	the	U.S.	Department	of	Energy,	

Office	of	Basic	Energy	Sciences,	Solar	Photochemistry	Program	under	Award	Number	DE-

SC0021197,	Photosynthetic	Systems	Program	under	Award	Number	DE-	SC0010847	and	

National	Science	Foundation,	Chemistry	of	Life	Processes	under	Award	number	1904655.	

I’d	like	to	thank	the	financial	support	through	Alfred	J.	and	Ruth	Zeits	Endowed	Fellowship	

from	the	College	of	Natural	Science	and	the	Rogowski	Chemistry	Graduate	Fellowship	from	

the	Department	of	Chemistry	at	Michigan	State	University.	

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TABLE	OF	CONTENTS	

LIST	OF	TABLES	.......................................................................................................................................................	ix	

LIST	OF	FIGURES	......................................................................................................................................................	x	

LIST	OF	ABBREVIATIONS	..................................................................................................................................	xix	

Overview	of	the	Dissertation	...............................................................................................................................	1	

Chapter	1:	Introduction	to	Carotenoids	and	Semiconductor	Quantum	Dots	.................................	4	
1.1	Nonradiative	Relaxation	Mechanisms	................................................................................................	4	
1.2	Orange	Carotenoid	Protein:	An	Overview	.........................................................................................	5	
1.3	Photophysics	of	Carotenoids	...................................................................................................................	6	
1.3.1	Nonradiative	Decay	in	Carotenoids	......................................................................................	8	
1.4	Semiconductor	Quantum	Dots	............................................................................................................	11	
1.4.1	Electronic	Structure	and	Surface	of	Colloidal	CdSe	QDs	..........................................	13	
1.4.2	Hot	Carrier	Cooling	in	QDs	....................................................................................................	15	
1.5	Multidimensional	Electronic	Spectroscopy	...................................................................................	18	
1.5.1	Excitation	Pulse	Sequence	in	2DES	...................................................................................	19	
1.5.2	Third-Order	Nonlinear	Optical	Responses	.....................................................................	20	
1.5.3	Quantum	Coherences	in	2DES	.............................................................................................	25	
1.6	Instrumentation	.........................................................................................................................................	30	
1.7	Data	Processing	and	Analysis	..............................................................................................................	35	
REFERENCES	......................................................................................................................................................	37	

Chapter	2:	Broadband	2DES	Detection	of	Vibrational	Coherence	in	the	Sx	State	of	
Ketocarotenoid	Canthaxanthin	........................................................................................................................	51	
2.1	Introduction	................................................................................................................................................	52	
2.2	Experimental	Methods	............................................................................................................................	54	
2.2.1	Samples	..........................................................................................................................................	54	
2.2.2	Linear	Spectroscopy	.................................................................................................................	55	
2.2.3	Two-Dimensional	Electronic	Spectroscopy	...................................................................	55	
2.3	Results	............................................................................................................................................................	57	
2.3.1	Linear	Spectroscopy	.................................................................................................................	57	
2.3.2	2DES	Spectra	...............................................................................................................................	59	
2.3.3	Global	and	Target	Modeling	of	the	2DES	spectra	........................................................	61	
2.3.4	Vibrational	Coherence.............................................................................................................	66	
2.3.5	Anisotropy	....................................................................................................................................	73	
2.4	Discussion	.....................................................................................................................................................	77	
REFERENCES	......................................................................................................................................................	83	
APPENDIX	............................................................................................................................................................	88	

Chapter	3:	Electronic-Vibrational	Coherences	in	Oleate-capped	CdSe	Quantum	Dots	...........	96	
3.1	Introduction	................................................................................................................................................	97	

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3.2	Experimental	Methods	............................................................................................................................	99	
3.2.1	CdSe	Quantum	Dot	Synthesis	and	Characterization	..................................................	99	
3.2.2	Linear	Spectroscopy	and	Photoluminescence	............................................................	102	
3.2.3	Two-Dimensional	Electronic	Spectroscopy	.................................................................	102	
3.3	Results	..........................................................................................................................................................	104	
3.3.1	Particle	Size	and	Surface	Characterization	..................................................................	104	
3.3.2	Linear	Spectroscopy	...............................................................................................................	105	
3.3.3	2DES	Spectra	.............................................................................................................................	107	
3.3.4	Global	Modeling	and	Coherence	Analysis	.....................................................................	109	
3.4	Discussion	...................................................................................................................................................	120	
REFERENCES	....................................................................................................................................................	124	
APPENDIX	..........................................................................................................................................................	128	

Chapter	4:	Vibronic	Coherences	Initiate	Photoinduced	Charge	Transfer	from	CdSe	Quantum	
Dots	to	Methyl	Viologen	...................................................................................................................................	130	
4.1	Introduction	..............................................................................................................................................	131	
4.2	Experimental	Methods	..........................................................................................................................	135	
4.2.1	CdSe	Quantum	Dot	Synthesis	and	Characterization	................................................	135	
4.2.2	Linear	Spectroscopy	and	Photoluminescence	............................................................	136	
4.2.3	Two-Dimensional	Electronic	Spectroscopy	.................................................................	137	
4.3	Results	..........................................................................................................................................................	138	
4.3.1	Linear	Absorption	and	Photoluminescence	................................................................	138	
4.3.2	Two-Dimensional	Electronic	Spectroscopy	.................................................................	140	
4.3.3	Global	Analysis	and	Coherence	Analysis	.......................................................................	142	
4.4	Discussion	...................................................................................................................................................	151	
REFERENCES	....................................................................................................................................................	155	
APPENDIX	..........................................................................................................................................................	159	

viii	

	
	
	
	
	
	
LIST	OF	TABLES	

Table	3.1.	Parameters	(frequency,	amplitude,	phase,	and	damping	time)	for	LPSVD	
analysis	of	X3	excitation	at	the	indicated	coordinates	in	2D	spectra.	These	coordinates	are	
indicated	in	the	2D	spectra	(Figure	3.6).	...................................................................................................	115	

Table	3.2.	Parameters	for	LPSVD	analysis	for	X2	excitation	at	the	indicated	coordinates	in	
2D	spectra.	These	coordinates	are	indicated	in	the	excitation	specific	coherence	map	
(Figure	3.11)	..........................................................................................................................................................	119	

Table	4.1.	Parameters	(frequency,	amplitude,	phase,	and	damping	time)	for	LPSVD	
analysis	of	X3	excitation	for	QDs	at	the	indicated	coordinates	in	2D	spectra.	..........................	148	

Table	4.2.	Parameters	(frequency,	amplitude,	phase,	and	damping	time)	for	LPSVD	
analysis	of	X3	excitation	for	QD-MV2+	at	the	indicated	coordinates	in	2D	spectra.	................	148	

ix	

	
	
	
	
	
	
LIST	OF	FIGURES	

Figure	1.1.	Structure	of	different	carotenoids.	...........................................................................................	7	

Figure	1.2.	Schematic	representations	for	the	potential	energy	surfaces	for	the	singlet	
states	of	a	carotenoid,	plotted	here	as	a	function	of	a	reaction	coordinate	composed	of	
sequential	displacements	from	the	Franck–Condon	geometry	of	the	optically	prepared	S2	
state	with	respect	to	the	C–C	and	C=C	stretching	and	out-of-plane	(φ)	coordinates	of	the	
isoprenoid	backbone.	Planar	and	distorted	conformations	are	divided	by	a	low	barrier	at	
the	structure	marked	‡	on	the	reaction	coordinate	axis.	The	mixed	S2,	S1,	and	S0	surfaces	
are	proposed	to	converge	near	the	geometry	of	the	S2	minimum	owing	to	a	conical	
intersection	(CI)	of	the	diabatic	surfaces.	Arrows	indicate	vertical	optical	transitions	from	
planar	and	distorted	conformations	to	the	S2	state.	Adapted	from	Gurchiek	et	al.29	..............	10	

Figure	1.3.	Illustration	of	the	quantum	confinement	compared	to	the	bulk	semiconductor.	
When	the	spatial	extent	of	wavefunction	is	smaller	than	the	Bohr	exciton	radius	(ab),	size-
dependent	optical	properties	are	observed.	Adapted	from	ref	47.47	..............................................	12	

Figure	1.4.	Illustration	of	different	surface	capping	ligands	and	their	possible	coupling	of	
vibrational	modes	with	QD	core	electronic	states.82	(a)	Ligands,	alkylamine	(I),	
trioctylphosphineoxide	(TOPO)(II),	and	alkylcarboxyl	group	(III),	where	R	represents	the	
alkyl	chain,	interacting	with	the	surface	of	CdSe	QDs.	(b)	Possible	coupling	of	energy	levels	
of	ligand	(solid	line	and	dashed	line	representing	bonding	orbital	and	antibonding	orbital,	
respectively)	to	core	electronic	states	and	(c)	exciton	manifold	for	excitons	(electron	hole	
pair)	X1	to	X4,	as	labelled.	(Reproduced	from	Ryan	Tilluck’s	dissertation.83)	...........................	14	

Figure	1.5.	Broadband	pulse	sequences	in	the	2DES	experiment.	The	red	Gaussian	pulse	
envelopes	depict	the	excitation	pulses	in	the	pulse	sequence.	The	blue	signals	represent	the	
coherences	emitted	from	the	sample	after	the	interaction	of	the	pulses.	The	first	pulse	
creates	coherence	that	evolves	over	time,	followed	by	the	interaction	of	the	second	pulse	to	
create	a	population.	The	third	pulse	interacts	with	the	system	to	create	another	coherence	
and	an	evolving	electric	field	(blue)	is	emitted	from	the	sample.	(Reproduced	from	Ryan	
Tilluck’s	dissertation,83	adapted	from	work	by	the	Jonas	group.121,133)	........................................	20	

Figure	1.6.	WMEL	diagram	(top)	and	Feynman	diagram	(bottom)	of	ground-state	
bleaching	signal.	The	figures	on	the	right	correspond	to	the	non-rephasing	pathway,	
whereas	those	on	the	left	correspond	to	the	rephasing	pathway.	In	the	WMEL	diagram,	
time	evolves	towards	the	right,	and	the	field	matter	interactions	are	numbered	as	1,	2,	and	
3	with	marked	time	delays.	The	solid	arrows	represent	the	field-matter	interaction	on	the	
ket	side	of	the	Feynman	diagram,	whereas	the	dashed	arrows	represent	the	interaction	on	
the	bra	side.	The	dotted	line	in	the	WMEL	and	dashed	arrow	in	the	Feynman	diagram	
represent	the	emitted	signal	after	a	series	of	field-matter	interactions.	The	vertical	line	in	
the	Feynman	diagram	represents	the	evolution	of	the	time.	.............................................................	22	

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Figure	1.7.	WMEL	diagram	(top)	and	Feynman	diagram	(bottom)	of	stimulated	emission	
signals.	The	figures	on	the	right	correspond	to	the	non-rephasing	pathway,	whereas	those	
on	the	left	correspond	to	the	rephasing	pathway.	..................................................................................	24	

Figure	1.8.	WMEL	diagram	(top)	and	Feynman	diagram	(bottom)	of	the	excited-state	
absorption	signal.	The	figures	on	the	right	correspond	to	the	non-rephasing	pathway,	
whereas	those	on	the	left	correspond	to	the	rephasing	pathway.	...................................................	25	

Figure	1.9.	Example	WMEL	diagram	for	electronic	coherences	between	excited	electronic	
states,	1	and	2.	The	figures	on	the	right	correspond	to	the	non-rephasing	pathway,	whereas	
those	on	the	left	correspond	to	the	rephasing	pathway.	......................................................................	27	

Figure	1.10.	Example	of	WMEL	diagram	for	vibrational	coherences	between	ground	and	
excited	electronic	state,	1.	Vibrational	states	are	indicated	by	v0	and	v1.	The	figures	on	the	
right	correspond	to	the	non-rephasing	pathway,	whereas	those	on	the	left	correspond	to	
the	rephasing	pathway.	.......................................................................................................................................	28	

Figure	1.11.	Example	WMEL	diagram	for	ground-state	vibrational	coherences	(stimulated	
Raman)	between	ground	and	excited	electronic	state.	Vibrational	states	are	indicated	by	v0	
and	v1.	The	figures	on	the	right	correspond	to	the	non-rephasing	pathway,	whereas	those	
on	the	left	correspond	to	the	rephasing	pathway.	..................................................................................	29	

Figure	1.12.	An	example	broadband	laser	spectrum	in	the	range	of	510-710	nm	used	in	
2DES	experiments.	The	full	width	at	half	maximum	(FWHM)	is	120	nm	and	the	transform	
limited	pulse	duration	was	6.8	fs.	...................................................................................................................	31	

Figure	1.13.	Interferometric	autocorrelation	of	the	pump	pulses,	determined	as	the	
integral	of	the	SHG-FROG	spectrogram156	(left	panel).	SHG-FROG158	spectrogram	for	the	
pump	pulses,	as	measured	with	scanned	pulse	pairs	prepared	by	the	pump	beam's	pulse	
shaper	in	the	2DES	spectrometer.	..................................................................................................................	33	

Figure	1.14.	Instrumentation	set	up	used	in	the	2DES	experiment.	The	Yb	laser	(4W,	100	
kHz,	1040	nm)	is	pumped	to	a	NOPA	to	generate	broadband	visible	pulses	ranging	from	
500-700	nm.	The	adaptive	pulse	shapers	and	the	pairs	of	chirp	mirrors	compress	the	pulse	
to	the	transform	limit.	The	pulse	shaper	on	the	pump	beam	is	manipulated	to	create	a	pulse	
pair	and	vary	the	time	between	the	pump	pulses.	A	time-of-flight	delay	stage	is	used	to	vary	
the	time	delay	between	the	pump	and	the	probe	beams.	The	emitted	signals	are	collected	
using	a	home-built	spectrograph	and	a	fast	CCD.	....................................................................................	34	

Figure	1.15.	Evolution	of	the	amplitude	obtained	after	FFT	of	the	pump-induced	change	in	
probe-transmission	with	respect	to	the	time,	integrated	along	the	detection	axis	for	CdSe	
QDs	with	7	fs	pulses.	The	coherent	oscillations	are	isolated,	mirrored	and	zero-padded	
prior	to	the	FFT	process.	....................................................................................................................................	36	

Figure	2.1.	Structure	of	canthaxanthin.	......................................................................................................	53	

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Figure	2.2.	Linear	absorption	spectrum	of	CAN	in	toluene	solvent	(blue	dotted	curve),	
plotted	with	respect	to	the	wavenumber	ν	as	the	relative	oscillator	strength,	ε(ν)/ν.	The	
14000–17000-cm−1	range	of	the	spectrum	is	also	plotted	with	a	×25	scaling	of	the	ordinate.	
The	laser	intensity	spectrum	from	the	broadband	excitation	pulses	used	in	the	2DES	
experiments	(red	solid	curve)	is	superimposed.	.....................................................................................	58	

Figure	2.3.	Evolution	of	total	amplitude	(𝐾)	2DES	spectra	from	CAN	in	toluene	at	six	
waiting	times	𝑇.	......................................................................................................................................................	60	

Figure	2.4.	2D	global	and	target	model	for	the	main	band	excitation	region	of	the	2DES	𝐾	
spectra	from	CAN	in	toluene.	(a)	Kinetic	scheme	and	time	constants	for	nonradiative	decay	
of	the	S2	state	via	an	intermediate,	Sx,	to	the	S1	state.	(b)	Time	dependence	of	the	
populations	for	the	S2	(blue),	Sx	(green	dotted),	and	S1	(red	dashed)	spectrokinetic	species.	
(c)	2D	evolution-associated	difference	spectra	(EADS)	for	the	three	spectrokinetic	species.	
The	EADS	are	scaled	relative	to	the	maximum	of	the	ESA	signal	in	the	S1	compartment.	....	63	

Figure	2.5.	2D	global	and	target	model	for	the	red	tail	excitation	region	of	the	2DES	𝐾	
spectra	from	CAN	in	toluene.	(a)	Kinetic	scheme	and	time	constants	for	nonradiative	decay	
of	the	S2	state	via	an	intermediate,	Sx,	to	the	S1	state.	(b)	Time	dependence	of	the	
populations	for	the	S2	(blue),	Sx	(green	dotted),	and	S1	(red	dashed)	spectrokinetic	species.	
(c)	2D	evolution-associated	difference	spectra	(EADS)	for	the	three	spectrokinetic	species.	
The	EADS	are	scaled	relative	to	the	maximum	of	the	ESA	signal	in	the	S1	compartment	in	
the	main	band	region	(Figure	2.4).	................................................................................................................	65	

Figure	2.6.	Oscillation	maps	for	the	principal	vibrational	coherences	detected	in	the	2DES	
𝐾	spectra	from	CAN	in	toluene.	.......................................................................................................................	69	

Figure	2.7.	Total	amplitude	𝐾	and	anisotropy	𝑟	transients	with	excitation	at	18200	cm−1	
and	detection	at	16750	cm−1	in	the	Sx	cross	peak	in	the	main	band	excitation	region.	(a)	𝐾	
transient,	with	the	fit	from	the	global	model	(from	Figure	2.4)	superimposed.	(b)	Residual	
(𝐾−global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	𝐾	residual	
over	the	𝑇	=	70-	500	fs	range.	(d)	Anisotropy	𝑟	transient,	with	a	fitted	exponential	(40	fs	
time	constant).	(e)	Residual	(𝑟−exponential	fit)	transient.	(f)	Fourier	transform	amplitude	
spectrum	of	the	𝑟	residual	over	the	𝑇	=	100-500	fs	range.	Error	bars	show	the	95%	
confidence	intervals	for	the	𝐾	and	𝑟	amplitudes.	....................................................................................	71	

Figure	2.8.	Total	amplitude	𝐾	and	anisotropy	𝑟	transients	with	excitation	at	17200	cm−1	
and	detection	at	16750	cm−1	in	the	Sx	cross	peak	in	the	red	tail	excitation	region.	(a)	𝐾	
transient,	with	the	fit	from	the	global	model	(Figure	2.5)	superimposed.	(b)	Residual	(𝐾-
global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	𝐾	residual	over	
the	𝑇	=	70-500	fs	range.	(d)	Anisotropy	𝑟	transient,	with	a	fitted	exponential	(92	fs	time	
constant).	(e)	Residual	(𝑟−exponential	fit)	transient.	(f)	Fourier	transform	amplitude	
spectrum	of	the	𝑟	residual	over	the	𝑇	=	100-500	fs	range.	Error	bars	show	the	95%	
confidence	intervals	for	the	𝐾	and	𝑟	amplitudes.	....................................................................................	72	

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Figure	2.9.	Schematic	representations	for	the	potential	energy	surfaces	for	the	singlet	
states	of	a	carotenoid,	plotted	here	as	a	function	of	a	reaction	coordinate	composed	of	
sequential	displacements	from	the	Franck–Condon	geometry	of	the	optically	prepared	S2	
state	with	respect	to	the	C–C	and	C=C	stretching	and	out-of-plane	(ϕ)	coordinates	of	the	
isoprenoid	backbone.	Planar	and	distorted	conformations	are	divided	by	a	low	barrier	at	
the	structure	marked	‡	on	the	reaction	coordinate	axis.	The	dashed	curve	indicates	that	the	
S2	surface	will	be	stabilized	by	displacements	with	respect	to	the	out-of-plane	coordinates	
when	the	isoprenoid	backbone	is	carbonyl	substituted,	as	in	CAN.	The	mixed	S2,	S1,	and	S0	
surfaces	are	proposed	to	converge	near	the	geometry	of	the	S2	minimum	owing	to	a	conical	
intersection	(CI)	of	the	diabatic	surfaces.	Arrows	indicate	vertical	optical	transitions	from	
planar	and	distorted	conformations	to	the	S2	state.	Adapted	from	Ref.	6.	...................................	80	

Figure	A2.1.	Laser	intensity	and	residual	phase	spectrum	for	the	laser	pulses	in	the	pump	
beam	of	the	2DES	spectrometer,	with	the	latter	determined	at	the	sample’s	position	by	
MIIPS	scans23	after	compression.	...................................................................................................................	88	

Figure	A2.2.	Laser	intensity	and	residual	phase	spectrum	for	the	laser	pulses	in	the	probe	
beam	of	the	2DES	spectrometer,	with	the	latter	determined	at	the	sample’s	position	by	
MIIPS	scans	after	compression.	.......................................................................................................................	89	

Figure	A2.3.	Interferometric	autocorrelation	and	SHG-FROG24	spectrograms	for	the	pump	
pulses,	as	measured	with	scanned	pulse	pairs	prepared	by	the	pump	beam’s	pulse	
shaper.	........................................................................................................................................................................	89	

Figure	A2.4.	1D	global	and	target	model	for	the	2DES	spectra	from	CAN	in	toluene,	with	
excitation	at	18500	cm−1	(540	nm).	(a)	Kinetic	scheme	for	nonradiative	decay	of	the	
resonant	S2	state	via	the	intermediate	Sx	to	the	S1	state.	(b)	Time	dependence	of	the	
populations	for	the	S2,	Sx,	and	S1	spectrokinetic	species.	(c)	Evolution-associated	difference	
spectra	(EADS)	for	the	three	spectrokinetic	species.	............................................................................	90	

Figure	A2.5.	Oscillation	map	for	vibrational	coherence	at	100	cm−1	detected	in	the	2DES	𝐾	
spectra	from	CAN	in	toluene.	............................................................................................................................	91	

Figure	A2.6.	Oscillation	map	for	vibrational	coherence	at	1800	cm−1	detected	in	the	2DES	
𝐾	spectra	from	CAN	in	toluene.	.......................................................................................................................	91	

Figure	A2.7.	Total	amplitude	𝐾	transient	and	modulation	spectrum	on	the	diagonal	in	the	
main	band	excitation	region.	(a)	𝐾	transient	with	excitation	at	18200	cm−1	and	detection	at	
18200	cm−1,	with	the	fit	from	the	global	model	(red	curve)	superimposed.	(b)	Residual	(𝐾−	
global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	residual	over	the	
𝑇	=	75-500	fs	range.	In	(b,c)	the	bars	show	the	95%	confidence	intervals	for	the	𝐾	
amplitudes.	...............................................................................................................................................................	92	

Figure	A2.8.	Total	amplitude	𝐾	transient	and	modulation	spectrum	in	the	S1	cross	peak	in	
the	main	band	excitation	region.	(a)	𝐾	transient	with	excitation	at	18200	cm−1	and	
detection	at	15500	cm−1,	with	the	fit	from	the	global	model	(red	curve)	superimposed.	(b)	

xiii	

	
	
	
Residual	(𝐾−	global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	
residual	over	the	𝑇	=	75-500	fs	range.	In	(b,c)	the	bars	show	the	95%	confidence	intervals	
for	the	𝐾	amplitudes.	...........................................................................................................................................	93	

Figure	A2.9.	Total	amplitude	𝐾	transient	and	modulation	spectrum	on	the	diagonal	in	the	
red	tail	excitation	region.	(a)	𝐾	transient	with	excitation	at	17200	cm−1	and	detection	at	
17200	cm−1,	with	the	fit	from	the	global	model	(red	curve)	superimposed.	(b)	Residual	(𝐾−	
global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	residual	over	the	
𝑇	=	75-500	fs	range.	In	(b,c)	the	bars	show	the	95%	confidence	intervals	for	the	𝐾	
amplitudes.	...............................................................................................................................................................	94	

Figure	A2.10.	Total	amplitude	𝐾	transient	and	modulation	spectrum	in	the	S1	cross	peak	in	
the	red	tail	excitation	region.	(a)	𝐾	transient	with	excitation	at	17200	cm−1	and	detection	at	
15500	cm−1,	with	the	fit	from	the	global	model	(red	curve)	superimposed.	(b)	Residual	(𝐾−	
global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	residual	over	the	
𝑇	=	75-500	fs	range.	In	(b,c)	the	bars	show	the	95%	confidence	intervals	for	the	𝐾	
amplitudes.	...............................................................................................................................................................	95	

Figure	3.1.	Schematic	representation	of	the	potential	energy	surface	representing	the	
relaxation	of	optical	excitation	via	a	cascade	of	conical	intersections	via	coherent	
wavepacket	motions.	Adapted	from	Tilluck	et	al.14	................................................................................	99	

Figure	3.2.	Schematics	of	DART-MS	analysis.	The	sample	was	heated	using	a	thermal	
desorption	module	where	the	ion	source	ionized	the	desorbed	molecules.	The	mass	
spectrometer	detects	ionized	ligand	molecules	and	shows	the	signatures	of	the	released	
species	in	the	mass	spectrum.	Inset	plot	shows	the	linear	temperature	ramp	applied	over	
certain	time.	...........................................................................................................................................................	101	

Figure	3.3.	Characterization	of	oleate	CdSe	(a)	Transmission	electron	microscopy	images	
of	oleate-capped	CdSe	quantum	dots	with	500,000x	magnification	and	5x	zoom.	(b)	Size	
distribution	of	CdSe	QDs,	245	total	particles	counted,	62	particles	6.98	nm.	The	mean	of	the	
size	distribution	is	6.97	nm	with	a	standard	deviation	of	0.50	nm.	Mass	spectra	collected	
from	TD-DART-MS	of	oleate-capped	CdSe	QDs.	The	ligands	are	desorbed	from	the	inorganic	
core	at	430	°C.	In	addition	to	the	major	peak	at	m/z	=	281.4	corresponding	to	the	oleate	
anion,	two	peaks	associated	with	subsequent	additions	of	oxygen	are	observed	at	m/z	=	
297.4	and	m/z	=	313.3.	Desorption	plot	obtained	from	DART-MS	for	m/z	=	281.4.	.............	105	

Figure	3.4.	Energy	level	diagram	of	CdSe	QDs.	On	the	left,	the	electron-hole	energy	levels	
are	marked	with	hole	levels	in	the	valence	band	(1S3/2,	1P3/2,	2S3/2,	3S1/2)	and	electron	
levels	(1Se	and	1Pe)	in	the	conduction	band.	The	band	edge	exciton	(1S3/2	1Se)	is	denoted	as	
X1,	the	second	exciton	(2S3/2	1Se)	is	denoted	as	X2,	the	third	exciton	(1P3/2	1Pe)	as	X3,	and	
the	fourth	exciton	(3S1/2	1Se)	as	X4.	The	figure	on	the	right	shows	the	exciton	energy	levels	
of	the	first	four	excitons	with	energy	in	eV	on	the	left	and	wavelength	on	the	right.	...........	106	

Figure	3.5.	Steady-state	spectroscopic	characterization	of	oleate-capped	QDs.	Linear	
absorption	spectrum	(blue	trace)	marked	with	various	exciton	energy	levels,	and	

xiv	

	
	
	
photoluminescence	spectrum	(orange	trace)	with	overlapping	laser	spectrum		
(gray	filled).	............................................................................................................................................................	107	

Figure	3.6.	Time	evolution	of	2DES	spectra	of	oleate	capped	CdSe	quantum	dots	with	
respect	to	the	population	time,	𝑇.	The	spectra	are	presented	with	evenly	spaced	contours	
and	are	tinted	with	colors	indicating	positive	(red,	GSB/SE)	and	negative	(blue,	ESA/PA)	
signals.	The	side	panels	plot	the	2DES	signal	amplitude	sliced	along	the	diagonal	at	𝑇	=	0	fs	
(blue)	superimposed	on	the	linear	absorption	oscillator	strength	(black	dotted)	and	
photoluminescence	(PL)	spectra	(orange).	Amplitude	transients	sampled	at	the	marked	
coordinates	(excitation	at	X3	and	detection	at	X3,	X1,	and	PL)	are	shown	in	Figure	3.7.	....	109	

Figure	3.7.	Global	analysis	of	the	population	response	of	the	X3	(2.066-2.194	eV)	
excitation	region	of	2DES	spectrum	of	oleate	capped	CdSe	quantum	dots.	(a)	Kinetic	
scheme	for	the	global	model	with	time	constants,	12	+	1	fs,	40	+	1	fs,	212	+	3	fs,	1.41	+	0.47	
ps,	and	186	+	40	ps	for	each	relaxation	pathway.	(b)	Evolution	of	population	with	respect	to	
time	for	each	compartment.	(c)	Evolution	associated	difference	spectra	(EADS)	for	each	
compartment	in	the	kinetic	scheme.	(d)	Transients	at	various	coordinates,	(X3,	X3)	(blue	
trace),	(X3,	X1)	(green	trace)	and	(X3,	PL)	(maroon	trace).	The	lower	panels	show	the	
residual	for	each	coordinate	overlapped	with	the	fit	obtained	from	the	LPSVD	analysis.	..	112	

Figure	3.8.	Coherence	analysis	accompanying	the	relaxation	of	X3.	(a)	Excitation-specific	
coherence	map	at	X3	excitation	(from	10-200	fs).	The	side	panel	includes	the	steady	state	
absorption	spectrum	(b)	LPSVD	spectra	for	coordinates	(X3,	X3),	(X3,	X1)	and	(X3,	PL)	for	
time	range	10-	500	fs.	........................................................................................................................................	114	

Figure	3.9.	3DES	spectra/mode	specific	oscillation	of	modulations	for	rapidly	damped	
modulations	of	frequencies,	(a)	280	cm-1,	(b)	380	cm-1,	(c)	640	cm-1,	and	(d)	720	cm-1.	....	116	

Figure	3.10.	Global	analysis	of	the	population	response	of	the	X2	(1.952-2.016	eV)	
excitation	region	of	2DES	spectrum	of	oleate	capped	CdSe	quantum	dots.	(a)	Kinetic	
scheme	for	the	global	model	with	time	constants,	17	+	1	fs,	165	+	3	fs,	2.10	+	0.4	ps,	and	164	
+	40	ps	for	each	relaxation	pathway.	(b)	Evolution	of	population	with	respect	to	time	for	
each	compartment.	(c)	Evolution	associated	difference	spectra	(EADS)	for	each	
compartment	in	the	kinetic	scheme.	(d)	Transients	at	various	coordinates,	(X3,	X3)	(blue	
trace),	(X3,	X1)	(green	trace)	and	(X3,	PL)	(maroon	trace).	Lower	panels	show	the	residual	
for	each	coordinate	overlapped	with	the	fit	obtained	from	the	LPSVD	analysis.	....................	117	

Figure	3.11.	Coherence	analysis	accompanying	the	relaxation	of	X2.	(a)	Excitation	specific	
coherence	map	at	X3	excitation	(from	10-200	fs).	Side	panel	includes	the	steady	state	
absorption	spectrum	(b)	LPSVD	spectra	for	coordinates	(X2,	X2),	(X2,	X1)	and	(X2,	PL)	for	
time	range	10-	500	fs.	........................................................................................................................................	118	

Figure	3.12.	Vector	representation	of	the	420	cm-1,	650	cm-1	and	950	cm-1	obtained	from	
the	Raman	spectra	calculation	of	Cd	oleate	complex.	Purple	arrows	indicate	the	direction	of	
displacement	of	each	atom	from	its	equilibrium	position.	................................................................	121	

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Figure	A3.1.	Residual	phase	and	intensity	spectra	of	the	femtosecond	laser	pulses	used	in	
the	broadband	multidimensional	electronic	spectroscopy	experiments.	Top	panel	shows	
residual	phase	spectra	after	compression	of	the	laser	pulses	used	in	the	2DES	experiment	
for	the	pump	beam	(solid),	and	for	the	probe	beam	(dashed),	as	determined	by	MIIPS	
scans.20	Bottom	panel	is	the	intensity	spectrum	of	the	laser	pulses.	............................................	128	

Figure	A3.2.	SHG-FROG21	spectrogram	for	the	pump	pulses,	as	measured	with	scanned	
pulse	pairs	prepared	by	the	pump	beam's	pulse	shaper	in	the	2DES	spectrometer.	............	129	

Figure	A3.3.	Interferometric	autocorrelation	of	the	pump	pulses,	determined	as	the	
integral	of	the	SHG-FROG	spectrogram	(Figure	A3.2).	........................................................................	129	

Figure	4.1.	Energy	level	diagram	for	the	photoinduced	electron	transfer	from	CdSe	QD	core	
to	methyl	viologen	dication	(MV2+)	inspired	by	Morris-Cohen	et	al.15	On	the	left,	the	
electron	(1Se	and	1Pe)	and	hole	energy	levels	of	the	QDs	are	marked	with	solid	lines.	The	
conduction	band	(CB)	and	valence	band	(VB)	of	the	QDs	are	marked	with	shaded	regions.	
Exciton	formation	upon	optical	pulse	interaction	is	indicated	by	the	red	arrow.	On	the	right	
side,	the	lowest	unoccupied	molecular	orbital	(LUMO)	and	highest	occupied	molecular	
orbital	(HOMO)	levels	of	MV2+	are	shown.	Upon	photoexcitation,	an	electron-hole	pair	is	
formed	in	the	QDs.	This	electron	is	transferred	from	the	1Se	state	of	the	QD	to	the	LUMO	of	
the	MV2+	The	dotted	arrow	represents	the	electron	recombination	from	the	MV+•	to	the	
hole	in	the	VB.	.......................................................................................................................................................	134	

Figure	4.2.	Spectroscopic	characterization	of	methyl	viologen.	(a)	Structure	of	1,1′-
dimethyl-4,4′-bipyridinium	dication.	(b)	Absorption	spectra	at	298	K	and	of	methyl	
viologen	dication	(blue	trace)	and	radical	cation	in	ethanol	(red	trace,	redrawn	from	
Watanabe	et	al.23).	...............................................................................................................................................	135	

Figure	4.3.	Energy	level	diagram	of	CdSe	QDs	and	steady-state	spectroscopic	
characterization	of	QD-	MV2+.	(a)	On	the	top	left,	the	electron-hole	energy	levels	are	marked	
with	hole	levels	in	the	valence	band	and	electron	levels	in	the	conduction	band.	The	vertical	
lines	depict	different	excitons:	X1	(red),	X2	(green),	and	X3	(blue).	The	figure	on	the	right	
shows	the	exciton	energy	levels	with	energy	in	eV	on	the	left	and	wavelength	on	the	right.	
(b)	Linear	absorption	spectrum	(blue	trace)	marked	exciton	energy	levels,	and	
photoluminescence	(PL)	spectrum	(orange	trace)	with	overlapping	laser	spectrum	(gray	
filled).	The	brown	trace	is	the	photoinduced	absorption	spectrum	of	MV+•	radical	cation	
adapted	from	Zhao	et	al.19	The	purple	trace	is	the	PL	of	the	QD-MV2+	complex.	.....................	139	

Figure	4.4.	Time	evolution	of	2D	spectra	of	oleate-capped	QD	and	QD-MV2+	with	respect	to	
the	population	time,	𝑇.	The	2D	spectra	on	the	left	are	those	of	the	oleate-capped	QDs	used	
in	the	control	experiment.	The	2D	spectra	of	the	QD-MV2+	complex	are	shown	on	the	right	
side.	The	intensities	of	the	2D	spectra	are	auto	scaled	with	respect	to	the	maxima	of	the	
signal	at	a	given	time,	𝑇.	The	side	panels	plot	the	linear	absorption	oscillator	strength	
(blue),	photoinduced	absorption	spectrum	of	MV+•	(brown),	and	photoluminescence	(PL)	
spectra	(orange).	The	amplitude	transients	sampled	at	the	marked	coordinates	(excitation	
at	X3	and	detection	at	X3,	X1,	and	PL)	are	shown	in	Figure	4.5.	.....................................................	141	

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Figure	4.5.	Global	analysis	of	the	population	response	of	the	X3	(2.102-2.214	eV)	
excitation	region	of	2DES	spectrum	of	QD-MV2+	complex.	On	the	left	is	the	kinetic	scheme	
for	the	global	model	with	time	constants	for	each	relaxation	pathway.	Evolution	associated	
difference	spectra	(EADS)	for	each	compartment	in	the	kinetic	scheme	are	present	on	the	
right.	The	final	component	of	the	model	is	enhanced	15	times	to	project	out	the		
amplitudes.	.............................................................................................................................................................	143	

Figure	4.6.	Amplitude	transient	comparison	of	QDs	and	QD-MV2+at	various	coordinates.	
(a)	2D	spectra	of	the	QD-MV2+	complex	with	marked	coordinates	(X3,	X3)	(blue),	(X3,	X1)	
(green)	and	(X3,	PL)	(maroon).	The	side	panels	plot	the	linear	absorption	oscillator	
strength	(blue),	photoinduced	absorption	spectrum	of	MV+•	(brown),	and	
photoluminescence	(PL)	spectra	(orange).	(b)	Amplitude	transients	at	for	the	QDs	(top	
panel)	and	QD-MV2+	(bottom	panel)	for	the	marked	coordinates	in	the	2D	spectra.	............	146	

Figure	4.7.	Frequency	analysis	of	the	residuals	of	the	transients	shown	in	Figure	4.6.	(a)	
Residuals	of	the	transients	presented	in	the	Figure	4.6.	The	green	traces	correspond	to	the	
coordinate	(X3,	X1)	and	the	maroon	trace	correspond	to	the	coordinate	(X3,	PL).	The	
LPSVD	fit	function	is	plotted	as	the	black	trace	overlapping	on	the	residuals	of	the	
transients.	(b)	LPSVD	models	for	the	oscillations	observed	in	the	residuals.	The	dotted	lines	
represent	the	amplitude	spectra	of	the	QDs,	and	the	solid	lines	represent	the	amplitude	
spectra	of	the	QD-MV2+	of	the	complex.	The	model	parameters	are	provided	in	Tables	4.1	
and	4.2.	.....................................................................................................................................................................	147	

Figure	4.8.	Comparison	of	excitation-specific	coherence	map	at	X3	excitation	(from	10-
200	fs)	for	QD	and	QD-MV2+	complex.	The	side	panels	plot	the	linear	absorption	oscillator	
strength	(blue),	photoinduced	absorption	spectrum	of	MV+•	(brown),	and	PL	spectra	
(orange).	The	blue	box	illustrates	the	portion	of	the	excitation-specific	coherence	map	
where	significant	amplitude	differences	between	QD	and	QD-MV2+	are	evident.	..................	150	

Figure	4.9.	Vector	representation	of	the	vibrational	modes	obtained	from	the	Raman	
spectra	calculation	of	MV2+	for	340-450	cm-1	region.	Purple	arrows	indicate	the	direction	of	
displacement	of	each	atom	from	its	equilibrium	position	during	the	vibrations.	..................	151	

Figure	4.10.	Schematic	representation	of	the	potential	energy	surface	representing	the	
relaxation	of	X3	optical	excitation	via	a	cascade	of	conical	intersections	via	coherent	
wavepacket	motions.	The	red	potential	energy	curve	depicts	the	bridging	coherent	charge	
transfer	intermediate	in	the	QD-MV2+	complex.	....................................................................................	153	

Figure	A4.1.	Residual	phase	and	intensity	spectra	of	the	femtosecond	laser	pulses	used	in	
the	broadband	multidimensional	electronic	spectroscopy	experiments.	Top	panel	shows	
residual	phase	spectra	after	compression	of	the	laser	pulses	used	in	the	2DES	experiment	
for	the	pump	beam	(solid),	and	for	the	probe	beam	(dashed),	as	determined	by	MIIPS	
scans.27	Bottom	panel	is	the	intensity	spectrum	of	the	laser	pulses.	............................................	159	

Figure	A4.2.	SHG-FROG28	spectrogram	for	the	pump	pulses,	as	measured	with	scanned	
pulse	pairs	prepared	by	the	pump	beam's	pulse	shaper	in	the	2DES	spectrometer.	............	160	

xvii	

	
	
	
Figure	A4.3.	Interferometric	autocorrelation	of	the	pump	pulses,	determined	as	the	
integral	of	the	SHG-FROG	spectrogram	(Figure	A4.2).	........................................................................	160	

xviii	

	
	
	
	
	
	
LIST	OF	ABBREVIATIONS	

2DES	

Two-Dimensional	Electronic	Spectroscopy	

CAN	

CB	

CCD	

CI	

CT	

Canthaxanthin	

Conduction	Band	

Charge-Coupled	Device	

Conical	Intersection	

Charge	Transfer	

CTD	

C-Terminal	Domain	

DART	

Direct	Analysis	in	Real	Time	

EADS	

Evolution	Associated	Difference	Spectra	

ESA	

FFT	

Excited	State	Absorption	

Fast	Fourier	Transform	

FROG	

Frequency	Resolved	Optical	Gating	

FT	

Fourier	Transform	

FWHM	

Full	Width	at	Half	Maximum	

GSB	

Ground	State	Bleaching	

HOMO	

Highest	Occupied	Molecular	Orbital	

HOOP	

Hydrogen-Out-of-Plane	

HPLC	

High	Performance	Liquid	Chromatogrpahy	

ICT	

IR	

LED	

Intramolecular	Charge	Transfer	

Infrared	

Light	Emitting	Diode	

xix	

	
	
	
LH	

LO	

Light	Harvesting	

Longitudinal	Optical	

LPSVD	

Linear	Prediction	Singular	Value	Decomposition	

LUMO	

Lowest	Unoccupied	Molecular	Orbital	

MBE	

Molecular	Beam	Epitaxy	

MG	

Milligram	

MIIPS	

Multiphoton	Intrapulse	Interference	Scan	

MOCVD	

Metalorganic	Chemical	Vapor	Deposition		

MS	

Mass	Spectrometry	

MTSU	

Middle	Tennessee	State	University	

NIR	

Near	Infrared	

NOPA	

Noncollinear	Optical	Parametric	Amplifier	

NTD	

OCP	

N-Terminal	Domain	

Orange	Carotenoid	Protein	

OCPO	

Orange	Carotenoid	Protein-Orange	state	

OCPR	

Orange	Carotenoid	Protein-Red	state	

ODE	

PL	

PTC	

QD	

SE	

Octadecene	

Photoluminescence	

Phenyldithiocarbamate	

Quantum	Dots	

Stimulated	Emission	

SHG	

Second	Harmonic	Generation	

xx	

	
	
	
SLM	

Spatial	Light	Modulator	

TA	

TD	

TDM	

TEM	

THG	

Transient	Absorption	

Thermal	Desorption	

Transition	Dipole	Moment	

Transmission	Electron	Microscopy	

Third	Harmonic	Generation	

TOPO	

Trioctylphosphineoxide	

UV	

VB	

Ultraviolet	

Valence	Band	

WMEL	

Wave-Mixing	Energy	Level	Diagram	

xxi	

	
	
	
	
Overview	of	the	Dissertation	

The	purpose	of	the	work	presented	in	this	dissertation	is	to	address	the	role	of	

electronic-vibrational	(vibronic)	quantum	coherences	in	nonradiative	relaxation	

mechanism	of	carotenoids	and	semiconductor	quantum	dots	(QDs)	as	well	as	the	

photoinduced	charge	transfer	from	QD	core	to	an	acceptor	molecule.	We	employed	

multidimensional	spectroscopic	techniques	on	samples	of	ketocarotenoid	molecule,	

canthaxanthin	and	CdSe	QDs	to	understand	the	dynamics	of	nonradiative	relaxation	and	

photoinduced	electron	transfer.	The	correlation	nature	of	multidimensional	spectroscopic	

techniques	enables	us	to	determine	the	relaxation	of	excitation	energy	via	a	series	of	

excited	energy	levels.	The	vibronic	coherences	manifest	as	amplitude	modulations	in	the	

2D	spectra,	and	their	frequencies	provide	the	structural	information	on	the	vibrational	

motions	involved	in	these	processes.	Using	the	time-evolution	of	the	2D	spectra	along	with	

the	vibronic	coherence	characterization,	we	address	the	following	questions:	

1.  What	are	the	electronic	and	vibrational	dynamics	accompanying	the	formation	of	

intermediate,	Sx	in	the	nonradiative	decay	of	S2	in	the	ketocarotenoid	

canthaxanthin?	

