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THESIS

LIBRARE

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3 1293 01682 6293

 

                       

               

 

 

 

 

This is to certify that the

dissertation entitled

Zwitterionic Excited States of the Delta-Manifold

of Quadruply Bonded Metal Dimers

presented by

Daniel Scott Engebretson

has been accepted towards fulfillment
of the requirements for

PhD Chemistry

degree in

 

 

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MSU is an Affirmative Action ’Equal Opportunity Institution 0-12771

 

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1193 Macs-p.14

 

ZWITTERIONIC EXCITED STATES OF THE DELTA-MANIF OLD OF
QUADRUPLY BONDED METAL DIMERS

By

Daniel Scott Engebretson

A Dissertation

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1998

ABSTRACT

ZWITTERIONIC EXCITED STATES OF THE DELTA-MANIFOLD OF
QUADRUPLY BONDED METAL DIMERS

By

Daniel Scott Engebretson

Photoinitiated multielectron chemistry is one of the fundamental processes of life;
without it, carbon dioxide could not be converted to simple sugars and water could not be
split to provide oxygen. While photoinitiated multielectron chemistry is ubiquitous in
natural systems, it is rarely observed in man-made systems. Zwitterionic excited states,
by virtue of having a pair of electrons associated with one nucleus, are a promising
intermediate to photoinitiated multielectron chemistry.

Two electrons in two weakly coupled orbitals give rise to two states (diradical)
with electrons residing in separate orbitals and two states (zwitterionic) with both
electrons paired in one orbital or the other. This two-center, two-electron state manifold
has eluded experimental confirmation because the zwitterionic states have been diflicult
to locate. Two-photon excitation of fluorescence of quadruply bonded metal dimers has
been utilized to reveal the zwitterionic nature of the singlet excited states of the
8-manifold of quadruply bonded metal dimers. The assignment of the band observed in
the two-photon fluorescence excitation spectra to the hidden zwitterionic state (2‘Alg)
has been aided by measuring the quadratic dependence of the fluorescence on the
incident laser intensity and measuring the relative intensity when two circularly polarized

photons are used as compared to two linearly polarized photons.

Based on these two—photon fluorescence excitation measurements for a number of
different quadruply bonded dimers it has been possible to assess the zwitterionic
character of the excited states. It is observed that when the 8-bond is fully formed in the
M2X4L4 series of compounds, the excited states are approximately 80% ionic. However,
when the S-bond is partially broken in the M02Cl4(PrI’)2 series of compounds, the ionic
character approaches 85%. Furthermore, with this latter series of compounds, the entire
manifold of states can be spectroscopically measured. This is the first case where all of

the electronic states of a two-center, two-electron bond have been observed.

Dedicated to my family, past, present, and future

iv

ACKNOWLEDGMENTS

The work reported here would not have been possible without the excellent
facilities provided at Michigan State University. In particular I would like to thank the
faculty of the LASER laboratory for providing such a wonderfully equipped facility in
which to play. Also, I would like to thank Dr. Tom Carter, the manager of the LASER
laboratory, for his help over the years.

I have had the opportunity to work with a number of great people during my
graduate career; all have helped me grow both scientifically and personally. The
members of the Leroi and Nocera groups could always be counted on to discuss problems
and thoughts on my project -— usually while drinking a beer or catching a fish (actually,
not too many were ever caught). While everyone I worked with was greatly appreciated,
I would like to single out Jeff Zaleski. He was my mentor when I first began and he
taught me a great deal about how to approach and deal with problems in experimental
physical chemistry.

I would also like to thank the support staff in the Chemistry Department. Without
Manfred, Scott and Keki in the glass shop my fingers would eternally blistered since I
always forget hot glass looks just like cold glass. Russ, Dick and Sam were always
willing to build strange little doo-hickeys to hold sample cells, optics, and contain my
experiments. I would also like to thank Ron and Scott in the electronic shop for doing
their best at keeping me from getting electrocuted when I did not have everything
properly grounded.