2.  How	do	the	vibrations	of	surface	ligands	and	the	QD	core	facilitate	hot-carrier	

cooling	of	electrons	and	holes	in	oleate-capped	QDs?	

3.  Do	vibronic	excitons	involving	the	core	and	ligand	vibrational	modes	initiate	

photoinduced	charge	transfer	from	the	QD	core	to	the	acceptor	molecule?	

The	dissertation	is	organized	as	follows:	

Chapter	1	provides	a	brief	introduction	to	carotenoids	and	semiconductor	quantum	

dots.	This	chapter	discusses	nonradiative	relaxation	in	carotenoids	and	reviews	relevant	

1	

	
	
literature.	The	second	section	provides	an	introduction	to	semiconductor	quantum	dots	

and	their	previously	suggested	nonradiative	relaxation	mechanisms.	In	the	final	section	of	

this	chapter,	a	brief	introduction	to	third-order	nonlinear	signals	is	provided	along	with	

experimental	implementation	of	two-dimensional	electronic	spectroscopy	(2DES).		

Chapter	2	reports	the	results	from	the	study	of	the	nonradiative	relaxation	mechanism	

in	ketocarotenoid	canthaxanthin	using	multidimensional	spectroscopy.	We	report	the	

spectroscopic	signature	and	vibrational	coherence	of	the	intermediate,	Sx,	that	is	involved	

in	the	nonradiative	decay	of	bright	S2	state	to	the	dark	S1	state.	The	results	indicate	that	the	

Sx	evolves	along	out-of-plane	coordinates	of	the	isoprenoid	backbone	as	it	relaxes	to	S1	

state.	

Chapter	3	presents	the	results	from	the	multidimensional	spectroscopy	that	determine	

the	coherent	vibronic	exciton	mechanism	of	hot	carrier	cooling	in	oleate-capped	CdSe	QDs.	

This	process	involves	excited-state	coherent	wavepacket	motions	through	a	cascade	of	

conical	intersections	between	exciton	potential-energy	surfaces.	The	results	indicate	that	

the	ligand	vibrations	are	quantum	coherently	mixed	with	the	core	electronic	states	of	the	

QDs.	Using	coherence	analyses	we	isolate	the	vibrational	motions	that	aid	the	electron	and	

hole	relaxation	in	these	QDs.	

In	the	Chapter	4,	we	present	the	results	from	the	multidimensional	spectroscopy	that	

determines	the	role	of	vibronic	excitons	on	the	photoinduced	charge	transfer	from	CdSe	QD	

core	to	a	surface	electron	acceptor	methyl	viologen	(MV).	We	observe	coherent	wavepacket	

motions	with	frequencies	of	lattice-vibrations	and	the	out-of-plane	deformations	of	MV2+.	

These	observations	are	consistent	with	a	charge	transfer	intermediate	with	a	mixed	QD-MV	

2	

	
	
	
character,	and	this	intermediate	initiates	the	photoinduced	charge	transfer	from	the	core	of	

the	QD	to	the	surface	acceptor	molecule.	

3	

	
	
	
Chapter	1:	Introduction	to	Carotenoids	and	Semiconductor	Quantum	
Dots		

Nonradiative	relaxation	of	excited	states	has	been	observed	in	both	naturally	existing	

photosynthetic	light-harvesting	structures	and	energy	materials	such	as	semiconductor	

quantum	dots.	The	mechanism	of	nonradiative	relaxation	observed	in	these	systems	

involves	relaxation	of	the	optically	prepared	excited	states	via	the	coupling	of	electronic	

and	nuclear	motions.1–3	This	chapter	covers	the	background	of	the	nonradiative	relaxation	

observed	in	carotenoids,	along	with	a	review	of	the	literature	to	date.	The	second	part	of	

the	chapter	provides	a	background	on	semiconductor	quantum	dots	and	the	previously	

proposed	mechanisms	of	nonradiative	relaxation	(hot-carrier	cooling).	We	employed	

multidimensional	electronic	spectroscopic	techniques	to	address	the	nonradiative	

relaxation	mechanisms	of	these	systems.	The	experimental	implementation	of	this	

spectroscopic	technique	is	discussed	in	the	final	section	of	this	chapter.	

1.1	Nonradiative	Relaxation	Mechanisms	

Photosynthetic	light	harvesting	systems	and	solar	energy	materials	consist	of	a	

manifold	of	excited	states	including	several	vibrational	energy	levels.	Upon	an	electric	field	

interaction	from	an	optical	pulse,	a	wavepacket	is	created	in	the	excited	state	which	

consists	of	both	electronic	and	vibrational	energy	levels.	This	electronic-vibrational	

(vibronic)	wavepacket	evolves	through	the	excited	state	potential	energy	surfaces	and	lose	

its	excitation	energy	into	vibrations	in	the	form	of	nonradiative	relaxation.	The	

nonradiative	relaxation	is	considered	as	a	nonadiabatic	mechanism	which	occurs	beyond	

the	Born-Oppenheimer	regime.4–6	In	the	Born-Oppenheimer	regime,	the	motions	of	

electrons	and	nuclei	evolve	independently	of	each	other	owing	to	their	large	differences	in	

4	

	
	
mass.	However,	in	nonadiabatic	mechanisms,	the	electrons	couple	to	the	nuclear	motions	

of	the	molecules	that	allow	for	energy	relaxation.	Nonadiabatic	processes	occurs	in	the	

regions	where	the	optically	prepared	wavepacket	crosses	the	potential	energy	surfaces	at	

the	intersections	called	conical	intersections	(CI).4,7	

	Several	powerful	experimental	techniques	employing	ultrafast	lasers	have	been	

applied	to	create	and	investigate	excited	states,	enabling	experimental	investigations	of	the	

relaxation	of	excited	states	through	these	nonadiabatic	processes.	Some	of	the	

experimental	techniques	include	transient	absorption	spectroscopy,	multidimensional	

spectroscopy,	and	single	molecule	spectroscopy.	These	mechanisms	have	been	used	to	

explain	several	photophysical	processes	including	coherent	vibronic	dynamics	in	energy	

transfer	mechanisms8–11	and	photochemical	reactions.12–14	

1.2	Orange	Carotenoid	Protein:	An	Overview	

Carotenoid	molecules	are	an	integral	component	of	light-harvesting	systems	in	plants	

and	photosynthetic	organisms.15,16	In	cyanobacteria,	ketocarotenoids	serve	as	

chromophores	for	ambient	light	sensing	in	the	orange	carotenoid	protein	(OCP).15,17–23	The	

OCP	facilitates	the	nonphotochemical	quenching	of	bilin	chromophores	in	the	core	of	light-

harvesting	protein	complexes,	phycobilisomes.23	The	OCP	consists	of	two	protein	domains,	

C-terminal	domain	(CTD)	and	N-terminal	domain	(NTD).	The	ketocarotenoid	is	located	at	

the	interface	between	the	NTD	and	CTD.	Upon	excitation	of	the	ketocarotenoid	in	the	OCP	

using	mid-visible	photons,	it	gets	photoactivated	from	the	resting	orange	state	(OCPO)	to	

the	active	red	state	(OCPR).	The	absorption	spectra	of	the	OCPR	exhibits	a	redshift	of	50	nm	

compared	to	that	of	the	OCPO.23,24	In	terms	of	protein	structure,	the	process	of	

photoactivation	involves	translocation	of	the	carotenoid	molecule	into	the	NTD	and	

5	

	
	
	
displacement	of	the	CTD.23,25	The	NTD	of	OCPR	then	binds	to	the	core	of	the	phycobilisome	

to	facilitate	nonphotochemical	quenching.	The	photoactivation	process	of	OCP	from	OCPO	

to	OCPR	involves	significant	changes	in	the	conformation	and	position	of	the	carotenoid	

molecule.23,26	However,	the	impact	of	photoactivation	on	the	electronic	structure	of	the	

ketocarotenoid	is	still	under	investigation.	As	an	initial	stage,	it's	crucial	to	understand	the	

impact	of	photoexcitation	on	carotenoid	molecules	before	delving	into	their	response	to	

photoactivation	in	OCP.	The	next	section	gives	an	overview	of	the	structure	and	

photophysical	processes	in	carotenoids.	

1.3	Photophysics	of	Carotenoids	

Carotenoid	molecules	consist	of	a	long-conjugated	isoprenoid	backbone	with	various	

functional	groups	at	their	ends.	Examples	include	canthaxanthin,	β-carotene,	peridinin,	and	

zeaxanthin	(Figure	1.1).	Owing	to	the	planar	structure	of	these	molecules,	they	fall	under	

the	C2h	symmetry	group.	Therefore,	the	ground	state	S0	has	1Ag

-	symmetry,	while	the	first	

excited	state,	S1,	and	second	excited	state,	S2,	have	symmetries	2Ag

-	and	1Bu

+,	respectively.27	

The	absorption	spectrum	of	a	typical	carotenoid	consists	of	a	strong	band	in	the	mid-visible	

region.	The	first	excited	state,	S1,	is	considered	a	dark	state	owing	to	the	lack	of	dipole-

allowed	transitions	from	the	ground	state,	S0.	Consequently,	the	strong	absorption	band	in	

the	mid-visible	region	of	the	absorption	spectrum	is	attributed	to	the	transition	from	the	S0	

to	the	second	excited	state,	S2.28,29	These	transitions	are		π	→	π∗	excitations	of	the	long-

conjugated	isoprenoid	backbone.27,30,31	The	energies	of	these	transitions	are	similar	to	the	

particle-in-a	box	problem,	where	an	increase	in	the	conjugation	length	results	in	a	decrease	

in	the	energy	gap.32	Additionally,	most	carotenoid	molecules	also	exhibit	vibronic		

6	

	
	
	
Lycopene
Lycopene

The Journal
of Chemical Physics

Lycopene

β-carotene 
!-carotene
!-carotene

!-carotene

O
O

O

HO
HO

O

HO

Violaxanthin
Canthaxanthin 
Violaxanthin

FIG. 1. Structure of canthaxanthin.

Violaxanthin

O
O

O

ARTICLE

scitation.org/journal/jcp

O

OH
OH

OH

For femtosecond spectroscopy, samples of CAN were dissolved in
toluene (Sigma-Aldrich 179418) to obtain an absorbance of 0.3 at
1) for a 1-mm path length static cuvette and then
545 nm (18 350 cm
centrifuged in a desktop microcentrifuge at 17 000g to pellet light-
−
scattering particles. The CAN samples were kept in the dark prior
to performing femtosecond spectroscopy experiments. The linear
absorption spectrum was measured before and after exposure to the
laser. Neither changes in the absorbance nor changes in the shape of
the linear spectrum were observed after the samples were used in the
recording of 2DES spectra, but a fresh sample was put in place after
three iterations of the data acquisition process.

OH
OH

OH

O
O

HO
HO

Zeaxanthin

Our finding that the lifetime of Sx is considerably longer in
Zeaxanthin
the carbonyl-substituted carotenoid peridinin, however, raises the
Zeaxanthin 
Zeaxanthin
possibility that Sx should be assigned instead to a conformationally
HO
distorted S2 structure moving along out-of-plane coordinates of the
isoprenoid backbone toward a conical intersection (CI) seam8 with
the S1 state.3,11,19,20 This general idea has found additional support
from recent fluorescence studies. The Sx state is the likely origin
15'
of a broad fluorescence emission band in β-carotene solutions at
15
cryogenic temperatures. The fluorescence anisotropy measured for
15'
Peridinin
β-carotene in aprotic solutions at room temperature indicates that
O
15'
Peridinin
the emission transition dipole moment (TDM) is rotated as much as
HO
?5.1/7()8@;!L*)0.*0)(&!,9!.,88,-!.+),*(-,%'&;!
50
relative to that of the Franck–Condon S2 state. These observa-
Peridinin
?5.1/7()8@;!L*)0.*0)(&!,9!.,88,-!.+),*(-,%'&;!
Peridinin 
tions suggest that torsional and pyramidal distortions near the center
of the isoprenoid backbone are initiated in Sx.6

?5.1/7()8@;!L*)0.*0)(&!,9!.,88,-!.+),*(-,%'&;!

HO
HO
•
HO
•

O
O
11
11

HO
HO

11'
11'

15
15

O
O

11'

11

O

O

•

○

OCOCH3
OCOCH3

OCOCH3

B. Linear spectroscopy

Linear absorption spectra of CAN samples were recorded at
C) with a Shimadzu UV-2600 spectrometer.

room temperature (23

○

C. Femtosecond spectroscopy

!
!

2DES spectra were recorded using a pump–probe optical con-
figuration with adaptive pulse shaping22 to compress the laser pulses
and to prepare the excitation pulse sequence (pulse 1–τ–pulse 2)
required for the three-pulse stimulated photon-echo experiment.16
The instrumentation and methods were introduced in an earlier
publication.23

!

)8@8)(!+/0=72053($<0=0A<;>5,>(
)8@8)(!+/0=72053($<0=0A<;>5,>(

?+),*(-,%'&! /(1,-4! *,! +! .1+&&! ,9! 1%-(+)! .,-304+*('! 5,12(-(&! A%*$! (M*(-'('!

90-.*%,-+1! 4),05&! +-'! (-'! 4),05&;! ! R%40)(!";H! &$,A&! +! 9(A! (M+851(&! ,9! .,88,-!

cF(1(.*),-! &2&*(8&! ,9! B+)2%-4! .,-304+*%,-! 1(-4*$&! >a@6! A$%.$! .,-*+%-! B+)%,0&!

In this article, we report that broadband 2DES can be used
to detect the formation of the Sx state in toluene solutions of the
Figure	1.1.	Structure	of	different	carotenoids.	
?+),*(-,%'&! /(1,-4! *,! +! .1+&&! ,9! 1%-(+)! .,-304+*('! 5,12(-(&! A%*$! (M*(-'('!
)8@8)(!+/0=72053($<0=0A<;>5,>(
ketocarotenoid canthaxanthin (CAN). The structure of CAN dif-
?+),*(-,%'&! /(1,-4! *,! +! .1+&&! ,9! 1%-(+)! .,-304+*('! 5,12(-(&! A%*$! (M*(-'('!
fers from that of β-carotene only by the addition of a carbonyl to
cF(1(.*),-! &2&*(8&! ,9! B+)2%-4! .,-304+*%,-! 1(-4*$&! >a@6! A$%.$! .,-*+%-! B+)%,0&!
each of the β-ionone (cyclohexene) end rings (Fig. 1). The carbonyls
cF(1(.*),-! &2&*(8&! ,9! B+)2%-4! .,-304+*%,-! 1(-4*$&! >a@6! A$%.$! .,-*+%-! B+)%,0&!
are thought to be essential to the role served by CAN as a light
sensor in the orange carotenoid protein, which mediates photopro-
90-.*%,-+1! 4),05&! +-'! (-'! 4),05&;! ! R%40)(!";H! &$,A&! +! 9(A! (M+851(&! ,9! .,88,-!
tective nonphotochemical quenching mechanisms in the phycobil-
90-.*%,-+1! 4),05&! +-'! (-'! 4),05&;! ! R%40)(!";H! &$,A&! +! 9(A! (M+851(&! ,9! .,88,-!
isome in cyanobacteria.21 The 2DES spectra shown in this paper
.+),*(-,%'&;! ! d+-2! ,9! *$(! %-*()(&*%-4! 5$2&%.+1! 5),5()*%(&! ,9! .+),*(-,%'&! +)(!
20 fs after optical preparation of the S2
establish that Sx forms in
.+),*(-,%'&;! ! d+-2! ,9! *$(! %-*()(&*%-4! 5$2&%.+1! 5),5()*%(&! ,9! .+),*(-,%'&! +)(!
state of CAN by transitions in the main absorption band. Further-
more, it is shown that Sx is formed directly by vertical transitions
of molecules in the ground-state ensemble that contribute to the
`!
broad low frequency onset of the main absorption band. Charac-
`!
terization of the high-frequency vibrational coherences in the 2DES
spectrum establishes that Sx and S1 are displaced structurally from
the Franck–Condon S2 state along out-of-plane modes of the iso-
prenoid backbone. Despite the presence of the carbonyl substituents,
which substantially lengthen the lifetime of Sx to 440 fs, the results
indicate that radiationless decay from Sx to S1 occurs in CAN with
retention of vibrational coherence.

Excitation pulses were obtained from a noncollinear optical
parametric amplifier (NOPA, Spectra-Physics Spirit-NOPA-3H),
which was pumped by the third harmonic of a 1.04 ￿m amplified
Yb laser (Spectra-Physics Spirit-4W, 400 fs pulses at a 100 kHz rep-
etition rate, 4 W average power). The pump and probe beams in
the spectrometer were split from the NOPA output by a broad-
band dielectric beamsplitter (Layertec, Mellingen), processed by an
adaptive pulse shaper (FemtoJock and FemtoJock P, respectively,
Biophotonic Solutions), and then compressed by multiple reflec-
tions on pairs of broadband chirped mirrors (Ultrafast Innovations,
Munich). For the present experiments, the NOPA’s signal beam out-
put spectrum (Fig. 1) was centered at 590 nm (
520–700 nm usable range). The excitation pulse energy was atten-
uated to 4.5 nJ per pulse, as measured at the sample’s position. The
pump beam’s plane of linear polarization was rotated 45
of the probe beam by a thin achromatic half-wave retarder plate.
The two beams were focused by off-axis parabolic mirrors to 100 ￿m
spots overlapped spatially just after the front window of the sample
cuvette. The excitation pulses in both beams were characterized by
MIIPS scans24 conducted with a thin β-barium borate crystal, which
was placed at the sample’s position following a single cuvette win-
dow. The estimated pulse duration for both beams at the sample
position was 7.8 fs. Residual phase plots (Figs. S1 and S2), calcu-

55 nm FWHM;

∼

from that

○

.+),*(-,%'&;! ! d+-2! ,9! *$(! %-*()(&*%-4! 5$2&%.+1! 5),5()*%(&! ,9! .+),*(-,%'&! +)(!

7	

!
!

`!

<

!

II. EXPERIMENTAL

A. Samples

lated temporal profiles from the MIIPS scans (Fig. S3), and SHG-

FROG spectrograms25 (Fig. S4) are presented in the supplementary

CAN was used as received from Sigma-Aldrich (32993-2MG).

material.

In order to assess its purity, reversed-phase high-performance liq-

2DES spectra were recorded by programming the pump beam’s

uid chromatography (HPLC) of CAN solutions in acetonitrile was

pulse shaper to scan the coherence time interval between the two

performed with a Waters Atlantis T3 5 ￿m analytical column (4.6

250 mm2) and detection with an Agilent Prostar 325 two-channel

pump pulses, τ, from 0 to 50 fs with 0.5 fs steps to obtain the exci-

tation axis after Fourier transformation. Longer τ scans produced

UV/vis detector at 480 and 364 nm. The chromatograms (not

identical spectra but with a lower signal/noise ratio. The detection

shown) establish that

95% of the eluted sample corresponds to the

axis of the 2DES spectrum was measured directly by measuring the

×

all-trans configuration and that shorter carotenoids are not present.

pump-induced change in probe transmission through the sample

>

J. Chem. Phys. 155, 035103 (2021); doi: 10.1063/5.0055598

Published under an exclusive license by AIP Publishing

155, 035103-2

	
	
	
	
	
	
	
structures	in	the	absorption	spectrum,	which	are	attributed	to	the	combination	of	

stretching	motions	of	the	C-C	(1150	cm-1)	and	C=C	(1530	cm-1)	bonds	of	the	polyene	

backbone.	

1.3.1	Nonradiative	Decay	in	Carotenoids	

In	carotenoids,	the	optically	prepared	S2	state	exhibits	a	very	short	lifetime	(<100	fs)	

and	relaxes	to	the	S1	state	via	ultrafast	nonradiative	processes.33–35	Several	studies	have	

shown	that	the	decay	of	S2	to	S1	involves	an	intermediate	state	that	is	detected	in	<	20	fs	

after	the	optical	preparation	of	S2.30,36,37	The	structural	and	spectroscopic	nature	of	this	

intermediate	remains	uncertain.	One	of	the	first	experimental	detection	of	the	intermediate	

state	was	with	resonance	Raman	excitation	studies	of	all-trans-spheroidene	by	Koyama	et	

al.38	Further	studies	using	sub-picosecond	time-resolved	experiments	on	all-trans-

neurosporene,	the	group	assigned	the	intermediate	to	a	discrete	1Bu

-	state39,40	as	predicted	

by	Tavan	and	Schulten.41	Subsequent	transient	absorption	(TA)	experiments	conducted	by	

Cerullo	group	using	15	fs	pulses	on	β-carotene	and	lutein	revealed	that	the	S2	state	decays	

in	12	fs,	giving	rise	to	a	distinctive	electronic	state	called	Sx,	characterized	by	an	excited	

state	absorption	in	the	800–900	nm	range.36	Like	earlier	studies,	this	intermediate	was	also	

attributed	to	the	1Bu

–	state.	Two-dimensional	electronic	spectroscopy	studies	from	Scholes	

group	on	LH2	light-harvesting	protein	have	detected	the	X	state	in	the	carotenoid.	The	X	

state	is	attributed	to	the	direct	excitation	of	the	1Bu

–	state	and	is	considered	to	borrow	

oscillator	strength	from	the	nearby	S2	state	via	the	Herzberg–Teller	coupling.42,43	The	

assignment	of	the	intermediate	state	to	1Bu

–	applies	only	to	planar	carotenoid	molecules	

with	a	C2h	geometry.	However,	studies	on	the	ground-state	structures	in	vacuum,	solution	

8	

	
	
	
and	proteins	show	that	these	carotenoids	have	asymmetric	conformations	with	distortion	

along	out-of-plane	coordinates.31,44		

Earlier	studies	from	our	group	raised	the	possibility	that	Sx	should	be	assigned	to	a	

conformationally	distorted	S2	structure	moving	along	the	out-of-plane	coordinates	of	the	

isoprenoid	backbone	towards	a	conical	intersection	(CI)	seam4	with	the	S1	state.31,34,35	

Upon	photoexcitation,	carotenoid	molecules	undergo	displacements	along	the	bond-

alternation	coordinates	from	the	Franck-Condon	geometry.	These	molecules	then	undergo	

vibrational	motions	along	out-of-plane	coordinates,	leading	to	a	twisted	conformation	

(Figure	1.2).	Fluorescence	anisotropy	measurements	on	β-carotene	in	aprotic	solutions	at	

room	temperature	show	a	50°	rotation	of	the	emission	transition	dipole	moment	(TDM)	

relative	to	the	Franck–Condon	S2	state,	implying	that	the	torsional	and	pyramidal	

distortions	are	initiated	in	the	Sx	state	near	the	center	of	the	isoprenoid	backbone.29		

The	first	part	of	this	dissertation	addresses	the	nonradiative	decay	mechanisms	of	the	

ketocarotenoid,	canthaxanthin	involving	an	intermediate	state,	Sx,	using	multidimensional	

spectroscopic	techniques.	The	nature	of	the	bridging	intermediate	state,	Sx,	involved	in	the	

nonadiabatic	mechanism	of	decay	of	optically	prepared	S2	state	to	dark	S1	state	in	the	

ketocarotenoid	is	to	be	established.	We	address	our	proposal	that	Sx	corresponds	to	

conformationally	distorted	molecules	evolving	along	the	out-of-plane	coordinates	of	the	

isoprenoid	backbone	near	a	low	barrier	between	the	planar	and	distorted	conformations	

on	the	S2	potential	surface.	The	spectroscopic	signature,	electronic	and	vibrational	

dynamics	of	Sx	formation	will	be	addressed	in	the	Chapter	2.	

9	

	
	
	
	
	
Sn

S2

S1

S0

y
g
r
e
n
E

l

a
i
t
n
e
t
o
P

planar

‡  φ

Sx
Reaction Coordinate

CI

Figure	1.2.	Schematic	representations	for	the	potential	energy	surfaces	for	the	singlet	
states	of	a	carotenoid,	plotted	here	as	a	function	of	a	reaction	coordinate	composed	of	
sequential	displacements	from	the	Franck–Condon	geometry	of	the	optically	prepared	S2	
state	with	respect	to	the	C–C	and	C=C	stretching	and	out-of-plane	(φ)	coordinates	of	the	
isoprenoid	backbone.	Planar	and	distorted	conformations	are	divided	by	a	low	barrier	at	
the	structure	marked	‡	on	the	reaction	coordinate	axis.	The	mixed	S2,	S1,	and	S0	surfaces	
are	proposed	to	converge	near	the	geometry	of	the	S2	minimum	owing	to	a	conical	
intersection	(CI)	of	the	diabatic	surfaces.	Arrows	indicate	vertical	optical	transitions	from	
planar	and	distorted	conformations	to	the	S2	state.	Adapted	from	Gurchiek	et	al.29	

10	

	
	
	
	
	
	
	
 
1.4	Semiconductor	Quantum	Dots	

Semiconductor	materials	have	a	fixed	energy	gap	(or	band	gap)	between	the	conduction	

band	(CB)	and	valence	band	(VB),	depending	on	the	composition	of	the	materials.	However,	

when	these	semiconductor	crystals	are	<	10	nm	in	size,	their	bandgaps	are	no	longer	fixed.	

In	this	size	regime,	semiconductor	crystals	exhibit	quantum	size	effects	and	are	therefore	

called	quantum	dots	(QDs).	QDs	contain	anywhere	from	100	to	10000	atoms	per	

nanocrystals.	They	can	be	viewed	as	materials	between	the	molecules	and	bulk	materials.	

Quantum	effects	are	observed	when	the	size	of	the	nanocrystals	is	comparable	to	or	

smaller	than	the	spatial	separation	between	the	electron	and	hole	or	the	Bohr	exciton	

radius	(Figure	1.3).	Their	size-dependent	electronic	energy	gaps	have	been	modeled	using	

the	particle-in-a-sphere	approximation.45,46	The	energy	of	a	particle	in	a	sphere	of	radius	R	

is	strongly	dependent	on	size	and	is	proportional	to	1/R2.	The	wavefunctions	of	the	particle	

in	a	sphere	are	similar	to	the	atomic	orbitals	of	H-atom.	Thus,	they	are	labeled	by	quantum	

numbers	n	(1,	2,…),	l	(S,	P,	D,	…),	and	m.	According	to	the	derived	selection	rules,	optical	

transitions	occur	only	at	energy	levels	with	the	same	l	quantum	numbers.	Owing	to	the	

quantum	confinement	in	these	particles,	smaller	QDs	exhibit	optical	properties	in	the	blue	

region	of	the	spectra	compared	to	larger	ones.	

QDs	can	be	composed	of	single	elements	like	Si	or	C,	binary	compounds	of	II-IV	(e.g.	

CdSe,	CdTe,	ZnS,	etc.),	III-V	elements	(InP,	GaN,	GaP,	etc.),	and	IV-VI	elements	(PbSe,	PbTe,	

GeTe,	etc.).	Several	synthetic	approaches	have	been	devised	to	prepare	QDs	with	identical	

shapes,	sizes,	and	properties.	These	approaches	include	physical	processes	such	as	

molecular-beam-epitaxy	(MBE)48–50	and	metalorganic-chemical-vapor-deposition		

11	

	
	
	
Figure	1.3.	Illustration	of	the	quantum	confinement	compared	to	the	bulk	semiconductor.	
When	the	spatial	extent	of	wavefunction	is	smaller	than	the	Bohr	exciton	radius	(ab),	size-
dependent	optical	properties	are	observed.	Adapted	from	ref	47.47	

12	

	
	
	
	
	
	
(MOCVD)50,51	and	chemical	methods	such	as	colloidal	nanocrystalline	synthesis.52–54	

This	dissertation	focusses	on	colloidal	CdSe	quantum	dots.	Colloidal	CdSe	quantum	dots	

(QDs)	have	been	widely	recognized	as	a	model	system	for	the	fundamental	research	of	

electronic	and	optical	properties	of	QDs.55	This	is	primarily	because	they	can	be	

synthesized	with	ease,	resulting	in	high-quality,	monodisperse	QDs.		

1.4.1	Electronic	Structure	and	Surface	of	Colloidal	CdSe	QDs	

To	obtain	a	complete	picture	of	the	electronic	structure	and	size-dependent	optical	

properties,	several	optical	spectroscopic	techniques	have	been	employed,	including	

transient	differential	absorption,56–60	photoluminescence	excitation56,61–63	and	fluorescence	

line	narrowing.64,65	In	QDs,	the	VB	contains	a	high	density	of	states	and	the	CB	has	a	lower	

density	of	states.	This	means	that	the	hole	energy	levels	in	the	VB	are	closer	to	each	other	

than	the	electronic	energy	levels	in	the	CB.	The	electronic	energy	levels	in	the	CB	and	the	

hole	energy	levels	in	the	VB	are	shown	in	Figure	1.3.	Electronic	transitions	following	

selection	rules	occur	from	the	S	and	P	states	in	the	VB	to	the	corresponding	S	and	P	states	

in	the	CB.	The	lower-energy	exciton	(1S3/2	1Se)	is	often	termed	as	the	band-edge	exciton.	

Due	to	their	tunable	size-dependent	energy	gap,	narrow-linewidth	emission,	surface	

chemistry,	and	charge	transport	properties,	they	have	wide	range	of	applications.47	Some	of	

the	QD	applications	include	their	use	in	displays,66–69	lasers,70–72	optical	sensing	and	

imaging,73–75	solar	cells,76–78		and	photo	and	electrocatalysis.79–81		

In	colloidal	solution,	the	surface	of	the	quantum	dots	is	passivated	with	organic	

molecules	called	surface	capping	ligands	(Figure	1.4).	These	ligand	molecules	satisfy	

valencies	of	the	surface	atoms	of	the	nanocrystal,	protect	the	surface	from	the	

13	

	
	
	
the effective masses of the electron and hole independently, while the selection rules govern only 

transitions between levels with the same quantum number. In strongly confined QDs, the valence 

band contains a higher density of states when compared to the conduction band, which 

introduces complexities in describing the hole levels of a QD. Experimental results from 

absorption spectra,73 photoluminescence excitation,74 and hole burning experiments75 have been 

used to describe the valence band quantitatively. Figure 1.2 below illustrates the general 

surroundings,	and	control	nucleation	and	kinetics	during	the	colloidal	synthesis.84–86	QDs	

electronic structure of CdSe QDs featured in the experiments in this dissertation. The QDs were 

have	large	surface-to-volume	ratio	and	spatially	confined	excitonic	wavefunctions.	

colloidal, and therefore capped with organic surface ligands. Each state is assigned a principal 

quantum number (1,2), angular momentum (S, P, D), and total angular momentum (1/2, 3/2).  

Figure	1.4.	Illustration	of	different	surface	capping	ligands	and	their	possible	coupling	of	
Figure 1.2. Examples of surface capping ligands and possible coupling of core electronic states 
vibrational	modes	with	QD	core	electronic	states.82	(a)	Ligands,	alkylamine	(I),	
in QDs with ligand vibrations, after Lifshitz.76 (a) Alkylamine (I), trioctylphosphineoxide 
(TOPO, II), and alkylcarboxyl (III) ligands and ligation to metal cation (e.g. Cd2+) and anion 
trioctylphosphineoxide	(TOPO)(II),	and	alkylcarboxyl	group	(III),	where	R	represents	the	
(chalcogen, e.g. Se2−) sites, with R representing alkane or alkene substituents. (b) Coupling of 
alkyl	chain,	interacting	with	the	surface	of	CdSe	QDs.	(b)	Possible	coupling	of	energy	levels	
core QD electronic (black) states and ligand bonding (solid red) and antibonding (dashed red) 
of	ligand	(solid	line	and	dashed	line	representing	bonding	orbital	and	antibonding	orbital,	
states. (c) Exciton manifold for the first four bound electron-hole pairs formed upon excitation, 
respectively)	to	core	electronic	states	and	(c)	exciton	manifold	for	excitons	(electron	hole	
labeled X1 through X4. 
pair)	X1	to	X4,	as	labelled.	(Reproduced	from	Ryan	Tilluck’s	dissertation.83)	

Therefore,	the	properties	of	QDs	can	be	significantly	altered	largely	by	modifying	their	

surface	using	capping	ligands.	Surface-to-ligand	bonding	characteristics	are	classified	into	

three	categories	by	exploring	the	photoluminescence	quantum	yield	dependence	on	

13 

ligands.82,86–88	They	are	L-type,	X-type	and	Z-type	based	on	Green’s	Covalent	Bond	

Classification.89	The	L-type	ligands	are	neutral	two-electron	donors	with	lone	pairs	such	as	

amines	and	phosphines.	These	ligands	donate	two	electrons	to	the	vacant	orbitals	of	the	

metal	ions.	X-type	ligands	are	one-electron	Lewis	bases,	such	as	carboxylates,	chlorides,	

14	

	
	
	
	
	
 
 
 
 
and	sulfides.	Two	X-type	ligands	can	coordinate	with	a	divalent	cation	such	as	Cd2+	or	Pb2+	

to	form	covalent	bonds.86	In	larger	quantum	dots,	a	surface	monolayer	of	divalent	cations	is	

formed,	which	can	coordinate	with	two	X-type	ligands	to	form	MX2	complexes,	where	M2+	is	

the	divalent	cation	known	as	the	Z-type	ligand.90	Due	to	the	different	types	of	interactions	

of	ligands	to	the	electronic	core,	the	coupling	strengths	between	the	vibrational	modes	to	

electronic	wavefunctions	would	be	quite	different.	

1.4.2	Hot	Carrier	Cooling	in	QDs	

Charge	carriers	are	considered	to	be	‘hot’	when	they	occupy	energy	levels	higher	than	

the	bandgap	upon	photoexcitation.	They	lose	this	excess	energy	via	a	nonradiative	process	

called	hot-carrier	cooling.	In	a	photoexcited	quantum	dot,	the	electrons	that	occupy	higher	

energy	levels	(1Pe)	above	the	band	gap	relax	very	quickly	(subpicosecond	regime)	and	

nonradiatively	to	a	lower	energy	state.91	Consequently,	due	to	the	irreversible	loss	of	

excitation	energy,	quantum	dots	exhibit	low	photoconversion	efficiency	in	photovoltaic	

applications.92	Understanding	the	mechanisms	of	hot	carrier	cooling	are	of	very	high	

importance	to	ensure	better	performance	of	these	materials	in	light	harvesting	

applications.93	Several	mechanisms	were	proposed	to	understand	the	nature	and	

mechanism	of	hot	carrier	cooling	in	recent	years.91,94–96	Early	theoretical	studies	proposed	

that	the	nonradiative	relaxation	is	mediated	by	coupling	of	the	exciton	to	lattice	phonons.94	

But,	the	intraband	spacings	in	the	quantum	dots	are	in	the	order	of	hundreds	of	meV	while	

the	energy	of	phonons	is	tens	of	meV	(for	example,	phonons	have	an	energy	of	30	meV	in	

CdSe	QDs)	which	suggests	that	the	relaxation	could	be	a	slow	multiphonon	process	known	

as	phonon-bottleneck.97,98	Alternative	mechanisms	proposed	for	the	hot	carrier	cooling	

include	nonradiative	relaxation	facilitated	by	Auger	recombination.91,96	Auger	

15	

	
	
	
recombination	occurs	when	the	excess	energy	of	photoexcited	electron	is	transferred	to	

hole	in	the	valence	band.	The	Auger	process	is	mediated	by	strong	Coulombic	attraction	

between	electrons	and	holes.99,100	The	high	density	of	states	in	the	valence	band	of	the	QDs	

would	facilitate	the	hole	relaxation	to	the	band	edge.	The	hole	relaxes	nonradiatively	by	

transferring	energy	to	the	lattice	vibrations/phonons	through	a	multiphonon	process.	In	

contradiction	to	Auger	recombination	mechanism,	the	hole	relaxation	rates	observed	in	

smaller	quantum	dots	with	higher	energy	gaps	were	much	faster	than	larger	quantum	

dots.91,100–102		

Further	studies	on	hot	carrier	cooling	studies	on	CdSe	QDs	with	different	surface	

modifications	using	inorganic	and	organic	molecules	revealed	that	surface	ligands	play	an	

important	role	in	the	process.99	These	results	have	initiated	investigations	on	the	role	of	

surface	and	surface-capping	ligands	in	the	hot	carrier	cooling.	Guyot-Sionnest	and	

coworkers	studied	the	rates	and	mechanism	of	intraband	relaxation	in	QDs	capped	with	

several	ligands	using	transient	absorption	spectroscopy.95,103	They	performed	transient	

absorption	studies	on	CdSe	QDs	capped	with	trioctylphosphine	oxide	(TOPO),	oleic	acid,	

oleylamine,	thiols	and	concluded	that	the	intraband	relaxation	rates	are	ligand-dependent	

in	nature.	They	proposed	that	the	intraband	relaxation	occurs	via	incoherent	energy	

transfer	to	the	vibrational	modes	of	the	surface	ligand	via	dipole-dipole	interaction.103,104	

Kambhampati	group	has	shown	that	the	electronic-to-vibrational	energy	transfer	and	

Auger	recombination	mechanism	are	highly	sensitive	to	QD’s	structure	and	surface	

chemistry.	Their	study	shows	that	the	intraband	relaxation	can	be	slowed	down	by	

decoupling	the	electronic	states	of	the	QD	with	vibrational	states	of	the	ligands	using	ZnS	

16	

	
	
	
layer.105,106	They	point	out	that	the	surface	vibrations	induce	nonadiabatic	pathways	for	the	

hole	relaxation	in	colloidal	CdSe	QDs.105		

Owing	to	spatially	confined	excitonic	wavefunctions,	the	core	electronic	states	are	

quantum	mechanically	mixed	with	ligand	vibrational	modes	by	bonding	interactions,	which	

leads	to	the	delocalization	of	core	electronic	states	to	the	surface	of	the	QDs	(Figure	1.4).	

Therefore,	our	group	proposed	that	hot-carrier	cooling	in	semiconductor	quantum	dots	is	

mediated	by	a	nonadiabatic	radiationless	mechanism,	in	which	branching	or	promoting	

modes	principally	involve	vibrational	modes	of	surface	capping	ligands.	In	Tilluck	et	al.,107	

we	provided	the	first	evidence	that	coherent	vibronic	wavepacket	motions	involving	mid-

frequency	modes	of	the	surface	ligands	promote	hot	carrier	cooling	of	electrons	to	the	band	

edge	by	a	nonadiabatic	mechanism.	The	study	involved	understanding	the	mechanism	of	

hot	carrier	cooling	in	hexadecylamine-capped	CdSe	QDs.		

In	the	Chapter	3	of	this	dissertation,	the	nature	of	the	structural,	vibrational,	and	kinetic	

processes	involved	in	the	vibronic	exciton	mechanism	of	the	nonradiative	relaxation	of	

excitons	in	oleate-capped	QDs	will	be	addressed.	As	an	extension	of	the	vibronic	exciton	

mechanism,	we	propose	that	photoinduced	charge	transfer	from	the	QD	core	to	the	surface	

ligand	acceptor	molecule	is	initiated	via	a	coherent	intermediate.	In	Chapter	4,	the	nature	

of	the	electronic-vibrational	coupling	that	initiates	charge	transfer	in	the	QD-acceptor	

complex	needs	to	be	established.		

Studies	of	exciton	relaxation	dynamics	in	QDs	were	predominantly	carried	out	using	

conventional	spectroscopic	techniques,	such	as	time-resolved	fluorescence	studies	and	

transient	absorption	spectroscopy	using	pulses	of	about	~100	fs	long.91,95,99,103,104	Recently,	

several	groups	have	employed	two-dimensional	electronic	spectroscopy	(2DES)	to	study	

17	

	
	
	
the	energy	transfer	mechanisms	in	semiconductor	nanocrystals.108–113	Advantages	of	2DES	

over	conventional	pump-probe	spectroscopy	are	described	in	the	experimental	section.	

Several	groups	have	detected	electronic	coherences	between	exciton	levels	of	QDs	and	

vibronic	coherences	arising	from	electron-phonon	coupling.109,110,114,115	Earlier	studies	

have	also	demonstrated	the	capability	to	distinguish	the	fine	structure	resulting	from	single	

and	biexciton	excitations	in	CdSe	quantum	dots,	even	in	the	presence	of	significant	line	

broadening	caused	by	variations	in	size	and	shape.116–118	

In	the	next	section,	the	experimental	methods	used	to	study	the	nonradiative	relaxation	

mechanisms	in	carotenoids	and	semiconductor	quantum	dots	are	discussed.	This	section	

provides	a	brief	introduction	necessary	for	interpreting	the	results	obtained	from	the	

multidimensional	spectroscopy.	An	overview	of	third-order	nonlinear	signals,	such	as	

ground	state	bleaching,	stimulated	emission,	excited	state	absorption,	and	quantum	

coherences	and	their	corresponding	Feynman	diagrams	will	be	discussed.	Subsequently,	

the	experimental	implementation	of	the	2DES	is	described.	

1.5	Multidimensional	Electronic	Spectroscopy	

Two-dimensional	electronic	spectroscopy	(2DES)121–125	is	a	powerful	technique	to	

study	the	energy	transfer	mechanism	in	photosynthetic	light	harvesting11,126–131	and	

semiconductor	quantum	dots.107,108,111,113,116,132	Additionally,	2DES	has	also	been	employed	

to	investigate	the	quantum	coherences	in	ground	and	excited	states	in	several	systems.	As	

discussed	earlier,	many	studies	on	carotenoid	photophysics	and	QDs	have	been	conducted	

using	ultrafast	(~100	fs	pulses)	transient	absorption	and	transient	grating	spectroscopy.	

2DES	offers	several	advantages	over	conventional	transient	absorption	spectroscopy	or	

femtosecond	pump-probe	spectroscopy.	As	a	correlation	spectroscopy	technique,	2DES	

18	

	
	
	
projects	out	the	correlation	between	the	excitation	energy	and	emitted	energy,	which	is	

crucial	for	studying	the	energy	transfer	mechanisms	in	light	harvesting.	The	exciton	

relaxation	pathways	manifest	as	the	time	evolution	of	off-diagonal	crosspeaks	in	the	2D	

spectra.121,123	The	broadband	laser	spectrum	used	to	perform	2DES	can	span	several	

excited	states	simultaneously.	This	enables	us	to	probe	the	excitation	energy	flow	through	

a	cascade	of	energy	levels	and	the	subsequent	relaxation	to	the	ground	state.	The	short	

pulses	employed	in	2DES	provide	partial	relief	from	the	inhomogeneous	broadening	of	

spectral	features.	Furthermore,	short	pulses	that	are	smaller	than	the	electronic	dephasing	

of	energy	levels	allow	us	to	probe	the	electronic	coherences.	These	short	pulses	also	aid	in	

accessing	time-resolved	vibrational	coherences	of	energy	up	to	3000	cm-1.		

1.5.1	Excitation	Pulse	Sequence	in	2DES	

Two-dimensional	electronic	spectroscopy	is	a	nonlinear	spectroscopic	technique	

performed	using	three	very	short	pulses	of	duration,	6-7	fs	scanned	over	two	different	time	

delays	(Figure	1.5).	The	time	delay	between	the	first	and	second	pulses	is	the	coherence	

time	𝜏,	and	that	between	the	second	and	third	pulses	is	the	population	time	𝑇.	The	first	two	

pulses	are	the	excitation	pulses,	and	the	third	pulse	is	the	probe	pulse.	The	first	two	pump	

pulses	are	generated	and	the	time	delay	between	them	are	controlled	using	an	adaptive	

pulse	shaper.	When	the	first	pulse	interacts	with	the	sample,	a	coherence	is	created	in	the	

sample.	Coherence	is	a	linear	superposition	of	ground	and	excited	states.	The	coherence	

evolves	with	respect	to	the	coherence	time	𝜏	and	undergoes	free-induction	decay.	In	the	

meantime,	the	second	pulse	interacts	with	the	system	and	drive	the	evolving	coherence	

into	a	population.	The	population	created	by	the	pulse	pairs	evolves	along	the	population	

time	𝑇,	after	which	a	third	pulse	and	a	probe	pulse	interact	with	the	system.	This	pulse	

19	

	
	
	
creates	another	coherence	that	in	turn	emits	an	electric	field.	The	emitted	signal	travels	

Broadband Multidimensional Electronic Spectroscopy (2DES)

along	the	probe	beam	and	is	detected	as	a	pump-induced	change	in	the	probe	transmission.	

Hot carrier cooling studies using 2DES with 6.7 fs pulses

τ

T

t

Figure	1.5.	Broadband	pulse	sequences	in	the	2DES	experiment.	The	red	Gaussian	pulse	
envelopes	depict	the	excitation	pulses	in	the	pulse	sequence.	The	blue	signals	represent	the	
coherences	emitted	from	the	sample	after	the	interaction	of	the	pulses.	The	first	pulse	
creates	coherence	that	evolves	over	time,	followed	by	the	interaction	of	the	second	pulse	to	
create	a	population.	The	third	pulse	interacts	with	the	system	to	create	another	coherence	
and	an	evolving	electric	field	(blue)	is	emitted	from	the	sample.	(Reproduced	from	Ryan	
Tilluck’s	dissertation,83	adapted	from	work	by	the	Jonas	group.121,133)	

1.5.2	Third-Order	Nonlinear	Optical	Responses	

The	three	types	of	signals	detected	using	2DES	are:	ground-state	bleaching	(GSB),	

y
g
r
e
n
E
n
o
i
t
c
e
t
e
D

E2

E1

E1

E2

Excitation Energy

stimulated	emission	(SE),	and	excited-state	absorption	(ESA).122,133	The	theoretical	

Grumstrup et al. Opt. Express 2007, 15, 16681.

formulation	for	two-dimensional	electronic	correlations	were	developed	by	Jonas	group	

Shim et al.  Phys. Chem. Chem. Phys. 2009, 11, 748.

and	Fleming	group.121,122,133,134	The	phenomenological	interpretation	of	the	signals	is	

adapted	in	this	section	are	based	on	the	works	of	Mukamel,135	Hamm,	and	Zanni.136	In	

Tekavec et al.  Opt. Lett. 2009, 34, 1390.

5

order	to	provide	a	brief	description	of	the	above-mentioned	signals,	Albrecht	wave	mixing	

energy	level	diagram	(WMEL)137	and	double-sided	Feynman	diagrams	will	be	used	in	this	

section.	In	the	WMEL	diagrams,	a	system	with	three	energy	levels	is	used	to	understand	the	

origin	of	the	signals.	The	horizontal	lines	in	the	WMEL	represent	different	energy	levels	in	

the	system.	The	energy	levels	are	labeled	as	‘g’	for	ground	state,	‘1’	for	the	first	excited	

energy	level,	and	‘f’	for	the	second	excited	state	at	a	higher	energy	level.	The	red	arrows	in	

20	

	
	
	
	
 
the	WMEL	represent	the	interaction	of	each	laser	pulse	electric	field	with	the	system.	In	

WMEL,	the	time	progresses	from	left	to	right.		

In	the	double-sided	Feynman	diagram,	the	left	side	represents	the	ket	part	of	the	

wavefunction,	whereas	the	right	side	represents	the	bra	part	of	the	wavefunction.	The	

vertical	lines	show	the	evolution	of	the	wavefunctions	with	each	field-matter	interaction.	

The	field-matter	interactions	are	represented	by	solid	arrows	and	the	emitted	signal	is	

represented	by	dashed	arrows.	The	momentum	vectors	are	represented	by	𝒌n,	where	n	is	

the	order	of	their	interactions	with	the	system.	To	draw	a	connection	between	the	two	

representations,	the	solid	arrows	within	a	WMEL	represent	a	field	matter	interaction	on	

the	left	side	or	ket	side	of	the	Feynman	diagram,	while	the	dashed	arrow	represents	an	

interaction	on	the	right	side	or	bra	side	of	the	Feynman	diagram.		

Ground	state	bleaching	(GSB)	is	the	signal	emitted	by	the	system	after	the	preparation	

of	the	population	in	the	ground	state	during	the	first	two	pump	interactions	(Figure	1.6).	

The	ground	state	is	represented	as	gg	in	the	system.	The	first	interaction	with	the	pump	

pulse	creates	a	coherence	in	the	system,	where	gg	evolves	to	1g	or	g1.	The	system	evolves	

to	1g	when	the	field-matter	interaction	occurs	at	the	ket	side	of	the	Feynman	diagram	

whereas	the	interaction	at	the	bra	side	results	in	g1.	This	coherence	evolves	with	respect	to	

the	coherence	time	𝜏.	After	a	short	interval	of	time,	the	second	pulse	interacts	with	the	

system	and	converts	the	evolving	coherence	into	a	population	in	the	ground	state,	

represented	by	gg.	The	third	pulse	creates	another	coherence	1g	or	g1	in	the	system	which	

emits	an	electric	field	signal	that	can	be	detected.	Depending	on	the	phase	of	the	two	

coherences	created	in	the	system,	there	are	two	types	of	pathways:	rephasing	and	non-

rephasing.	When	the	coherences	induced	by	the	first	and	third	pulses	are	of	the	same	

21	

	
	
	
phase,	the	resulting	pathway	is	termed	as	non-rephasing	pathway.	In	contrast,	when	the	

coherence	has	an	opposite	phase,	the	pathway	is	referred	to	as	the	rephasing	pathway.	

GSB NR

GSB R

f

1

g

t

T

τ 

0

gg 1g

gg

1g

τ 

1

2

T

t

3

-ks

-k2

+k3

+k1

g g

1 g

g g

1 g

g g

f

1

g

t

T

τ 

0

gg 1g

gg

g1

τ 

1

2

T

t

3

+ks

-k3

g g

g 1

g g

1 g

g g

-k2

+k1

Figure	1.6.	WMEL	diagram	(top)	and	Feynman	diagram	(bottom)	of	ground-state	
bleaching	signal.	The	figures	on	the	right	correspond	to	the	non-rephasing	pathway,	
whereas	those	on	the	left	correspond	to	the	rephasing	pathway.	In	the	WMEL	diagram,	
time	evolves	towards	the	right,	and	the	field	matter	interactions	are	numbered	as	1,	2,	and	
3	with	marked	time	delays.	The	solid	arrows	represent	the	field-matter	interaction	on	the	
ket	side	of	the	Feynman	diagram,	whereas	the	dashed	arrows	represent	the	interaction	on	
the	bra	side.	The	dotted	line	in	the	WMEL	and	dashed	arrow	in	the	Feynman	diagram	
represent	the	emitted	signal	after	a	series	of	field-matter	interactions.	The	vertical	line	in	
the	Feynman	diagram	represents	the	evolution	of	the	time.		

22	

	
	
	
	
	
	
Stimulated	emission	(SE)	is	the	signal	emitted	by	the	system	after	the	preparation	of	the	

population	in	the	excited	state	during	the	first	two	pump	interactions	(Figure	1.7).	The	first	

interaction	with	the	pump	pulse	creates	a	coherence	in	the	system	where	gg	evolves	to	1g	

or	g1.	The	second	pulse	interacts	with	the	system	and	converts	the	evolving	coherence	into	

a	population	in	the	excited	state,	which	is	represented	by	11.	The	third	pulse	drives	an	

interaction	downwards	and	creates	another	coherence	1g	or	g1	in	the	system;	this	

coherence	emits	an	electric	field	signal	that	can	be	detected	as	SE.		

For	excited	state	absorption	(ESA),	the	first	interaction	with	the	pump	pulse	creates	a	

coherence	in	the	system,	where	gg	evolves	to	1g	or	g1	(Figure	1.8).	The	second	pulse	

interacts	with	the	system	and	converts	the	evolving	coherence	into	a	population	in	the	

excited	state	represented	by	11.	The	third	pulse	drives	the	population	in	the	excited	state	to	

another	excited	state,	f,	to	create	coherences,	1f	or	f1,	in	the	system.	This	coherence	emits	

an	electric	field	signal	with	a	frequency	of	the	energy	difference	between	states	1	and	f.	

This	signal	corresponds	to	the	absorption	from	the	first	excited	state	of	1.	

By	applying	the	law	of	conservation	of	momentum,	the	signals	after	three	field-matter	

interactions	can	be	detected	along	the	directions,	𝒌1 − 𝒌2 + 𝒌3	for	nonrephasing	pathways	

and	−𝒌1 + 𝒌2 + 𝒌3	for	the	rephasing	pathways.	In	practice,	the	beams	are	arranged	in	a	

boxcar	geometry	for	the	detection	these	signals.	In	boxcar	experimental	implementation,	

the	first	three	pulses	are	aligned	such	that	they	form	the	corners	of	a	box,	while	the	signal	is	

emitted	along	the	fourth	corner	of	the	box.	To	detect	the	rephasing	and	nonrephasing	

pathways,	the	ordering	of	the	first	two	pulses	is	interchanged.	

23	

	
	
SE NR

SE R

f

1

g

t

T

τ 

0

gg 1g

11

1g

τ 

1

2

T

t

3

-ks

+k1

g g

1 g

1 1

1 g

g g

+k3

-k2

f

1

g

t

T

τ 

0

gg 1g

11

g1

τ 

1

2

T

t

3

+ks

-k2

g g

g 1

1 1

1 g

g g

-k3

+k1

Figure	1.7.	WMEL	diagram	(top)	and	Feynman	diagram	(bottom)	of	stimulated	emission	
signals.	The	figures	on	the	right	correspond	to	the	non-rephasing	pathway,	whereas	those	
on	the	left	correspond	to	the	rephasing	pathway.	

24	

	
	
	
	
	
ESA NR

ESA R

f

1

g

t

T

τ 

0

f1

gg 1g

11

τ 

1

2

T

t

3

-ks

+k3

+k1

1 1

f 1

1 1

1 g

g g

-k2

f

1

g

t

T

τ 

0

1f

gg 1g

11

τ 

1

2

T

t

3

+ks

-k3

-k2

1 1

1 f

1 1

1 g

g g

+k1

Figure	1.8.	WMEL	diagram	(top)	and	Feynman	diagram	(bottom)	of	the	excited-state	
absorption	signal.	The	figures	on	the	right	correspond	to	the	non-rephasing	pathway,	
whereas	those	on	the	left	correspond	to	the	rephasing	pathway.	

1.5.3	Quantum	Coherences	in	2DES	

The	broadband	spectrum	accompanied	by	short	pulses	in	the	2DES	experiments	spans	

a	wide	range	of	electronic	states	and	vibrational	states	within	both	excited	and	ground	

states	which	allows	us	to	monitor	the	evolution	of	coherent	wavepacket	motions.138–141	In	

2DES	experiments,	various	kinds	of	coherences	can	be	detected,	including	electronic	

coherence,	vibrational	coherence,	and	vibronic	coherences.121,123,142,143	These	coherences	

25	

	
	
	
	
exhibit	distinct	characteristics,	such	as	differences	in	damping	times	and	their	position	in	

the	2D	spectrum.		

Electronic	coherences	are	observed	in	strongly	coupled	chromophores	with	a	common	

ground	state.	They	can	be	identified	by	the	crosspeak	positions	and	the	frequency	

oscillations.	For	example,	consider	two	electronic	states,	1	and	2,	with	a	common	ground	

state	g.	The	first	field-matter	interaction	creates	coherence	g1,	followed	by	a	second	

interaction	that	drives	the	system	to	21.	In	this	case,	a	coherence	is	created	between	the	

excited	states	1	and	2	which	evolves	along	the	population	time,	𝑇.	The	frequency	of	this	

electronic	coherence	is	equal	to	the	energy	difference	between	states,	1	and	2	(Figure	1.9).	

Since	electronic	coherences	are	observed	owing	to	the	superposition	of	electronic	states,	

they	are	detected	at	the	crosspeaks	of	the	two	states	involved	in	the	coherence	in	2D	

spectra.	The	electronic	coherences	appear	symmetric	with	respect	to	the	diagonal.	The	

damping	times	of	these	coherences	are	typically	a	few	tens	of	femtoseconds.	

Vibrational	coherences,	unlike	electronic	coherences,	are	observed	between	the	

vibrational	energy	levels	in	both	the	ground	and	excited	states.	Depending	on	the	Franck-

Condon	overlap	of	the	excited	state	energy	levels,	vibrational	coherence	peak	patterns	can	

be	observed	throughout	the	2D	spectrum.144,145	The	peak	patterns	are	spaced	according	to	

the	vibrational	quanta	along	the	detection	axis	in	the	2D	spectrum.	They	exhibit	a	greater	

intensity	along	the	lower	energies	of	the	excited	states.144,146,147	As	an	example	for	the	

origin	of	vibrational	coherence	in	the	excited	state	or	vibronic	coherence,	consider	a	two-

level	system	with	ground	electronic	state	g	and	excited	state	1	with	vibrational	levels	v	=	0,	

1	(Figure	1.10).	

26	

	
	
	
NR

R

2

1

g

2

1

g

gg g1

21

g2

τ 

1

2

T

t

3

gg

g2

12

g2

τ 

1

2

T

t

3

2

1

g

2

1

g

gg 1g

12

g2

τ 

1

2

T

t

3

gg 2g

21

g1

τ 

1

2

T

t

3

Figure	1.9.	Example	WMEL	diagram	for	electronic	coherences	between	excited	electronic	
states,	1	and	2.	The	figures	on	the	right	correspond	to	the	non-rephasing	pathway,	whereas	
those	on	the	left	correspond	to	the	rephasing	pathway.	

27	

	
	
	
	
	
	
NR

R

1

g0g0 11g0 1110 11g0

τ 

1

2

T

t

3

g

1

g0g0 10g0 g1g0 11g0

g

τ 

1

2

T

t

3

v1
v0

v1
v0

v1
v0

v1
v0

1

g0g0 g010 1110 11g1

τ 

1

2

T

t

3

g

1

g0g0 g011 1011 10g0

g

τ 

1

2

T

t

3

v1
v0

v1
v0

v1
v0

v1
v0

Figure	1.10.	Example	of	WMEL	diagram	for	vibrational	coherences	between	ground	and	
excited	electronic	state,	1.	Vibrational	states	are	indicated	by	v0	and	v1.	The	figures	on	the	
right	correspond	to	the	non-rephasing	pathway,	whereas	those	on	the	left	correspond	to	
the	rephasing	pathway.	

The	first	interaction	drives	the	system	to	the	first	vibrational	state	of	1	represented	by	

11g0,	and	the	second	interaction	drives	the	system	to	1110.	After	the	second	interaction,	a	

coherence	is	created	between	the	vibrational	states	of	the	first	excited	state,	1.	This	

coherence	evolves	with	respect	to	the	population	time	𝑇	in	the	excited	state,	with	the	

frequency	of	the	energy	difference	between	the	two	vibrational	states.	Vibronic	coherences	

are	characteristics	of	the	excited	state.	They	provide	information	on	the	vibrational	

motions	activated	in	the	excited	states	upon	excitation.	The	damping	times	of	vibronic	

coherences	are	dependent	on	the	coupling	between	the	electronic	states	and	vibrational	

motions	and	the	lifetime	of	the	excited	states.148,149	We	have	previously	detected	rapidly	

28	

	
	
	
	
damped	vibronic	wavepacket	motions	in	the	excited	states	in	several	light-harvesting	

systems	undergoing	rapid	relaxation	processes	from	the	excited	states.11,107,131	Some	of	the	

vibronic	coherences	are	long	lived	and	can	be	detected	at	the	product	states	after	the	

relaxation	of	excitation	to	the	lower	energy	states.150		
Gr st coh

NR

R

1

g0g0 10g0 1010 10g1

g

τ 

1

2

T

t

3

v1
v0

v1
v0

1

g0g0 g011 1111 11g1

g

τ 

1

2

T

t

3

v1
v0

v1
v0

Figure	1.11.	Example	WMEL	diagram	for	ground-state	vibrational	coherences	(stimulated	
Raman)	between	ground	and	excited	electronic	state.	Vibrational	states	are	indicated	by	v0	
and	v1.	The	figures	on	the	right	correspond	to	the	non-rephasing	pathway,	whereas	those	
on	the	left	correspond	to	the	rephasing	pathway.	

Ground-state	vibrational	coherences	are	observed	when	the	first	two	excitation	pulses	

create	coherences	in	the	ground	vibrational	states	of	the	system.	An	example	of	ground-

state	coherence	is	stimulated	Raman	signals	(Figure	1.11).	The	first	interaction	drives	a	

coherence	between	the	g0	and	10,	and	the	second	interaction	creates	a	population	in	the	10	

state.	The	third	interaction	drives	the	system	to	10g1.	This	interaction	creates	a	coherence	

between	the	vibrational	levels	in	the	ground	state.	The	coherence	that	evolves	with	respect	

to	𝑇	exhibits	the	frequency	of	vibrational	motion	in	ground	state	with	a	damping	time	of	

vibrational	dephasing	(several	hundreds	of	fs).		

29	

	
	
	
	
The	natural	light-harvesting	systems	are	significantly	complex	in	terms	of	presence	of	

multiple	electronic	states	and	vibrational	states.	Hence,	the	vibronic	coherences	in	these	

systems	are	much	more	intricate.	The	2DES	presents	an	additional	advantage	over	TA	to	

understand	the	vibronic	mechanism	of	nonradiative	relaxation	by	correlation	of	the	

coherences	to	excitation	and	detection	energies.	Short	pulses	aid	in	detection	of	a	wide	

range	of	coherences	from	low	to	high	frequencies	which	would	not	be	resolved	with	100	fs	

pulses.		

1.6	Instrumentation	

The	earlier	implementation	of	2DES	involved	a	diffractive	optics-based	approaches	

from	the	Miller	group125,151,152	and	Fleming	group.122	The	current	2DES	setup	in	this	thesis	

is	based	on	the	approach	by	Zanni	and	coworkers153,154	and	Ogilvie	and	coworkers155	

where	a	pump-probe	geometry	is	implemented	(Figure	1.14).	In	the	pump-probe	

configuration,	the	momentum	vectors	𝒌1 = 	𝒌2;	therefore,	the	signal	travels	along	𝒌3,	which	

is	the	direction	of	the	probe	beam.	In	addition,	the	signal	detected	in	pump-probe	geometry	

is	the	sum	of	both	nonrephasing	and	rephasing	pathways.	An	adaptive	pulse	shaper	is	

programmed	to	create	a	pulse	pair	in	the	pump	beam.156	The	detection	scheme	in	the	

current	experimental	setup	employs	a	lock-in	detection	method	following	the	work	from	

Zigmantas	and	coworkers.157	

The	excitation	pulses	are	obtained	from	a	Yb	laser	(Spectra-Physics	Spirit-4W)	with	a	4	

W	output	at	100	kHz	repetition	rate	centered	at	1040	nm.	The	noncollinear	optical	

parametric	amplifier	(Spectra-Physics	Spirit-NOPA-3H)	pumped	by	the	Yb	laser	is	used	to	

generate	broadband	pulses	in	the	visible	region.	Inside	the	NOPA,	the	fundamental	beam	is	

split	into	two,	one-part	passes	through	a	white	light	continuum	and	the	second	part	passes	

30	

	
	
	
through	a	series	of	second	harmonic	generation	(SHG)	and	a	third	harmonic	generation	

(THG).	The	third	harmonic	is	mixed	with	the	white	light	continuum	at	two	amplification	

stages	involving	nonlinear	crystals	to	generate	a	broadband	(520-700	nm,	centered	at	600	

nm)	laser	spectrum	for	the	experiments	(Figure	1.12).		

The	output	beam	from	the	NOPA	is	further	split	into	two	beams	using	a	broadband	

dielectric	beamsplitter	(Layertec,	Mellingen)	to	generate	the	pump	and	probe	beams.	Each	

pump	and	probe	beams	are	processed	using	a	programmable	adaptive	pulse	shaper156			

y
t
i
s
n
e
t
n
I

0

550

600

650

700

Wavelength (nm)

Figure	1.12.	An	example	broadband	laser	spectrum	in	the	range	of	510-710	nm	used	in	
2DES	experiments.	The	full	width	at	half	maximum	(FWHM)	is	120	nm	and	the	transform	
limited	pulse	duration	was	6.8	fs.	

(FemtoJock	and	FemtoJock	P,	Biophotonic	Solutions	Inc.).	The	pulse	shapers	consist	of	128-

pixel	spatial	light	modulators	(SLM)	that	are	used	to	manipulate	the	phase	and	amplitude	

of	the	transmitted	pulses.	The	FemtoJock	on	the	pump	beam	contains	two	SLMs	that	are	

used	to	manipulate	both	the	phase	and	amplitude	of	the	pulses,	whereas	FemtoJock	P	has	

only	one	SLM	that	is	used	to	manipulate	only	the	phase	of	the	pulses.	Using	the	FemtoJock,	

31	

	
	
	
	
the	pump	pulses	are	split	into	two	identical	pump	pulses,	and	the	delay	between	them	are	

varied	by	manipulating	the	phase	and	the	amplitude	of	the	electric	field.		

A	detailed	derivation	of	the	pulse	splitting	to	create	a	pulse	replica	and	vary	the	time	

delay	between	them	is	provided	in	Ryan	Tilluck’s	dissertation.	In	short,	to	create	a	pulse	

replica	of	incoming	electric	field,	𝐸in(𝜔)	and	with	a	time	delay	𝜏	and	a	phase	difference	

𝜙	between	them,	a	phase	and	amplitude	function,	𝑀(𝜔)	is	applied	such	that,	

where	𝑀(𝜔) = 	 |cos(𝜔𝜏 + 𝜙)|	and	phase	mask,	Φ(𝜔) = arg	[1 + 𝑒!"($%&’)]	and	

𝐸out(𝜔) = 	𝑀(𝜔)	𝐸in(𝜔)	

(1.1)	

transmission	mask,	𝑇(𝜔) = [1 + 𝑒!"($%&’)]).	

The	adaptive	pulse	shapers	use	multiphoton	intrapulse	interference	phase	scan	(MIIPS)	

to	measure	and	compensate	for	the	chirp	on	the	pulses.156	The	output	from	thin	second	

harmonic	generation	(SHG)	crystal,	beta-Barium	borate	crystal	at	sample	position	is	used	

for	the	MIIPS	scans.	The	pulse	duration	of	the	compressed	pulses	is	characterized	by	

interferometric	autocorrelation	of	the	pump	pulse	pairs.	The	SHG-frequency-resolved-

optical	gating	(FROG)	is	also	measured	during	the	autocorrelation	process	(Figure	1.13).	

Additionally,	multiple	reflections	on	a	pair	of	chirp	mirrors	(Ultrafast	Innovations,	Munich)	

also	aid	to	compensate	the	chirp	on.	The	combination	of	adaptive	pulse	shapers	and	chirp	

mirrors	yield	compressed	pulses	with	transform-limited	durations.	

A	thin	achromatic	half-wave	retarder	plate	on	the	pump	beam	is	used	to	rotate	the	

polarization	of	the	excitation	pulses	to	magic	angle	(54.7°)	with	respect	to	the	probe	for	the	

2DES	experiments	on	the	QDs.	The	probe	beam	is	horizontally	polarized	with	respect	to	the	

optical	bench.	To	calculate	the	nonlinear	anisotropy	signals,	the	polarization	of	the	

excitation	pulses	is	at	45°	with	respect	to	the	polarization	of	the	probe	beam.	A	polarization	

32	

	
	
	
of	45°	will	result	in	equal	intensity	of	the	electric	field	of	the	pulses	along	both	the	parallel	

and	perpendicular	directions.	The	population	time	𝑇,	that	is,	the	time	delay	between	the	

1.0

0.8

0.6

0.4

0.2

y
t
i
s
n
e

t

n

I

0
−100

−50

0
Time (fs)

50

100

)

m
n

(

y
t
i
s
n
e
t
n
I

h
t
g
n
e
e
v
a
W

l

1.0
340

0.8
320

0.6
300

0.4

280
0.2

260
0
−100

−50

0
Time (fs)

50

100

Figure	1.13.	Interferometric	autocorrelation	of	the	pump	pulses,	determined	as	the	
integral	of	the	SHG-FROG	spectrogram156	(left	panel).	SHG-FROG158	spectrogram	for	the	
pump	pulses,	as	measured	with	scanned	pulse	pairs	prepared	by	the	pump	beam's	pulse	
shaper	in	the	2DES	spectrometer.	

second	and	third	pulses,	is	controlled	using	a	time-of-flight	delay	stage	controlled	by	

nanomovers	(Melles	Griot).	The	pump	and	probe	beams	are	focused	and	overlapped	just	

after	the	cuvette	window	to	a	beam	size	of	100	microns	at	the	sample	position	using	an	off-

axis	parabolic	mirror.	The	pump	beam	is	terminated	after	the	sample	position.	

The	probe	beam,	along	with	the	signal	from	the	sample,	was	passed	through	an	

analyzer	polarizer	with	its	axis	aligned	parallel	to	the	polarization	of	the	probe	beam.	This	

analyzer	polarizer	can	be	rotated	using	a	motorized	stage	(Thorlabs)	to	select	the	linear	

components	of	the	signals	parallel	and	perpendicular	to	the	polarization	of	the	excitation	

pulses.	Further,	the	beam	is	focused	using	lens	and	spatially	filtered	to	eliminate	any	

straylight	using	a	lens.	The	spectrograph	of	the	detection	scheme	consists	of	a	spherical	

mirror	followed	by	a	300	gr/mm	grating,	which	disperses	the	beam	into	the	constituent	

33	

	
	
	
	
 
 
wavelengths.	Another	spherical	mirror	is	used	to	focus	the	beam	on	to	the	CCD	(Newton	

Andor	940).		

Figure	1.14.	Instrumentation	set	up	used	in	the	2DES	experiment.	The	Yb	laser	(4W,	100	
kHz,	1040	nm)	is	pumped	to	a	NOPA	to	generate	broadband	visible	pulses	ranging	from	
500-700	nm.	The	adaptive	pulse	shapers	and	the	pairs	of	chirp	mirrors	compress	the	pulse	
to	the	transform	limit.	The	pulse	shaper	on	the	pump	beam	is	manipulated	to	create	a	pulse	
pair	and	vary	the	time	between	the	pump	pulses.	A	time-of-flight	delay	stage	is	used	to	vary	
the	time	delay	between	the	pump	and	the	probe	beams.	The	emitted	signals	are	collected	
using	a	home-built	spectrograph	and	a	fast	CCD.		

The	2D	spectrometer	employs	lock-in	detection	scheme	based	on	design	by	Augulis	and	

Zigmantas157	to	detect	the	signals.	The	pump	beam	is	amplitude-modulated	using	a	

mechanical	chopper	(Thorlabs)	at	a	frequency	of	400	Hz.	In	the	pump-probe	geometry	of	

the	experimental	setup,	the	signals	are	heterodyned	along	the	probe	beam.	The	CCD	

acquires	spectra	at	a	rate	of	1	kHz.	The	CCD	comprises	of	2048	W	×	512	H	pixels,	of	which	

the	bottom	10	pixels	are	used	to	detect	the	signals.	The	signals	are	detected	as	pump	

induced	change	in	probe	intensity	at	the	chopper	frequency	of	400	Hz.	The	signal	intensity	

on	the	CCD	is	binned	by	a	factor	of	8	and	undergoes	shift	register	to	single	line.	The	CCD	is	

set	to	acquire	800	spectra	with	a	1	millisecond	exposure	for	each	spectrum.	The	signals	are	

34	

	
	
	
	
isolated	by	performing	a	fast	Fourier	transform	(FFT)	of	the	time	series	of	intensity	

obtained	at	each	detection	wavelength.		

1.7	Data	Processing	and	Analysis	

During	a	2DES	experiment,	a	series	of	spectra	are	collected	for	each	population	time	𝑇.	

The	time	𝑇	spans	from	-3	picosecond	(ps)	to	several	tens	or	hundreds	of	ps	depending	on	

the	nature	of	the	sample	and	the	nature	of	the	relaxation	kinetics	being	probed.	These	

spectra	contain	the	amplitudes	detected	for	each	binned	pixel	of	the	CCD	for	each	time	

point	of	the	coherence	time	tau.	In	the	experiments	presented	in	this	thesis,	there	were	101	

spectra	for	Tau	time	points	(0-50	fs	in	0.5	fs	steps).	Each	data	file	consists	of	256	x	101	

array	of	amplitudes	where	256	is	the	total	number	of	the	binned	CCD	pixels.	The	data	

processing	is	performed	using	MATLAB	scripts	in	the	initial	stages.		

The	amplitude	of	the	FFT	for	pump-induced	change	in	probe-transmission	undergoes	

decays	with	respect	to	time	and	damps	out	at	about	20	fs	(Figure	1.15).	An	offset	

subtraction	is	carried	out	to	bring	the	oscillations	centered	around	zero.	The	time	points	

after	the	decay	are	removed	and	replaced	with	zeros.	Owing	to	the	symmetric	nature	of	the	

signal	oscillations,	the	amplitude	at	each	detection	wavelength	is	mirrored	and	

concatenated.	The	data	is	further	zero-padded	to	create	2N	data	points	for	the	FFT	analysis.	

The	FFT	output	contains	both	real	and	imaginary	components,	out	of	which	the	real	

components	are	extracted	and	plotted	as	a	contour	with	excitation	energy	on	the	x-axis	and	

detection	energy	on	the	y-axis.	These	steps	are	repeated	for	each	𝑇	to	generate	a	series	of	

2D	spectra	and	associated	data.	Several	iterations	of	the	𝑇-scans	are	analyzed	individually	

and	averaged	to	increase	the	signal-to-noise	ratio	of	a	particular	run.	The	95%	confidence	

interval	of	the	amplitudes	at	each	𝑇	point	is	also	calculated	during	the	averaging	process.		

35	

	
	
	
e
d
u
t
i
l

p
m
A

0

−50

−40

−30

−20

−10

0

10

20

30

40

50

Time (fs)

Figure	1.15.	Evolution	of	the	amplitude	obtained	after	FFT	of	the	pump-induced	change	in	
probe-transmission	with	respect	to	the	time,	integrated	along	the	detection	axis	for	CdSe	
QDs	with	7	fs	pulses.	The	coherent	oscillations	are	isolated,	mirrored	and	zero-padded	
prior	to	the	FFT	process.		

To	perform	kinetic	modeling	of	the	energy	relaxation	processes	in	these	systems,	a	part	

of	the	response	along	a	desired	excitation	energy	is	averaged.	This	data	contains	

amplitudes	of	the	signals	at	all	the	detection	wavelengths	that	evolve	with	time	𝑇.	The	

signals	are	subjected	to	global	modeling159	performed	using	the	CarpetView	software	

package	(Light	Conversion).	The	kinetic	models	are	subtracted	from	the	signal	responses	at	

each	coordinate	in	the	2D	spectra	to	obtain	the	residuals.	These	residuals	are	subjected	to	

FFT	using	Julia	codes	to	obtain	information	on	the	frequencies	of	the	modulations.	Specific	

details	of	the	coherence	analysis	used	for	each	study	are	described	in	the	following	

chapters.	To	characterize	the	frequencies	and	damping	times	of	the	modulations,	linear	

prediction	singular	value	decomposition	(LPSVD)	analysis	is	performed	using	MATLAB	

scripts.	

36	

	
	
	
	
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50	

	
	
	
	
Chapter	2:	Broadband	2DES	Detection	of	Vibrational	Coherence	in	the	Sx	
State	of	Ketocarotenoid	Canthaxanthin	

The	nonadiabatic	mechanism	that	mediates	nonradiative	decay	of	the	bright	S2	state	to	

the	lower	energy	dark	S1	state	of	carotenoids	involves	population	of	an	intermediate	state,	

Sx,	in	several	instances.	The	nature	of	Sx	remains	to	be	determined	definitively,	but	it	has	

been	recently	suggested	that	Sx	corresponds	to	conformationally	distorted	molecules	

evolving	along	out-of-plane	coordinates	of	the	isoprenoid	backbone	near	a	low	barrier	

between	planar	and	distorted	conformations	on	the	S2	potential	surface.	In	this	chapter,	the	

electronic	and	vibrational	dynamics	accompanying	the	formation	of	Sx	in	toluene	solutions	

of	the	ketocarotenoid	canthaxanthin	(CAN)	are	characterized	with	broadband	two-	

dimensional	electronic	spectroscopy	(2DES)	with	7.8	fs	excitation	pulses	and	detection	of	

the	linear	polarization	components	of	the	third-order	nonlinear	optical	signal.	A	

stimulated-emission	cross	peak	in	the	2DES	spectrum	accompanies	the	formation	of	Sx	in	<	

20	fs	following	excitation	of	the	main	absorption	band.	Sx	is	prepared	instantaneously,	

however,	with	excitation	of	hot-band	transitions	associated	with	distorted	conformations	

of	CAN’s	isoprenoid	backbone	in	the	low	frequency	onset	of	the	main	absorption	band.	

Vibrational	coherence	oscillation	maps	and	modulated	anisotropy	transients	show	that	Sx	

undergoes	displacements	from	the	Franck–Condon	S2	state	along	out-of-	plane	coordinates	

as	it	passes	to	the	S1	state.	The	results	are	consistent	with	the	conclusion	that	CAN’s	

carbonyl-substituted	β-ionone	rings	impart	an	intramolecular	charge-transfer	character	

that	frictionally	slows	the	passage	from	Sx	to	S1	compared	to	carotenoids	lacking	carbonyl	

substitution.	Despite	the	longer	lifetime,	the	S1	state	of	CAN	is	formed	with	retention	of	

vibrational	coherence	after	passing	through	a	conical	intersection	seam	with	the	Sx	state.		

51	

	
	
The	work	presented	in	this	chapter	has	been	adapted	from	J.	Chem.	Phys.	2021,	155,	

035103.	

2.1	Introduction	

The	light-harvesting	functions	performed	by	carotenoids	in	photosynthetic	organisms	

chiefly	employ	the	lowest	two	excited	singlet	states,	S1	and	S2,	which	are	π	→	π∗	excitations	

of	a	carotenoid’s	conjugated	isoprenoid	backbone.1–4	The	S2	state	can	be	prepared	optically	

by	transitions	in	the	strong	mid-visible	absorption	band;	S1	is	considered	a	“dark”	state,	

lacking	electric-dipole	allowed	optical	transitions	to	or	from	the	ground	state,	S0.5,6	In	

condensed	phases	and	in	the	binding	sites	of	proteins,	the	S2	state	decays	non-	radiatively	

to	the	S1	state	usually	in	<200	fs	after	absorption	of	light.	Owing	to	the	extremely	short	

timescale,	the	relaxation	process	is	accompanied	by	only	a	few	vibrations	of	the	skeletal	

normal	modes	of	the	isoprenoid	backbone.	The	decay	to	the	S1	state	is	accordingly	very	

likely	to	be	mediated	by	a	nonadiabatic	mechanism,7,8	involving	strong	coupling	of	

electronic	and	vibrational	motions.		

Considerable	evidence	has	accumulated,	however,	showing	that	the	S2	state	does	not	

directly	decay	to	the	S1	state.	An	intermediate,	usually	labeled	Sx,	is	detected	in	<20	fs	after	

optical	preparation	of	the	S2	state	in	several	carotenoids.2,9,10	The	structural	and	

spectroscopic	nature	of	Sx	remains	uncertain.	The	measured	lifetime	of	Sx	in	unsubstituted	

carotenoids9,11	is	consistent	with	the	fluorescence	life-	time	usually	stated	for	S2.2	An	

assignment	of	Sx	to	the	1B−

u	state12,13	was	suggested	early	on	by	Zhang	et	al.14	and	by	

Cerullo	et	al.,9	but	this	assignment	would	apply	formally	only	to	a	planar	carotenoid	with	

C2h	symmetry.	Ostroumov	et	al.15	assigned	the	X	state	they	detected	in	two-dimensional	

electronic	spectroscopy	(2DES)16	studies	of	carotenoids	in	the	LH2	light-harvesting	protein	

52	

	
	
	
from	purple	bacteria	to	a	direct	excitation	to	the	1B−

u	state.	In	their	picture,	the	1B−

u	state	

borrows	oscillator	strength	for	absorption	transitions	from	the	nearby	S2	state	via	a	

Herzberg–Teller	coupling;17,18	in	the	absence	of	symmetry	breaking,	the	1B−

The Journal
of Chemical Physics

expected	to	be	a	dark	state.9	

u	state	would	be	

ARTICLE

scitation.org/journal/jcp

For femtosecond spectroscopy, samples of CAN were dissolved in
toluene (Sigma-Aldrich 179418) to obtain an absorbance of 0.3 at
1) for a 1-mm path length static cuvette and then
545 nm (18 350 cm
centrifuged in a desktop microcentrifuge at 17 000g to pellet light-
−
scattering particles. The CAN samples were kept in the dark prior
to performing femtosecond spectroscopy experiments. The linear
absorption spectrum was measured before and after exposure to the
laser. Neither changes in the absorbance nor changes in the shape of
the linear spectrum were observed after the samples were used in the
recording of 2DES spectra, but a fresh sample was put in place after
three iterations of the data acquisition process.

Figure	2.1.	Structure	of	canthaxanthin.	

FIG. 1. Structure of canthaxanthin.

Our	finding	that	the	lifetime	of	Sx	is	considerably	longer	in	the	carbonyl-substituted	

conformationally	distorted	S2	structure	moving	along	out-of-plane	coordinates	of	the	

isoprenoid	backbone	toward	a	conical	intersection	(CI)	seam	with	the	S1	state.3,11,19,20	This	

Our finding that the lifetime of Sx is considerably longer in
carotenoid	peridinin,	however,	raises	the	possibility	that	Sx	should	be	assigned	instead	to	a	
the carbonyl-substituted carotenoid peridinin, however, raises the
possibility that Sx should be assigned instead to a conformationally
distorted S2 structure moving along out-of-plane coordinates of the
isoprenoid backbone toward a conical intersection (CI) seam8 with
the S1 state.3,11,19,20 This general idea has found additional support
from recent fluorescence studies. The Sx state is the likely origin
of a broad fluorescence emission band in β-carotene solutions at
cryogenic temperatures. The fluorescence anisotropy measured for
the	likely	origin	of	a	broad	fluorescence	emission	band	in	β-carotene	solutions	at	cryogenic	
β-carotene in aprotic solutions at room temperature indicates that
the emission transition dipole moment (TDM) is rotated as much as
relative to that of the Franck–Condon S2 state. These observa-
50
temperatures.	The	fluorescence	anisotropy	measured	for	β-carotene	in	aprotic	solutions	at	
tions suggest that torsional and pyramidal distortions near the center
of the isoprenoid backbone are initiated in Sx.6

general	idea	has	found	additional	support	from	recent	fluorescence	studies.	The	Sx	state	is	

room	temperature	indicates	that	the	emission	transition	dipole	moment	(TDM)	is	rotated	

○

as	much	as	50°	relative	to	that	of	the	Franck–Condon	S2	state.	These	observations	suggest	

that	torsional	and	pyramidal	distortions	near	the	center	of	the	isoprenoid	backbone	are	

initiated	in	Sx.6	In	this	article,	we	report	that	broadband	2DES	can	be	used	to	detect	the	

formation	of	the	Sx	state	in	toluene	solutions	of	the	ketocarotenoid	canthaxanthin	(CAN).	

The	structure	of	CAN	differs	from	that	of	β-carotene	only	by	the	addition	of	a	carbonyl	to	

In this article, we report that broadband 2DES can be used
to detect the formation of the Sx state in toluene solutions of the
ketocarotenoid canthaxanthin (CAN). The structure of CAN dif-
fers from that of β-carotene only by the addition of a carbonyl to
each of the β-ionone (cyclohexene) end rings (Fig. 1). The carbonyls
are thought to be essential to the role served by CAN as a light
sensor in the orange carotenoid protein, which mediates photopro-
tective nonphotochemical quenching mechanisms in the phycobil-
isome in cyanobacteria.21 The 2DES spectra shown in this paper
20 fs after optical preparation of the S2
establish that Sx forms in
state of CAN by transitions in the main absorption band. Further-
more, it is shown that Sx is formed directly by vertical transitions
of molecules in the ground-state ensemble that contribute to the
broad low frequency onset of the main absorption band. Charac-
terization of the high-frequency vibrational coherences in the 2DES
53	
spectrum establishes that Sx and S1 are displaced structurally from
the Franck–Condon S2 state along out-of-plane modes of the iso-
prenoid backbone. Despite the presence of the carbonyl substituents,
which substantially lengthen the lifetime of Sx to 440 fs, the results

<

B. Linear spectroscopy

Linear absorption spectra of CAN samples were recorded at
C) with a Shimadzu UV-2600 spectrometer.

room temperature (23

○

C. Femtosecond spectroscopy

2DES spectra were recorded using a pump–probe optical con-
figuration with adaptive pulse shaping22 to compress the laser pulses
and to prepare the excitation pulse sequence (pulse 1–τ–pulse 2)
required for the three-pulse stimulated photon-echo experiment.16
The instrumentation and methods were introduced in an earlier
publication.23

Excitation pulses were obtained from a noncollinear optical
parametric amplifier (NOPA, Spectra-Physics Spirit-NOPA-3H),
which was pumped by the third harmonic of a 1.04 ￿m amplified
Yb laser (Spectra-Physics Spirit-4W, 400 fs pulses at a 100 kHz rep-
etition rate, 4 W average power). The pump and probe beams in
the spectrometer were split from the NOPA output by a broad-
band dielectric beamsplitter (Layertec, Mellingen), processed by an
adaptive pulse shaper (FemtoJock and FemtoJock P, respectively,
Biophotonic Solutions), and then compressed by multiple reflec-
tions on pairs of broadband chirped mirrors (Ultrafast Innovations,
Munich). For the present experiments, the NOPA’s signal beam out-
put spectrum (Fig. 1) was centered at 590 nm (
520–700 nm usable range). The excitation pulse energy was atten-
uated to 4.5 nJ per pulse, as measured at the sample’s position. The
pump beam’s plane of linear polarization was rotated 45
of the probe beam by a thin achromatic half-wave retarder plate.
The two beams were focused by off-axis parabolic mirrors to 100 ￿m
spots overlapped spatially just after the front window of the sample
cuvette. The excitation pulses in both beams were characterized by

55 nm FWHM;

∼

from that

○

indicate that radiationless decay from Sx to S1 occurs in CAN with

retention of vibrational coherence.

II. EXPERIMENTAL

A. Samples

MIIPS scans24 conducted with a thin β-barium borate crystal, which

was placed at the sample’s position following a single cuvette win-

dow. The estimated pulse duration for both beams at the sample

position was 7.8 fs. Residual phase plots (Figs. S1 and S2), calcu-

lated temporal profiles from the MIIPS scans (Fig. S3), and SHG-

FROG spectrograms25 (Fig. S4) are presented in the supplementary

CAN was used as received from Sigma-Aldrich (32993-2MG).

material.