My advisors, Dan and George, will always be fondly remembered. I cannot thank
them enough for the guidance they have given me. Dan could always be counted on to
share his zeal for science. Usually that went hand in hand with late nights trying to get
data or figures for a talk — tomorrow, but he showed me how much fun science can be.

George was a great stabilizing force. His love for science and discovery was more muted

than Dan’s (isn’t everyone’s?), but his passion was clear. I would also like to thank
George for his willingness to accept me into the graduate program here at Michigan
State, and also helping me leave.

Amy, Ariel and my son (we’ll name him when he gets here) have to be thanked
for their unending love and emotional support. Without Amy, I probably would not have
gone to graduate school and despite a few bad days I have really enjoyed the decision.
She was also very understanding when I would call and say “I’m working with Nocera..”.
I would also like to thank my parents and Amy’s parents. Though I don’t think they
really understand what a zwitterionic excited state is they always provided a great deal of
encouragement. I would also like to thank Lowell McCann. While he was not part of the

chemistry department, the friendship we developed over the years will never be forgotten.

vi

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. ix
LIST OF FIGURES ............................................................................................................. x
Chapter I .............................................................................................................................. 1
Introduction ..................................................................................................................... 1
LA Zwitterionic Excited States ...................................................................................... 5
I.A.l. History of the Delta Bond .................................................................................. l6
1.A.2. Electronic States of the S-Manifold ................................................................... 17
LB. Nonlinear Spectroscopy ........................................................................................ 19
1.8.1 Phenomenological Aspects of Spectroscopy ........................................................ l9
l.B.2. Mathematical Aspects of Spectroscopy ............................................................. 23
I.B.2.a. Selection Rules ................................................................................................ 28
I.B.2.b. Power Dependence .......................................................................................... 31
I.B.2.c. Polarization Dependence ................................................................................. 32
Chapter II ........................................................................................................................... 37
Experimental Methods .................................................................................................. 37
HA. Materials and Standard Instrumentation .............................................................. 38
II.A.l. Synthesis of M02C14(I§P)2 compounds ............................................................. 39
II.A.1.a. Synthesis of M02C14(S,S-dppb)2 .................................................................... 39
HA. I .b. Synthesis of M02C14(depe)2 ........................................................................... 40
HA. 1 .c. Synthesis of M02C14(dppe)2 ........................................................................... 4O
II.A.2. Spectroscopic Solvents and Materials .............................................................. 41
II.A.3. Standard Instrumentation. ................................................................................. 42
11.8. Two-Photon Fluorescence Excitation (TPE) ....................................................... 42
II.B.l. TPE Instrumentation ......................................................................................... 42
II.B.l.a. TPE Measurment ............................................................................................ 51
II.B.1.b. Power Dependence Measurement .................................................................. 53
II.B.2.c. Polarization Dependence Measurement ......................................................... 53
Chapter III ......................................................................................................................... 55
Two-Photon Spectroscopy of M02C14(PrP)2 Complexes ............................................... 55
III.A. Experimental Background of M2X4(PP)2 .......................................................... 55
III.B. Two-Photon Spectroscopic Results for M02C14(PP)2 Compounds. .................. 58
IIIHBI. M02Cl4(S,S,'dppb)2 ......................................................................................... 61
III.B.2. M02C14(depe)2 ................................................................................................. 67
111.83. M02C14(dppe)2. ................................................................................................ 7O
III.B.4. M02C14(dmpm)2. ............................................................................................. 7O
III.C. Discussion ........................................................................................................... 74
Chapter IV ......................................................................................................................... 77
Two-Photon Spectroscopy of M2X4L4 Complexes ....................................................... 77
WA. Spectroscopic Background for M2X4L4 Compounds”54 .................................. 77

vii

IV.B. Theoretical Observations on M2X4L4 Compounds. ........................................... 8]