In order to assess its purity, reversed-phase high-performance liq-

2DES spectra were recorded by programming the pump beam’s

uid chromatography (HPLC) of CAN solutions in acetonitrile was

pulse shaper to scan the coherence time interval between the two

performed with a Waters Atlantis T3 5 ￿m analytical column (4.6

250 mm2) and detection with an Agilent Prostar 325 two-channel

pump pulses, τ, from 0 to 50 fs with 0.5 fs steps to obtain the exci-

tation axis after Fourier transformation. Longer τ scans produced

×

UV/vis detector at 480 and 364 nm. The chromatograms (not

identical spectra but with a lower signal/noise ratio. The detection

shown) establish that

95% of the eluted sample corresponds to the

axis of the 2DES spectrum was measured directly by measuring the

all-trans configuration and that shorter carotenoids are not present.

pump-induced change in probe transmission through the sample

>

J. Chem. Phys. 155, 035103 (2021); doi: 10.1063/5.0055598

Published under an exclusive license by AIP Publishing

155, 035103-2

	
	
	
	
each	of	the	β-ionone	(cyclohexene)	end	rings	(Figure	2.1).	The	carbonyls	are	thought	to	be	

essential	to	the	role	served	by	CAN	as	a	light	sensor	in	the	orange	carotenoid	protein,	which	

mediates	photoprotective	nonphotochemical	quenching	mechanisms	in	the	phycobilisome	

in	cyanobacteria.21	The	2DES	spectra	shown	in	this	Chapter	establish	that	Sx	forms	in	<20	fs	

after	optical	preparation	of	the	S2	state	of	CAN	by	transitions	in	the	main	absorption	band.	

Further-	more,	it	is	shown	that	Sx	is	formed	directly	by	vertical	transitions	of	molecules	in	

the	ground-state	ensemble	that	contribute	to	the	broad	low	frequency	onset	of	the	main	

absorption	band.	Characterization	of	the	high-frequency	vibrational	coherences	in	the	

2DES	spectrum	establishes	that	Sx	and	S1	are	displaced	structurally	from	the	Franck–

Condon	S2	state	along	out-of-plane	modes	of	the	isoprenoid	backbone.	Despite	the	presence	

of	the	carbonyl	substituents,	which	substantially	lengthen	the	lifetime	of	Sx	to	440	fs,	the	

results	indicate	that	radiationless	decay	from	Sx	to	S1	occurs	in	CAN	with	retention	of	

vibrational	coherence.	

2.2	Experimental	Methods	

2.2.1	Samples	

CAN	was	used	as	received	from	Sigma-Aldrich	(32993-2MG).	In	order	to	assess	its	

purity,	reversed-phase	high-performance	liquid	chromatography	(HPLC)	of	CAN	solutions	

in	acetonitrile	was	performed	with	a	Waters	Atlantis	T3	5	μm	analytical	column	(4.6	×	250	

mm2)	and	detection	with	an	Agilent	Prostar	325	two-channel	UV/vis	detector	at	480	and	

364	nm.	The	chromatograms	establish	that	>95%	of	the	eluted	sample	corresponds	to	the	

all-trans	configuration	and	that	shorter	carotenoids	are	not	present.	For	femtosecond	

spectroscopy,	samples	of	CAN	were	dissolved	in	toluene	(Sigma-Aldrich	179418)	to	obtain	

an	absorbance	of	0.3	at	545	nm	(18350	cm−1)	for	a	1-mm	path	length	static	cuvette	and	

54	

	
	
	
then	centrifuged	in	a	desktop	microcentrifuge	at	17	000g	to	pellet	light-scattering	particles.	

The	CAN	samples	were	kept	in	the	dark	prior	to	performing	femtosecond	spectroscopy	

experiments.	The	linear	absorption	spectrum	was	measured	before	and	after	exposure	to	

the	laser.	Neither	changes	in	the	absorbance	nor	changes	in	the	shape	of	the	linear	

spectrum	were	observed	after	the	samples	were	used	in	the	recording	of	2DES	spectra,	but	

a	fresh	sample	was	put	in	place	after	three	iterations	of	the	data	acquisition	process.	

2.2.2	Linear	Spectroscopy		

Linear	absorption	spectra	of	CAN	samples	were	recorded	at	room	temperature	(23	°C)	

with	a	Shimadzu	UV-2600	spectrometer.	

2.2.3	Two-Dimensional	Electronic	Spectroscopy		

2DES	spectra	were	recorded	using	a	pump–probe	optical	configuration	with	adaptive	

pulse	shaping22	to	compress	the	laser	pulses	and	to	prepare	the	excitation	pulse	sequence	

(pulse	1–𝜏–pulse	2)	required	for	the	three-pulse	stimulated	photon-echo	experiment.16	The	

instrumentation	and	methods	were	introduced	in	an	earlier	publication.22	Excitation	pulses	

were	obtained	from	a	noncollinear	optical	parametric	amplifier	(NOPA,	Spectra-Physics	

Spirit-NOPA-3H),	which	was	pumped	by	the	third	harmonic	of	a	1.04	μm	amplified	Yb	laser	

(Spectra-Physics	Spirit-4W,	400	fs	pulses	at	a	100	kHz	repetition	rate,	4	W	average	power).	

The	pump	and	probe	beams	in	the	spectrometer	were	split	from	the	NOPA	output	by	a	

broadband	dielectric	beamsplitter	(Layertec,	Mellingen),	processed	by	an	adaptive	pulse	

shaper	(FemtoJock	and	FemtoJock	P,	respectively,	Biophotonic	Solutions),	and	then	

compressed	by	multiple	reflections	on	pairs	of	broadband	chirped	mirrors	(Ultrafast	

Innovations,	Munich).	For	the	present	experiments,	the	NOPA’s	signal	beam	output	

spectrum	(Figure	2.2)	was	centered	at	590	nm	(∼55	nm	FWHM;	520–700	nm	usable	

55	

	
	
	
range).	The	excitation	pulse	energy	was	attenuated	to	4.5	nJ	per	pulse,	as	measured	at	the	

sample’s	position.	The	pump	beam’s	plane	of	linear	polarization	was	rotated	45°	from	that	

of	the	probe	beam	by	a	thin	achromatic	half-wave	retarder	plate.	The	two	beams	were	

focused	by	off-axis	parabolic	mirrors	to	100	μm	spots	overlapped	spatially	just	after	the	

front	window	of	the	sample	cuvette.	The	excitation	pulses	in	both	beams	were	

characterized	by	MIIPS	scans23	conducted	with	a	thin	β-barium	borate	crystal,	which	was	

placed	at	the	sample’s	position	following	a	single	cuvette	window.	The	estimated	pulse	

duration	for	both	beams	at	the	sample	position	was	7.8	fs.	Residual	phase	plots	(Figures	

A2.1	and	A2.2),	and	SHG-FROG	spectrograms24	(Figure	A2.3)	are	presented	in	the	appendix.	

2DES	spectra	were	recorded	by	programming	the	pump	beam’s	pulse	shaper	to	scan	

the	coherence	time	interval	between	the	two	pump	pulses,	𝜏,	from	0	to	50	fs	with	0.5	fs	

steps	to	obtain	the	excitation	axis	after	Fourier	transformation.	Longer	𝜏	scans	produced	

identical	spectra	but	with	a	lower	signal/noise	ratio.	The	detection	axis	of	the	2DES	

spectrum	was	measured	directly	by	measuring	the	pump-induced	change	in	probe	

transmission	through	the	sample	with	a	home-built	0.2	m	spectrograph	(300	gr/mm	

diffraction	grating)	and	a	fast	CCD	detector	(Andor	Newton	940)	using	a	phase-sensitive	

detection	protocol	and	amplitude	modulation	of	the	pump	pulses.25	The	waiting	time	

interval	between	the	second	pump	pulse	and	the	probe	pulse,	𝑇,	was	scanned	by	a	time-of-

flight	delay	line	from	0	to	20	fs	with	a	2.5	fs	spacing;	the	25	to	500	fs	range	was	then	

sampled	at	5	fs	intervals.	An	additional	dataset,	with	scans	reaching	out	to	𝑇	=	20,000	fs,	

was	used	to	measure	the	lifetime	of	the	S1	state.	Each	reported	2DES	spectrum	was	

determined	as	the	average	of	the	spectra	from	six	successive	𝑇	scans.	Owing	to	the	use	of	

the	pump–probe	optical	geometry	and	amplitude	modulation	of	the	pump–pulse	pair,	the	

56	

	
	
	
2DES	spectra	reported	here	are	intrinsically	autophased.	The	spectra	obtained	using	this	

approach	are	the	sum	of	those	from	the	rephasing	and	non-rephasing	nonlinear	optical	

pathways.22	

Linear	polarization	components	of	the	2DES	signal	were	measured	by	analyzing	the	

transmitted	probe	beam	after	collimation	and	prior	to	the	input	of	the	spectrograph	with	a	

calcite	Glan-laser	polarizer.	The	polarizer	was	rotated	by	a	motorized	stage	in	successive	𝑇	

scans	to	select	the	parallel	and	perpendicular	signal	components,	𝐴∥	and	𝐴+,	respectively,	

relative	to	the	pump	beam’s	plane	of	linear	polarization.	A	dichroism-free	total-amplitude	

signal,	𝐾,	is	obtained	from	the	two	components	as	

𝐾 = 𝐴∥ + 2𝐴+			
where	𝐾	is	proportional	to	the	excited-state	population	prepared	by	the	pump	pulses.26	

(2.1)	

The	anisotropy,	

𝐴∥ − 𝐴+
𝐴∥ + 2𝐴+
measures	the	depolarization	resulting	from	changes	in	the	orientation	of	the	excited-state	

(2.2)	

𝑟 =

TDM	by	internal	motions	or	by	global	rotations	of	the	entire	molecular	framework.	In	some	

cases,	the	anisotropy	signal	includes	contributions	from	electronic	coherence	of	degenerate	

excited	states.27–29	Because	the	pump–probe	spectra	of	carotenoids	exhibit	zero	crossings	

when	ground-state	bleaching	(GSB)	or	stimulated	emission	(SE)	bands	overlap	with	

excited-state	absorption	(ESA)	bands,	𝑟	is	useful	only	where	the	total	amplitude	𝐾	≠	0.	

2.3	Results	

2.3.1	Linear	Spectroscopy	

Figure	2.2	shows	the	linear	absorption	spectrum	of	CAN	in	toluene	solvent	at	room	

temperature	(23	°C).	The	spectrum	is	plotted	as	the	oscillator	strength,	ε(ν)/ν,	which	is	

obtained	from	the	absorption	spectrum,	ε(ν),	and	the	wavenumber	ν	(cm−1).	The	spectrum	

57	

	
	
	
			
The Journal

of Chemical Physics

A

and A

∥

￿

from the two components as

the pump pulses.27 The anisotropy,

K

A

2A

,

=

∥ +

￿

A

A

r

=

∥ −

∥ +

A

2A

￿

,

￿

of	the	excitation	pulses	used	in	the	2DES	experiment	is	plotted	superimposed.	The	

oscillator-strength	spectrum	of	CAN	is	smooth	and	unstructured;	in	comparison,	the	

absorption	spectrum	of	β-carotene	exhibits	a	partially	resolved	vibronic	progression	with	

respect	to	the	C=C	and	C–C	stretching	modes	of	the	isoprenoid	backbone.	Numerical	

simulations	performed	previously	with	the	multimode	Brownian	oscillator	model11,30	

indicate	that	the	carbonyl	substituents	on	the	β-ionone	end	rings	(Figure	2.1)	broaden	the	

spectrum	by	increasing	the	system–bath	coupling	(or	solvation	reorganization	energy),	λ.	

scitation.org/journal/jcp

ARTICLE

with a home-built 0.2 m spectrograph (300 gr/mm diffraction grat-
ing) and a fast CCD detector (Andor Newton 940) using a phase-
sensitive detection protocol and amplitude modulation of the pump
pulses.26 The waiting time interval between the second pump pulse
and the probe pulse, T, was scanned by a time-of-flight delay line
from 0 to 20 fs with a 2.5 fs spacing; the 25 to 500 fs range was then
sampled at 5 fs intervals. An additional dataset, with scans reach-
20 000 fs, was used to measure the lifetime of the
S1 state. Each reported 2DES spectrum was determined as the aver-
age of the spectra from six successive T scans. Owing to the use of
the pump–probe optical geometry and amplitude modulation of the
pump–pulse pair, the 2DES spectra reported here are intrinsically
autophased. The spectra obtained using this approach are the sum
of those from the rephasing and non-rephasing nonlinear optical

ing out to T

=

pathways.22

Linear polarization components of the 2DES signal were mea-
sured by analyzing the transmitted probe beam after collimation and
prior to the input of the spectrograph with a calcite Glan-laser polar-
izer. The polarizer was rotated by a motorized stage in successive
T scans to select the parallel and perpendicular signal components,
, respectively, relative to the pump beam’s plane of linear
polarization. A dichroism-free total-amplitude signal, K, is obtained

FIG. 2. Linear absorption spectrum of CAN in toluene solvent (blue dotted curve),
Figure	2.2.	Linear	absorption	spectrum	of	CAN	in	toluene	solvent	(blue	dotted	curve),	
plotted with respect to the wavenumber ν as the relative oscillator strength,
plotted	with	respect	to	the	wavenumber	ν	as	the	relative	oscillator	strength,	ε(ν)/ν.	The	
25
ε
14000–17000-cm−1	range	of	the	spectrum	is	also	plotted	with	a	×25	scaling	of	the	ordinate.	
scaling of the ordinate. The laser intensity spectrum from the broadband excitation
The	laser	intensity	spectrum	from	the	broadband	excitation	pulses	used	in	the	2DES	
pulses used in the 2DES experiments (red solid curve) is superimposed.
(
experiments	(red	solid	curve)	is	superimposed.	

1 range of the spectrum is also plotted with a
ν. The 14 000–17 000-cm
−

)￿

×

ν

	The	carbonyl	substituents	accentuate	an	additional	feature	in	the	absorption	spectrum	

spectrum by increasing the system–bath coupling (or solvation reor-
ganization energy), λ. The carbonyl substituents accentuate an addi-
tional feature in the absorption spectrum of ketocarotenoids over
of	ketocarotenoids	over	the	14000–18000	cm−1	range,	a	broad	“tail”	in	the	low	frequency	
1 range, a broad “tail” in the low frequency
the 14 000–18 000 cm
onset of the main absorption band. This region of the linear absorp-
−
onset	of	the	main	absorption	band.	This	region	of	the	linear	absorption	spectrum	has	been	
tion spectrum has been assigned to vertical transitions to the 1B
u
state15 or to hot-band transitions of thermally excited molecules with
−
distorted conformations of the isoprenoid backbone.32

(1)

where K is proportional to the excited-state population prepared by

measures the depolarization resulting from changes in the orien-

tation of the excited-state TDM by internal motions or by global

rotations of the entire molecular framework. In some cases, the

anisotropy signal includes contributions from electronic coherence

of degenerate excited states.28–30 Because the pump–probe spectra

of carotenoids exhibit zero crossings when ground-state bleaching

(GSB) or stimulated emission (SE) bands overlap with excited-state

absorption (ESA) bands, r is useful only where the total amplitude

K

0.

≠

III. RESULTS

A. Linear spectroscopy

(2)

B. 2DES spectra

58	

Figure 3 presents 2DES K spectra acquired at several T delays
500 fs dataset from CAN in toluene. The

selected from the 0

NOPA spectrum used in these experiments spans the red tail and

includes a portion of the main absorption band (Fig. 2), which allows

⋅ ⋅ ⋅

both regions to be characterized in parallel in the same 2DES exper-

iment. A comparable laser tuning was used previously in the broad-

band 2DES study by Ostroumov et al.15 of carotenoids in the LH2

protein from purple bacteria. Sugisaki et al.10 used tunable 20 fs

pulses to excite corresponding regions of the absorption spectrum

of β-carotene in separate transient grating experiments. The CAN

concentration was adjusted for the 2DES experiments to obtain an

optical density of 0.3 at 18 350 cm

1, approximately where the nor-

malized laser and absorption spectra cross. These conditions are

−

optimal for excitation of molecules in the main absorption band.

The 2DES spectra presented in Fig. 3 are normalized by the laser

Figure 2 shows the linear absorption spectrum of CAN in

intensity spectrum along both axes.

toluene solvent at room temperature (23

C). The spectrum is plot-

The 2DES K spectra exhibit distinct responses along the

ted as the oscillator strength, ε

ν

ν, which is obtained from the

○

excitation axis in the red tail and main absorption band regions.

absorption spectrum, ε

ν

, and the wavenumber ν (cm

At short delays T, a diagonal band of positive-going signal

spectrum of the excitation pulses used in the 2DES experiment

−

derived from GSB and SE from the S2 state is superimposed on

is plotted superimposed. The oscillator-strength spectrum of CAN

a broader band of negative-going ESA transitions to a manifold

(

)￿

(

)

1). The

is smooth and unstructured; in comparison, the absorption spec-

of higher energy singlet states, Sn. The positive band oscil-

trum of β-carotene exhibits a partially resolved vibronic progres-

sion with respect to the C

C and C–C stretching modes of the

lates parallel to the diagonal of the spectrum over the T

0,

. . ., 50 fs range, with a recurrence back to the diagonal observed at

isoprenoid backbone. Numerical simulations performed previously

with the multimode Brownian oscillator model11,31 indicate that the

==

T

35 fs, which indicates directly that the spectrum is strongly

modulated by

vibrational

coherences.

Scanning

frame-by-

carbonyl substituents on the β-ionone end rings (Fig. 1) broaden the

frame through the entire dataset

reveals

strong amplitude

=

=

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155, 035103-3

	
	
	
	
assigned	to	vertical	transitions	to	the	1B−

u	state15	or	to	hot-band	transitions	of	thermally	

excited	molecules	with	distorted	conformations	of	the	isoprenoid	backbone.31	

2.3.2	2DES	Spectra	

Figure	2.3	presents	2DES	𝐾	spectra	acquired	at	several	𝑇	delays	selected	from	the	0-

500	fs	dataset	from	CAN	in	toluene.	The	NOPA	spectrum	used	in	these	experiments	spans	

the	red	tail	and	includes	a	portion	of	the	main	absorption	band	(Figure	2.2),	which	allows	

both	regions	to	be	characterized	in	parallel	in	the	same	2DES	experiment.	A	comparable	

laser	tuning	was	used	previously	in	the	broadband	2DES	study	by	Ostroumov	et	al.15	of	

carotenoids	in	the	LH2	protein	from	purple	bacteria.	Sugisaki	et	al.10	used	tunable	20	fs	

pulses	to	excite	corresponding	regions	of	the	absorption	spectrum	of	β-carotene	in	

separate	transient	grating	experiments.	The	CAN	concentration	was	adjusted	for	the	2DES	

experiments	to	obtain	an	optical	density	of	0.3	at	18350	cm−1,	approximately	where	the	

normalized	laser	and	absorption	spectra	cross.	These	conditions	are	optimal	for	excitation	

of	molecules	in	the	main	absorption	band.	The	2DES	spectra	presented	in	Figure	2.3	are	

normalized	by	the	laser	intensity	spectrum	along	both	axes.	

The	2DES	𝐾	spectra	exhibit	distinct	responses	along	the	excitation	axis	in	the	red	tail	

and	main	absorption	band	regions.	At	short	delays	𝑇,	a	diagonal	band	of	positive-going	

signal	derived	from	GSB	and	SE	from	the	S2	state	is	superimposed	on	a	broader	band	of	

negative-going	ESA	transitions	to	a	manifold	of	higher	energy	singlet	states,	Sn.	The	positive	

band	oscillates	parallel	to	the	diagonal	of	the	spectrum	over	the	𝑇	=	0-50	fs	range,	with	a	

recurrence	back	to	the	diagonal	observed	at	𝑇	=	35	fs,	which	indicates	directly	that	the	

spectrum	is	strongly	modulated	by	vibrational	coherences.	Scanning	frame-by-frame	

through	the	entire	dataset	reveals	strong	amplitude	oscillations	over	most	of	the	spectrum.	

59	

	
	
	
The Journal
of Chemical Physics

However,	as	𝑇	advances,	a	resolved	SE	cross	peak	spanning	from	the	17500	cm−1	region	to	
scitation.org/journal/jcp
the	lower	frequency	limit	of	the	detection	axis	develops	in	the	main	band	excitation	region	

ARTICLE

FIG. 3. Total amplitude (K) 2DES spectra from CAN in toluene at six waiting times T.

Figure	2.3.	Evolution	of	total	amplitude	(𝐾)	2DES	spectra	from	CAN	in	toluene	at	six	
waiting	times	𝑇.	
oscillations over most of
(The supplementary
material includes a movie with Fig. S5 including the entire set
500 fs range.) However, as T
of 2DES spectra over the T
0
1
advances, a resolved SE cross peak spanning from the 17 500 cm
⋅ ⋅ ⋅
region to the lower frequency limit of the detection axis develops
−

20 fs onward and
in the main band excitation region from T
disappears at T
10-fs spectra show that
a comparable region of SE can be observed in the red tail region at
=
shorter delays T than in the main band. At longer delays, the red tail
region exhibits a series of alternating SE and ESA regions spaced by

the spectrum.

100 fs. The T

0 and T

=

>

=

>

60	

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155, 035103-4

	
	
	
	
from	𝑇	>	20	fs	onward	and	disappears	at	𝑇	>	100	fs.	The	𝑇	=	0	and	𝑇	=	10-fs	spectra	show	

that	a	comparable	region	of	SE	can	be	observed	in	the	red	tail	region	at	shorter	delays	𝑇	

than	in	the	main	band.	At	longer	delays,	the	red	tail	region	exhibits	a	series	of	alternating	

SE	and	ESA	regions	spaced	by	∼500	cm−1,	which	is	consistent	with	interference	of	the	SE	

and	ESA	transitions	due	to	vibronic	progressions	of	modes	of	the	isoprenoid	backbone,	as	

discussed	in	the	following.	Finally,	relatively	strong	regions	of	ESA	characteristic	of	the	S1	

state	develop	below	the	diagonal	at	𝑇	>	150	fs	in	both	excitation	regions.	The	ESA	spectrum	

observed	at	𝑇	=	400	fs	dominates	the	entire	spectrum	from	the	main	excitation	band	well	

into	the	red	tail,	and	it	persists	throughout	as	the	S1	state	decays	to	S0	over	the	𝑇	=	1–10-ps	

range.	

2.3.3	Global	and	Target	Modeling	of	the	2DES	spectra		

The	time	evolution	of	the	non-oscillatory	population	signals	in	the	2DES	𝐾	spectra	

during	the	nonradiative	relaxation	from	S2	to	S1	can	be	approximately	described	by	global	

and	target	modeling.32	This	approach	fits	the	2DES	spectra	using	a	linear	combination	of	

evolution-associated	difference	spectra	(EADS)	for	each	of	the	spectrokinetic	species	in	a	

kinetic	model,	here	describing	the	nonradiative	decay	pathway	between	the	singlet	excited	

states	of	CAN.	The	kinetic	scheme	used	in	these	global	models	defines	a	population	

compartment	labeled	Sx	that	serves	as	an	intermediate	between	the	S2	state	prepared	by	

the	excitation	pulses	and	the	S1	state.	The	EADS	are	weighted	in	the	global	model	by	the	

waiting	time	𝑇	dependence	of	the	populations	for	the	spectrokinetic	species.	The	main	

band	and	red	tail	regions	of	the	excitation	axis	were	modeled	separately.	Figure	2.4	shows	

the	two-dimensional	(2D)	global	model	for	the	main	absorption	band	region	from	17700	to	

18750	cm−1.	The	EADS	from	the	S2	state	contains	alternating	ESA	and	GSB/SE	features	

61	

	
	
	
parallel	to	the	diagonal	of	the	spectrum	spaced	by	∼1200	cm−1,	which	indicates	a	vibronic	

progression	principally	due	to	displacements	of	the	ground	state	S0,	the	resonant	S2	state,	

and	a	higher	singlet	excited	state	Sn	with	respect	to	the	C–C	and	C=C	stretching	modes	of	

the	isoprenoid	backbone	of	CAN.	The	vibronic	structure	is	partially	resolved	at	short	𝑇	

delays	compared	to	the	electronic	dephasing	time	owing	to	partial	relief	of	the	

inhomogeneous	broadening	evident	in	the	linear	absorption	spectrum.	(The	global	model	

is	convoluted	with	a	12-fs	Gaussian-shaped	instrument-response	function	centered	

at	𝑇	=	0	fs.)		

The	instantaneous	compartment	from	the	S2	state	decays	very	rapidly	in	the	global	

model,	in	13.6	±	1.2	fs,	to	yield	the	Sx	intermediate.	This	time	constant	is	comparable	to	

those	determined	previously	for	β-carotene11	and	for	peridinin19	in	heterodyne	transient	

grating	experiments.	The	rise	of	Sx	is	temporally	and	spectrally	well-resolved	from	the	S2	

compartment	in	terms	of	the	delayed	formation	of	its	off-diagonal	cross	peak,	which	

consists	of	a	broad	band	of	net	SE	character	spanning	most	of	the	detection	axis.	The	EADS	

from	Sx	also	incorporates	a	GSB	signal	along	the	diagonal	of	the	spectrum,	which	is	initially	

obscured	by	the	diagonal	ESA	band	from	the	S2	state.	This	finding	confirms	that	S2	and	Sx		

share	the	same	electronic	ground	state.	The	Sx	compartment	decays	in	440	±	10	fs	to	S1,	

which	is	associated	with	a	broad	band	of	ESA	centered	at	16000	cm−1.	As	determined	with	a	

second	dataset	with	a	longer	𝑇	axis	reaching	out	to	20	ps,	the	lifetime	of	S1	for	excitations	in	

the	main	band	is	4.1	±	0.2	ps.	This	value	is	consistent	with	that	determined	previously	in	1D	

pump–probe	experiments	with	excitation	nearer	to	the	absorption	maximum.33	Owing	to	

the	short	time	axis	for	the	𝑇	=	0-500	fs	dataset	of	the	global	model,	we	did	not	include	a	

62	

	
	
	
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of Chemical Physics

compartment	for	the	S0

∗	state,	a	long-lived	(ps	lifetime)	ground-state	intermediate	that	has	

ARTICLE

scitation.org/journal/jcp

been	often	observed	following	radiationless	decay	from	the	S1	state	in	carotenoids.2	

−

∼

500 cm

1, which is consistent with interference of the SE and ESA
transitions due to vibronic progressions of modes of the isoprenoid
backbone, as discussed in the following. Finally, relatively strong
regions of ESA characteristic of the S1 state develop below the
150 fs in both excitation regions. The ESA spectrum
400 fs dominates the entire spectrum from the main
excitation band well into the red tail, and it persists throughout as

observed at T

diagonal at T

>

the S1 state decays to S0 over the T

1–10-ps range.

=

=

C. Global and target modeling of the 2DES spectra

The time evolution of the non-oscillatory population signals
in the 2DES K spectra during the nonradiative relaxation from S2
to S1 can be approximately described by global and target model-
ing.33 This approach fits the 2DES spectra using a linear combination
of evolution-associated difference spectra (EADS) for each of the
spectrokinetic species in a kinetic model, here describing the non-
radiative decay pathway between the singlet excited states of CAN.
The kinetic scheme used in these global models defines a population
compartment labeled Sx that serves as an intermediate between the
S2 state prepared by the excitation pulses and the S1 state. The EADS
are weighted in the global model by the waiting time T dependence
of the populations for the spectrokinetic species. The main band and
red tail regions of the excitation axis were modeled separately.

Figure 4 shows the two-dimensional (2D) global model for the
1. The EADS
main absorption band region from 17 700 to 18 750 cm
from the S2 state contains alternating ESA and GSB/SE features
−
1,
parallel to the diagonal of the spectrum spaced by
which indicates a vibronic progression principally due to displace-
−
∼
ments of the ground state S0, the resonant S2 state, and a higher
singlet excited state Sn with respect to the C–C and C
C stretching
modes of the isoprenoid backbone of CAN. The vibronic structure
is partially resolved at short T delays compared to the electronic
dephasing time owing to partial relief of the inhomogeneous broad-
ening evident in the linear absorption spectrum. (The global model
is convoluted with a 12-fs Gaussian-shaped instrument-response

1200 cm

==

FIG. 4. 2D global and target model for the main band excitation region of the
Figure	2.4.	2D	global	and	target	model	for	the	main	band	excitation	region	of	the	2DES	𝐾	
2DES K spectra from CAN in toluene. (a) Kinetic scheme and time constants for
spectra	from	CAN	in	toluene.	(a)	Kinetic	scheme	and	time	constants	for	nonradiative	decay	
nonradiative decay of the S2 state via an intermediate, Sx, to the S1 state. (b)
of	the	S2	state	via	an	intermediate,	Sx,	to	the	S1	state.	(b)	Time	dependence	of	the	
Time dependence of the populations for the S2 (blue), Sx (green dotted), and S1
populations	for	the	S2	(blue),	Sx	(green	dotted),	and	S1	(red	dashed)	spectrokinetic	species.	
(red dashed) spectrokinetic species. (c) 2D evolution-associated difference spec-
(c)	2D	evolution-associated	difference	spectra	(EADS)	for	the	three	spectrokinetic	species.	
tra (EADS) for the three spectrokinetic species. The EADS are scaled relative to
the maximum of the ESA signal in the S1 compartment.
The	EADS	are	scaled	relative	to	the	maximum	of	the	ESA	signal	in	the	S1	compartment.		

function centered at T

0 fs.)

=

rapidly in the global model, in 13.6

The instantaneous compartment from the S2 state decays very
1.2 fs, to yield the Sx intermedi-
ate. This time constant is comparable to those determined previously
for β-carotene11 and for peridinin20 in heterodyne transient grating
experiments. The rise of Sx is temporally and spectrally well-resolved
from the S2 compartment in terms of the delayed formation of its
off-diagonal cross peak, which consists of a broad band of net SE
character spanning most of the detection axis. The EADS from Sx
also incorporates a GSB signal along the diagonal of the spectrum,

±

ground-state intermediate that has been often observed following
radiationless decay from the S1 state in carotenoids.2

Slices of the 2DES spectra at specific excitation wavenumbers
in the main absorption band were modeled separately in a series of
63	
one-dimensional (1D) global models to probe the dependence of the
response as the excitation is tuned toward the red tail region and to
allow comparison of the fitted set of EADS with the line shapes deter-
100-fs excitation pulses. Figure
mined in earlier experiments with

which is initially obscured by the diagonal ESA band from the S2

S6 in the supplementary material presents the 1D model for exci-

state. This finding confirms that S2 and Sx share the same electronic

tation at 18 500 cm

1. The EADS for Sx in this model is broader

∼

ground state.

The Sx compartment decays in 440

10 fs to S1, which is

associated with a broad band of ESA centered at 16 000 cm

determined with a second dataset with a longer T axis reaching

−

±

1. As

and substantially red-shifted of that determined for the S2 state of

−

β-carotene by de Weerd et al.35 with pump–probe spectroscopy

and from the time-resolved fluorescence upconversion spectrum

reported by Macpherson and Gillbro.36 As the excitation frequency

out to 20 ps, the lifetime of S1 for excitations in the main band is

is scanned over the main band region toward the red tail of the

4.1

0.2 ps. This value is consistent with that determined previ-

absorption spectrum, the lifetime of the S2 state shortens markedly,

ously in 1D pump–probe experiments with excitation nearer to

the absorption maximum.34 Owing to the short time axis for the

but the lifetime of the Sx state remains mostly constant.

The global model determined for the 16 700–17 700 cm

1 part

500 fs dataset of the global model, we did not include

of the red tail region of the excitation axis of the 2DES spectrum of

−

a compartment

for the S0

state, a long-lived (ps lifetime)

CAN is reported in Fig. 5. This model indicates that the Sx state is

±

0

T

=

⋅ ⋅ ⋅

∗

J. Chem. Phys. 155, 035103 (2021); doi: 10.1063/5.0055598

Published under an exclusive license by AIP Publishing

155, 035103-5

	
	
	
	
	
	
Slices	of	the	2DES	spectra	at	specific	excitation	wavenumbers	in	the	main	absorption	

band	were	modeled	separately	in	a	series	of	one-dimensional	(1D)	global	models	to	probe	

the	dependence	of	the	response	as	the	excitation	is	tuned	toward	the	red	tail	region	and	to	

allow	comparison	of	the	fitted	set	of	EADS	with	the	line	shapes	determined	in	earlier	

experiments	with	∼100-fs	excitation	pulses.	Figure	A2.4	in	the	supplementary	material	

presents	the	1D	model	for	excitation	at	18500	cm−1.	The	EADS	for	Sx	in	this	model	is	

broader	and	substantially	red-shifted	of	that	determined	for	the	S2	state	of	β-carotene	by	

de	Weerd	et	al.34	with	pump–probe	spectroscopy	and	from	the	time-resolved	fluorescence	

upconversion	spectrum	reported	by	Macpherson	and	Gillbro.35	As	the	excitation	frequency	

is	scanned	over	the	main	band	region	toward	the	red	tail	of	the	absorption	spectrum,	the	

lifetime	of	the	S2	state	shortens	markedly,	but	the	lifetime	of	the	Sx	state	remains	mostly	

constant.	The	global	model	determined	for	the	16700–17700	cm−1	part	of	the	red	tail	

region	of	the	excitation	axis	of	the	2DES	spectrum	of	CAN	is	reported	in	Figure	2.5.	This	

model	indicates	that	the	Sx	state	is	the	first	state	in	the	kinetic	scheme	for	this	region	of	the	

absorption	spectrum	with	an	appreciable	lifetime.	

64	

	
	
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that of Sx in the main band, but its decay to S1 is considerably more
rapid; however, the lifetime of S1 determined in the global model for
the red tail excitation region, 5.4
that obtained for S1 in the main band. The different lifetimes deter-
mined for Sx and S1 in the red tail suggest that the structures for these
states are somewhat different from those obtained with excitation in
the main absorption band.

0.3 ps, is somewhat longer than

±

D. Vibrational coherence

The 2DES spectrum from CAN is strongly modulated by vibra-
tional coherences associated with modes of the isoprenoid backbone.
Analysis of the overlapping contributions from excited state and
ground state coherences is aided by the oscillation maps provided in
Fig. 6, each of which shows the Fourier amplitude at a selected fre-
quency ωT as a function of the
spectrum. These frequencies were selected from the principal com-
ponents observed in the Fourier amplitude spectra determined at
several coordinates sampled from the 2DES spectra, in particular,
in the region of the Sx cross peak; Figs. 7 and 8 include examples of
the K transients and the corresponding Fourier amplitude spectra
observed near the cross peak from Sx. Additional maps, at 100 cm
1 (Fig. S8), are included in the supplementary
(Fig. S7) and 1800 cm
material. The maps were generated by Fourier transformation with
−
respect to the waiting time T after subtracting the nonoscillating
population signal fit by an overdetermined global model. The resid-
ual transients were zero padded to interpolate the frequency axis, but
the intrinsic resolution, 77 cm
range from 70 to 500 fs. The T
to avoid contamination from oscillatory signals at short delays T,
including those associated with temporal overlap of the second and
third excitation pulses and those from instantaneous nonresonant
responses in the red tail region.

ωex, ωdet

coordinates in the 2DES

(

)

1

−

1, is determined by the sampled T

−

70 fs range was discarded in order

<

1 mode is assigned to C

C in-plane stretch-

==

ing vibrations of the isoprenoid backbone of a carotenoid. (The
numbering adopted here is as commonly used in the literature
on resonance Raman spectroscopy of carotenoids, as reviewed by
Robert et al.37,38) For the excitation region corresponding to the
main absorption band, the most intense peak in the oscillation map
for the ω1 mode is observed near to the diagonal of the spectrum.
Two additional peaks are observed below the diagonal at intervals
nearly matching the mode frequency. The spacing of the peaks is
consistent with the intensity pattern anticipated for a displaced pair
of harmonic oscillator potentials, as modeled by Butkus et al.39 and
by Egorova,40 with the additional provision that the patterns for the
rephasing and nonrephasing nonlinear optical pathways are super-
imposed here. Peaks would be expected in a similar progression
spaced by ω1 above the diagonal of the oscillation map, but the pat-
tern is truncated in the high-frequency corner of the 2DES spectrum
by the tuning of the laser spectrum.

1520 cm

The ω1

=

−

FIG. 5. 2D global and target model for the red tail excitation region of the 2DES
Figure	2.5.	2D	global	and	target	model	for	the	red	tail	excitation	region	of	the	2DES	𝐾	
K spectra from CAN in toluene. (a) Kinetic scheme and time constants for non-
spectra	from	CAN	in	toluene.	(a)	Kinetic	scheme	and	time	constants	for	nonradiative	decay	
radiative decay of the S2 state via an intermediate, Sx, to the S1 state. (b) Time
of	the	S2	state	via	an	intermediate,	Sx,	to	the	S1	state.	(b)	Time	dependence	of	the	
dependence of the populations for the S2 (blue), Sx (green dotted), and S1 (red
populations	for	the	S2	(blue),	Sx	(green	dotted),	and	S1	(red	dashed)	spectrokinetic	species.	
dashed) spectrokinetic species. (c) 2D evolution-associated difference spectra
(c)	2D	evolution-associated	difference	spectra	(EADS)	for	the	three	spectrokinetic	species.	
(EADS) for the three spectrokinetic species. The EADS are scaled relative to the
The	EADS	are	scaled	relative	to	the	maximum	of	the	ESA	signal	in	the	S1	compartment	in	
maximum of the ESA signal in the S1 compartment in the main band region (Fig. 4).
the	main	band	region	(Figure	2.4).	

the first state in the kinetic scheme for this region of the absorp-
tion spectrum with an appreciable lifetime. The instantaneous S2
compartment in this model can be mainly attributed to a nonres-
onant response, given its amplitude compared to the subsequent
population-dependent compartments and its very short lifetime,
7.3
0.7 fs, which is shorter than the 12-fs instrument-response
width estimated in these experiments. The Sx compartment exhibits
10 fs, than the 440-fs lifetime for
a significantly shorter lifetime, 90
Sx in the main absorption band, but it persists long enough to make it
±
clear that it is due to excited-state population produced by resonant
65	
excitation of molecules absorbing in the red tail. The EADS for the
Sx intermediate here includes overlapping net ESA and net SE bands
displaced well below the diagonal of the spectrum, but as noted

±

above, a fast moving off-diagonal SE band can be observed in this

In the red tail region of the excitation axis, peaks are also

excitation region at short delays in the 2DES spectra. The S1 species

that is produced upon decay of Sx shares the off-diagonal spectral

observed in the ω1 oscillation map above and below the diagonal

in partially resolved sum and difference combinations,18,41 which

profile of the S1 state in the main absorption band, but its ampli-

arise from mixing with the other principal modes of the isoprenoid

tude decreases as the absorption oscillator strength decays toward

backbone. The distinct

500 cm

lower frequencies along the excitation axis. These findings strongly

combinations of ω1 with the ω3

−

1005 cm

suggest that excitations of CAN in the red tail region of the ground-

modes. Combination bands are also observed in the red tail region

−

−

state absorption spectrum promptly prepare a structure analogous to

of the oscillation maps at other mode frequencies. This finding is

=

∼

=

1 spacing likely corresponds to

1 and/or ω4

960 cm

1

J. Chem. Phys. 155, 035103 (2021); doi: 10.1063/5.0055598

Published under an exclusive license by AIP Publishing

155, 035103-6

	
	
	
	
	
The	instantaneous	S2	compartment	in	this	model	can	be	mainly	attributed	to	a	

nonresonant	response,	given	its	amplitude	compared	to	the	subsequent	population-

dependent	compartments	and	its	very	short	lifetime,	7.3	±	0.7	fs,	which	is	shorter	than	the	

12-fs	instrument-response	width	estimated	in	these	experiments.	The	Sx	compartment	

exhibits	a	significantly	shorter	lifetime,	90	±	10	fs,	than	the	440-fs	lifetime	for	Sx	in	the	main	

absorption	band,	but	it	persists	long	enough	to	make	it	clear	that	it	is	due	to	excited-state	

population	produced	by	resonant	excitation	of	molecules	absorbing	in	the	red	tail.	The	

EADS	for	the	Sx	intermediate	here	includes	overlapping	net	ESA	and	net	SE	bands	displaced	

well	below	the	diagonal	of	the	spectrum,	but	as	noted	above,	a	fast	moving	off-diagonal	SE	

band	can	be	observed	in	this	excitation	region	at	short	delays	in	the	2DES	spectra.	The	S1	

species	that	is	produced	upon	decay	of	Sx	shares	the	off-diagonal	spectral	profile	of	the	S1	

state	in	the	main	absorption	band,	but	its	amplitude	decreases	as	the	absorption	oscillator	

strength	decays	toward	lower	frequencies	along	the	excitation	axis.	These	findings	strongly	

suggest	that	excitations	of	CAN	in	the	red	tail	region	of	the	ground	state	absorption	

spectrum	promptly	prepare	a	structure	analogous	to	that	of	Sx	in	the	main	band,	but	its	

decay	to	S1	is	considerably	more	rapid;	however,	the	lifetime	of	S1	determined	in	the	global	

model	for	the	red	tail	excitation	region,	5.4	±	0.3	ps,	is	somewhat	longer	than	that	obtained	

for	S1	in	the	main	band.	The	different	lifetimes	determined	for	Sx	and	S1	in	the	red	tail	

suggest	that	the	structures	for	these	states	are	somewhat	different	from	those	obtained	

with	excitation	in	the	main	absorption	band.	

2.3.4	Vibrational	Coherence		

The	2DES	spectrum	from	CAN	is	strongly	modulated	by	vibrational	coherences	

associated	with	modes	of	the	isoprenoid	backbone.	Analysis	of	the	overlapping	

66	

	
	
	
contributions	from	excited	state	and	ground	state	coherences	is	aided	by	the	oscillation	

maps	provided	in	Figure	2.6,	each	of	which	shows	the	Fourier	amplitude	at	a	selected	

frequency	ωT	as	a	function	of	the	(ωex,	ωdet)	coordinates	in	the	2DES	spectrum.	These	

frequencies	were	selected	from	the	principal	components	observed	in	the	Fourier	

amplitude	spectra	determined	at	several	coordinates	sampled	from	the	2DES	spectra	in	the	

region	of	the	Sx	cross	peak;	Figure	2.7	and	2.8	include	examples	of	the	𝐾	transients	and	the	

corresponding	Fourier	amplitude	spectra	observed	near	the	cross	peak	from	Sx.	Additional	

maps,	at	100	cm−1	(Figure	A2.5)	and	1800	cm−1	(Figure	A2.6),	are	included	in	the	

supplementary	material.	The	maps	were	generated	by	Fourier	transformation	with	respect	

to	the	waiting	time	𝑇	after	subtracting	the	nonoscillating	population	signal	fit	by	an	

overdetermined	global	model.	The	residual	transients	were	zero	padded	to	interpolate	the	

frequency	axis,	but	the	intrinsic	resolution,	77	cm−1,	is	determined	by	the	sampled	𝑇	range	

from	70	to	500	fs.	The	𝑇	<	70	fs	range	was	discarded	to	avoid	contamination	from	

oscillatory	signals	at	short	delays	𝑇,	including	those	associated	with	temporal	overlap	of	

the	second	and	third	excitation	pulses	and	those	from	instantaneous	nonresonant	

responses	in	the	red	tail	region.	

The	ω1	=	1520	cm−1	mode	is	assigned	to	C=C	in-plane	stretching	vibrations	of	the	

isoprenoid	backbone	of	a	carotenoid.	(The	numbering	adopted	here	is	as	commonly	used	in	

the	literature	on	resonance	Raman	spectroscopy	of	carotenoids,	as	reviewed	by	Robert	et	

al.36,37)	For	the	excitation	region	corresponding	to	the	main	absorption	band,	the	most	

intense	peak	in	the	oscillation	map	for	the	ω1	mode	is	observed	near	to	the	diagonal	of	the	

spectrum.	Two	additional	peaks	are	observed	below	the	diagonal	at	intervals	nearly	

matching	the	mode	frequency.	The	spacing	of	the	peaks	is	consistent	with	the	intensity	

67	

	
	
	
pattern	anticipated	for	a	displaced	pair	of	harmonic	oscillator	potentials,	as	modeled	by	

Butkus	et	al.38	and	by	Egorova,39	with	the	additional	provision	that	the	patterns	for	the	

rephasing	and	nonrephasing	nonlinear	optical	pathways	are	superimposed	here.	Peaks	

would	be	expected	in	a	similar	progression	spaced	by	ω1	above	the	diagonal	of	the	

oscillation	map,	but	the	pattern	is	truncated	in	the	high-frequency	corner	of	the	2DES	

spectrum	by	the	tuning	of	the	laser	spectrum.	

In	the	red	tail	region	of	the	excitation	axis,	peaks	are	also	observed	in	the	ω1	oscillation	

map	above	and	below	the	diagonal	in	partially	resolved	sum	and	difference	

combinations,18,40	which	arise	from	mixing	with	the	other	principal	modes	of	the	

isoprenoid	backbone.	The	distinct	∼500	cm−1	spacing	likely	corresponds	to	combinations	

of	ω1	with	the	ω3	=	1005	cm−1	and/or	ω4	=	960	cm−1	modes.	Combination	bands	are	also	

observed	in	the	red	tail	region	of	the	oscillation	maps	at	other	mode	frequencies.	This	

finding	is	consistent	with	the	proposal	that	the	photoselected	molecules	in	the	red	tail	

region	assume	a	distribution	of	non-planar	conformations31	because	the	vibrational	modes	

of	distorted	conformations	of	the	isoprenoid	backbone	would	be	more	strongly	mixed	than	

those	for	planar	all-trans	configurations.	A	partially	resolved	node	between	the	main	band	

and	red	tail	excitation	regions	of	the	oscillation	map	can	be	explained	by	interference	of	the	

signals	in	the	two	regions,	which	would	be	expected	due	to	the	shift	of	phase	that	

accompanies	detuning	from	the	center	of	a	spectral	band.38,41	Note	also	that	the	toluene	

solvent	contributes	a	nonresonant	background	at	several	vibrational	frequencies	close	to	

those	of	CAN,	increasingly	as	the	inner-filter	attenuation	of	the	laser	intensity	by	the	CAN	

solute	molecules	decreases,	but	the	restriction	of	the	peak	patterns	along	the	excitation	

axis	as	observed	here	indicates	predominantly	resonant	excitations.	Furthermore,	linear		

68	

	
	
	
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FIG. 6. Oscillation maps for the principal vibrational coherences detected in the 2DES K spectra from CAN in toluene.

Figure	2.6.	Oscillation	maps	for	the	principal	vibrational	coherences	detected	in	the	2DES	
𝐾	spectra	from	CAN	in	toluene.		

The oscillation map observed for the ω2

whereas the vibrational dephasing time for toluene vibrations in the
liquid is 5 ps.43

prediction	singular-value	decomposition	models	of	modulated	transients	at	key	

consistent with the proposal that the photoselected molecules in the
red tail region assume a distribution of non-planar conformations32
because the vibrational modes of distorted conformations of the iso-
prenoid backbone would be more strongly mixed than those for
planar all-trans configurations.

main	band	region,	whereas	the	vibrational	dephasing	time	for	toluene	vibrations	in	the	

coordinates	of	the	2DES	spectrum	(not	shown)	indicate	that	the	damping	times	for	the	
A partially resolved node between the main band and red tail
excitation regions of the oscillation map can be explained by inter-
modulation	components	are	typically	<	400	fs,	which	is	similar	to	the	lifetime	of	Sx	in	the	
ference of the signals in the two regions, which would be expected
due to the shift of phase that accompanies detuning from the center
of a spectral band.39,42 Note also that the toluene solvent contributes
a nonresonant background at several vibrational frequencies close to
those of CAN, increasingly as the inner-filter attenuation of the laser
intensity by the CAN solute molecules decreases, but the restric-
tion of the peak patterns along the excitation axis as observed here
indicates predominantly resonant excitations. Furthermore, linear
prediction singular-value decomposition models of modulated tran-
sients at key coordinates of the 2DES spectrum (not shown) indicate
that the damping times for the modulation components are typically
400 fs, which is similar to the lifetime of Sx in the main band region,

1 mode
is analogous to that of ω1, but some interesting differences are
−
observed in the intensity patterns. The ω2 mode arises from C–C
stretching vibrations coupled to in-plane C–H bending motions near
the center of the isoprenoid backbone.44 In the main band exci-
tation region, the peaks below the diagonal of the spectrum are
not as well resolved as in the ω1 map, perhaps due to differences
in excited-state and ground-state mode frequencies for the over-
lapping SE and GSB peaks, respectively. Furthermore, unlike the
oscillation maps for the other modes, the peaks observed for ω2
in the red tail excitation region are weaker than the diagonal peak
observed in the main band. This observation is consistent with the
idea that the red tail region includes molecules with out-of-plane
distortions. The normal coordinate analysis of β-carotene discussed
by Koyama et al.44 indicates that the resonance Raman intensity of
the ω2 mode is weaker in cis configurations compared to all-trans
configurations.

but	some	interesting	differences	are	observed	in	the	intensity	patterns.	The	ω2	mode	arises	

The	oscillation	map	observed	for	the	ω2	=	1160	cm−1	mode	is	analogous	to	that	of	ω1,	

liquid	is	5	ps.42		

1160 cm

=

<

from	C–C	stretching	vibrations	coupled	to	in-plane	C–H	bending	motions	near	the	center	of	

J. Chem. Phys. 155, 035103 (2021); doi: 10.1063/5.0055598

Published under an exclusive license by AIP Publishing

69	

155, 035103-7

	
	
	
	
the	isoprenoid	backbone.43	In	the	main	band	excitation	region,	the	peaks	below	the	

diagonal	of	the	spectrum	are	not	as	well	resolved	as	in	the	ω1	map,	perhaps	due	to	

differences	in	excited-state	and	ground-state	mode	frequencies	for	the	overlapping	SE	and	

GSB	peaks,	respectively.	Furthermore,	unlike	the	oscillation	maps	for	the	other	modes,	the	

peaks	observed	for	ω2	in	the	red	tail	excitation	region	are	weaker	than	the	diagonal	peak	

observed	in	the	main	band.	This	observation	is	consistent	with	the	idea	that	the	red	tail	

region	includes	molecules	with	out-of-plane	distortions.	The	normal	coordinate	analysis	of	

β-carotene	discussed	by	Koyama	et	al.43	indicates	that	the	resonance	Raman	intensity	of	

the	ω2	mode	is	weaker	in	cis	configurations	compared	to	all-trans	configurations.	

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1 and detection at 16 750 cm
−

transients with excitation at
FIG. 7. Total amplitude K and anisotropy r
FIG. 8. Total amplitude K and anisotropy r
Figure	2.7.	Total	amplitude	𝐾	and	anisotropy	𝑟	transients	with	excitation	at	18200	cm−1	
1 in the Sx cross peak in the main
1 in the Sx cross peak in the red
18 200 cm
17 200 cm
band excitation region. (a) K transient, with the fit from the global model (from
and	detection	at	16750	cm−1	in	the	Sx	cross	peak	in	the	main	band	excitation	region.	(a)	𝐾	
tail excitation region. (a) K transient, with the fit from the global model (Fig. 5)
−
−
global model) transient. (c) Fourier trans-
Fig. 4) superimposed. (b) Residual (K
superimposed. (b) Residual (K-global model) transient. (c) Fourier transform
transient,	with	the	fit	from	the	global	model	(from	Figure	2.4)	superimposed.	(b)	Residual	
form amplitude spectrum of the K residual over the T
70, . . . , 500 fs range. (d)
amplitude spectrum of the K residual over the T
(𝐾−global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	𝐾	residual	
Anisotropy r transient, with a fitted exponential (40 fs time constant). (e) Resid-
−
Anisotropy r transient, with a fitted exponential (92 fs time constant). (e) Resid-
exponential fit) transient. (f) Fourier transform amplitude spectrum of the r
ual (r
exponential fit) transient. (f) Fourier transform amplitude spectrum of the r
ual (r
over	the	𝑇	=	70-	500	fs	range.	(d)	Anisotropy	𝑟	transient,	with	a	fitted	exponential	(40	fs	
100, . . . , 500 fs range. Error bars show the 95% confidence
residual over the T
100, . . . , 500 fs range. Error bars show the 95% confidence
residual over the T
time	constant).	(e)	Residual	(𝑟−exponential	fit)	transient.	(f)	Fourier	transform	amplitude	
intervals for the K and r amplitudes.
intervals for the K and r amplitudes.
=
spectrum	of	the	𝑟	residual	over	the	𝑇	=	100-500	fs	range.	Error	bars	show	the	95%	
confidence	intervals	for	the	𝐾	and	𝑟	amplitudes.	

transients with excitation at

70, . . . , 500 fs range. (d)

=

1 and detection at 16 750 cm
−

−

−

=

=

=

The oscillation map shown in Fig. 6 for 1000 cm

1 displays
unresolved contributions in the spectra from two modes, ω3 and
−
1 mode is assigned to in-plane rocking
ω4. The ω3
1005 cm
motions of methyl groups near the center of the isoprenoid back-
−
1 mode is assigned to hydrogen-out-
bone, whereas the ω4
960 cm
C bonds.
of-plane (HOOP) motions coupled to torsions of the C
−
This mode is usually quite weak in the resonance Raman spectrum
of all-trans carotenoids.44–46 A similar pattern in the oscillation map
1 in
is observed for the local HOOP vibration at ωHOOP
785 cm
the red tail and main band excitation regions. This mode was also
−
detected by Liebel et al.47,48 in impulsive pump–continuum probe
71	

==

=

=

experiments with β-carotene. That this vibration is prominent in the
2DES spectrum from CAN is a strong indication that Sx and/or S1
undergo out-of-plane distortions that weaken the conjugation near
the center of the isoprenoid backbone.

The displacement well below the diagonal of the oscillation map
of the strongest peaks for the ω3 and/or ω4 and the ωHOOP modes
resolves the patterns due to excited-state vibrational coherences40 in
Sx and/or S1 from the overlapping ground-state vibrational coher-
ences from S2. The T range employed for the Fourier transformation
principally monitors the Sx compartment, but it also includes the rise
of the S1 compartment, especially in the red tail. The short lifetime

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18 200 cm

−

ual (r

residual over the T

−

=

ω4. The ω3

1005 cm

bone, whereas the ω4

=

−

=

FIG. 7. Total amplitude K and anisotropy r

transients with excitation at
Figure	2.8.	Total	amplitude	𝐾	and	anisotropy	𝑟	transients	with	excitation	at	17200	cm−1	
1 in the Sx cross peak in the main
1 and detection at 16 750 cm
band excitation region. (a) K transient, with the fit from the global model (from
and	detection	at	16750	cm−1	in	the	Sx	cross	peak	in	the	red	tail	excitation	region.	(a)	𝐾	
−
Fig. 4) superimposed. (b) Residual (K
global model) transient. (c) Fourier trans-
transient,	with	the	fit	from	the	global	model	(Figure	2.5)	superimposed.	(b)	Residual	(𝐾-
form amplitude spectrum of the K residual over the T
70, . . . , 500 fs range. (d)
Anisotropy r transient, with a fitted exponential (40 fs time constant). (e) Resid-
global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	𝐾	residual	over	
exponential fit) transient. (f) Fourier transform amplitude spectrum of the r
the	𝑇	=	70-500	fs	range.	(d)	Anisotropy	𝑟	transient,	with	a	fitted	exponential	(92	fs	time	
100, . . . , 500 fs range. Error bars show the 95% confidence
constant).	(e)	Residual	(𝑟−exponential	fit)	transient.	(f)	Fourier	transform	amplitude	
spectrum	of	the	𝑟	residual	over	the	𝑇	=	100-500	fs	range.	Error	bars	show	the	95%	
confidence	intervals	for	the	𝐾	and	𝑟	amplitudes.		

transients with excitation at
FIG. 8. Total amplitude K and anisotropy r
1 in the Sx cross peak in the red
17 200 cm
tail excitation region. (a) K transient, with the fit from the global model (Fig. 5)
−
superimposed. (b) Residual (K-global model) transient. (c) Fourier transform
amplitude spectrum of the K residual over the T
70, . . . , 500 fs range. (d)
Anisotropy r transient, with a fitted exponential (92 fs time constant). (e) Resid-
exponential fit) transient. (f) Fourier transform amplitude spectrum of the r
ual (r
residual over the T
100, . . . , 500 fs range. Error bars show the 95% confidence
intervals for the K and r amplitudes.

1 and detection at 16 750 cm
−

intervals for the K and r amplitudes.

−

−

=

=

=

The oscillation map shown in Fig. 6 for 1000 cm

1 displays
unresolved contributions in the spectra from two modes, ω3 and
−
1 mode is assigned to in-plane rocking
motions of methyl groups near the center of the isoprenoid back-
1 mode is assigned to hydrogen-out-
960 cm
of-plane (HOOP) motions coupled to torsions of the C
C bonds.
−
This mode is usually quite weak in the resonance Raman spectrum
of all-trans carotenoids.44–46 A similar pattern in the oscillation map
1 in
is observed for the local HOOP vibration at ωHOOP
the red tail and main band excitation regions. This mode was also
−
detected by Liebel et al.47,48 in impulsive pump–continuum probe

785 cm

==

=

experiments with β-carotene. That this vibration is prominent in the
2DES spectrum from CAN is a strong indication that Sx and/or S1
undergo out-of-plane distortions that weaken the conjugation near
the center of the isoprenoid backbone.

The displacement well below the diagonal of the oscillation map
of the strongest peaks for the ω3 and/or ω4 and the ωHOOP modes
resolves the patterns due to excited-state vibrational coherences40 in
Sx and/or S1 from the overlapping ground-state vibrational coher-
ences from S2. The T range employed for the Fourier transformation
principally monitors the Sx compartment, but it also includes the rise
of the S1 compartment, especially in the red tail. The short lifetime
72	

J. Chem. Phys. 155, 035103 (2021); doi: 10.1063/5.0055598

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155, 035103-8

	
	
	
	
	
	
The	oscillation	map	shown	in	Figure	2.6	for	1000	cm−1	displays	unresolved	

contributions	in	the	spectra	from	two	modes,	ω3	and	ω4.	The	ω3	=	1005	cm−1	mode	is	

assigned	to	in-plane	rocking	motions	of	methyl	groups	near	the	center	of	the	isoprenoid	

backbone,	whereas	the	ω4	=	960	cm−1	mode	is	assigned	to	hydrogen-out-of-plane	(HOOP)	

motions	coupled	to	torsions	of	the	C=C	bonds.	This	mode	is	usually	quite	weak	in	the	

resonance	Raman	spectrum	of	all-trans	carotenoids.43–45	A	similar	pattern	in	the	oscillation	

map	is	observed	for	the	local	HOOP	vibration	at	ωHOOP	=	785	cm−1	in	the	red	tail	and	main	

band	excitation	regions.	This	mode	was	also	detected	by	Liebel	et	al.46,47	in	impulsive	

pump–continuum	probe	experiments	with	β-carotene.	That	this	vibration	is	prominent	in	

the	2DES	spectrum	from	CAN	is	a	strong	indication	that	Sx	and/or	S1	undergo	out-of-plane	

distortions	that	weaken	the	conjugation	near	the	center	of	the	isoprenoid	backbone.	

The	displacement	well	below	the	diagonal	of	the	oscillation	map	of	the	strongest	peaks	

for	the	ω3	and/or	ω4	and	the	ωHOOP	modes	resolves	the	patterns	due	to	excited-state	

vibrational	coherences39	in	Sx	and/or	S1	from	the	overlapping	ground-state	vibrational	

coherences	from	S2.	The	𝑇	range	employed	for	the	Fourier	transformation	principally	

monitors	the	Sx	compartment,	but	it	also	includes	the	rise	of	the	S1	compartment,	especially	

in	the	red	tail.	The	short	lifetime	of	S2	limits	its	contributions	over	the	sampled	𝑇	range	to	

stimulated	Raman	(ground-state)	coherences,	which	is	consistent	with	the	strongest	peaks	

in	the	oscillation	maps	from	ω1	and	ω2	being	on	the	diagonal	of	the	2DES	spectrum.	

2.3.5	Anisotropy	

The	general	conclusion	from	the	oscillation	maps	discussed	above	is	that	Sx	and	

perhaps	S1	exhibit	vibrational	coherences	in	out-of-plane	modes	of	the	isoprenoid	

backbone	of	CAN,	and	the	pattern	of	amplitudes	is	different	from	those	observed	in	

73	

	
	
	
resonance	Raman	spectra.	These	points	can	be	further	considered	by	examining	anisotropy	

transients	sampled	below	the	diagonal	of	the	2DES	spectrum	in	regions	associated	with	Sx	

in	the	global	models.	In	the	simplest	picture,	the	anisotropy	provides	information	on	the	

orientation	of	the	TDM	relative	to	the	photoselected	direction	for	the	optically	prepared	S2	

state.	Figures	2.7	and	2.8	compare	the	𝐾	and	𝑟	transients	sampled	in	the	main	band	and	red	

tail	excitation	regions,	respectively,	near	the	maximum	amplitude	of	the	Sx	EADS.	The	𝑟	

transients	are	limited	to	𝑇	>	100	fs	to	avoid	the	zero-crossing	by	𝐾	in	the	main	band.	

(Additional	𝐾	transients	sampled	on	the	diagonal	for	S2	and	off-diagonal	for	the	S1	EADS	

are	included	in	the	supplementary	material	as	Figs.	A2.7–A10.)	

In	the	main	band	excitation	region,	the	𝑟	transient	[Figure	2.7(d)]	exhibits	oscillations	

yielding	a	simplified	Fourier	amplitude	spectrum	[Figure	2.7(f)],	with	the	in-plane	ω1	and	

ω2	components	significantly	attenuated	compared	to	their	counterparts	in	the	spectrum	

[Figure	2.7(c)]	from	the	𝐾	transient	[Figure	2.7(a)].	The	amplitude	oscillations	in	𝐾	can	be	

described	as	an	interference	pattern,	with	repeating	partial	cancellation	and	recurrence	

regions	along	the	𝑇	axis	arising	mainly	from	the	superpositions	of	the	oscillations	from	the	

∼1000	and	1160	cm−1	modes	with	those	from	the	more	resolved	1520	cm−1	mode.	Modes	

with	out-of-plane	character	are	clearly	more	prominent	in	the	𝑟	spectrum,	and	ω4	

apparently	contributes	a	partially	resolved	peak	in	the	∼950	cm−1	region	next	to	the	peak	

for	ω3.	In	comparison,	the	Fourier	amplitude	spectra	of	𝐾	[Figure	2.8(c)]	and	𝑟	[Figure	

2.8(f)]	are	more	similar	with	excitation	in	the	red	tail,	and	the	785	cm−1	component	is	

stronger	than	in	the	main	band.	The	out-of-plane	modes	would	be	expected	to	modulate	

the	direction	of	the	excited-state	TDM	of	a	carotenoid,	so	their	appearance	in	the	𝑟	

transients	should	be	expected	if	Sx	is	displaced	along	those	coordinates	from	the	Franck–

74	

	
	
	
Condon	geometry.	Note	that	if	a	twisted	or	pyramidal	distortion	near	the	center	of	the	

isoprenoid	backbone	occurs,	even	the	ω3	wagging	mode	would	likely	cause	the	direction	of	

the	TDM	to	wobble,	and	it	appears	prominently	in	the	𝑟	spectrum	in	both	excitation	

regions.	Of	course,	a	normal	coordinate	analysis	for	an	all-trans	configuration	of	a	

carotenoid	can	only	be	used	in	a	limited	way	here	to	infer	the	character	of	motion,	

especially	if	an	out-of-plane	distortion	results	in	mixing	of	the	modes	of	the	isoprenoid	

backbone	as	suggested	by	the	oscillation	maps.	In	contrast,	the	ω1	and	ω2	modes	are	mainly	

modulations	of	the	bond	lengths	along	the	direction	of	the	isoprenoid	backbone;	these	

modes	would	not	be	expected	to	modulate	the	TDM	direction	as	strongly.	

The	𝑟	transients	shown	in	Figures	2.7	and	2.8	also	indicate	exponentially	rising	trends	

with	shorter	time	constants	than	those	for	the	decay	of	Sx.	The	initially	lower	average	𝑟	

values	observed	at	𝑇	=	100	fs	are	consistent	with	the	suggestion	that	the	isoprenoid	

backbone	of	CAN	undergoes	an	out-of-plane	displacement	shortly	after	optical	preparation	

of	the	S2	state.	The	fluorescence	anisotropy	from	CAN	in	toluene	exhibits	a	value	of	0.30	

with	excitation	in	the	main	band	region	used	here	(results	not	shown),	which	corresponds	

to	an	average	value	for	the	internal	rotation	of	the	excited-state	TDM	of	∼25°	relative	to	

that	of	the	photoselected	Franck–Condon	S2	state.6	The	rising	𝑟	trend	observed	

subsequently	is	in	general	agreement	with	the	previous	proposal	by	de	Weerd	et	al.34	in	the	

case	of	β-carotene	that	the	isoprenoid	backbone	relaxes	toward	a	planar	conformation	in	S1	

after	undergoing	twisting	deformations	in	the	S2	state,	but	their	picture	would	expect	a	

slower	response	accompanying	vibrational	cooling	in	S1	after	nonradiative	decay	from	Sx.	

An	additional	issue	to	consider,	however,	is	raised	by	the	work	of	Jonas	and	co-workers,48,49	

who	have	pointed	out	that	the	pump–probe	anisotropy	carries	distinct	information	content	

75	

	
	
	
from	that	of	the	fluorescence	anisotropy	when	ESA	signals	are	present	owing	to	the	

involvement	of	a	second	higher-energy	excited	electronic	state	in	the	third-order	nonlinear	

optical	response.	In	the	present	case,	the	strength	of	the	ESA	contributions	to	the	signal	at	

the	Sx	cross	peak	increases	with	respect	to	𝑇	as	population	is	transferred	between	Sx	and	S1.	

The	Sn	states	involved	in	the	ESA	transitions	in	carotenoids	are	likely	to	exhibit	TDMs	

oriented	more	or	less	along	the	direction	of	the	isoprenoid	backbone,6,50	but	they	would	not	

necessarily	be	perfectly	aligned	with	that	of	the	resonant	S2	state	because	the	TDMs	of	the	

singlet	states	of	the	carotenoids	are	calculated	to	be	displaced	by	a	few	degrees	relative	to	

the	molecular	framework.6	This	displacement	introduces	a	possible	electronic	state	

dependence	for	the	orientation	of	the	photoselected	TDMs	contributing	to	the	nonlinear	

optical	signal	during	the	nonradiative	decay	process.	This	issue	might	account	for	the	

observation	that	an	𝑟	>	0.4	value	is	reached	at	the	end	of	the	recordings,	especially	in	

Figure	2.7	for	the	main	band	region.	

In	sum,	these	findings	indicate	that	while	the	oscillations	in	the	anisotropy	are	

potentially	useful	for	determining	the	character	of	motion	in	the	vibrational	coherence	in	

the	Sx	state,	the	relaxation	response	from	the	anisotropy	is	complicated	owing	to	the	

superposition	of	the	trajectory	taken	in	the	S2	and	Sx	states	with	its	projection	onto	the	

higher	Sn	potential	surfaces	for	the	ESA	transitions.	As	already	discussed	for	the	case	of	β-

carotene,	we	anticipate	that	a	direct	use	of	information	from	fluorescence	anisotropy	

measurements	will	allow	a	more	detailed	discussion	about	the	TDM	direction	taken	by	CAN	

upon	optical	excitation	to	the	S2	state.	

76	

	
	
	
2.4	Discussion		

The	broadband	2DES	studies	of	CAN	in	toluene	solution	presented	herein	provide	some	

important	new	details	of	the	structural	dynamics	that	follow	optical	preparation	of	the	S2	

state	of	a	carotenoid	by	transitions	in	the	main	absorption	band	by	demonstrating	that	the	

Sx	state	intermediate	can	be	temporally	and	spectroscopically	resolved	in	terms	of	a	broad	

SE	cross	peak	in	the	2DES	spectrum.	Additionally,	the	results	indicate	that	vertical	

transitions	in	the	red	tail	region	of	the	linear	absorption	spectrum	prepare	Sx	directly,	but	

the	subsequent	decay	to	the	S1	state	is	faster	than	with	excitation	in	the	main	absorption	

band.	Taken	together,	these	findings	clarify	that	the	nonradiative	decay	mechanism	is	

initiated	by	C–C	and	C=C	stretching	displacements	from	the	Franck–Condon	geometry	

followed	by	out-of-plane	vibrational	distortions	of	the	isoprenoid	backbone.	The	out-of-

plane	character	of	Sx	and	S1	is	revealed	especially	by	the	mixing	of	the	character	of	the	

vibrational	modes	from	the	isoprenoid	backbone	that	contribute	to	the	excited-state	

vibrational	coherence	and	by	their	prominence	in	the	anisotropy.	

The	general	hypothesis	that	has	emerged	from	our	work	on	carotenoids	so	far	is	that	

although	the	S0	state	tends	to	favor	essentially	planar,	all-trans	structures,	absorption	of	

light	causes	the	S2	state	to	evolve	rapidly	toward	a	pyramidal	conformation	near	a	seam	of	

CIs	with	the	S1	state.	Figure	2.9	provides	a	schematic	description	of	this	picture	by	

sketching	how	the	potential	energy	surfaces	of	the	singlet	excited	states	of	a	carotenoid	

depend	on	a	reaction	coordinate	initiated	by	optical	excitation	to	the	S2	state.	The	key	event	

in	the	proposed	nonradiative	decay	pathway	from	S2	to	S1	is	the	passage	over	a	low	barrier	

on	the	S2	potential	surface	that	divides	the	regions	favoring	planar	and	out-of-plane	

77	

	
	
	
distorted	structures.	The	present	results	emphasize	that	most	of	these	events,	even	passage	

to	S1,	occur	on	timescales	shorter	than	those	for	pure	vibrational	dephasing.	

The	Sx	state	is	attributed	in	this	picture	to	molecules	that	have	begun	out-of-plane	

deformations	near	the	barrier	region	on	the	S2	surface	after	an	initial	displacement	

principally	along	the	ω1	and	ω2,	C=C	and	C–C	stretching	modes	of	the	isoprenoid	backbone.	

The	initial	displacement	from	the	Franck–Condon	geometry	contributes	to	the	change	in	

bond-length	alternation	along	the	isoprenoid	backbone	that	is	noted	upon	excitation	to	the	

S2	state,51	and	it	gives	rise	to	the	ground-state	vibrational	coherences	that	contribute	to	the	

oscillation	maps	near	the	diagonal	of	the	2DES	spectrum.	In	a	previous	review,3	we	

suggested	that	the	presence	of	low	barriers	on	the	potential	surfaces	for	the	singlet	excited	

states	provides	a	ready	explanation	for	the	time	evolution	of	the	ESA	signals	in	the	near-IR	

assigned	to	Sx,	as	observed	by	Cerullo	et	al.9	in	their	broadband	pump–probe	experiments.	

The	barrier	on	the	S2	surface	has	the	additional	implication	that	tuning	of	the	excitation	

energy	controls	the	fraction	of	the	S2	molecules	having	enough	potential	energy	to	cross	

over	the	barrier.6	Depending	on	the	energy	of	the	Franck–Condon	geometry	relative	to	the	

height	of	the	barrier,	the	Sx	state	would	be	formed	by	crossing	the	barrier	within	a	

vibrational	period	of	the	C=C	and	C–C	stretching	modes	or	the	S2	state	would	be	retained	in	

the	planar	minimum	region.	Given	that	global	modeling	of	the	main	band	excitation	region	

of	the	2DES	spectra	from	CAN	does	not	require	a	branched	radiationless	decay	pathway,	

we	suggest	that	the	carbonyl	substituents	lower	the	effective	barrier	height	significantly	

compared	to	that	of	an	unsubstituted	carotenoid	like	β-carotene	by	stabilizing	the	gradient	

region	of	the	potential	surface,	which	develops	an	ICT	character	as	the	molecule	advances	

along	the	out-of-plane	coordinates	to	the	CI	seam	near	the	S2	(Sx)	minimum.	

78	

	
	
	
The	scheme	shown	in	Figure	2.9	suggests	that	excitations	in	the	red	tail	region	would	

prepare	Sx	directly	via	vertical	optical	transitions	directly	to	the	out-of-plane	gradient	of	

the	S2	potential	surface.	The	results	are	consistent	with	this	idea	because	the	global	model	

for	the	red	tail	excitation	region	of	the	2DES	spectrum	indicates	that	the	Franck–Condon	S2	

state	has	a	negligible	lifetime	prior	to	evolution	to	the	Sx	compartment	and	because	these	

molecules	eventually	yield	an	S1	compartment	exhibiting	a	spectral	profile	matching	that	

for	S1	with	the	main	band	excitation.	The	oscillation	maps	indicate	that	excitations	of	this	

region	of	the	spectrum	results	in	enhanced	mixing	of	the	vibrational	modes	of	the	

isoprenoid	backbone	compared	to	excitations	of	the	main	band	region	of	the	linear	

absorption	spectrum	because	the	combination	peaks	are	more	prominent	than	in	the	main	

band	region.	

For	molecules	passing	over	the	barrier	after	excitation	in	the	main	absorption	band	or	

optically	prepared	past	the	barrier	in	the	red	tail	region,	the	scheme	shown	in	Figure	2.9	

further	suggests	that	the	S1	state	is	formed	by	evolution	down	the	S2	gradient	and	through	

a	seam	of	CIs	near	the	S2	minimum.	The	lifetime	of	Sx	detected	in	the	red	tail	region	is	

considerably	shorter,	by	a	factor	of	four,	than	that	detected	in	the	main	band;	the	larger	

initial	force	of	displacement	that	would	arise	from	a	direct	optical	transition	to	the	Sx	

gradient	and	the	shorter	distance	along	the	reaction	coordinate	from	the	Franck–Condon	

geometry	to	the	CI	seam	may	contribute	to	this	shortening	of	the	lifetime.	In	both	cases,	

however,	solvent	friction	would	retard	the	evolution	along	the	reaction	coordinate	near	the	

CI	seam	owing	to	the	induction	of	ICT	character	that	accompanies	increasing	out-of-plane	

displacement	of	a	conjugated	polyene.52,53	It	should	be	kept	in	mind,	however,	that	this	

picture	for	the	potential	energy	surfaces	is	intrinsically	multicoordinate.	The	structural	

79	

	
	
	
The Journal

of Chemical Physics

ARTICLE

scitation.org/journal/jcp

Sx and S1 is revealed especially by the mixing of the character of the

to Sx, as observed by Cerullo et al.9 in their broadband pump–probe

vibrational modes from the isoprenoid backbone that contribute to

experiments. The barrier on the S2 surface has the additional impli-

the excited-state vibrational coherence and by their prominence in

cation that tuning of the excitation energy controls the fraction of

the anisotropy.

The general hypothesis that has emerged from our work on

the S2 molecules having enough potential energy to cross over the

barrier.6 Depending on the energy of the Franck–Condon geome-

carotenoids so far is that although the S0 state tends to favor essen-

try relative to the height of the barrier, the Sx state would be formed

tially planar, all-trans structures, absorption of light causes the S2

by crossing the barrier within a vibrational period of the C

C and

state to evolve rapidly toward a pyramidal conformation near a seam

C–C stretching modes or the S2 state would be retained in the pla-

of CIs with the S1 state. Figure 9 provides a schematic description of

nar minimum region. Given that global modeling of the main band

this picture by sketching how the potential energy surfaces of the

excitation region of the 2DES spectra from CAN does not require a

singlet excited states of a carotenoid depend on a reaction coordi-

branched radiationless decay pathway, we suggest that the carbonyl

==

nate initiated by optical excitation to the S2 state. The key event in

substituents lower the effective barrier height significantly compared

the proposed nonradiative decay pathway from S2 to S1 is the passage

to that of an unsubstituted carotenoid like β-carotene by stabiliz-

over a low barrier on the S2 potential surface that divides the regions

ing the gradient region of the potential surface, which develops

favoring planar and out-of-plane distorted structures. The present

an ICT character as the molecule advances along the out-of-plane

results emphasize that most of these events, even passage to S1, occur

coordinates to the CI seam near the S2 (Sx) minimum.

on timescales shorter than those for pure vibrational dephasing.

The scheme shown in Fig. 9 suggests that excitations in the red

The Sx state is attributed in this picture to molecules that have

tail region would prepare Sx directly via vertical optical transitions

begun out-of-plane deformations near the barrier region on the S2

directly to the out-of-plane gradient of the S2 potential surface. The

==

surface after an initial displacement principally along the ω1 and ω2
C
C and C–C stretching modes of the isoprenoid backbone. The
initial displacement from the Franck–Condon geometry contributes
to the change in bond-length alternation along the isoprenoid back-
bone that is noted upon excitation to the S2 state,52 and it gives rise to
the ground-state vibrational coherences that contribute to the oscil-
lation maps near the diagonal of the 2DES spectrum. In a previous
review,3 we suggested that the presence of low barriers on the poten-
due	to	excitation	in	the	red	tail	region	may	be	considerably	different	from	that	after	
tial surfaces for the singlet excited states provides a ready explana-
tion for the time evolution of the ESA signals in the near-IR assigned

excitation	in	the	main	band,	which	implies	that	the	S1	structures	produced	upon		

trajectory	taken	following	a	vertical	excitation	to	the	gradient	on	the	S2	potential	surface	

results are consistent with this idea because the global model for the
red tail excitation region of the 2DES spectrum indicates that the
Franck–Condon S2 state has a negligible lifetime prior to evolution
to the Sx compartment and because these molecules eventually yield
an S1 compartment exhibiting a spectral profile matching that for
S1 with the main band excitation. The oscillation maps indicate that
excitations of this region of the spectrum results in enhanced mix-
ing of the vibrational modes of the isoprenoid backbone compared
to excitations of the main band region of the linear absorption spec-
trum because the combination peaks are more prominent than in
the main band region.

For molecules passing over the barrier after excitation in the
main absorption band or optically prepared past the barrier in the
red tail region, the scheme shown in Fig. 9 further suggests that the
S1 state is formed by evolution down the S2 gradient and through
a seam of CIs near the S2 minimum. The lifetime of Sx detected
in the red tail region is considerably shorter, by a factor of four,
than that detected in the main band; the larger initial force of dis-
placement that would arise from a direct optical transition to the Sx
gradient and the shorter distance along the reaction coordinate from
the Franck–Condon geometry to the CI seam may contribute to this
shortening of the lifetime. In both cases, however, solvent friction
would retard the evolution along the reaction coordinate near the
CI seam owing to the induction of ICT character that accompanies
increasing out-of-plane displacement of a conjugated polyene.53,54 It
should be kept in mind, however, that this picture for the potential
energy surfaces is intrinsically multicoordinate. The structural tra-
jectory taken following a vertical excitation to the gradient on the
S2 potential surface due to excitation in the red tail region may be
considerably different from that after excitation in the main band,
which implies that the S1 structures produced upon nonradiative
decay might have different conformations. This idea is suggested by
the finding that the lifetime of S1 is somewhat longer with excitation
in the red tail region than in the main absorption band.

Despite the solvent friction near to the CI seam, the results
show definitively that the S1 state is formed with retention of vibra-
tional coherence after passing from the Sx part of the S2 potential
surface. This finding is in agreement with the conclusions by Liebel
et al.48 for β-carotene, where excited-state vibrational coherence in

FIG. 9. Schematic representations for the potential energy surfaces for the sin-
Figure	2.9.	Schematic	representations	for	the	potential	energy	surfaces	for	the	singlet	
glet states of a carotenoid, plotted here as a function of a reaction coordinate
states	of	a	carotenoid,	plotted	here	as	a	function	of	a	reaction	coordinate	composed	of	
composed of sequential displacements from the Franck–Condon geometry of the
sequential	displacements	from	the	Franck–Condon	geometry	of	the	optically	prepared	S2	
C stretching and
optically prepared S2 state with respect to the C–C and C
state	with	respect	to	the	C–C	and	C=C	stretching	and	out-of-plane	(ϕ)	coordinates	of	the	
out-of-plane (ϕ) coordinates of the isoprenoid backbone. Planar and distorted con-
isoprenoid	backbone.	Planar	and	distorted	conformations	are	divided	by	a	low	barrier	at	
formations are divided by a low barrier at the structure marked ‡ on the reaction
the	structure	marked	‡	on	the	reaction	coordinate	axis.	The	dashed	curve	indicates	that	the	
coordinate axis. The dashed curve indicates that the S2 surface will be stabilized
S2	surface	will	be	stabilized	by	displacements	with	respect	to	the	out-of-plane	coordinates	
by displacements with respect to the out-of-plane coordinates when the isoprenoid
when	the	isoprenoid	backbone	is	carbonyl	substituted,	as	in	CAN.	The	mixed	S2,	S1,	and	S0	
backbone is carbonyl substituted, as in CAN. The mixed S2, S1, and S0 surfaces
surfaces	are	proposed	to	converge	near	the	geometry	of	the	S2	minimum	owing	to	a	conical	
are proposed to converge near the geometry of the S2 minimum owing to a conical
intersection	(CI)	of	the	diabatic	surfaces.	Arrows	indicate	vertical	optical	transitions	from	
intersection (CI) of the diabatic surfaces. Arrows indicate vertical optical transitions
planar	and	distorted	conformations	to	the	S2	state.	Adapted	from	Ref.	6.	
from planar and distorted conformations to the S2 state. Adapted from Ref. 6.

==

J. Chem. Phys. 155, 035103 (2021); doi: 10.1063/5.0055598

Published under an exclusive license by AIP Publishing

80	

155, 035103-10

	
	
	
	
	
	
nonradiative	decay	might	have	different	conformations.	This	idea	is	suggested	by	the	

finding	that	the	lifetime	of	S1	is	somewhat	longer	with	excitation	in	the	red	tail	region	than	

in	the	main	absorption	band.	

Despite	the	solvent	friction	near	to	the	CI	seam,	the	results	show	definitively	that	the	S1	

state	is	formed	with	retention	of	vibrational	coherence	after	passing	from	the	Sx	part	of	the	

S2	potential	surface.	This	finding	is	in	agreement	with	the	conclusions	by	Liebel	et	al.47	for	

β-carotene,	where	excited-state	vibrational	coherence	in	several	modes	lacking	resonance	

Raman	activity	was	observed	in	S1.	Figures	A2.8	and	A2.10	indicate,	however,	that	the	

vibrational	coherence	near	the	center	of	the	ESA	cross	peak	from	S1	is	stronger	in	the	red	

tail	than	with	excitation	in	the	main	band.	This	finding	is	consistent	with	the	shorter	

lifetime	observed	for	Sx	for	the	red	tail	region.	The	modulated	waveform	detected	for	the	

main	band	excitation	(Figure	A2.8)	in	this	case	is	relatively	weak	compared	to	the	

confidence	intervals	for	the	amplitude	samples,	but	even	here	the	results	indicate	that	S1	is	

formed	with	retention	of	vibrational	coherence	because	peaks	are	evident	below	the	

diagonal	in	the	oscillation	maps	at	1800	cm−1	(Figure	A2.6).	Owing	to	partial	inversion	of	

the	C–C/C=C	bond-length	alternation	pattern	in	the	S1	state,51	the	mode	frequency	for	the	

C=C	bond	upshifts	markedly	to	1785	cm−1	from	the	1520	cm−1	natural	frequency	observed	

in	the	resonance	Raman	spectrum	for	all-trans	or	cis	configurations,	respectively.35,46,47,54,55	

The	present	results	regrettably	do	not	provide	definitive	information	on	the	vibrational	

modes	that	promote	nonradiative	decay	from	Sx	to	S1	for	CAN.	The	principal	modes	of	the	

isoprenoid	backbone	have	relatively	short	damping	times,	<400	fs,	which	is	similar	to	the	

lifetime	of	Sx,	but	they	undergo	several	vibrational	recurrences	during	the	passage	from	the	

Franck–Condon	region	to	the	CI	seam.	Accordingly,	these	components	are	likely	to	be	

81	

	
	
	
serving	as	spectator	modes	rather	than	driving	progress	along	the	reaction	coordinate.	In	

contrast,	especially	considering	the	probable	contribution	from	solvent	friction	as	the	ICT	

character	develops,	the	reaction-coordinate	modes	ought	to	be	much	more	rapidly	damped.	

Indeed,	the	tuning	and	coupling	modes	that	define	the	branching	plane56	for	the	CI	seam	

with	S1	might	be	expected	only	to	carry	out	only	a	single	excursion	after	being	launched	by	

the	onset	of	the	Sx	gradient.	Alternative	candidates	for	the	branching	modes	for	the	

nonadiabatic	mechanism	would	include	delocalized	torsional	modes	of	the	isoprenoid	

backbone	at	natural	frequencies	in	the	300–700	cm−1	region.43	These	modes	would	be	

expected	to	be	strongly	damped	near	the	CI	seam,	but	their	half	periods	are	compatible	

with	the	anisotropy	kinetics	and	the	Sx	lifetimes	determined	in	the	global	models.

82	

	
	
	
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https://doi.org/10.1098/rsif.2017.0504.	

(38)	Butkus,	V.;	Zigmantas,	D.;	Valkunas,	L.;	Abramavicius,	D.	Vibrational	vs.	Electronic	

Coherences	in	2D	Spectrum	of	Molecular	Systems.	Chem.	Phys.	Lett.	2012,	545,	40–43.	

(39)	Egorova,	D.	Self-Analysis	of	Coherent	Oscillations	in	Time-Resolved	Optical	Signals.	J.	

Phys.	Chem.	A	2014,	118	(44),	10259–10267.	

(40)	Farfan,	C.	A.;	Turner,	D.	B.	Interference	among	Multiple	Vibronic	Modes	in	Two-

Dimensional	Electronic	Spectroscopy.	Sci.	China	Ser.	A	Math.	2020,	8	(2),	157.	

(41)	Butkus,	V.;	Zigmantas,	D.;	Abramavicius,	D.;	Valkunas,	L.	Distinctive	Character	of	

Electronic	and	Vibrational	Coherences	in	Disordered	Molecular	Aggregates.	Chem.	
Phys.	Lett.	2013,	587,	93–98.	

(42)	Niu,	K.;	Lee,	S.-Y.	Analysis	of	Time	Resolved	Femtosecond	and	

Femtosecond/Picosecond	Coherent	Anti-Stokes	Raman	Spectroscopy:	Application	to	
Toluene	and	Rhodamine	6G.	J.	Chem.	Phys.	2012,	136	(6),	064504.	

(43)	Koyama,	Y.;	Takatsuka,	I.;	Nakata,	M.;	Tasumi,	M.	Raman	and	Infrared	Spectra	of	the	

All-Trans,	7-Cis,	9-Cis,	13-Cis	and	15-Cis	Isomers	of	β-Carotene:	Key	Bands	
Distinguishing	Stretched	or	Terminal-Bent	Configurations	Form	Central-Bent	
Configurations.	J.	Raman	Spectrosc.	1988,	19	(1),	37–49.	

(44)	Okamoto,	H.;	Sekimoto,	Y.;	Tasumi,	M.	Assignment	and	Anharmonicity	Analysis	of	

Overtone	and	Combination	Bands	Observed	in	the	Resonance	Raman	Spectra	of	
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(45)	Ou-Yang,	S.-L.;	Wu,	N.-N.;	Tian,	Y.-J.	Effect	of	High	Pressure	on	the	Molecular	Structure	
and	π-Electrons	Delocalization	of	Canthaxanthin	as	Revealed	by	Raman	Spectra.	
Journal	of	Spectroscopy	2015,	2015.	https://doi.org/10.1155/2015/467089.	

(46)	Liebel,	M.;	Kukura,	P.	Broad-Band	Impulsive	Vibrational	Spectroscopy	of	Excited	
Electronic	States	in	the	Time	Domain.	J.	Phys.	Chem.	Lett.	2013,	4	(8),	1358–1364.	