WC. Two-Photon Spectroscopic Results of M2X4L4 complexes. .............................. 82
IV.C.l. MozCl4(PMe3)4 ............................................................................................... 82
IV.C.2. MozBr4(PMe3)4 ............................................................................................... 88
IV.C.3. M0214(PMe3)4 .................................................................................................. 88
IV.C.4. MozCl4(PEt3)4 ................................................................................................. 93
IV.C.S. M02C14(AsMe3)4 ............................................................................................. 93
IV.C.6. W2Cl4(PMe3)4 ................................................................................................. 98
IV.C.7. MoWCl4(PMe3)4 ............................................................................................. 98
IV.C.8. cis-M02C12(mhp)2(PMe2Ph)2 ........................................................................ 103
IV.D. Discussion ........................................................................................................ 107
IV.D.l. Effect of Halogen Substitution on the 5-manifold. ....................................... 107
IV.D.2. Effect of o—donating ligand on the 8—manifold. ............................................ 112
IV.D.3. Effect of Metal Substitution on the 8-manifold. ........................................... 113
IV.D.4. cis-M02C12(mhp)2(PMe2Ph)2 ......................................................................... l 13
IV.B. Zwitterionic Character of the 85* and 8*2 States. ............................................ 114
Appendix I ....................................................................................................................... 116
Appendix II ...................................................................................................................... 123
References ....................................................................................................................... 1 26

viii

LIST OF TABLES

Table 1.1. Values for the polarization functions F, G, and H, depending on the eight
polarization cases. From References 34 and 36. ...................................................... 34

Table 1.2. Two-photon tensor patterns and the polarization ratio expected for each
transition in the D2d point group. From References 34, 36, and 38. ........................ 35

Table 11.1. The twist angle (x) for each of the compounds studied. The ligand
abbreviations are given in the text. M02C14(PMe3)4 corresponds to a 90° twist.
Values taken from Reference 26b. ............................................................................ 38

Table 111.1. Spectroscopic and structural data for M02C14(PrP)2 compounds. 1(5 -) 5*)
is the transition energy in cm", a is the extinction coefficient for the I(5 —) 5*)
transition at the maximum in M'lcm", 3(5 —> 5*) is the transition energy in cm" and
x is the twist angle in degrees. NM not measurable. Except as noted, the data was
taken from Reference 26. .......................................................................................... 59

Table 1V.1. The entries are in the form of nm (M‘lcm'l). a reference 54a, 5 reference 40,
and c reference 54b d reference 54c. IThis band was only reported in the
fluorescence spectrum and the extinction coefficient was not measured .................. 80

Table IV.2. Summary of data for the 1(5 —-) 5*) and 1(52 -) 5*2) transition energies and
the energy gap (AB) separating the 55* and 5‘“2 states as determined from the band
maxima. The energies are in cm". ......................................................................... 108

Table IV.3. The metal-metal bond distance (in A), overlap (S) of parent dxy orbitals and

one- (AW) and two-electron (K) energies in cm". * S was determined from the
oscillator strengths using Mulliken’s relationship (Equation 1.1), the references are
for the oscillator strengths. NM not measured. ** This value is for cis-
M02C12(mhp)2(PEt3)2 .............................................................................................. 109

Table IV.4. The 2(5 —-) 5*) transition energies for the M02X4(PMe3)4+/' series of
compounds. From Reference 61. ............................................................................ 111

Table IV.5. Results of calculation to determine the percentage of zwitterionic character
of the excited state. .................................................................................................. 114

ix

LIST OF FIGURES

Figure 1.1 A general scheme for photoinitiated multielectron chemistry in natural
systems. A photon is absorbed at the receptor and the excited state which is
produced initiates a chain of electron transfer reactions where the electron is moved
further and further away from the receptor. Ultimately, the requisite number of
electrons are stored at the multielectron site where the chemical reaction occurs. ..... 2

Figure 1.2. Diagram of the thylakoid membrane of chloroplast showing the components
of the electron-transfer scheme in green plants. P680 and P700 are the chlorophyll
molecules that initiate the photoinduced electron transfer processes. Q represents
the plastoquinone molecules. Cyt are the cytochrome molecules. FeS are the iron-
sulfur proteins. A are the electron accepting chlorophyll molecules. Fd is
ferrodoxin. FAD is ferrodoxin NADP+ reductase and PC denotes the blue copper
protein plastocyanin. ................................................................................................... 3