86	

	
	
	
(47)	Liebel,	M.;	Schnedermann,	C.;	Kukura,	P.	Vibrationally	Coherent	Crossing	and	Coupling	
of	Electronic	States	during	Internal	Conversion	in	β-Carotene.	Phys.	Rev.	Lett.	2014,	
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Polarization	Anisotropy:	Application	to	Square	Symmetric	Molecules	and	
Perpendicular	Chromophore	Pairs.	J.	Chem.	Phys.	2003,	119	(3),	1611–1622.	

(49)	Farrow,	D.	A.;	Smith,	E.	R.;	Qian,	W.;	Jonas,	D.	M.	The	Polarization	Anisotropy	of	

Vibrational	Quantum	Beats	in	Resonant	Pump-Probe	Experiments:	Diagrammatic	
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Chem.	Phys.	2000,	259	(2),	273–295.	

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Photoisomerization	of	a	Model	Protonated	Schiff	Base	in	Solution.	J.	Phys.	Chem.	A	
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(54)	Hashimoto,	H.;	Koyama,	Y.	The	C (cid:0) C	Stretching	Raman	Lines	of	[β-Carotene	Isomers	
in	the	S1	State	as	Detected	by	Pump-Probe	Resonance	Raman	Spectroscopy.	Chem.	
Phys.	Lett.	1989,	154	(4),	321–325.	

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Intersections.	J.	Chem.	Phys.	1991,	95	(3),	1862–1876.	

87	

	
	
	
APPENDIX	

Laser 
Phase

2

1

0

−1

−2

P
h
a
s
e

(
r
a
d
s
)

)
.
u
.
a
(

y
t
i
s
n
e
t
n
I

1.0

0.8

0.6

0.4

0.2

0

16,000
Frequency (cm-1)

18,000

Figure	A2.1.	Laser	intensity	and	residual	phase	spectrum	for	the	laser	pulses	in	the	pump	
FIG. S1. Laser intensity and residual phase spectrum for the laser pulses in the pump beam of the 2DES
beam	of	the	2DES	spectrometer,	with	the	latter	determined	at	the	sample’s	position	by	
spectrometer, with the latter determined at the sample’s position by MIIPS scans1 after compression.
MIIPS	scans23	after	compression.		

)
.
u
.
a
(

y
t
i
s
n
e

t

n

I

1.0

0.8

0.6

0.4

0.2

0

Laser 
Phase

2

1

0

−1

−2

P
h
a
s
e

(
r
a
d
s
)

16,000
Frequency (cm-1)

18,000

FIG. S2. Laser intensity and residual phase spectrum for the laser pulses in the probe beam of the 2DES

spectrometer, with the latter determined at the sample’s position by MIIPS scans1 after compression.

88	

2

	
	
	
 
 
 
 
)

.

u

.

a

(

y

t

i

s

n

e

t

n

I

1.0

0.8

0.6

0.4

0.2

0

Laser 

Phase

2

1

0

−1

−2

P

h

a

s

e

(

r

a

d

s

)

16,000
Frequency (cm-1)

18,000

FIG. S1. Laser intensity and residual phase spectrum for the laser pulses in the pump beam of the 2DES

spectrometer, with the latter determined at the sample’s position by MIIPS scans1 after compression.

)
.
u
.
a
(

y
t
i
s
n
e
t
n
I

1.0

0.8

0.6

0.4

0.2

0

Laser 
Phase

2

1

0

−1

−2

P
h
a
s
e

(
r
a
d
s
)

16,000
Frequency (cm-1)

18,000

FIG. S3. Calculated temporal profile for the electric field of the pump pulses, as determined by the MIIPS
Figure	A2.2.	Laser	intensity	and	residual	phase	spectrum	for	the	laser	pulses	in	the	probe	
FIG. S2. Laser intensity and residual phase spectrum for the laser pulses in the probe beam of the 2DES
beam	of	the	2DES	spectrometer,	with	the	latter	determined	at	the	sample’s	position	by	
spectrometer, with the latter determined at the sample’s position by MIIPS scans1 after compression.
MIIPS	scans	after	compression.		

scans.1

2

FIG. S4. Interferometric autocorrelation and SHG-FROG2 spectrograms for the pump pulses, as measured
Figure	A2.3.	Interferometric	autocorrelation	and	SHG-FROG24	spectrograms	for	the	pump	
pulses,	as	measured	with	scanned	pulse	pairs	prepared	by	the	pump	beam’s	pulse	shaper.		

with scanned pulse pairs prepared by the pump beam’s pulse shaper.

3

89	

	
	
	
	
 
 
 
 
A

18 fs

S2

Sx

450 fs

S1

4.3 ps

S0

S2
Sx
S1

B

1.0

n
o

i
t

l

a
u
p
o
P

0.5

C

e
d
u
t
i
l

p
m
A

0

2
1
0
1

2

1

0

0

5

10

0

100

300

200
Delay T (fs)

400

500

S2S2

SxSx

S1

550

600

650

700

Wavelength (nm)

18500 cm

Figure	A2.4.	1D	global	and	target	model	for	the	2DES	spectra	from	CAN	in	toluene,	with	
FIG. S6. 1D global and target model for the 2DES spectra from CAN in toluene, with excitation at
excitation	at	18500	cm−1	(540	nm).	(a)	Kinetic	scheme	for	nonradiative	decay	of	the	
1 (540 nm). (a) Kinetic scheme for nonradiative decay of the resonant S2 state via the inter-
resonant	S2	state	via	the	intermediate	Sx	to	the	S1	state.	(b)	Time	dependence	of	the	
mediate Sx to the S1 state. (b) Time dependence of the populations for the S2, Sx, and S1 spectrokinetic
populations	for	the	S2,	Sx,	and	S1	spectrokinetic	species.	(c)	Evolution-associated	difference	
spectra	(EADS)	for	the	three	spectrokinetic	species.		

species. (c) Evolution-associated difference spectra (EADS) for the three spectrokinetic species.

5

90	

	
	
	
	
Figure	A2.5.	Oscillation	map	for	vibrational	coherence	at	100	cm−1	detected	in	the	2DES	𝐾	
spectra	from	CAN	in	toluene.		

FIG. S7. Oscillation map for vibrational coherence at 100 cm
FIG. S7. Oscillation map for vibrational coherence at 100 cm
in toluene.
in toluene.

1 detected in the 2DES K spectra from CAN
1 detected in the 2DES K spectra from CAN

Figure	A2.6.	Oscillation	map	for	vibrational	coherence	at	1800	cm−1	detected	in	the	2DES	
𝐾	spectra	from	CAN	in	toluene.		

FIG. S8. Oscillation map for vibrational coherence at 1800 cm
FIG. S8. Oscillation map for vibrational coherence at 1800 cm
CAN in toluene.
CAN in toluene.

1 detected in the 2DES K spectra from
1 detected in the 2DES K spectra from

6
6

91	

	
	
	
	
	
e
d
u
t
i
l

p
m
A

l

i

a
u
d
s
e
R

20

0

!20

20

0

!20

A

B

0

100

200

300

400

500

Delay T (fs)

e
d
u

t
i
l

p
m
A

1.0

0.5

0

0

C

500

1000
Frequency (cm-1)

1500

2000

Figure	A2.7.	Total	amplitude	𝐾	transient	and	modulation	spectrum	on	the	diagonal	in	the	
FIG. S9. Total amplitude K transient and modulation spectrum on the diagonal in the main band excita-
main	band	excitation	region.	(a)	𝐾	transient	with	excitation	at	18200	cm−1	and	detection	at	
18200	cm−1,	with	the	fit	from	the	global	model	(red	curve)	superimposed.	(b)	Residual	(𝐾−	
1, with the fit from
tion region. (a) K transient with excitation at 18200 cm
global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	residual	over	the	
the global model (red curve) superimposed. (b) Residual (K
global model) transient. (c) Fourier trans-
𝑇	=	75-500	fs	range.	In	(b,c)	the	bars	show	the	95%	confidence	intervals	for	the	𝐾	
amplitudes.		
form amplitude spectrum of the residual over the T = 75


500 fs range. In (b,c) the bars show the 95%

1 and detection at 18200 cm

· · ·

confidence intervals for the K amplitudes.

92	

7

	
	
	
	
	
	
e
d
u
t
i
l

p
m
A

l

i

a
u
d
s
e
R

e
d
u
t
i
l

p
m
A

A

B

0

100

200

300

400

500

Delay T (fs)

C

0

!20

!40

!60

10

0

!10

!20

1.0

0.5

0

0

500

1000
Frequency (cm-1)

1500

2000

Figure	A2.8.	Total	amplitude	𝐾	transient	and	modulation	spectrum	in	the	S1	cross	peak	in	
FIG. S10. Total amplitude K transient and modulation spectrum in the S1 cross peak in the main band
the	main	band	excitation	region.	(a)	𝐾	transient	with	excitation	at	18200	cm−1	and	
detection	at	15500	cm−1,	with	the	fit	from	the	global	model	(red	curve)	superimposed.	(b)	
excitation region. (a) K transient with excitation at 18200 cm
Residual	(𝐾−	global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	
from the global model (red curve) superimposed. (b) Residual (K
residual	over	the	𝑇	=	75-500	fs	range.	In	(b,c)	the	bars	show	the	95%	confidence	intervals	
for	the	𝐾	amplitudes.		
transform amplitude spectrum of the residual over the T = 75

500 fs range. In (b,c) the bars show the

1 and detection at 15500 cm

global model) transient. (c) Fourier

1, with the fit



· · ·

95% confidence intervals for the K amplitudes.

93	

8

	
	
	
	
	
	
e
d
u

t
i
l

p
m
A

l

i

a
u
d
s
e
R

e
d
u
t
i
l

p
m
A

A

B

0

100

200

300

400

500

Delay T (fs)

C

20

0

!20

10

0

!10

1.0

0.5

0

0

500

1000
Frequency (cm-1)

1500

2000

Figure	A2.9.	Total	amplitude	𝐾	transient	and	modulation	spectrum	on	the	diagonal	in	the	
FIG. S11. Total amplitude K transient and modulation spectrum on the diagonal in the red tail excitation re-
red	tail	excitation	region.	(a)	𝐾	transient	with	excitation	at	17200	cm−1	and	detection	at	
17200	cm−1,	with	the	fit	from	the	global	model	(red	curve)	superimposed.	(b)	Residual	(𝐾−	
1, with the fit from the global
gion. (a) K transient with excitation at 17200 cm
global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	residual	over	the	
model (red curve) superimposed. (b) Residual (K
global model) transient. (c) Fourier transform ampli-
𝑇	=	75-500	fs	range.	In	(b,c)	the	bars	show	the	95%	confidence	intervals	for	the	𝐾	

amplitudes.		
tude spectrum of the residual over the T = 75
500 fs range. In (b,c) the bars show the 95% confidence

1 and detection at 17200 cm

· · ·

intervals for the K amplitudes.

94	

9

	
	
	
	
	
	
0

!10

!20

e
d
u

t
i
l

p
m
A

10

0

!10

1.0

0.5

l

i

a
u
d
s
e
R

e
d
u
t
i
l

p
m
A

A

B

0

100

200

300

400

500

Delay T (fs)

C

0

0

500

1000
Frequency (cm-1)

1500

2000

Figure	A2.10.	Total	amplitude	𝐾	transient	and	modulation	spectrum	in	the	S1	cross	peak	in	
FIG. S12. Total amplitude K transient and modulation spectrum in the S1 cross peak in the red tail ex-
the	red	tail	excitation	region.	(a)	𝐾	transient	with	excitation	at	17200	cm−1	and	detection	at	
15500	cm−1,	with	the	fit	from	the	global	model	(red	curve)	superimposed.	(b)	Residual	(𝐾−	
1, with the fit
citation region. (a) K transient with excitation at 17200 cm
global	model)	transient.	(c)	Fourier	transform	amplitude	spectrum	of	the	residual	over	the	
from the global model (red curve) superimposed. (b) Residual (K
global model) transient. (c) Fourier
𝑇	=	75-500	fs	range.	In	(b,c)	the	bars	show	the	95%	confidence	intervals	for	the	𝐾	
amplitudes.		
transform amplitude spectrum of the residual over the T = 75

500 fs range. In (b,c) the bars show the

1 and detection at 15500 cm



· · ·

95% confidence intervals for the K amplitudes.

95	

10

	
	
	
	
	
	
	
Chapter	3:	Electronic-Vibrational	Coherences	in	Oleate-capped	CdSe	
Quantum	Dots	

Exciton	relaxation	in	semiconductor	quantum	dots	(QDs)	is	strongly	dependent	on	the	

nature	and	extent	of	passivation	of	the	surface	by	organic	ligands.	To	determine	how	the	

ligands	participate	in	nonradiative	decay	mechanisms,	we	characterized	preparation	of	

CdSe	QDs	capped	oleate	ligands	using	broadband	multidimensional	spectroscopy	with	7-fs	

laser	pulses.	Population	transfer	to	the	band	edge	and	then	to	the	photoluminescent	state	

after	optical	preparation	of	the	X3	exciton	(1Pe	state)	is	revealed	in	two-dimensional	

electronic	spectra	(2DES)	by	the	time	evolution	of	an	off-diagonal	cross	peak.	This	process	

involves	excited-state	coherent	wavepacket	motions	through	a	cascade	of	conical	

intersections	between	exciton	potential-energy	surfaces.	Excitation	and	mode	specific	

oscillation	maps	allow	us	to	probe	excited	state	wavepacket	motions	at	frequencies	

matching	the	vibrational	modes	of	the	organic	ligands.	These	observations	indicate	that	the	

ligand	vibrations	are	quantum	coherently	mixed	with	the	core	electronic	states	of	the	QDs.	

These	results	raise	new	opportunities	for	engineering	photoinduced	electron	transfer	

processes	in	QDs	through	control	of	electronic-vibrational	coupling	with	organic	ligands.	

96	

	
	
3.1	Introduction	

Semiconductor	quantum	dots	(QDs)	are	of	high	interest	because	their	optoelectronic	

properties	can	be	tuned	by	varying	size,	shape,	and	surface	chemistry.1–3	As	a	result,	QDs	

are	used	in	several	applications	including	solar	cells,	lasers,	catalysis,	biomedical	sensing,	

and	imaging.4,5,58,61,64,67	In	a	photoexcited	QD,	the	electrons	that	occupy	higher	energy	levels	

(1Pe)	above	the	band	gap	rapidly	(subpicosecond	regime)	relax	to	a	lower	energy	state	via	

nonradiative	relaxation.5,6	This	irreversible	loss	of	excitation	energy	in	QDs	contributes	to	

low	efficiency	in	photovoltaic	applications.	The	nonradiative	relaxation	mechanism	in	QDs	

is	strongly	influenced	by	the	interaction	of	QD	core	with	the	organic	molecules	on	the	

surface.7,8		

Early	reports	from	Guyot-Sionnest	group	have	proposed	that	the	surface	ligands	

facilitate	intraband	relaxation	via	ligand	vibrations.	In	such	mechanism,	ligand	vibrational	

modes	are	considered	to	accept	energy	and	serve	as	a	sink	to	the	electron	relaxation	from	

higher	to	lower	electronic	state.7	Further	studies	from	Pandey	and	Guyot-Sionnest	have	

shown	that	the	intraband	relaxation	can	be	significantly	slowed	by	isolating	the	QD	core	

from	the	surface	ligands	by	incorporating	a	ZnSe	inorganic	shell.8	The	studies	from	

Kambhampati	group	have	reported	the	influence	of	surface	and	surface	ligands	in	multiple	

aspects	of	carrier	relaxation	including	electronic-to-vibrational	energy	transfer,	electron-

phonon	coupling	and	Auger	relaxation	rates.9	They	have	shown	that	the	holes	in	colloidal	

CdSe	QDs	relax	through	a	surface	based	nonadiabatic	channel	while	the	electrons	relax	

primarily	through	Auger	mechanism.10	

Owing	to	spatially	confined	excitonic	wavefunctions,	the	core	electronic	states	are	

quantum	mechanically	mixed	with	surface	ligands	by	bonding	interactions,	which	leads	to	

97	

	
	
the	delocalization	of	core	electronic	states	to	the	surface	ligands.	Weiss	and	coworkers	

have	investigated	the	relaxation	of	exciton	confinement	in	QDs	via	delocalization	of	the	

core	wavefunction	to	the	surface	ligands	using	phenyldithiocarbamate	(PTC)	molecule.	11,12	

The	orbital	overlap	of	PTC	molecule	with	the	QD	core	results	in	delocalization	of	the	hole-

wavefunction.11	This	delocalization	of	the	wavefunction	increases	the	exciton	confinement	

radius	of	the	QDs	resulting	in	lower	optical	band	gaps	and	thus	a	red-shift	in	the	absorption	

spectrum.	They	have	further	manipulated	these	interactions	to	achieve	photoinduced	hole	

transfer	form	CdS	QDs	to	phenothiazine	molecular	acceptor.13		

The	recent	study	from	our	group	demonstrated	that	the	vibrational	motions	of	the	

surface	ligands	promote	the	nonradiative	relaxation	pathway	in	hexadecylamine-capped	

CdSe	QDs	via	mixing	of	core	electronic	states	of	the	quantum	dot	and	vibrational	states	of	

the	surface	ligands.14	Modulations	corresponding	to	torsional,	wagging	and	scissoring	

modes	of	the	alkylamine	entities	where	observed	during	the	relaxation	from	the	X3	exciton	

energy	level	to	lower	energy	levels	like	X1	and	PL.	This	study	proposed	a	nonadiabatic	

mechanism	for	the	relaxation	of	X3	via	a	cascade	of	conical	intersections	(CIs)15	where	

coherent	wavepacket	motions	are	following	the	optical	excitation	of	X3	(Figure	3.1).		

In	this	chapter,	results	from	broadband	multidimensional	spectroscopic	studies	of	vibronic	

coherences	aiding	the	hot	carrier	cooling	in	oleate-capped	CdSe	quantum	will	be	presented.	

Additionally,	a	global	analysis	of	X3	is	being	carried	out	on	these	quantum	dots	to	

characterize	the	nature	and	kinetics	of	the	exciton	relaxation.	The	main	results	indicate	

that	the	stretching	and	rocking	vibrational	motions	of	the	carboxylate	along	with	mixed	

vibrations	of	QD	core	facilitate	the	vibronic	exciton	mechanism	of	hot-carrier	cooling.		

98	

	
	
	
	
The Journal of Physical Chemistry Letters

pubs.acs.org/JPCL

Letter

CdSe nanoparticle. A schematic illustration of the nonradiative
decay pathway and the three computed minimal energy conical
intersection (MECI) structures are pictured in Figure 4. The

Figure	3.1.	Schematic	representation	of	the	potential	energy	surface	representing	the	
relaxation	of	optical	excitation	via	a	cascade	of	conical	intersections	via	coherent	
wavepacket	motions.	Adapted	from	Tilluck	et	al.14	

Figure 4. (A) Schematic representation of molecular potential
surfaces in a QD,
illustrating how cooling through a cascade of
conical intersections leads to coherent wavepacket motions along an
associated branching coordinate, with retention of vibrational
coherence observed at the band-edge state. Dotted potential energy
curves depict a relaxation process to the photoluminescent state
following nonradiative relaxation to X1. (B−D) Optimized minimal
energy conical intersections (MECIs) responsible for cooling from X4
to X1 in a Cd26Se26(NH3)25 cluster. MECI energies are presented in
The	2DES	studies	on	CdSe	quantum	dots	presented	in	this	chapter	were	synthesized	by	
Tables S1 and S2.

3.2.1	CdSe	Quantum	Dot	Synthesis	and	Characterization	

3.2	Experimental	Methods	

of	these	particles,	cadmium	oxide	(99.5%	metals	basis)	and	oleic	acid	(99%)	were	

purchased	from	Sigma	Aldrich,	St.	Louis,	MO.	Chloroform	(A.C.S.	reagent	grade)	was	

the	Van	Patten	laboratory	at	Middle	Tennessee	State	University	(MTSU).	For	the	synthesis	
intersections are accessed upon local displacement of the
surface atoms. Analysis of the CI geometries suggests that
energy is deposited during the nonradiative relaxation pathway
to the band edge into a complex combination of modes,
including various bending modes of the ammonia ligands
(including the wagging mode described above), ammonia
twisting modes, Cd−N stretching modes, and surface Cd−Se
stretching modes. A more detailed, quantitative analysis of the
(Newburyport,	MA).	Octadecene	(90%)	was	purchased	from	Acros	Organics	
relative importance of
to be
presented in a subsequent publication.

obtained	from	Alfa	Aesar	(Haverhill,	MA).	Selenium	powder	was	purchased	from	STREM	

these modes is underway,

(Geel,Belgium).		

We propose that coherent wavepacket motion is launched
along these ligand modes upon optical preparation of the
exciton states in CdSe QDs. It is this wavepacket motion that
contributes the rapidly damped modulations we observe at
ligand-derived frequencies to the 2DES spectra; slowly damped
coherences are likely to indicate contributions from spectator
modes, which are not as strongly coupled to the reaction
coordinate for the nonradiative relaxation processes. The
oscillation maps indicate that vibrational coherence in these

99	

modes is retained in the product X1 state; further, strong

oscillation amplitudes coincide with the energy of

the

photoluminescent band-edge transition. This

is a clear

indication of a coherent nonadiabatic mechanism, involving

phase-coherent displacements of the ligand modes from the

optically prepared exciton state and persisting to the band edge

and photoluminescent states.

The 2DES spectra reported in this work establish that

nonradiative relaxation between the photoexcited exciton levels

in CdSe QDs is strongly coupled to vibrations of the surface-
capping ligands. These results are consistent with the vibronic
exciton hypothesis proposed in the introduction. Further, the
finding that nonradiative relaxation and photoluminescence in
QDs involves a coherent nonadiabatic mechanism implicates
specific structural motions of the surface-capping ligands in the
control of the rate and yield of competing photophysical
pathways. In support of this proposal, electronic structure
calculations have identified a cascade of conical intersections in
a small CdSe nanoparticle with amine ligands consistent with
ultrafast, coherent relaxation from X4 to X1. These discoveries
raise new opportunities involving ligand chemistry to improve
the function of QDs in luminescence, solar energy capture, and
photocatalysis applications.

■ EXPERIMENTAL METHODS

the contents

Sample Preparation. Large (6.9 nm), amine-capped CdSe QDs
were prepared using a modification of a previously described
method.10 A 100 mL round-bottom flask was charged with
0.167 g of cadmium stearate, 0.1 g of hexadecyl palmitate, 1.0 g
of hexadecylamine (HDA), 4.0 g of octadecane, 4.0 g of 1-
octadecene, and a stir bar. The flask was connected to a
vacuum/inert gas manifold and evacuated at a temperature of
100 °C for 1 h with vigorous stirring. While the flask was
evacuating, two other solutions were prepared in an inert gas
glovebox, and these solutions were drawn into two syringes for
later injection into the reaction mixture. Injection solution #1
prepared by combining 31 mg of Se powder with 2.5 mL of
trioctylphosphine (TOP) and stirring until
completely dissolved. Injection solution #2 was prepared by
combining 50.0 mg of cadmium stearate, 7.0 mg of Se powder,
and 0.8 mL of TOP and stirring until the contents completely
dissolved. After the 1 h evacuation, the flask was removed from
vacuum and then continuously purged with N2
remainder of the process. The flask temperature was quickly
raised to 320 °C, at which point injection solution #1 was
swiftly injected. The reaction temperature was maintained at
275 °C for 1 h after injection to allow complete reaction and
growth of the CdSe particles. After 1 h of growth, injection
solution #2 was slowly injected dropwise over a period of
about 15 min while the reaction temperature was maintained at
275 °C. Once the second injection was complete, the reaction
temperature was lowered to 150 °C for 3 h before the products
were cooled to room temperature and exposed to air. The QDs
were purified by first spinning in a microcentrifuge at 17 000g.
The clear, colorless supernatant was discarded, and the QDs
were resuspended in chloroform (equal
volume), followed by precipitation with 100% ethanol and
centrifugation.

to the original

the

for

For femtosecond spectroscopy, the QDs were resuspended
in toluene solvent to obtain an absorbance of 0.3 at 630 nm in
a static quartz cuvette of 1 mm path length.

Linear and Photoluminescence Spectra. Linear absorption

spectra of

the QD preparations were recorded at

room

temperature (23 °C) with a Shimadzu UV-2600 spectrometer.

The room-temperature photoluminescence spectrum was

recorded with a home-built fluorescence spectrometer32

employing a broadband visible LED and a compact double

monochromator as an excitation source and a spectrograph

and a CCD camera as the detector.

Femtosecond Spectroscopy. 2DES spectra were recorded using

a pump−probe optical configuration with adaptive pulse

shaping33 as discussed previously.13 Excitation pulses (6.8 fs,

9681

https://doi.org/10.1021/acs.jpclett.1c02630

J. Phys. Chem. Lett. 2021, 12, 9677−9683

	
	
	
	
CdSe	QDs	were	synthesized	following	a	modified	phosphine-free	synthesis	previously	

reported	by	Jasieniak	et	al.16		A	Se	precursor	stock	solution	was	prepared	by	evacuating	

0.1280	g	of	Se	in	16	mL	of	octadecene	(ODE)	for	30	min	and	then	heating	under	nitrogen	at	

200°C	for	2	h.	A	separate	stock	solution	of	Cd-oleate	was	prepared	by	evacuating	0.0478	g	

of	CdO	and	1.0163	g	of	99%	oleic	acid	in	12	mL	of	ODE	for	30	min.	The	Cd	solution	was	

then	heated	under	nitrogen	at	100	°C	for	1	h.	The	Cd-oleate	solution	was	then	heated	to	

285	°C,	and	3.6	mL	of	the	Se	precursor	was	rapidly	injected.	The	growth	temperature	was	

maintained	at	265	°C	for	30	min.	After	the	first	growth	step,	UV/Vis	measurements	were	

taken	using	a	modernized	Cary	14	spectrophotometer,	and	the	absorbance	was	measured	

at	618	nm	(5.49	nm	diameter).	A	second	injection	was	performed	by	heating	the	QD	

solution	to	265	°C	and	slowly	injecting	1	mL	of	the	Se	precursor	using	a	New	Era	Pump	

Systems	NE-300	syringe	pump	at	a	rate	of	80	µL/min.	The	QD	solution	was	then	allowed	to	

grow	for	an	additional	30	min,	after	which	UV/Vis	measurements	were	taken,	and	the	

absorbance	was	measured	at	640	nm	(6.95	nm	diameter).	The	resulting	QD	solution	was	

purified	by	two	cycles	of	precipitation	by	spinning	in	a	microcentrifuge	at	17000	×	g	and	

resuspension	using	a	chloroform/acetonitrile	solvent/antisolvent	combination.		

To	verify	the	size	of	the	QDs,	transmission	electron	micrographs	(TEM)	were	obtained	

using	a	Hitachi	7650	transmission	electron	microscope.	A	single	drop	of	purified	QDs	

suspended	in	toluene	was	deposited	onto	a	carbon-coated	copper	TEM	grid,	which	was	

then	placed	in	a	petri	dish	on	filter	paper	and	allowed	to	dry	overnight.	The	microscope	

was	operated	at	an	accelerating	voltage	of	100	kV	and	at	500,000×	direct	magnification.	

The	size	distribution	was	determined	using	ImageJ	software.	

100	

	
	
2. Characterization of QD ligands : DART-MS 

Direct analysis in Real Time

DART mass spectrometry coupled 
with thermal desorption has been 
used to detect surface ligands on 

QD surfaces.

Various chemical species can be 
differentiated by spectral signature 

with high sensitivity.

Bound (chemisorbed) species can 
be distinguished from unbound or 
physisorbed species. Strongly-
bound ligands are observed at later 

times (higher T) than weakly-

associated molecules.

s
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n
o

I

2

s
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o

Figure	3.2.	Schematics	of	DART-MS	analysis.	The	sample	was	heated	using	a	thermal	
desorption	module	where	the	ion	source	ionized	the	desorbed	molecules.	The	mass	
spectrometer	detects	ionized	ligand	molecules	and	shows	the	signatures	of	the	released	
species	in	the	mass	spectrum.	Inset	plot	shows	the	linear	temperature	ramp	applied	over	
certain	time.	

281.4 C18H33O2- 

The	surface	ligands	of	the	QDs	were	analyzed	using	Thermal	Desorption	Direct	Analysis	

297.4 C18H33O3- 

in	Real	Time	Mass	Spectrometry	(TD-DART-MS),	as	previously	described	by	Frazier	et	al	

313.3 C18H33O4- 

(Figure	3.2).17	In	TD-DART-MS,	a	temperature	ramp	is	applied	with	respect	to	time	while	

200

300

400

500

600

m/z
measuring	the	mass	spectrum	of	the	ionized	species.	Using	mass	spectrometry,	different	

0
100

ligand	molecules	can	be	distinguished	from	their	mass	spectrum	with	very	high	selectivity	

m/z = 281.4

4.37 min

467 ℃

and	sensitivity.	The	chemically	bound	species	on	the	surface	of	the	QDs	can	be	readily	

distinguished	from	the	physisorbed	species.	The	weakly	bound	or	the	unbound	species	

arrive	at	the	detector	at	low	temperatures	and	early	time.	Conversely,	strongly	bound	or	

I

1.37 min

167 ℃

chemically	bonded	species	arrive	at	higher	temperature	and	at	later	time.	Using	a	Thermo	

0
0

300
200
300
200
LTQ	XL	mass	spectrometer	coupled	with	a	DART	ion	source	and	an	IonRocket	temperature	
Temperature (℃ )
Temperature (°C)
gradient	system,	5	µL	of	the	sample	was	analyzed	at	a	time.	The	analysis	of	each	sample	

400
400

500
500

100
100

was	conducted	using	a	temperature	profile	that	increased	from	30	to	530	°C	at	a	rate	of	

101	

	
	
	
 
 
 
100	°C/min,	with	a	30-s	hold	at	530	°C	to	ensure	the	complete	desorption	of	ligands	from	

the	copper	substrate.	Additionally,	each	scan	monitored	m/z	ranges	from	50-1000,	and	the	

DART	ion	source	He	gas	stream	temperature	was	set	to	400	°C.	

3.2.2	Linear	Spectroscopy	and	Photoluminescence	

The	QDs	were	dispersed	in	hexane	to	obtain	an	absorbance	of	0.3	at	562	nm	for	the	

2DES	experiments.	The	absorption	spectrum	is	measured	using	a	Schimadzu-2600	UV-Vis-

NIR	spectrophotometer.	The	room	temperature	fluorescence	was	measured	using	a	home-

built	fluorescence	spectrometer	employing	a	broadband	visible	LED	and	a	compact	double	

monochromator	as	an	excitation	source	and	a	spectrograph	and	a	CCD	camera	as	the	

detector.18	

3.2.3	Two-Dimensional	Electronic	Spectroscopy	

2DES	spectra	were	recorded	using	a	pump–probe	optical	configuration	with	adaptive	

pulse	shaping19	to	compress	the	laser	pulses	and	to	generate	the	excitation	pulse	sequence	

(pulse	1–𝜏–pulse	2)	required	for	the	three-pulse	stimulated	photon-echo	experiment.	

Excitation	pulses	were	obtained	from	a	noncollinear	optical	parametric	amplifier	(NOPA,	

Spectra-Physics	Spirit-NOPA-3H),	which	was	pumped	by	the	third	harmonic	of	a	1.04	μm	

amplified	Yb	laser	(Spectra-Physics	Spirit-4W,	400	fs	pulses	at	a	100	kHz	repetition	rate,	

4	W	average	power).	The	pump	and	probe	beams	in	the	spectrometer	were	split	from	the	

NOPA	output	by	a	broadband	dielectric	beamsplitter	(Layertec,	Mellingen),	processed	by	

an	adaptive	pulse	shaper	(FemtoJock	and	FemtoJock	P,	respectively,	Biophotonic	

Solutions),	and	then	compressed	by	multiple	reflections	on	pairs	of	broadband	chirped	

mirrors	(Ultrafast	Innovations,	Munich).	For	the	present	experiments,	the	NOPA’s	signal	

beam	output	spectrum	(Figure	3.5)	was	centered	at	600	nm	(∼110	nm	FWHM;	520–700	

102	

	
	
	
nm	usable	range).	The	excitation	pulse	energy	was	attenuated	to	3.75	nJ	per	pulse,	as	

measured	at	the	sample’s	position.	The	pump	beam’s	plane	of	linear	polarization	was	

rotated	magic	angle	(54.7°)	from	that	of	the	probe	beam	by	a	thin	achromatic	half-wave	

retarder	plate.	The	two	beams	were	focused	by	off-axis	parabolic	mirrors	to	100	μm	spots	

overlapped	spatially	just	after	the	front	window	of	the	sample	cuvette.	The	excitation	

pulses	in	both	beams	were	characterized	by	MIIPS	scans20	conducted	with	a	thin	β-barium	

borate	crystal,	which	was	placed	at	the	sample’s	position	following	a	single	cuvette	

window.	The	estimated	pulse	duration	for	both	beams	at	the	sample	position	was	6.9	fs.	

Residual	phase	plots	(Figures	A3.1),	SHG-FROG	spectrograms21	(Figure	A3.2),	and	

autocorrelation	(Figure	A3.3)	are	presented	in	the	appendix.	

2DES	spectra	were	recorded	by	programming	the	pump	beam’s	pulse	shaper	to	scan	

the	coherence	time	interval	between	the	two	pump	pulses,	𝜏,	from	0	to	50	fs	with	0.5	fs	

steps	to	obtain	the	excitation	axis	after	Fourier	transformation.	The	detection	axis	of	the	

2DES	spectrum	was	measured	directly	by	measuring	the	pump-induced	change	in	probe	

transmission	through	the	sample	with	a	home-built	0.2	m	spectrograph	(300	gr/mm	

diffraction	grating)	and	a	fast	CCD	detector	(Andor	Newton	940)	using	a	phase-sensitive	

detection	protocol	and	amplitude	modulation	of	the	pump	pulses.22	The	population	time	𝑇	

is	scanned	by	a	time-of-flight	delay	stages	with	a	spacing	of	2.5	fs	from	0-30	fs,	5	fs	spacing	

from	30-500	fs,	10	fs	spacing	from	500-800	fs,	50	fs	spacing	from	800-1000	fs	and	1	ps	

spacing	from	1-10	ps.	Each	2D	spectrum	was	an	average	of	seven	consecutive	𝑇	scans.	

Owing	to	the	use	of	the	pump–probe	optical	geometry	and	amplitude	modulation	of	the	

pump–pulse	pair,	the	2DES	spectra	reported	here	are	intrinsically	autophased.	The	spectra	

103	

	
	
	
obtained	using	this	approach	are	the	sum	of	those	from	the	rephasing	and	non-rephasing	

nonlinear	optical	pathways.22	

3.3	Results		

3.3.1	Particle	Size	and	Surface	Characterization	

To	study	the	vibronic	character	of	the	exciton	relaxation	in	oleate-capped	CdSe	QDs,	

nanoparticles	with	a	size	of	~7	nm	were	used	to	perform	the	2DES	experiment.	

Transmission	Electron	Microscopy	(TEM)	has	been	carried	out	on	these	QDs	to	understand	

the	size	distribution	(Figure	3.3a).	TEM	images	show	that	the	particles	are	highly	

monodisperse	in	shape	and	size	(Figure	3.3b)	and	exhibit	a	zincblende	crystal	structure	

owing	to	their	cubic	symmetry.	The	mass	spectra	collected	during	the	thermal	desorption	

DART-MS	showed	that	the	desorbed	ionic	species	detected	were	primarily	oleate	ions	and	

its	different	ionic	forms	(Figure	3.3c).	The	temperature	desorption	profile	of	the	sample	at	

m/z	=	281.4	indicates	that	the	oleate	ions	were	desorbed	from	the	surface	of	the	QD	at	

460	°C	(Figure	3.3d).	This	confirms	that	the	oleate	ligands	are	the	only	surface	ligands	that	

are	chemically	bound	to	the	QDs.		

104	

	
	
	
A

C

s
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I

0
100

σ = 6.97 
± 0.5 nm

6

4
Diameter (nm)

8

10

12

B

60

l

s
e
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i
t
r
a
P

f
o

.

o
N

0

0

2

m/z = 281.4

D

2

s
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I

0
0

281.4 C18H33O2- 

297.4 C18H33O3- 

313.3 C18H33O4- 

200

300

400

500

600

m/z

100
100

300
200
300
200
Temperature (℃ )
Temperature (°C)

400
400

500
500

X3

X4

X2

X1

X4

2.0

1.5

2.3

2.2

550

E

1Pe
1Se

F
Figure	3.3.	Characterization	of	oleate	CdSe	(a)	Transmission	electron	microscopy	images	
of	oleate-capped	CdSe	quantum	dots	with	500,000x	magnification	and	5x	zoom.	(b)	Size	
525
distribution	of	CdSe	QDs,	245	total	particles	counted,	62	particles	6.98	nm.	The	mean	of	the	
X4
size	distribution	is	6.97	nm	with	a	standard	deviation	of	0.50	nm.	Mass	spectra	collected	
from	TD-DART-MS	of	oleate-capped	CdSe	QDs.	The	ligands	are	desorbed	from	the	inorganic	
core	at	430	°C.	In	addition	to	the	major	peak	at	m/z	=	281.4	corresponding	to	the	oleate	
anion,	two	peaks	associated	with	subsequent	additions	of	oxygen	are	observed	at	m/z	=	
297.4	and	m/z	=	313.3.	Desorption	plot	obtained	from	DART-MS	for	m/z	=	281.4.	

Wavelength (nm)

575
600
625
650
675

y
t
i
s
n
e
t
n
I

700 675

W
a
v
e
e
n
g
t
h

y
g
r
e
n
E

y
g
r
e
n
E

PL

X1

X3

X2

575

625

650

550

600

V
e
(

V
e
(

(
n
m

2.0

1.8

1.9

2.1

1.0

0.5

X3

X1

X2

)

)

)

l

3.3.2	Linear	Spectroscopy	

0

1S3/2
1P3/2
2S3/2
3S1/2

0

Upon	incidence	of	photons,	electrons	are	excited	from	the	hole	states	in	the	valence	

Energy (eV)

1.8

1.9

2.0

2.1

2.2

2.3

band	to	the	electronic	states	in	the	conduction	band.	In	the	7-nm	CdSe	QDs,	the	lowest	

energy	transition	or	the	band	edge	exciton	(1S3/2	1Se)	is	denoted	as	X1	(1.90	eV),	the	

second	exciton	(2S3/2	1Se)	is	denoted	as	X2	(1.99	eV),	the	third	exciton	(1P3/2	1Pe)	as	X3	

(2.12	eV),	and	the	fourth	exciton	(3S1/2	1Se)	as	X4	(2.31	eV).	Figure	3.4a	shows	the	various	

excitons	created	within	the	CdSe	QDs,	illustrating	their	positions	in	both	the	electron-hole	

105	

	
	
	
 
 
 
 
 
 
 
 
 
 
A

C

281.4 C18H33O2- 

s
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energy	level	and	the	exciton	energy	domain.	These	distinct	excitons	are	represented	by	

297.4 C18H33O3- 

different	colors	(X1-red,	X2-green,	X3-blue,	and	X4-magenta)	in	the	absorption	spectrum	

313.3 C18H33O4- 

(Figure	3.5).	The	broadband	laser	spectrum	spans	the	first	three	excitons	very	well	in	this	

study.	Coverage	of	the	broadband	spectrum	allows	us	to	study	the	population	relaxation	
300

600

400

500

200

0
100

σ = 6.97 

± 0.5 nm

0

2

4

6

8

10

12

Diameter (nm)

D

m/z = 281.4

B

60

s

e

l

c

i

t

r

a

P

f

o

.

o

N

0

2

s
t
n
u
o
C
n
o

I

0
0

100
100

200

200

300

300

400

400

500

500

Temperature (℃ )

Temperature (°C)

A

Wavelength (nm)

700 675

650

625

600

575

550

525

y
t
i
s
n
e
n

t

I

X4

PL

X1

X2

X3

1.8

1.9

2.0

2.1

2.2

2.3

Energy (eV)

and	coherent	wavepacket	dynamics	from	all	three	exciton	levels	simultaneously.		

m/z

A

X3

2.0

X1

X2

X4

1Pe
1Se

)

V
e
(

y
g
r
e
n
E

1.5

1.0

0.5

0

1S3/2
1P3/2
2S3/2
3S1/2

X4

X3

X2

X1

550

575
600
625
650
675

W
a
v
e
e
n
g
t
h

l

(
n
m

)

)

V
e
(

y
g
r
e
n
E

2.3

2.2

2.1

2.0

1.9

1.8

0

Figure	3.4.	Energy	level	diagram	of	CdSe	QDs.	On	the	left,	the	electron-hole	energy	levels	
are	marked	with	hole	levels	in	the	valence	band	(1S3/2,	1P3/2,	2S3/2,	3S1/2)	and	electron	
levels	(1Se	and	1Pe)	in	the	conduction	band.	The	band	edge	exciton	(1S3/2	1Se)	is	denoted	as	
X1,	the	second	exciton	(2S3/2	1Se)	is	denoted	as	X2,	the	third	exciton	(1P3/2	1Pe)	as	X3,	and	
the	fourth	exciton	(3S1/2	1Se)	as	X4.	The	figure	on	the	right	shows	the	exciton	energy	levels	
of	the	first	four	excitons	with	energy	in	eV	on	the	left	and	wavelength	on	the	right.	

106	

	
	
	
	
 
 
 
 
 
 
 
 
 
 
σ = 6.97 

± 0.5 nm

0

2

4

6

8

10

12

Diameter (nm)

D

m/z = 281.4

B

60

s

e

l

c

i

t

r

a

P

f

o

.

o

N

0

2

s

t

n

u

o

C

n

o

I

0
0

100
100

300
200
300
200
Temperature (℃ )
Temperature (°C)

400
400

500
500

A

C

s

t

n

u

o

C

n

o

I

0

)

V

e

(

y

g

r

e

n

E

1.5

1.0

0.5

0

281.4 C18H33O2- 

297.4 C18H33O3- 

313.3 C18H33O4- 

100

200

300

400

500

600

A

X3

2.0

X1

X2

X4

1Pe

1Se

m/z

)

V
e
(

y
g
r
e
n
E

2.3

2.2

2.1

2.0

1.9

1.8

0

1S3/2

1P3/2

2S3/2

3S1/2

X4

X3

X2

X1

550

575
600
625
650
675

l

W
a
v
e
e
n
g
t
h
(
n
m

)

Wavelength (nm)

700 675

650

625

600

575

550

525

y
t
i
s
n
e
t
n
I

PL

X1

X2

X3

X4

1.8

1.9

2.0

2.1

2.2

2.3

Energy (eV)

Figure	3.5.	Steady-state	spectroscopic	characterization	of	oleate-capped	QDs.	Linear	
absorption	spectrum	(blue	trace)	marked	with	various	exciton	energy	levels,	and	
photoluminescence	spectrum	(orange	trace)	with	overlapping	laser	spectrum	(gray	filled).	

3.3.3	2DES	Spectra	

A	series	of	2D	spectra	with	the	absorption	spectrum	and	overlapped	laser	spectra	are	

shown	in	the	Figure	3.6.	In	the	short	time	delay,	the	2D	spectra	exhibit	partially	resolved	

positive	peaks	along	the	diagonal	resulting	from	the	ground	state	bleaching	(GSB)	and	

stimulated	emission	(SE).	The	formation	of	diagonal	peaks	indicates	preparation	of	

population	at	different	exciton	energy	levels	after	the	photoexcitation	from	the	pump	

pulses.	An	early	time	diagonal	slice	of	2D	spectrum	shows	well	resolved	peaks	that	arise	

due	to	the	fine	structure	of	excitons	in	the	QDs	(solid	blue	line	of	side	panel,	Figure	3.5).	

The	origin	of	the	fine	structure	of	excitons	in	QDs	is	a	combination	of	strong	spin-orbit	

coupling,	exchange	interaction	for	singlet	and	triplet	states	and	crystal	field	splitting	arising	

from	shape	anisotropy.23,24	Early	reports	from	Bawendi	group	investigated	the	fine	

structure	in	QDs	using	steady-state	photoluminescence	excitation	and	fluorescence	line	

narrowing	experiments.24	These	experiments	where	performed	at	very	low	temperatures	

107	

	
	
	
	
 
 
 
 
 
 
 
 
 
 
of	10	K	and	lacked	time-resolved	dynamics	information.	Previously	several	groups	have	

used	2DES	studies	to	understand	the	fine	structure	of	CdSe	and	PbS	QDs.23,25,26	However,	

these	studies	exclusively	focused	on	probing	the	fine	structure	of	the	band	edge	exciton.	

Using	broadband	short	pulses	in	this	experiment	allows	us	to	monitor	the	fine	structure	of	

multiple	excitons	before	the	resultant	spectral	features	undergo	inhomogeneous	

broadening	owing	to	interaction	with	the	surroundings.	

As	the	population	time	𝑇	evolves,	the	diagonal	peaks	broaden	due	to	inhomogeneous	

broadening	or	loss	of	memory	of	the	excitation	owing	to	interactions	with	the	

surroundings.	Apart	from	the	broadening	of	spectral	features,	a	strong	cross	peak	appears	

at	lower	energies	corresponding	to	X1,	X2,	and	PL	excited	at	higher	energies.	The	formation	

of	the	cross	peak	in	this	region	is	due	to	the	population	relaxation	from	X3.	Crosspeak	

formation	can	be	observed	at	very	short	delays	𝑇,	as	short	as	20	fs,	suggesting	that	

population	relaxation	occurs	very	rapidly.		

The	2D	spectra	also	shows	negative	blue	signals	corresponding	to	excited	state	

absorption	signals	(ESA)	arising	from	formation	of	trap	states	or	biexcitons.23,27–29	The	ESA	

signal	that		arise	from	the	biexciton	formation	which	can	be	viewed	as	transition	from	an	

excited	state,	X	to	a	doubly	excited	state,	XX	in	the	QDs.28	In	a	2DES	experiment,	the	pump	

pulses	create	a	coherence	between	the	ground	state	and	exciton	level	X,	the	second	pulse	

create	a	population	in	the	excited	state	X	the	third	probe	pulse	creates	a	coherence	

between	X	and	biexcitonic	state	XX	which	emits	a	signal	with	frequency	of	energy	gap	

between	X	and	XX.	The	ESA	features	observed	at	detection	energy,	1.85	eV	with	a	wide	

range	of	excitation	energies	from	1.85-2.2	eV	is	likely	to	arise	from	biexctonic	interaction	of	

the	X1	with	that	of	X1,	X2	and	X3.	The	ESA	has	also	been	observed	during	the	formation	of	

108	

	
	
	
)

V
e

(

y
g
r
e
n
E
n
o
i
t
c
e
t
e
D

2.3

2.2

2.1

2.0

1.9

1.8

2.3

2.2

2.1

2.0

1.9

1.8

T = 0 fs

T = 10 fs

T = 25 fs

1

3

.

2

2

.

2

1

.

2

0

0

.

2

9

.

1

)

V
e
(

y
g
r
e
n
E

8

.

1

(cid:1138)1
1

T = 50 fs

T = 200 fs

T = 1 ps

)

V
e
(

y
g
r
e
n
E

3

.

2

2

.

2

1

.

2

0

0

.

2

9

.

1

X4

X3

X2

X1

PL

Intensity

X4

X3

X2

X1

PL

1.8 1.9 2.0 2.1 2.2 2.3

1.8 1.9 2.0 2.1 2.2 2.3

1.8 1.9 2.0 2.1 2.2 2.3

Excitation Energy (eV) 

8
.
1

(cid:1138)1

Intensity

525

550

575

600

625

650

675
700

525

550

575

600

625

650

675
700

D
e
t
e
c
t
i
o
n
W
a
v
e
e
n
g
t
h

l

(

n
m

)

Figure	3.6.	Time	evolution	of	2DES	spectra	of	oleate	capped	CdSe	quantum	dots	with	
respect	to	the	population	time,	𝑇.	The	spectra	are	presented	with	evenly	spaced	contours	
and	are	tinted	with	colors	indicating	positive	(red,	GSB/SE)	and	negative	(blue,	ESA/PA)	
signals.	The	side	panels	plot	the	2DES	signal	amplitude	sliced	along	the	diagonal	at	𝑇	=	0	fs	
(blue)	superimposed	on	the	linear	absorption	oscillator	strength	(black	dotted)	and	
photoluminescence	(PL)	spectra	(orange).	Amplitude	transients	sampled	at	the	marked	
coordinates	(excitation	at	X3	and	detection	at	X3,	X1,	and	PL)	are	shown	in	Figure	3.7.		

surface	trap	states	when	the	surface	of	QDs	is	poorly	passivated,	with	the	unpassivated	

sites	on	the	QDs'	surface	serving	as	carrier	traps	for	electrons	and	holes.	The	2D	spectra	at	

population	times	𝑇	=	200	fs	and	𝑇	=	1	ps	show	a	high	intensity	crosspeak	at	lower	energies	

indicating	that	the	population	from	X3	has	completely	relaxed	to	lower	energy	states,	X1	

and	PL.	The	relaxation	of	X3	is	also	apparent	from	the	low	amplitude	of	GSB/SE	signals	on	

the	diagonal	of	the	2D	spectrum	at	(X3,	X3).	

3.3.4	Global	Modeling	and	Coherence	Analysis	

To	understand	the	dynamics	of	X3	relaxation,	the	amplitude	of	the	evolution	of	the	

nonoscillatory	kinetic	response	excited	at	the	energy	level	of	X3	is	subjected	to	global	

analysis	(Figure	3.7).	Global	analysis	models	the	evolution	of	spectral	response	as	a	linear	

109	

	
	
	
	
 
 
 
 
 
 
 
 
combination	of	evolution-associated	difference	spectra	(EADS)	of	different	spectrokinetic	

species.30	Each	of	the	EADS	in	the	global	model	can	be	viewed	as	the	average	spectral	

signature	of	the	different	components	of	the	model	(Figure	3.7c).	For	each	excitation,	the	

sequence	of	species	in	the	kinetic	model	is	the	simplest	one	that	fits	the	2DES	amplitude	as	

a	function	of	the	delay	𝑇.	To	determine	the	simplest	model	to	describe	the	kinetics,	the	

residual	(the	difference	between	data	and	the	fitted	values)	across	the	spectrum	is	

monitored	to	make	sure	the	intensity	is	around	zero.	To	describe	the	kinetic	response	of	

X3,	the	global	model	required	five	different	spectrokinetic	species	(see	kinetic	scheme	in	

Figure	3.7a).	The	character	of	these	kinetic	species	is	a	combination	of	ground-state	

bleaching	(GSB),	stimulated	emission	(SE),	and	negative-going	excited-state	absorption	

(ESA).	The	first	component	is	the	response	from	the	X3	exciton	upon	excitation.	The	EADS	

of	this	component	has	a	positive	GSB	and	SE	signals	at	the	excitation	energy	corresponding	

to	the	X3	exciton	on	the	detection	energy	axis.	Additionally,	there	is	a	positive	signal	at	the	

energies	of	X1	and	X2,	this	can	be	attributed	to	the	shared	ground	state	nature	of	all	the	

excitations.	The	first	two	compartments	rapidly	evolve	with	time	constant	of	12	fs	and	40	fs	

indicative	of	a	coherent	relaxation	dynamics.	This	coherent	relaxation	process	also	

contributes	to	a	small	increase	in	the	intensity	of	GSB/SE	amplitude	at	X1	and	X2.	Another	

notable	event	during	this	time	frame	is	the	shift	and	decrease	of	the	ESA	character	at	1.85	

eV.	The	ESA	signal	observed	here	is	due	to	the	formation	of	biexcitons	of	X3	with	that	of	X1	

(1.85	eV)	and	X2	(1.93	eV).	The	decrease	in	the	ESA	can	be	attributed	to	the	overlapping	SE	

signal	produced	during	the	relaxation	of	X3	to	X1	and	X2.	The	third	spectrokinetic	

component	evolves	with	a	time	constant	of	200	fs.	A	significant	decrease	in	the	positive	

EADS	amplitude	at	X3	energy	is	observed	and	at	the	same	time	there	is	increase	in	the	

110	

	
	
	
amplitude	of	at	X1	and	X2.	The	evolution	of	the	third	component	to	the	fourth	component	is	

due	to	the	hot	electron	cooling	from	the	1Pe	electronic	state	to	the	1Se	electronic	state	in	an	

electron-hole	picture	of	the	QDs.6,9	It	should	be	noted	that	excitons	X1	and	X2	have	the	

same	electronic	energy	level,	1Se.	Therefore,	when	the	electron	relaxes	from	1Pe	to	1Se,	the	

SE	amplitude	simultaneously	increases	at	detection	energies	of	both	X1	and	X2.	The	

evolution	of	fourth	species	to	fifth	species	has	a	time	constant	of	1.4	ps.	In	terms	of	EADS	

evolution,	there	is	an	increase	in	the	ESA	at	about	2.0	eV	as	well	as	a	decrease	in	X2	

intensity.	These	intensity	changes	most	likely	indicate	hole	trapping	on	the	surface	of	the	

QDs.	The	final	component	is	the	relaxation	of	the	band-edge	exciton	to	the	ground	state.	

This	process	is	slow	and	takes	several	hundred	picoseconds	to	complete.		

111	

	
	
	
A

C

12 fs

1

2

38 fs

3

4

215 fs

1.39 ps

186 ps

5

G

PL

X1

X2

X3

e
d
u
t
i
l

p
m
A
S
D
A
E

0

0

0

0

0

1.8

1.9

1.0

0.8

0.6

0.4

0.2

0

1.0

0.5

0

B

D

l

n
o
i
t
a
u
p
o
P

e
d
u
t
i
l

p
m
A

−0.5

e
d
u
t
i
l

p
m
A

e
d
u
t
i
l

p
m
A

l

0.1

0

−0.1
0.05

0

i

a
u
d
s
e
R

−0.05
(cid:1138)

0.1

0

−0.1

0
0

100

1000

10000

Delay T (fs)

(X3,X1)

(X3,PL)

(X3,X3)

(X3,X3)

(X3,X1)

(X3,PL)

2.0

2.2
Detection Energy (eV)

2.1

2.3

0

100

300
200
Delay T (fs)

400

500

Figure	3.7.	Global	analysis	of	the	population	response	of	the	X3	(2.066-2.194	eV)	
excitation	region	of	2DES	spectrum	of	oleate	capped	CdSe	quantum	dots.	(a)	Kinetic	
scheme	for	the	global	model	with	time	constants,	12	+	1	fs,	40	+	1	fs,	212	+	3	fs,	1.41	+	0.47	
ps,	and	186	+	40	ps	for	each	relaxation	pathway.	(b)	Evolution	of	population	with	respect	to	
time	for	each	compartment.	(c)	Evolution	associated	difference	spectra	(EADS)	for	each	
compartment	in	the	kinetic	scheme.	(d)	Transients	at	various	coordinates,	(X3,	X3)	(blue	
trace),	(X3,	X1)	(green	trace)	and	(X3,	PL)	(maroon	trace).	The	lower	panels	show	the	
residual	for	each	coordinate	overlapped	with	the	fit	obtained	from	the	LPSVD	analysis.		

112	

	
	
	
	
	
	
	
 
 
The	amplitude	vs	population	time	delay	at	different	coordinates	in	the	2D	spectra	are	

plotted	to	show	the	population	dynamics	(Figure	3.7d).	The	blue	trace	is	extracted	at	(X3,	

X3)	which	shows	the	population	relaxation	after	the	optical	preparation	of	the	X3	state.	The	

green	transient	(X3,	X1)	and	the	maroon	(X3,	PL)	show	the	transients	at	coordinates	

excited	at	X3	and	detected	at	lower	energy	levels.	The	signal	amplitude	at	these	coordinates	

rises	as	the	population	from	X3	relaxes	to	the	X1	and	PL	energy	levels.	

The	population	relaxation	in	the	signal	response	is	accompanied	by	rapidly	and	slowly	

damped	modulations.	The	rapidly	damped	modulations	have	damping	times	~50	fs	and	

frequencies	derived	from	oleate-ligand	vibrational	motions.	To	characterize	these	rapidly	

damped	modulations,	an	excitation-specific	coherence	map	(Figure	3.8a)	was	generated	by	

performing	the	FFT	of	residuals	in	the	time	range	(10-200	fs).	In	this	excitation	specific	

coherence	map,	the	amplitude	of	the	FFT	at	each	coordinate	is	plotted	with	frequency	on	

the	x-axis	and	detection	energy	on	the	y-axis.	These	maps	encompass	all	the	frequency	

information	of	the	coherent	dynamics	at	a	given	excitation	energy.	In	the	case	of	oleate-

capped	CdSe	QDs,	the	coherence	map	reveals	prominent	modulations	occurring	across	

several	lower	energy	levels,	with	the	most	significant	intensities	observed	at	X2,	X1,	and	PL	

energy	levels.	This	suggests	that,	upon	excitation	from	the	ground	state,	the	coherent	

wavepacket	persists	during	the	relaxation	process	towards	these	lower	energy	levels.	

The	principal	modulation	components	at	the	key	coordinates,	(X3,	X3),	(X3,	X1)	and	

(X3,	PL)	were	analyzed	using	linear	prediction,	singular	value	decomposition	(LPSVD)	

analysis	(Figure	3.8b).	The	advantages	of	LPSVD	over	FTs	include	the	additional	

information	on	the	phase	and	the	damping	times	of	modulations.	The	data	from	0-10	fs	are	

113	

	
	
	
excluded	from	the	analysis	as	to	avoid	any	contributions	from	the	pulse	overlap	effect	in	

A

)

V
e

(

y
g
r
e
n
E
n
o
i
t
c
e
t
e
D

2.3

2.2

2.1

2.0

1.9

1.8

0

)

V
e
(

y
g
r
e
n
E

3
.
2

2
.
2

1
.
2

0
.
2

9
.
1

8
.
1

1000 1500

500
Coherence Frequency (cm−1)

2000

2500 3000

X4

X3

X2

X1

PL

Intensity

B

e
d
u
t
i
l

p
m
A

0.4

0.2

0

0.2

0.1

0

0.1

0

0

(X3,X3)

(X3,X1)

(X3,PL)

500

1000
Coherence Frequency (cm−1)
Frequency (cm-1)

1500

2000

y
g
r
e
n
E
n
o
i
t
c
e
t
e
D

2.1

2.0

1.9

1.8

D

y
g
r
e
n
E
n
o
i
t
c
e
t
e
D

2.1

2.0

1.9

1.8

)

V
e
(

y
g
r
e
n
E

1
.
2

0
.
2

9
.
1

8
.
1

X3

X2

PL

C

2.3

650 cm−1

Figure	3.8.	Coherence	analysis	accompanying	the	relaxation	of	X3.	(a)	Excitation-specific	
X4
coherence	map	at	X3	excitation	(from	10-200	fs).	The	side	panel	includes	the	steady	state	
absorption	spectrum	(b)	LPSVD	spectra	for	coordinates	(X3,	X3),	(X3,	X1)	and	(X3,	PL)	for	
time	range	10-	500	fs.		

725 cm−1

V
e

V
e

2.3

2.2

2.2

3
.
2

2
.
2

)

(

)

(

the	early	time	response.	The	LPSVD	is	carried	out	in	the	time	range	10-500	fs	to	resolve	

both	rapidly	damped	and	slowly	damped	modulations	simultaneously.	The	components	of	
X1

LPSVD	analysis	can	be	categorized	to	two,	the	low-frequencies,	0-300	cm-1,	and	mid-

Intensity
frequencies	in	300-700	cm-1	region.	In	the	low	frequency	region,	there	are	two	types	of	

2.3

1.8

1.8

2.1

2.3

2.0

1.9
Excitation Energy (eV) 

2.1

2.2

2.0

1.9
Excitation Energy (eV) 

2.2

E

modulation,	rapidly	damped	and	slowly	damped	modulations	(Table	3.1).	The	example	of	

G

F

slowly	damped	modulation	is	210	cm-1	mode	which	aligns	with	the	stimulated	Raman	

signal	due	to	the	longitudinal	optical	(LO)	phonon	in	a	typical	CdSe	QD.	Stimulated	Raman	

650 cm−1

coherence	wavepackets	dampen	out	in	the	vibrational	dephasing	times	which	are	in	the	

picosecond	time	domain.	As	a	guide	to	understand	the	nature	of	these	modulations,	an	

147 cm−1

692 cm−1

electronic	structure	optimization	and	vibrational	analysis	of	bidendate	Cadmium	oleate	

[Cd(C18H33O2)]+	is	carried	out	using	Gaussian	software.31	The	ground	state	optimization	

and	the	normal	mode	analysis	were	carried	out	using	B3LYP	functional	6-

311g(d,p)/LANL2DZ	level	of	theory.		

114	

	
	
	
	
 
 
 
 
 
 
 
 
 
 
 
Table	3.1.	Parameters	(frequency,	amplitude,	phase,	and	damping	time)	for	LPSVD	
analysis	of	X3	excitation	at	the	indicated	coordinates	in	2D	spectra.	These	coordinates	are	
indicated	in	the	2D	spectra	(Figure	3.6).	

Coordinate	 Frequency	 Amplitude	

Phase	
(radians)	

Damping	
time	

(X3,	X3)	

49	cm-1	

210	cm-1	

339	cm-1	

(X3,	X1)	

250	cm-1	

642	cm-1	

(X3,	PL)	

126	cm-1	

280	cm-1	

381	cm-1	

718	cm-1	

0.72	

0.05	

3.02	

0.98	

1.23	

0.26	

0.70	

0.02	

0.82	

2.76	

2.29	

2.04	

0.22	

4.12	

0.89	

0.44	

1.27	

0.84	

117	fs	

1616	fs	

20	fs	

65	fs	

34	fs	

116	fs	

37	fs	

455	fs	

46	fs	

To	locate	the	amplitude	of	the	vibrational	motions	in	the	given	excitation	and	detection	

of	the	2DES,	a	3DES	is	produced.	The	entire	signal	response	from	a	2DES	experiment	is	

subjected	to	background	exponential	subtraction	to	isolate	the	residual.	These	residuals	

are	the	amplitudes	of	oscillations	owing	to	different	coherent	wavepacket	dynamics.	The	

residual	at	each	coordinate	is	subjected	to	FFT	and	to	make	a	3DES	spectrum,	the	

amplitude	of	a	particular	frequency	at	each	coordinate	is	plotted	with	respect	to	the	

excitation	and	detection	energies.	The	3DES	spectrum	for	280	cm-1,	380	cm-1,	650	cm-1	and	

720	cm-1	are	shown	in	the	Figure	3.9.	The	major	intensity	of	the	3DES	spectrum	is	seen	

along	the	relaxation	pathway	of	the	relaxation	of	X3	excitation.	Another	interesting	feature	

is	that	the	peaks	are	approximately	spaced	by	the	mode	frequency	along	the	detection	

115	

	
	
	
	
	
	
	
	
	
		
energy	axis,	which	indicates	that	the	peaks	arise	due	to	vibrational	coherences.32	These	

observations	indicate	that	the	vibrational	motions	accompany	the	nonadiabatic	relaxation	

of	X3	exciton.			

A

C

)

V
e

(

y
g
r
e
n
E
n
o
i
t
c
e
t
e
D

)

V
e

(

y
g
r
e
n
E
n
o
i
t
c
e
t
e
D

2.3

2.2

2.1

2.0

1.9

1.8

2.3

2.2

2.1

2.0

1.9

1.8

1.8

280 cm−1

B

380 cm−1

640 cm−1

D

720 cm−1

X4

X3

X2

X1

PL

Intensity

X4

X3

X2

X1

PL

)

V
e
(

y
g
r
e
n
E

)

V
e
(

y
g
r
e
n
E

3
.
2

2
.
2

1
.
2

0
.
2

9

.

1

8

.

1

3

.

2

2

.

2

1

.

2

0

.

2

9

.

1

8

.

1

2.0

1.9
Excitation Energy (eV) 

2.1

2.2

2.3

1.8

2.0

1.9
Excitation Energy (eV) 

2.1

2.2

2.3

Intensity

Figure	3.9.	3DES	spectra/mode	specific	oscillation	of	modulations	for	rapidly	damped	
modulations	of	frequencies,	(a)	280	cm-1,	(b)	380	cm-1,	(c)	640	cm-1,	and	(d)	720	cm-1.		

Global	analysis	was	also	performed	on	the	X2	excitation	(1.952-2.016	eV)	to	understand	

the	relaxation	mechanism	(Figure	3.10).	The	X2	exciton	has	an	excited	hole	in	the	valence	

band	unlike	the	X3	with	an	excited	electron	in	the	conduction	band.	The	relaxation	of	the	

X2	exciton	can	be	visualized	as	relaxation	of	the	excited	hole	to	the	band	edge.	An		

116	

	
	
	
	
 
 
 
 
 
 
 
 
A

C

17 fs

2

1

165 fs

3

4

2.10 ps

164 ps

G

PL

X1

X2

X3

e
d
u

t
i
l

p
m
A
S
D
A
E

0

0

0

0

1.8

1.9

l

n
o
i
t
a
u
p
o
P

B

D

e
d
u
t
i
l

p
m
A

e
d
u

t
i
l

p
m
A

e
d
u
t
i
l

p
m
A

1.0

0.8

0.6

0.4

0.2

0

1

0

−1

0.1

0

−0.1

0.05

0

l

i

a
u
d
s
e
R

-
−0.05
0.1

0

−0.1

0
0

100

1000

10000

Delay T (fs)

(X2,X2)

(X2,X1)

(X2,PL)

(X2,X2)

(X2,X1)

(X2,PL)

2.0

2.2
Detection Energy (eV)

2.1

2.3

0

100

300
200
Delay T (fs)

400

500

Figure	3.10.	Global	analysis	of	the	population	response	of	the	X2	(1.952-2.016	eV)	
excitation	region	of	2DES	spectrum	of	oleate	capped	CdSe	quantum	dots.	(a)	Kinetic	
scheme	for	the	global	model	with	time	constants,	17	+	1	fs,	165	+	3	fs,	2.10	+	0.4	ps,	and	164	
+	40	ps	for	each	relaxation	pathway.	(b)	Evolution	of	population	with	respect	to	time	for	
each	compartment.	(c)	Evolution	associated	difference	spectra	(EADS)	for	each	
compartment	in	the	kinetic	scheme.	(d)	Transients	at	various	coordinates,	(X3,	X3)	(blue	
trace),	(X3,	X1)	(green	trace)	and	(X3,	PL)	(maroon	trace).	Lower	panels	show	the	residual	
for	each	coordinate	overlapped	with	the	fit	obtained	from	the	LPSVD	analysis.		

117	

	
	
	
	
	
	
	
 
 
important	point	to	keep	in	mind	is	that	the	transitions	in	QDs	are	very	broad	and	the	

FWHM	of	the	transition	increases	as	with	increase	in	energy	of	transition.27	Due	to	the	

broad	nature	of	these	transitions,	there	could	be	some	contribution	from	the	X3	exciton	at	

the	X2	energy	level	as	well.	The	global	model	requires	four	different	spectrokinetic	species	

to	model	the	relaxation	dynamics.	The	first	component	has	GSB	and	SE	signals	at	the	

excitation	frequencies	of	X1	and	X2	which	are	indicative	of	shared	ground	state.	ESA	signals		

A

)

V
e

(

y
g
r
e
n
E
n
o
i
t
c
e
t
e
D

2.3

2.2

2.1

2.0

1.9

1.8

X4

X3

X2

X1

PL

)

V
e
(

y
g
r
e
n
E

3
.
2

2
.
2

1
.
2

0
.
2

9
.
1

8
.
1

B

e
d
u
t
i
l

p
m
A

e
d
u
t
i
l

p
m
A

0.2

0.1

0
0.2

0.1

0
0.15

0.10

0.05

(X2,X2)

(X2,X1)

(X2,PL)

0

500

1000 1500

2000

2500 3000

Intensity

0

Coherence Frequency (cm-1)

500

1000
Frequency (cm-1)
Coherence Frequency (cm-1)

1500

2000

Figure	3.11.	Coherence	analysis	accompanying	the	relaxation	of	X2.	(a)	Excitation	specific	
coherence	map	at	X3	excitation	(from	10-200	fs).	Side	panel	includes	the	steady	state	
absorption	spectrum	(b)	LPSVD	spectra	for	coordinates	(X2,	X2),	(X2,	X1)	and	(X2,	PL)	for	
time	range	10-	500	fs.		

are	observed	at	1.85	eV	and	2.05	eV	which	arises	due	to	the	biexciton	formation	of	X2	with	

X1	and	X3	respectively.	This	component	undergoes	decay	with	a	time	constant	of	17	fs.	

During	evolution,	the	ESA	at	energy	levels	1.85	eV	and	2.05	eV	have	disappeared.	This	is	

due	to	the	overlap	of	SE	arising	due	to	the	population	relaxation	to	X1	energy	level.	The	

second	component	has	a	major	GSB/SE	intensity	at	the	X1	and	X2	excitation	energies	and	

decays	with	a	time	constant	of	165	fs.	As	it	evolves	the	X1	peak	is	shifted	to	higher	energy.	

118	

	
	
	
	
 
 
 
 
The	third	component	evolves	with	a	time	constant	of	2.1	ps,	the	amplitude	of	the	ESA	at	

2.05	eV	increases	owing	to	the	surface	traps	(hole	trap)	on	the	QD.	The	final	component	

relaxes	in	several	hundreds	of	ps	just	like	the	final	state	in	X3	excitation.		

The	excitation	specific	coherence	for	X2	excitation	exhibits	presence	of	coherences	in	

the	lower	energy	regions	(Figure	3.11).	Enhanced	intensities	are	observed	in	the	low	

frequencies	and	400	cm-1	regions.	The	LPSVD	analysis	of	the	residuals	at	(X2,	X2)	and	(X2,	

X1)	shows	that	the	modulation	observed	in	the	400	cm-1	region	is	rapidly	damped	with	

damping	times	of	~50	fs.	However,	the	LPSVD	analysis	of	residual	at	(X2,	PL)	indicates	that	

the	400	cm-1	vibrational	mode	is	slowly	damped	and	persist	in	the	lowest	energy	region	

with	a	damping	time	~650	fs.	A	comparison	of	the	mode	analysis	between	the	X3	and	X2	

excitations	are	presented	in	the	discussion	section.	

Table	3.2.	Parameters	for	LPSVD	analysis	for	X2	excitation	at	the	indicated	coordinates	in	
2D	spectra.	These	coordinates	are	indicated	in	the	excitation	specific	coherence	map	
(Figure	3.11).	

Coordinate	 Frequency	

Amplitude	 Phase(radians)	 Damping	

0.24	

1.26	

1.07	

2.97	

1.76	

0.89	

0.44	

1.27	

time	

259	fs	

43	fs	

9	fs	

100	fs	

56	fs	

101	fs	

82	fs	

670	fs	

(X2,	X2)	

187	cm-1	

428	cm-1	

1.65	

6.10	

1094	cm-1	

15.59	

(X2,	X1)	

84	cm-1	

359	cm-1	

(X2,	PL)	

47	cm-1	

331	cm-1	

398	cm-1	

5.05	

7.21	

0.26	

0.70	

0.02	

119	

	
	
	
	
	
	
	
	
	
3.4	Discussion	

The	multidimensional	spectroscopic	study	of	coherent	wavepacket	dynamics	upon	

optical	preparation	of	excitons	in	oleate-capped	CdSe	quantum	dots	reveal	that	the	

vibrational	motions	that	facilitate	the	nonadiabatic	relaxation	mechanism.	The	global	

model	for	the	excitations	shows	rapid	population	relaxation	(time	constants	<15	fs	and	<40	

fs)	indicative	of	coherent	dynamics.	This	coherent	wavepacket	motions	give	rise	to	the	

rapidly	damped	modulations	that	accompany	the	exciton	relaxation	from	higher	energy	

levels.	The	short-time	excitation	specific	coherence	maps	for	X3	and	X2	excitations	exhibit	

low	and	mid-frequency	vibrations	in	the	lower	energy	levels.	These	modulations	exhibit	

peak	patterns	that	are	similar	to	the	vibrational	coherences	with	major	intensities	below	

the	diagonal	and	peaks	spaced	with	respect	to	the	frequency	of	vibrations.32,33			

The	rapidly	damped	modulations	like	130	cm-1,	187	cm-1	and	280	cm-1	in	the	low	

frequency	region	arises	due	to	the	mixing	of	QD	core	modes	with	the	vibrational	modes	of	

the	ligands.	This	mixing	of	core	vibrations	with	ligand	vibrations	gives	rise	to	frequencies	

that	are	higher	and	lower	than	the	lattice	vibrations	(eg.	LO	phonon).	The	modulations	in	

the	mid-frequency	are	assigned	to	the	scissoring,	rocking	and	wagging	modes	of	the	

carboxylate	group	attached	to	the	surface	of	the	QD.34	The	mode	analysis	obtained	from	

electronic	structure	calculations	of	Cd-oleate	are	shown	in	the	Figure	3.12.	The	purple	

vectors	depict	the	displacement	of	atoms	from	their	equilibrium	structures	during	the	

vibrational	motions.	The	vibrational	mode,	~400	cm-1	involves	rocking	vibrations	of	the	

carboxylate	attached	to	the	Cd2+	along	with	rocking	motions	of	CH2	groups	close	to	the	

carboxylates.	This	mode	is	rapidly	damped	in	the	excited	state	but	persist	for	a	long	time	in	

the	lower	energy	PL	state.	This	implies	that	the	wavepacket	rapidly	slides	down	the		

120	

	
	
	
420 cm−1

650 cm−1

950 cm−1

Figure	3.12.	Vector	representation	of	the	420	cm-1,	650	cm-1	and	950	cm-1	obtained	from	
the	Raman	spectra	calculation	of	Cd	oleate	complex.	Purple	arrows	indicate	the	direction	of	
displacement	of	each	atom	from	its	equilibrium	position.		

cascade	of	conical	intersections	to	reach	the	lower	energy	PL	level	and	persists	for	a	long	

time	(670	fs).	The	650	cm-1	mode	involves	out-of-plane	stretching	motions	of	the	

carboxylate	bound	to	the	Cd2+	ion	and	rocking	motions	of	the	adjacent	atoms.	Another	

mode	observed	in	the	calculation	that	is	closer	to	the	rapidly	damped	1090	cm-1	mode	seen	

at	X2	is	950	cm-1	mode.	This	involves	in-plane	symmetric	stretch	of	the	carboxylate	groups	

along	with	stretching	motions	of	the	carbon	chain.	Given	the	relatively	high	frequencies	of	

these	motions,	it	can	be	assessed	that	these	vibrational	motions	are	highly	localized	on	the	

surface	and	to	one	ligand	molecule.	If	there	were	multiple	ligands	aiding	the	relaxation	

121	

	
	
	
	
process	simultaneously,	the	effective	mass	of	the	atoms	involved	in	the	vibrational	motions	

would	be	very	high.	This	would	in	turn	result	in	very	low	frequency	of	the	vibrations.	The	

main	difference	in	the	rapidly	damped	modulations	of	the	X3	and	X2	excitation	turns	out	to	

be	the	ligand-derived	frequency.	The	relaxation	of	the	X3	exciton	essentially	probes	the		

relaxation	of	the	electron	from	1Pe	level	to	1Se.	At	the	same	time,	X3	has	an	excited	hole	that	

relaxes	to	the	band	edge.	The	origin	of	the	mid-frequency	vibrational	mode,	650	cm-1	

observed	in	the	X3	relaxation	is	due	to	the	mixing	of	electronic	wavefunction	with	the	

localized	in-plane	stretching	of	carboxylate	moiety	bound	to	the	surface	of	the	QD.	Whereas	

the	X2	excitation	primarily	probes	the	hole	relaxation,	and	the	400	cm-1	is	the	vibrational	

mode	that	interacts	with	the	hole	wavefunction	of	the	core	QD.	The	fact	that	the	400	cm-1	

mode	is	present	in	the	X3	as	well	as	X2	is	the	direct	indication	that	this	mode	is	mixed	with	

the	hole	wavefunction.	Another	important	aspect	of	the	hole	energy	level	is	that	they	are	

very	closely	spaced.	Therefore,	it	easy	to	visualize	the	presence	of	400	cm-1	mode	in	both	

X3	and	X2	relaxation.	This	demonstrates	the	use	of	excitation	specific	coherence	analysis	to	

distinguish	the	vibrational	motions	that	are	mixed	with	the	electronic	wavefunction	and	

the	hole	wavefunction.	Access	to	excitation	specific	coherence	analysis	turns	out	to	be	a	

unique	advantage	of	the	2DES	performed	with	a	broadband	spectrum	and	short	pulses.				

The	molecular	exciton	picture	for	the	nonadiabatic	relaxation	include	a	cascade	of	

potential	energy	surfaces	corresponding	to	different	excitons.	The	optically	prepared	

wavepacket	slides	via	multiple	potential	energy	surfaces	and	cross	conical	intersections	

(CIs)	during	exciton	relaxation.15,35	Upon	passage	of	the	wavepacket	via	CIs,	electronic	

energy	is	converted	into	vibrational	motions	along	certain	coordinates.	The	coherent	

wavepacket	motions	give	rise	to	rapidly	damped	modulations	with	frequencies	of	surface-

122	

	
	
	
ligand	vibrational	motions	along	the	pathway	of	exciton	relaxation.	Surface	ligand	

vibrations	serve	as	branching	modes	and	lifts	the	degeneracy	of	the	potential	energy	

surface	crossings	or	conical	intersections.14	The	vibrational	modes	that	undergo	

displacement	during	the	nonadiabatic	relaxation	of	the	exciton	in	oleate-capped	CdSe	QDs	

are	assigned	to	the	low	frequency	modes	with	mixed	core-ligand	character	and	mid-

frequency	modes	of	the	carboxylates	bound	to	the	surface.	The	ability	to	determine	the	

effective	electronic–vibrational	coupling	using	ligand	coherences	will	lead	to	new	

discoveries,	especially	in	determining	structural	mechanisms	for	efficient	excitation	energy	

transfer	or	charge	transfer	to	acceptors	on	the	QD	surface.		

123	

	
	
	
	
	
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.

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APPENDIX	

1

0

−1

−2
1.0

0.8

0.6

0.4

0.2

)
d
a
r
(

e
s
a
h
P

y
t
i
s
n
e
t
n
I

1.8

1.9

2.0

2.1

2.2

2.3

Energy (eV)

Figure	A3.1.	Residual	phase	and	intensity	spectra	of	the	femtosecond	laser	pulses	used	in	
the	broadband	multidimensional	electronic	spectroscopy	experiments.	Top	panel	shows	
residual	phase	spectra	after	compression	of	the	laser	pulses	used	in	the	2DES	experiment	
for	the	pump	beam	(solid),	and	for	the	probe	beam	(dashed),	as	determined	by	MIIPS	
scans.20	Bottom	panel	is	the	intensity	spectrum	of	the	laser	pulses.	

128	

	
	
	
 
Figure	A3.2.	SHG-FROG21	spectrogram	for	the	pump	pulses,	as	measured	with	scanned	
pulse	pairs	prepared	by	the	pump	beam's	pulse	shaper	in	the	2DES	spectrometer.	

y
t
i
s
n
e
t
n
I

−100

−50

0
Time (fs)

50

100

Figure	A3.3.	Interferometric	autocorrelation	of	the	pump	pulses,	determined	as	the	
integral	of	the	SHG-FROG	spectrogram	(Figure	A3.2).		

129	

	
	
	
	
	
	
Chapter	4:	Vibronic	Coherences	Initiate	Photoinduced	Charge	Transfer	
from	CdSe	Quantum	Dots	to	Methyl	Viologen	

	We	studied	the	role	of	vibronic	coherences	in	photoinduced	charge	transfer	of	CdSe	

quantum	dots	(QDs)	in	the	presence	of	surface-bound	methyl	viologen	dication	(MV2+)	

acceptors	using	multidimensional	spectroscopy	with	broadband	(500–700	nm)	mid-visible	

excitation	pulses	of	<7	fs	duration.	Analysis	of	coherent	wavepacket	motions	in	two-

dimensional	electronic	spectra	of	oleate-capped	CdSe	QDs	treated	with	MV2+	reveal	

enhanced	activity	in	low	and	mid-frequency	vibrations	at	frequencies	corresponding	to	

core	lattice	vibrations	and	out-of-plane	deformations	of	the	MV2+	pyridine	rings.	The	rapid	

damping	of	these	coherences	is	consistent	with	their	assignment	to	excited-state	coherent	

wavepacket	motions	following	hot-carrier	cooling.	They	can	be	distinguished	from	slowly	

damped	stimulated	Raman	pathways	involving	the	core	longitudinal	optical	phonon	modes.	

We	assign	the	excited-state	wavepacket	motions	to	a	charge-transfer	state	of	mixed	QD	and	

MV2+	character,	which	is	populated	in	<200	fs	prior	to	transfer	of	a	valence	band	electron	to	

the	MV2+	acceptor	on	the	ps	timescale.	These	observations	are	potentially	significant	steps	

towards	understanding	how	to	use	coherences	focused	on	the	organic	ligands	and	

adsorbed	electron-	and	excitation-energy	acceptors	on	the	surface	of	QDs	to	optimize	their	

use	in	photocatalysis.			

130	

	
	
	
	
	
	
4.1	Introduction	

Solar	light	harvesting	offers	a	promising	solution	to	overcome	current	energy	

challenges,	particularly	the	extensive	use	of	nonrenewable	fossil	fuels.1	Semiconductor	

nanocrystalline	materials	are	great	potential	candidates	as	light-harvesting	materials	due	

to	their	tunable	size,	optical	and	redox	properties.2,3	In	particular,	colloidal	quantum	dots	

(QDs)	capped	with	various	surface	ligands	are	used	in	several	classes	of	solution-processed	

optoelectronic	devices	such	as	photovoltaic	cells,4	emissive	devices,5,6	and	photodetectors.7	

Furthermore,	photocatalysis	using	QDs	is	another	promising	application	that	can	utilize	the	

solar	energy	to	drive	chemical	reactions.8,9		

The	process	of	solar	light	harvesting	involves	the	absorption	of	photons	and	the	

subsequent	generation	of	electron-hole	(e-h)	pairs.	The	excellent	tunable	optical	properties	

of	the	QDs	can	be	used	to	absorb	photons	in	a	wide	range	of	energies	to	generate	e-h	pairs.	

Successful	implementation	of	QDs	in	solar	light	harvesting	relies	on	extracting	charge	

carriers	and	stabilizing	the	charge-separated	state.	The	charge	separation	in	photoexcited	

QDs	are	achieved	using	electron	or	hole	acceptors	(Figure	4.1).	These	acceptor	species	can	

then	be	utilized	for	various	applications,	such	as	catalyzing	redox	reactions	and	facilitating	

charge	transport.	The	chemistry	of	the	QD	surface	and	the	nature	of	surface	ligands	can	be	

tuned	to	achieve	efficient	extraction	of	photogenerated	charge	carriers	and	stabilization	of	

charge	separated	state.10–12		

One	of	the	most	interesting	ligand	candidates	for	such	a	charge	transfer	(CT)	are	

viologens	(V),	a	class	of	cationic	organic	molecules	with	conjugated	bi-pyridyl	functional	

groups	with	three	stable	forms:	dication,	radical	cation,	and	neutral	molecule.	The	dication	

viologen	molecule,	V2+,	can	be	sequentially	reduced	to	stable	radical	cation	and	neutral	

131	

	
	
molecule.	They	have	been	widely	used	as	an	electron	acceptor	for	charge	separation	from	

the	photoexcited	quantum	dots.13–15	Methyl	viologen	dichloride	or	1,1′-Dimethyl-4,4′-

bipyridinium	dichloride,	is	an	electrochromic	molecule.	The	dication	species	of	the	methyl	

viologen	has	a	spectroscopic	signature	in	the	UV	region,	whereas	the	reduced	form	of	the	

molecule,	the	methyl	viologen	radical,	has	a	distinct	spectroscopic	signature	in	the	visible	

region	(Figure	4.2).	Therefore,	in	the	event	of	electron	transfer	from	the	QDs,	radical	cation	

is	formed,	and	it	can	be	detected	using	a	visible	probe.	The	Weiss	group	have	studied	the	

photoinduced	CT	using	viologen	derivatives	and	the	mechanism	of	surface	ligand	

adsorption	in	CdSe	and	CdS	quantum	dot	systems	using	transient	absorption	

experiments.15–18	The	Lian	group	have	demonstrated	varying	range	of	CT	rates	with	

respect	to	several	functionalized	viologen	electron	acceptor	molecules.19	The	Smith	group	

has	investigated	the	electron	transfers	in	CdSe/CdS	core-shell	quantum	systems	using	

viologen	acceptors	and	demonstrated	that	the	charge	transfer	rates	decrease	with	increase	

in	the	shell	thickness.20		

Additionally,	there	have	been	several	reports	on	the	involvement	of	vibrational	

coherences	in	the	CT	processes	from	QDs	to	various	electron	acceptors.21,22	The	Zhu	group	

has	carried	out	hot	electron	extraction	from	PbSe	QDs	using	TiO2	electron	acceptors	and	

observed	vibrational	coherences	involving		the	surface	atoms	of	the	electron	acceptor	

TiO2.21	Vibrational	coherences	in	this	study	arises	when	optical	pulses	shorter	than	the	

vibrational	period	activate	electric	fields	near	the	surface.	Recently,	the	Scholes	group	have	

investigated	the	mechanism	of	ultrafast	electron	transfer	in	polymer-fullerene	blends	using	

vibrational	coherences.22		

132	

	
	
In	this	chapter,	we	present	the	photoinduced	CT	from	CdSe	QD	to	the	surface	bound	

electron	acceptor	molecule,	methyl	viologen	(MV).	The	CT	from	a	donor	to	acceptor	

requires	good	energy	level	alignment	of	donor-acceptor	states	with	donor	state	at	similar	

or	higher	energy	than	that	of	the	acceptor	state	and	a	good	wavefunction	overlap	between	

the	donor	and	acceptor	wavefunction.	In	the	QD-MV2+	presented	here,	the	lowest	electronic	

energy	level	of	CdSe	is	the	donor	state	while	the	lowest	unoccupied	molecular	orbital	

(LUMO)	is	the	electron	acceptor.	We	propose	that	the	orbital	overlap	of	the	donor	and	

acceptor	states	lead	to	mixing	of	electronic	states	of	QDs	with	vibrational	states	of	the	

MV2+.	This	mixing	lead	to	delocalization	of	the	surface	and	formation	of	vibronic	excitons.	

This	delocalized	intermediate	formed	between	QD	core	and	MV2+	initiates	the	

photoinduced	CT	from	QD	core	to	surface	ligand	electron-acceptor.	From	the	Chapter	3,	we	

learnt	how	the	vibronic	coherences	involving	surface	ligands	mediated	the	exciton	

relaxation	in	oleate-capped	CdSe	QDs.	Here,	the	electronic–vibrational	coupling	using	

ligand	coherences	will	be	extended	to	understand	the	structural	and	coherent	mechanisms	

for	efficient	photoinduced	charge	transfer	to	acceptors	on	the	QD	surface.			

In	this	chapter,	we	discuss	the	use	of	broadband	two-dimensional	electronic	

spectroscopy	(2DES)	to	study	the	kinetics	and	detect	the	vibronic	coherences	that	mediate	

photoinduced	charge	transfer	from	CdSe	QDs	to	the	MV2+.	The	2DES	enables	us	to	detect	

the	exciton	specific	electron	transfer	to	MV2+	as	the	radical	cation	exhibits	a	photoinduced	

absorption	in	the	visible	region.15,19	The	short-pulses	allows	us	to	detect	the	vibronic	

coherences	before	their	dephasing	times.	The	global	analysis	used	to	model	the	kinetics	of	

electron	transfer	from	QD	core	to	the	MV2+shows	that	the	electron	transfer	occurs	from	the	

133	

	
	
lowest	electronic	energy	level	(either	X1	or	X2)	of	the	QD	to	the	LUMO	of	MV2+.	The	

coherence	analysis	of	the	modulations	using	LPSVD	models	and	excitation	specific		

Figure	4.1.	Energy	level	diagram	for	the	photoinduced	electron	transfer	from	CdSe	QD	core	
to	methyl	viologen	dication	(MV2+)	inspired	by	Morris-Cohen	et	al.15	On	the	left,	the	
electron	(1Se	and	1Pe)	and	hole	energy	levels	of	the	QDs	are	marked	with	solid	lines.	The	
conduction	band	(CB)	and	valence	band	(VB)	of	the	QDs	are	marked	with	shaded	regions.	
Exciton	formation	upon	optical	pulse	interaction	is	indicated	by	the	red	arrow.	On	the	right	
side,	the	lowest	unoccupied	molecular	orbital	(LUMO)	and	highest	occupied	molecular	
orbital	(HOMO)	levels	of	MV2+	are	shown.	Upon	photoexcitation,	an	electron-hole	pair	is	
formed	in	the	QDs.	This	electron	is	transferred	from	the	1Se	state	of	the	QD	to	the	LUMO	of	
the	MV2+	The	dotted	arrow	represents	the	electron	recombination	from	the	MV+•	to	the	
hole	in	the	VB.		

134	

	
	
	
	
	
	
	
A

B

e
c
n
a
b
r
o
s
b
A

0

200

H3C

N+

N+ CH3

MV2+
MV+.

300

400

500

600

700

Wavelength (nm)

Figure	4.2.	Spectroscopic	characterization	of	methyl	viologen.	(a)	Structure	of	1,1′-
dimethyl-4,4′-bipyridinium	dication.	(b)	Absorption	spectra	at	298	K	and	of	methyl	
viologen	dication	(blue	trace)	and	radical	cation	in	ethanol	(red	trace,	redrawn	from	
Watanabe	et	al.23).		

coherence	map	shows	an	enhanced	activity	in	the	low	and	mid-frequency	vibrational	

modes.	These	vibrations	correspond	to	the	mixed	core	lattice	vibrations	of	CdSe	QD	and	

out-of-plane	deformations	of	the	pyridine	rings	of	MV2+	and	arise	from	a	mixed	

intermediate	charge-transfer	state	involving	the	core	of	the	QD	and	MV2+.	

4.2	Experimental	Methods	

4.2.1	CdSe	Quantum	Dot	Synthesis	and	Characterization	

The	2DES	studies	on	CdSe	quantum	dots	presented	in	this	chapter	were	synthesized	by	

the	Van	Patten	laboratory	at	MTSU.	The	detailed	procedure	for	QD	synthesis	is	presented	in	

Chapter	3	of	this	thesis.	In	short,	CdSe	QDs	were	synthesized	following	a	modified	

135	

	
	
	
phosphine-free	synthesis	previously	reported	by	Jasieniak	et	al.24	A	Se	precursor	stock	

solution	was	prepared	in	octadecene	(ODE)	for	30	min	and	then	heated	under	nitrogen	at	

200°C	for	2	h.	A	separate	stock	solution	of	Cd-oleate	was	prepared	by	dissolving	CdO	in	

oleic	acid	and	heated	under	nitrogen	at	100	°C	for	1	h.	The	Cd-oleate	solution	was	then	

heated	to	285	°C,	and	the	Se	precursor	was	rapidly	injected.	The	growth	temperature	was	

maintained	at	265	°C	for	30	min.	After	the	first	growth	step,	UV/Vis	measurements	were	

taken	using	a	modernized	Cary	14	spectrophotometer,	and	a	second	injection	of	the	Se	

precursor	was	performed	and	the	QD	solution	was	allowed	to	grow	at	265	°C	for	another	

30	mins.	The	resulting	QD	solution	was	purified	by	two	cycles	of	precipitation	by	spinning	

in	a	microcentrifuge	at	17000	×	g	and	resuspension	using	a	chloroform/acetonitrile	

solvent/antisolvent	combination.	The	surface	ligands	of	the	QDs	were	analyzed	using	TD-

DART-MS	as	previously	described	by	Frazier	et	al.	25		

4.2.2	Linear	Spectroscopy	and	Photoluminescence	

The	QDs	were	dispersed	in	chloroform	to	obtain	an	absorbance	of	0.3	at	565	nm	for	the	

2DES	experiments.	The	chloroform	solution	is	well	miscible	with	the	MV2+	in	methanol	and	

prevents	the	aggregation	of	QD-MV2+	complex.	The	absorption	spectra	were	measured	

using	a	Schimadzu-2600	UV-Vis-NIR	spectrophotometer.	The	room	temperature	

photoluminescence	(PL)	was	measured	using	Hitachi	F-4500	Fluorescence	

Spectrophotometer.	A	4	mM	stock	solution	of	methyl	viologen	dichloride	hydrate	

(purchased	from	Sigma-Aldrich)	was	prepared	in	methanol.	A	control	experiment	was	

performed	using	oleate-capped	CdSe	QDs.	To	prepare	the	QD-MV2+	complex,	5.6	µL	of	the	

MV2+	stock	solution	was	added	to	150	µL	of	the	QD	sample	to	obtain	a	1:50	ratio	of	the	

QD:MV2+.	

136	

	
	
4.2.3	Two-Dimensional	Electronic	Spectroscopy	

2DES	spectra	were	recorded	using	a	pump–probe	optical	configuration	with	adaptive	

pulse	shaping26	to	compress	the	laser	pulses	and	to	generate	the	excitation	pulse	sequence	

(pulse	1–𝜏–pulse	2)	required	for	the	three-pulse	stimulated	photon-echo	experiment.	

Excitation	pulses	were	obtained	from	a	noncollinear	optical	parametric	amplifier	(NOPA,	

Spectra-Physics	Spirit-NOPA-3H),	which	was	pumped	by	the	third	harmonic	of	a	1.04	μm	

amplified	Yb	laser	(Spectra-Physics	Spirit-4W,	400	fs	pulses	at	a	100	kHz	repetition	rate,	4	

W	average	power).	The	pump	and	probe	beams	in	the	spectrometer	were	split	from	the	

NOPA	output	by	a	broadband	dielectric	beamsplitter	(Layertec,	Mellingen),	processed	by	

an	adaptive	pulse	shaper	(FemtoJock	and	FemtoJock	P,	respectively,	Biophotonic	

Solutions),	and	then	compressed	by	multiple	reflections	on	pairs	of	broadband	chirped	

mirrors	(Ultrafast	Innovations,	Munich).	For	the	present	experiments,	the	NOPA’s	signal	

beam	output	spectrum	(Figure	4.3b)	was	centered	at	600	nm	(∼110	nm	FWHM;	520–700	

nm	usable	range).	The	excitation	pulse	energy	was	attenuated	to	3.75	nJ	per	pulse,	as	

measured	at	the	sample’s	position.	The	pump	beam’s	plane	of	linear	polarization	was	

rotated	magic	angle	(54.7°)	from	that	of	the	probe	beam	by	a	thin	achromatic	half-wave	

retarder	plate.	The	two	beams	were	focused	by	off-axis	parabolic	mirrors	to	100	μm	spots	

overlapped	spatially	just	after	the	front	window	of	the	sample	cuvette.	The	excitation	

pulses	in	both	beams	were	characterized	by	MIIPS	scans27	conducted	with	a	thin	β-barium	

borate	crystal,	which	was	placed	at	the	sample’s	position	following	a	single	cuvette	

window.	The	estimated	pulse	duration	for	both	beams	at	the	sample	position	was	7	fs.	

Residual	phase	plots	(Figures	A4.1),	SHG-FROG	spectrograms28	(Figure	A4.2),	and	

autocorrelation	(Figure	A4.3)	are	presented	in	the	appendix.	

137	

	
	
2DES	spectra	were	recorded	by	programming	the	pump	beam’s	pulse	shaper	to	scan	

the	coherence	time	interval	between	the	two	pump	pulses,	𝜏,	from	0	to	50	fs	with	0.5	fs	

steps	to	obtain	the	excitation	axis	after	Fourier	transformation.	The	detection	axis	of	the	

2DES	spectrum	was	measured	directly	by	measuring	the	pump-induced	change	in	probe	

transmission	through	the	sample	with	a	home-built	0.2	m	spectrograph	(300	gr/mm	

diffraction	grating)	and	a	fast	CCD	detector	(Andor	Newton	940)	using	a	phase-sensitive	

detection	protocol	and	amplitude	modulation	of	the	pump	pulses.29	The	population	time	𝑇	

is	scanned	by	a	time-of-flight	delay	stages	with	a	spacing	of	2.5	fs	from	0-20	fs,	5	fs	spacing	

from	30-400	fs,	10	fs	spacing	from	400-800	fs,	100	fs	spacing	from	800-1000	fs,	1	ps	

spacing	from	1-10	ps,	and	10	ps	from	10-150	ps.	Each	2D	spectrum	was	an	average	of	four	

consecutive	𝑇	scans.	The	signals	detected	in	the	2DES	in	the	pump-probe	configuration	

were	a	sum	of	rephasing	and	non-rephasing	responses	from	the	sample.	

4.3	Results	

4.3.1	Linear	Absorption	and	Photoluminescence	

To	study	the	vibronic	mechanism	of	the	photoinduced	charge	transfer	in	the	QD-MV2+	

complex,	oleate-capped	CdSe	QDs	with	a	size	of	~6.5	nm	were	used	to	perform	the	2DES	

experiment.	Upon	incidence	of	photons,	electrons	are	excited	from	the	hole	states	in	the	

valence	band	to	the	electronic	states	in	the	conduction	band.	In	the	6.5-nm	CdSe	QDs,	the	

lowest	energy	transition	or	the	band	edge	exciton	(1S3/21Se)	is	denoted	as	X1	at	1.94	eV,	the	

second	exciton	(2S3/21Se)	is	denoted	as	X2	at	2.04	eV,	and	the	third	exciton	(1P3/21Pe)	as	X3	

at	2.2	eV.	Figure	4.3a	shows	the	various	excitons	created	upon	photoexcitation	within	the	

CdSe	QDs,	illustrating	their	positions	in	both	the	electron-hole	energy	level	and	the	exciton		

138	

	
	
A

2.0

X1

X2

X3

1Pe
1Se

)

V
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1.0

0.5

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1S3/2
1P3/2
2S3/2

X3

X2

X1

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575
600
625
650
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1.9

1.8

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Wavelength (nm)

700 675

650

625

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575

550

525

y
t
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I

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1.8

1.9

2.0

2.1

2.2

2.3

Energy (eV)

Figure	4.3.	Energy	level	diagram	of	CdSe	QDs	and	steady-state	spectroscopic	
characterization	of	QD-	MV2+.	(a)	On	the	top	left,	the	electron-hole	energy	levels	are	marked	
with	hole	levels	in	the	valence	band	and	electron	levels	in	the	conduction	band.	The	vertical	
lines	depict	different	excitons:	X1	(red),	X2	(green),	and	X3	(blue).	The	figure	on	the	right	
shows	the	exciton	energy	levels	with	energy	in	eV	on	the	left	and	wavelength	on	the	right.	
(b)	Linear	absorption	spectrum	(blue	trace)	marked	exciton	energy	levels,	and	
photoluminescence	(PL)	spectrum	(orange	trace)	with	overlapping	laser	spectrum	(gray	
filled).	The	brown	trace	is	the	photoinduced	absorption	spectrum	of	MV+•	radical	cation	
adapted	from	Zhao	et	al.19	The	purple	trace	is	the	PL	of	the	QD-MV2+	complex.		

energy	domain.	These	distinct	excitons	are	represented	by	different	colors	(X1-red,	X2-

green,	and	X3-blue)	in	the	absorption	spectrum	(Figure	4.3b).	The	peak	positions	were	

determined	using	the	minima	of	second	derivative	of	the	absorption	spectrum.	The	PL	peak	

139	

	
	
	
 
 
 
maximum	was	observed	at	1.917	eV.	The	CdSe	QDs	presented	in	this	study	are	smaller	than	

the	QDs	in	the	Chapter	3.	Therefore,	the	absorption	spectrum	of	these	particles	is	blue	

shifted.	The	smaller	particles	were	chosen	for	the	experiment	to	decrease	the	overlap	of	QD	

signals	with	that	of	MV+•	and	to	detect	the	photoinduced	absorption	signal	from	the	MV+•.		

The	absorption	spectrum	of	the	QD-MV2+	complex	exhibits	the	same	profile	as	that	of	

the	QDs	in	the	visible	region	as	MV2+	does	not	absorb	in	this	region	(Figure	4.2b).	However,	

the	PL	from	the	QDs	was	quenched	after	formation	of	the	QD-MV2+	complex	(Figure	4.3b,	

purple	trace).	This	is	due	to	the	transfer	of	electron	from	the	QD	core	to	the	MV2+	ligand	

which	limits	the	radiative	recombination	of	the	e-h	in	the	QD.	The	broadband	laser	

spectrum	spanned	the	first	three	excitons	very	well	in	this	study.	The	coverage	of	the	

broadband	spectrum	allows	us	to	study	the	population	relaxation	and	coherent	

wavepacket	dynamics	from	all	three	exciton	levels	and	the	photoinduced	charge	transfer	to	

MV2+	by	simultaneously	detecting	the	MV+•	radical	cation.	

4.3.2	Two-Dimensional	Electronic	Spectroscopy	

A	series	of	2D	spectra	at	different	time	delays,	𝑇	are	shown	in	the	Figure	4.4.	The	left	

side	of	the	figure	shows	the	2D	spectrum	acquired	at	the	labeled	time	delays	from	the	2DES	

control	experiments	with	oleate-capped	QDs.	The	2D	spectra	obtained	from	the	QD-MV2+	

complex	is	shown	on	the	right.	The	side	panel	includes	the	absorption	spectrum	of	the	QDs	

with	marked	exciton	energy	levels,	the	laser	spectrum,	and	the	photoinduced	absorption	

spectrum	of	the	MV+•.	In	the	short	time	delay,	the	2D	spectra	exhibit	partially	resolved	

positive	peaks	along	the	diagonal	resulting	from	the	ground	state	bleaching	(GSB)	and	

stimulated	emission	(SE).	The	formation	of	diagonal	peaks	indicates	the	preparation	of	

population	at	different	exciton	energy	levels	after	the	excitation	from	the	pump	pulses.	

140	

	
	
Oleate

Oleate-MV2+

T = 10 fs

T = 10 fs

T = 50 ps

T = 50 ps

T = 150 ps

T = 150 ps

)

V
e

(

y
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2.3

2.2

2.1

2.0

1.9

1.8

2.3

2.2

2.1

2.0

1.9

1.8

2.3

2.2

2.1

2.0

1.9

1.8

)

V
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(

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2

2

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9

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3
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0
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9
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1

X3

MV

X2

X1

PL

0

Intensity

X3

MV

X2

X1

PL

0

Intensity

X3

MV

X2

X1

PL

0.02

-0.02

1.8 1.9 2.0 2.1 2.2 2.3

1.8 1.9 2.0 2.1 2.2 2.3

0

Intensity

Excitation Energy (eV) 

5
2
5

525

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550

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575
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(

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l

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700

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7

Figure	4.4.	Time	evolution	of	2D	spectra	of	oleate-capped	QD	and	QD-MV2+	with	respect	to	
the	population	time,	𝑇.	The	2D	spectra	on	the	left	are	those	of	the	oleate-capped	QDs	used	
in	the	control	experiment.	The	2D	spectra	of	the	QD-MV2+	complex	are	shown	on	the	right	
side.	The	intensities	of	the	2D	spectra	are	auto	scaled	with	respect	to	the	maxima	of	the	
signal	at	a	given	time,	𝑇.	The	side	panels	plot	the	linear	absorption	oscillator	strength	
(blue),	photoinduced	absorption	spectrum	of	MV+•	(brown),	and	photoluminescence	(PL)	
spectra	(orange).	The	amplitude	transients	sampled	at	the	marked	coordinates	(excitation	
at	X3	and	detection	at	X3,	X1,	and	PL)	are	shown	in	Figure	4.5.		

141	

	
	
	
	
	
 
 
 
 
 
 
 
 
 
 
 
 
There	were	no	significant	differences	observed	in	the	2D	spectra	of	the	control	oleate-

capped	QDs	and	the	QD-MV2+	complex	in	the	early	times.	The	peak	patterns	are	very		

similar	to	that	described	in	Chapter	3.	The	emerging	off-diagonal	SE	cross	peaks	during	

time	evolution	shows	the	relaxation	of	higher	energy	excitons	to	the	lower	energy	states.	

Similar	to	the	oleate,	the	2D	spectra	exhibited	an	excited	state	absorption	(ESA)	at	1.88	eV	

arising	from	the	formation	of	trap	states	or	biexcitons.	The	intensity	of	the	ESA	is	much	

higher	than	that	of	the	larger	QDs	presented	in	the	Chapter	3.	This	might	indicate	that	the	

ligand	coverage	on	the	surface	might	be	lower	for	this	set	of	QDs	giving	rise	to	more	trap	

states.	However,	in	the	later	time,	at	𝑇	=	50	ps	the	GSB/SE	signals	corresponding	to	the	

formation	of	X2	and	X1	decreases	significantly.	This	indicates	decay	of	population	from	

these	lower	energy	states	due	to	the	electron	transfer	from	X2,	X1	to	the	MV2+.	At	delay	

times,	𝑇	=	50	ps	and	𝑇	=	100	ps,	there	appears	an	ESA	signal	detected	at	1.85	eV	throughout	

most	of	the	excitation	energies.	This	ESA	corresponds	to	the	photoinduced	absorption	of	

the	MV+•	radical	formed	after	the	electron	transfer	from	the	core	of	the	QDs.	

4.3.3	Global	Analysis	and	Coherence	Analysis	

To	understand	the	kinetics	of	X3	relaxation	and	the	electron	transfer	from	QD	to	MV2+,	

the	amplitude	of	the	evolution	of	the	nonoscillatory	kinetic	response	excited	at	the	energy	

level	of	X3	was	subjected	to	global	analysis	(Figure	4.5).	Global	analysis	models	evolution	of	

spectral	response	as	a	linear	combination	of	evolution-associated	difference	spectra	

(EADS)	from	different	spectrokinetic	species.30	Each	of	the	EADS	in	the	global	model	can	be	

viewed	as	the	average	spectral	signature	of	the	different	component	of	the	model.	For	each	

excitation,	the	sequence	of	species	in	the	kinetic	model	is	the	simplest	one	that	fits	the	

2DES	amplitude	as	a	function	of	the	delay	𝑇.	To	determine	the	simplest	model	to	describe	

142	

	
	
the	kinetics,	the	residual	(the	difference	between	data	and	the	fitted	values)	across	the	

spectrum	is	monitored	to	make	sure	that	the	intensity	is	around	zero.		

17 fs

41 fs

1

2

3

223 fs

4.7 ps

30 ps

449 ps

4

5

6

G

T = 150 ps

)

V
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2.3

2.2

2.1

2.0

1.9

1.8

1.8 1.9 2.0 2.1 2.2 2.3

Excitation Energy (eV) 

0.02

X3

-0.02

X2

X1

MV

PL

525

550

575

600

625

650

675

700

D

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x15

Delay T (fs)

Figure	4.5.	Global	analysis	of	the	population	response	of	the	X3	(2.102-2.214	eV)	
excitation	region	of	2DES	spectrum	of	QD-MV2+	complex.	On	the	left	is	the	kinetic	scheme	
for	the	global	model	with	time	constants	for	each	relaxation	pathway.	Evolution	associated	
difference	spectra	(EADS)	for	each	compartment	in	the	kinetic	scheme	are	present	on	the	
right.	The	final	component	of	the	model	is	enhanced	15	times	to	project	out	the	amplitudes.		

To	describe	the	kinetic	response	of	X3,	the	global	model	required	six	different	

spectrokinetic	species	(see	kinetic	scheme	in	Figure	4.5).	The	character	of	these	kinetic	

species	is	a	combination	of	ground-state	bleaching	(GSB),	stimulated	emission	(SE),	and	

143	

	
	
	
 
 
 
 
 
 
negative-going	excited-state	absorption	(ESA).	The	first	component	is	the	response	from	

the	X3	after	excitation.	The	EADS	of	this	component	has	a	positive	GSB	and	SE	signals	at	the	

excitation	energy	corresponding	to	the	X3	exciton	on	the	detection-energy	axis.	

Additionally,	there	is	a	positive	signal	at	the	energies	of	X1	and	X2,	this	can	be	attributed	to	

the	shared	ground	state	nature	of	all	the	excitations.	The	first	two	compartments	rapidly	

evolve	with	time	constants	of	17	fs	and	41	fs	indicative	of	a	coherent	relaxation	dynamics.	

This	coherent	relaxation	process	also	contributes	to	a	small	increase	in	the	intensity	of	the	

GSB/SE	amplitude	at	X1	and	X2.	Another	notable	event	during	this	time	frame	is	the	shift	

and	decrease	in	the	ESA	character	at	1.88	eV.	The	ESA	signal	observed	here	is	due	to	the	

formation	of	biexcitons	of	X3	with	X1	(1.88	eV).	The	decrease	in	the	ESA	can	be	attributed	

to	two	processes:	first	the	overlapping	SE	signal	produced	during	the	relaxation	of	X3	to	X1	

and	X2	and	second	the	decay	of	the	ESA	due	to	the	decay	of	the	biexciton	state	of	X3	and	X1.		

The	third	spectrokinetic	component	evolves	with	a	time	constant	of	220	fs.	A	decrease	in	

the	positive	EADS	amplitude	at	X3	energy	is	observed	and	at	the	same	time	there	is	

increase	in	the	amplitude	of	at	X1	and	X2.	The	evolution	of	the	third	component	to	the	

fourth	component	is	due	to	the	hot	electron	cooling	from	the	1Pe	electronic	state	to	the	1Se	

electronic	state	in	an	electron-hole	picture	of	the	QDs.	It	should	be	noted	that	excitons	X1	

and	X2	have	the	same	electronic	energy	level,	that	is,	1Se.	Therefore,	when	the	electron	

relaxes	from	1Pe	to	1Se,	the	SE	amplitude	increases	simultaneously	at	detection	energies	of	

both	X1	and	X2.	The	kinetics	of	the	evolution	of	first	three	spectrokinetic	components	of	

QD-MV2+	are	very	similar	to	that	of	the	QDs.	The	evolution	of	fourth	species	to	fifth	species	

has	a	time	constant	of	4.7	ps.	In	terms	of	EADS	evolution,	there	is	a	decrease	in	the	SE	at	the	

energy	levels	of	X2	and	X1	owing	to	the	electron	transfer	from	these	states.	The	evolution	

144	

	
	
of	the	fifth	component	to	the	sixth	component	is	almost	complete	decay	of	the	X1	and	X2	SE	

signals	with	a	time	constant	of	30	ps.	This	evolution	indicates	the	electron	transfer	from	

these	levels	to	the	HOMO	of	MV2+.	The	sixth	component	has	a	very	small	signal	intensity	

compared	to	all	the	other	components.	The	significant	part	of	the	EADS	is	the	ESA	seen	at	

1.85	eV	and	2.1	eV	which	is	the	photoinduced	absorption	signal	from	the	methyl	viologen	

radical	cation.	This	signal	is	very	weak	compared	with	the	signals	from	the	QDs,	and	there	

is	a	large	spectral	overlap	of	the	X2	and	X1	excitons	in	this	region	which	makes	it	even	

more	difficult	to	detect	the	weak	ESA	from	MV+•.	The	weak	response	from	the	MV+•	can	be	

understood	in	terms	of	the	extinction	coefficient	ε	=	13800	M-1	cm-1	at	2.03	eV23	which	is	

100	times	smaller	than	that	of	the	CdSe	QDs.31	The	final	component	is	the	relaxation	of	the	

MV+•	to	the	ground	state.	This	process	is	slow	and	takes	several	hundred	picoseconds	or	

even	nanoseconds.15	

The	amplitude	vs.	population	time	delay	at	different	coordinates	in	the	2D	spectra	were	

plotted	to	show	the	population	dynamics	(Figure	4.6b).	The	blue	trace	is	extracted	at	

(X3,	X3)	which	shows	the	population	relaxation	after	the	optical	preparation	of	the	X3	

state.	The	green	transient	(X3,	X1)	and	the	maroon	(X3,	PL)	show	the	transients	at	

coordinates	excited	at	X3	and	detected	at	lower	energy	levels,	X1	and	PL.	The	top	panel	of	

Figure	4.6b	are	the	transients	obtained	from	the	control	2DES	experiment	on	oleate-capped	

QDs	whereas	the	bottom	panel	show	the	transients	obtained	from	the	2DES	experiments	

on	the	QD-MV2+	complex.	Initially,	the	signal	amplitude	at	the	crosspeak	coordinates	rises	

as	the	population	from	X3	relaxes	to	these	lower	energy	levels.	In	oleate-capped	QDs,	the	

signal	amplitude	at	later	times,	that	is,	in	picosecond	time	range,	decays	very	slowly.	In	

contrast	to	this,	the	signal	intensity	at	the	crosspeak	of	the	QD-MV2+	complex	increases	in	

145	

	
	
5
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MV

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1.8 1.9 2.0 2.1 2.2 2.3

Excitation Energy (eV) 

0

Intensity

Oleate

Oleate-MV2+

A

B

)

V
e

(

y
g
r
e
n
E
n
o
i
t
c
e
t
e
D

2.3

2.2

2.1

2.0

1.9

1.8

1.0

0.5

0

−0.5

−1.0

1.0

e
d
u

t
i
l

p
m
A

0.5

0

−0.5

0
0

200

400

103

104

105

Delay T (fs)

Figure	4.6.	Amplitude	transient	comparison	of	QDs	and	QD-MV2+at	various	coordinates.	
(a)	2D	spectra	of	the	QD-MV2+	complex	with	marked	coordinates	(X3,	X3)	(blue),	(X3,	X1)	
(green)	and	(X3,	PL)	(maroon).	The	side	panels	plot	the	linear	absorption	oscillator	
strength	(blue),	photoinduced	absorption	spectrum	of	MV+•	(brown),	and	
photoluminescence	(PL)	spectra	(orange).	(b)	Amplitude	transients	at	for	the	QDs	(top	
panel)	and	QD-MV2+	(bottom	panel)	for	the	marked	coordinates	in	the	2D	spectra.		

146	

	
	
	
	
	
 
 
 
 
 
A

0.2

0

−0.2

0.2

0

−0.2

0.2

e
d
u

t
i
l

p
m
A

0

−0.2

0.2

0

−0.2

Oleate (X3,X1)
Oleate (X3,X1)
Oleate-MV2+ (X3,PL)
Oleate-MV2+ (X3,PL)

Oleate (X3,X1)

Oleate-MV2+ (X3,X1)

Oleate (X3,PL)

Oleate-MV2+ (X3,PL)

B

e
d
u

t
i
l

p
m
A

0.5

0.4

0.3

0.2

0.1

0

1.0

0.5

0
0

200

400

600

800

Delay T (fs)

0

0
0

500

1000
Frequency (cm-1)

1500

Figure	4.7.	Frequency	analysis	of	the	residuals	of	the	transients	shown	in	Figure	4.6.	(a)	
Residuals	of	the	transients	presented	in	the	Figure	4.6.	The	green	traces	correspond	to	the	
coordinate	(X3,	X1)	and	the	maroon	trace	correspond	to	the	coordinate	(X3,	PL).	The	
LPSVD	fit	function	is	plotted	as	the	black	trace	overlapping	on	the	residuals	of	the	
transients.	(b)	LPSVD	models	for	the	oscillations	observed	in	the	residuals.	The	dotted	lines	
represent	the	amplitude	spectra	of	the	QDs,	and	the	solid	lines	represent	the	amplitude	
spectra	of	the	QD-MV2+	of	the	complex.	The	model	parameters	are	provided	in	Tables	4.1	
and	4.2.		

the	fs	time	range	but	decays	in	picosecond	domain.	The	initial	rise	of	the	signal	is	due	to	the	

relaxation	of	X3	exciton	to	X2	and	X1	whereas	the	decay	in	the	ps	domain	is	the	signature	of	

photoinduced	charge	transfer	from	X2	and	X1	to	the	MV2+.	Another	notable	difference	in	

the	transients	are	the	modulation	and	their	amplitudes.	The	transients	of	the	QD-MV2+	

show	enhanced	amplitudes	of	modulations	at	the	crosspeak	coordinates	compared	to	the	

oleate-capped	QDs.	

147	

	
	
	
	
	
Table	4.1.	Parameters	(frequency,	amplitude,	phase,	and	damping	time)	for	LPSVD	
analysis	of	X3	excitation	for	QDs	at	the	indicated	coordinates	in	2D	spectra.	

	Coordinate	 Frequency		 Amplitude	 Phase	

(radians)	

Damping	
time		

(X3,	X1)	

96	cm-1	

0.015	

208	cm-1	

0.012	

374	cm-1	

0.037	

(X3,	PL)	

40	cm-1	

0.296	

196	cm-1	

0.009	

336	cm-1	

0.405	

0.44	

2.30	

3.12	

0.79	

0.44	

1.60	

120	fs	

874	fs	

74	fs	

88	fs	

2.02	ps	

38	fs	

Table	4.2.	Parameters	(frequency,	amplitude,	phase,	and	damping	time)	for	LPSVD	
analysis	of	X3	excitation	for	QD-MV2+	at	the	indicated	coordinates	in	2D	spectra.	

	Coordinate	 Frequency		 Amplitude	 Phase	

(radians)	

Damping	
time		

(X3,	X1)	

56	cm-1	

0.007	

201	cm-1	

0.014	

371	cm-1	

0.051	

(X3,	PL)	

48	cm-1	

0.003	

157	cm-1	

0.100	

209	cm-1	

0.032	

331	cm-1	

0.83	

2.69	

3.28	

2.40	

2.83	

1.62	

0.56	

0.94	

636	fs	

872	fs	

60	fs	

630	fs	

101	fs	

592	fs	

15	fs	

The	population	relaxation	in	the	signal	response	is	accompanied	by	rapidly	and	slowly	

damped	modulations.	The	rapidly	damped	modulations	have	damping	times	of	~50	fs	

148	

	
	
	
	
	
	
	
	
	
	
	
	
	
whereas	the	slowly	damped	modulations	have	damping	times	of	several	hundreds	of	

femtoseconds.	The	rapid	damping	of	the	coherences	is	consistent	with	their	assignment	to	

excited-state	coherent	wavepacket	motions	following	hot-carrier	cooling.	The	slowly	

damped	ones	are	mostly	stimulated	Raman	coherences	in	the	ground	state.	The	residuals	

of	the	crosspeaks	are	extracted	and	subjected	to	LPSVD	analysis.	The	LPSVD	is	carried	out	

in	the	time	range	of	10-800	fs	to	resolve	both	rapidly	damped	and	slowly	damped	

modulations	simultaneously.		

For	the	coordinate	(X3,	X1),	there	are	three	major	frequencies	at	96	cm-1,	208	cm-1	and	

374	cm-1	in	the	LPSVD	spectrum	(Table	1).	The	nature	of	the	LPSVD	spectrum	remains	very	

similar	in	case	of	the	QDs	and	the	QD-MV2+	complex.	The	low-frequency	peaks	are	

relatively	slowly	damped.	The	208	cm-1	peak	is	the	stimulated	Raman	signal	due	to	the	

lattice	vibration,	longitudinal	optical	(LO)	phonon	mode	in	a	typical	CdSe	QD.	Stimulated	

Raman	coherence	wavepackets	dampen	out	in	the	vibrational	dephasing	times,	which	are	

in	the	picosecond	time	domain.	The	374	cm-1	mode	that	is	very	similar	in	the	QD	and	QD-

MV2+	complex	is	likely	an	oleate	mode,	symmetric	in-plane	scissor	of	the	carboxylate	mixed	

with	C-H/C-C	stretching	along	the	long	alkyl	chain.	The	most	interesting	part	is	the	(X3,	PL)	

coordinate	where	the	vibrational	mode	patterns	are	quite	different	between	the	two	

samples.	In	the	QD-MV2+	complex,	there	appears	a	rapidly	damped	low	frequency	mode	at	

157	cm-1	which	is	not	present	in	the	QD	oleate.	The	frequency	is	lower	than	the	lattice	

mode	owing	to	the	mixing	of	these	modes.	Another	interesting	mode	is	the	330	cm-1	mode	

which	is	very	rapidly	damped.	The	336	cm-1	mode	in	the	oleate	is	replaced	by	this	rapidly	

damped	mode.	Since	the	damping	time	of	this	mode	is	short,	there	could	be	some	

uncertainty	regarding	the	peak	position.	To	understand	the	origin	of	this	mode,	a	

149	

	
	
Gaussian32	electronic	structure	calculation	and	vibrational	analysis	is	carried	out	on	the	

MV2+	molecule.	The	normal	mode	analysis	was	carried	out	using	the	B3LYP	functional	6-

311g(d,p)	level	of	theory.	The	detailed	mode	assignments	are	described	in	the	discussion	

section.		

To	compare	these	rapidly	damped	modulations	across	the	excitation	energy,	an	

excitation-specific	coherence	map	(Figure	4.8)	was	generated	by	performing	the	FFT	of	

residuals	in	the	time	range	(10-200	fs)	at	X3	excitation.	In	the	excitation-specific	coherence	

map,	the	amplitude	of	the	FFT	at	each	coordinate	is	plotted	with	frequency	on	the	x-axis	

and	detection	energy	on	the	y-axis.	These	maps	encompass	all	the	frequency	information	of	

Figure	4.8.	Comparison	of	excitation-specific	coherence	map	at	X3	excitation	(from	10-
200	fs)	for	QD	and	QD-MV2+	complex.	The	side	panels	plot	the	linear	absorption	oscillator	
strength	(blue),	photoinduced	absorption	spectrum	of	MV+•	(brown),	and	PL	spectra	
(orange).	The	blue	box	illustrates	the	portion	of	the	excitation-specific	coherence	map	
where	significant	amplitude	differences	between	QD	and	QD-MV2+	are	evident.		

the	coherent	dynamics	at	a	given	excitation	energy.	In	the	case	of	oleate-capped	CdSe	QDs,	

the	coherence	map	reveals	prominent	modulations	occurring	across	several	lower	energy	

levels,	with	the	most	significant	intensities	observed	at	the	X1	and	PL	energy	levels.	The	

major	peak	observed	are	~200	cm-1	corresponding	to	the	LO	phonon	mode.	At	the	same	

150	

	
	
	
time,	there	is	an	overall	enhancement	of	vibrational	amplitudes	in	the	excitation	specific	

coherence	map	of	QD-MV2+	complex.		

4.4	Discussion	

The	results	in	this	chapter	indicate	that	the	photoinduced	charge	transfer	from	CdSe	

QDs	to	the	MV2+	ligand	molecule	involves	a	coherent	vibronic	intermediate	(Figure	4.10).	

The	kinetic	analysis	and	global	modelling	indicate	that	the	X3	exciton	relaxes	to	the	lower	

energy	states,	X2	and	X1	similar	to	the	relaxation	kinetics	observed	in	oleate-capped	QDs	in	

Chapter	3.	The	X2	and	X1	state,	owing	to	their	shared	electronic	state,	1Se	donate	the	

electron	to	the	LUMO	of	the	MV2+.	The	charge	transfer	process	has	a	time	constant	of	30	ps	

in	this	case.	The	charge	transfer	rate	in	this	study	is	slower	compared	to	the	charge	transfer	

rates	observed	in	the	CdS	quantum	dots	because	of	the	low	driving	force	or	smaller	energy	

gap	between	the	donor	and	the	acceptor	states.14,15		

342 cm-1

385 cm-1

429 cm-1

442 cm-1

Figure	4.9.	Vector	representation	of	the	vibrational	modes	obtained	from	the	Raman	
spectra	calculation	of	MV2+	for	340-450	cm-1	region.	Purple	arrows	indicate	the	direction	of	
displacement	of	each	atom	from	its	equilibrium	position	during	the	vibrations.		

151	

	
	
	
The	comparison	of	short-time	excitation-specific	coherence	map	of	QD	and	QD-MV2+	

complex	reveals	the	enhancement	in	amplitudes	is	particularly	seen	in	the	mid	frequency	

regions.	Higher	vibrational	activity	seen	in	the	lowest	energy	region	at	~1.88	eV	region	

where	the	ESA	of	the	MV+•	is	being	observed	in	the	2D	spectra.	The	analysis	of	the	mode-

specific	character	of	the	coherences	reveals	the	structural	origin	of	the	electronic-ligand	

vibrational	coupling	present	in	the	intermediate	(Figure	4.9).	The	main	modes	found	in	this	

intermediate	is	the	~160	cm-1	which	corresponds	to	a	mixed	mode	with	the	lattice	

vibration	(LO	phonon)	and	ligand	vibrations.	This	mode	is	a	resultant	of	the	quantum	

coherent	mixing	of	the	core	electronic	states	with	the	vibrational	states	of	the	ligand.	Apart	

from	the	low	frequency	modes,	higher	amplitudes	are	also	observed	in	mid	frequency	

regions	at	~330	cm-1.	There	are	four	modes	that	were	isolated	from	the	MV2+	normal	mode	

analysis	in	the	340-450	cm-1	region.	A	342	cm-1	involves	the	out-of-plane	bending	modes	of	

the	pyridyl	rings	and	adjacent	hydrogens	on	the	methyl	group.	The	385	cm-1	corresponds	

to	the	in-plane	twisting	of	the	MV2+	molecule.	The	430	cm-1	and	440	cm-1	modes	are	very	

similar	in	nature	and	exclusively	involves	out-of-plane	motions	of	the	C	atoms	in	the	

bipyridyl	rings.	The	330	cm-1	mode	detected	in	the	LPSVD	model	could	be	either	one	of	

these	modes	or	a	mix	of	some	of	these	modes	and	the	core-QD	lattice	modes.	Therefore,	the	

mode	observed	~330	cm-1	is	assigned	to	the	in-plane	and	out-of-plane	bending	and	

deformation	of	the	bypyridyl	rings.33,34	An	enhancement	of	the	vibrational	amplitudes	

along	with	detection	of	MV-specific	vibrational	motions,	can	be	rationalized	in	terms	of	

presence	of	mixed	QD/MV2+	surface.	It	is	highly	unlikely	to	observe	MV2+	vibrations	in	

these	energy	regions	without	mixing	of	QD	core	with	MV2+,	owing	to	the	absence	of	direct	

excitation	and	very	small	extinction	coefficient	of	MV2+	compared	to	QDs.	These	

152	

	
	
observations	are	consistent	with	the	presence	of	an	intermediate	charge	transfer	state	

formed	via	coherent	wavepacket	motions.	In	summary,	the	exciton	relaxation	and	

photoinduced	charge	transfer	can	be	understood	in	terms	of	a	molecular	exciton	picture.		

E

X4

X3

X2

X1

CT

MV+

Branching Modes

Figure	4.10.	Schematic	representation	of	the	potential	energy	surface	representing	the	
relaxation	of	X3	optical	excitation	via	a	cascade	of	conical	intersections	via	coherent	
wavepacket	motions.	The	red	potential	energy	curve	depicts	the	bridging	coherent	charge	
transfer	intermediate	in	the	QD-MV2+	complex.		

This	picture	involves	a	cascade	of	potential	energy	surfaces	corresponding	to	different	

excitons.	Upon	photoexcitation,	a	coherent	wavepacket	is	prepared	at	the	X3	exciton.	This	

wavepacket	slides	via	multiple	potential	energy	surfaces	and	cross	conical	intersections	

(CIs)	during	exciton	relaxation.35,36	Upon	passage	of	the	wavepacket	via	CIs,	electronic	

energy	is	converted	into	vibrational	motions	along	certain	coordinates.	The	coherent	

wavepacket	motions	gives	rise	to	rapidly	damped	modulations	with	frequencies	of	surface-

ligand	vibrational	motions	along	the	pathway	of	relaxation	of	the	excitons.	Surface	ligand	

153	

	
	
	
vibrations	serve	as	branching	modes	and	lifts	the	degeneracy	of	the	potential	energy	

surface	crossings	or	conical	intersections.37	

In	other	words,	these	vibrational	modes	are	the	ones	that	experience	displacement	

during	the	nonadiabatic	relaxation	of	the	exciton.	In	the	study	presented	here,	the	X3	

exciton	relaxation	mechanism	and	coherences	are	quite	similar	in	the	initial	stages	for	the	

case	of	QDs	and	the	QD-MV2+	complex.	However,	the	presence	of	different	vibronic	

coherence	and	associated	peak	patterns	in	the	lower	energy	region	corresponding	to	

energy	levels	of	MV+•	indicate	that	there	is	a	charge	transfer	intermediate	formed	via	

coherent	wavepacket	motions.	This	intermediate	involves	coherent	wavepacket	motions	

that	are	resultant	of	mixed	vibrations	of	the	core	and	the	surface	electron	acceptor	

molecule	specifically	out-of-plane	motions	of	pyridyl	rings.	This	coherent	CT	intermediate	

initiates	the	photoinduced	CT	from	the	core	of	the	QDs	to	the	LUMO	of	the	surface	electron	

acceptor,	MV2+.	The	results	presented	in	this	chapter	are	consistent	with	the	proposed	

hypothesis	suggesting	a	presence	of	CT	intermediate	formed	via	vibronic	coherence	that	

initiates	the	photoinduced	CT	from	QD-MV2+.	These	findings	represent	promising	advances	

in	understanding	how	to	engineer	quantum	coherences	associated	with	organic	ligands	and	

adsorbed	electron-	and	excitation-energy	acceptors	on	quantum	dots'	surfaces	to	optimize	

and	enhance	the	efficiency	of	quantum	dots	in	photocatalysis.

154	

	
	
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APPENDIX	

)
d
a
r
(
e
s
a
h
P

y
t
i
s
n
e
t
n
I

1.0

0.5

0

1.0

0.8

0.6

0.4

0.2

1.8

1.9

2.0

2.1

2.2

2.3

Energy (eV)

Figure	A4.1.	Residual	phase	and	intensity	spectra	of	the	femtosecond	laser	pulses	used	in	
the	broadband	multidimensional	electronic	spectroscopy	experiments.	Top	panel	shows	
residual	phase	spectra	after	compression	of	the	laser	pulses	used	in	the	2DES	experiment	
for	the	pump	beam	(solid),	and	for	the	probe	beam	(dashed),	as	determined	by	MIIPS	
scans.27	Bottom	panel	is	the	intensity	spectrum	of	the	laser	pulses.	

159	

	
	
	
 
Figure	A4.2.	SHG-FROG28	spectrogram	for	the	pump	pulses,	as	measured	with	scanned	
pulse	pairs	prepared	by	the	pump	beam's	pulse	shaper	in	the	2DES	spectrometer.	

y
t
i
s
n
e
t
n
I

−100

−50

0
Time (fs)

50

100

Figure	A4.3.	Interferometric	autocorrelation	of	the	pump	pulses,	determined	as	the	
integral	of	the	SHG-FROG	spectrogram	(Figure	A4.2).	

160