Figure 1.3. The proposed simplified scheme of photoinduced multielectron chemistry.
As in Figure 1.1, the photon is absorbed by the receptor and multielectron chemistry
occurs at the multielectron site. ................................................................................... 6

Figure 1.4. (top) The molecular orbital diagram for H; that results when one electron is
placed in the molecular orbitals formed by the overlap of hydrogens’ atomic ls
orbitals. AW is the one-electron energy. (bottom) The four electronic states that
arise when two electrons are placed in the molecular orbitals of hydrogen. On the
left side of the diagram, the Is orbital of the hydrogen atom represents 0 on the
energy scale. AW is the one electron energy, and K is the two-electron exchange
energy. Since 02 and 6*2 are the same symmetry they mix together and gain some
two-electron character. The energy separating the state then becomes

2JAW2 + K2 ............................................................................................................ 7

Figure 1.5. The potential energy diagram for the hydrogen molecule, showing the
behavior of the states as the bond is stretched. In the strongly coupled limit AW
(which is much greater than K) dominates the energy of the electronic states. In the
weakly coupled limit, AW ~ 0 and K determines the energy of the states. ................. 9

Figure 1.6. The electronics states of ethylene as it is twisted about the C—C internuclear
axis ............................................................................................................................. 12

Figure 1.7. Molecular orbital diagram (D4,1 symmetry) showing the metal-metal bonding
in quadruply bonded dimers when two ML4 (D4h) fragments are brought together. 13

Figure 1.8. The 5-manifold of electronic states that results when two electrons are placed
in the 5 orbitals. ......................................................................................................... 15

Figure 1.9. The dependence of the electronic states of the 5-manifold on internuclear
twist angle (1). The 5-bond is broken at x = 45°. There is a mirror image of the
manifold from 45° — 90° that is not shown here ........................................................ 18

Figure 1.10. The toroidal shaped electric field that is generated by an Oscillating dipole.
................................................................................................................................... 21

Figure 1.11. View down the axes of three oscillating dipoles, along with the cross-
section of their emanating electric fields are shown. Constructive interference of the
electric fields only occurs in “forward” direction where the three electric fields
overlap. ...................................................................................................................... 21

Figure 1.12. The primary wave ('0') is at the frequency of the incident light. The
secondary wave (- - -) that is generated when the oscillating dipoles are accelerating
(at their turning points) is 90° out of phase with the primary wave. The refracted
wave (—) is the superposition of the primary and secondary waves. Its phase
relationship is determined by the 90° phase lag due to the secondary wave, plus a
component related to the intensities of the primary and secondary waves. .............. 22

Figure 1.13. When a dipole is exposed to a very high electric field, the dipole becomes
overdriven and can oscillate at multiples of the driving frequency. Here, the dipole
oscillates also at twice the driving frequency. ........................................................... 24

Figure 1.14. a.) Second harmonic generation is an example where two frequencies (hvl)

are mixed through the second order susceptibility tensor, x0), to yield a new
frequency (hvz), that is the sum of the incident frequencies. b.) In sum frequency

generation, three frequencies (hvl) are mixed through 1(2) to yield a new frequency
(hv3) that is the sum of the three incident frequencies. ............................................. 29

Figure 1.15. Two examples of nonlinear spectroscopy where a total of four frequencies
are mixed through 1(3). a.) Two-photon absorption (TPA), where two photons (v1)

populate the excited state that then relaxes to the ground state by two-photon
emission. b.) Coherent anti-Stokes Raman spectroscopy (CARS) is a more complex
process, where v, places the system in a virtual state that is driven down to a

vibrationally excited state by v2. This excited state interacts with a second photon
v, and ultimately the scattered photon at frequency V8 is detected. .......................... 30

xi

Figure 11.1. A schematic drawing of the instrumentation used to perform TPE
measurements. L1 is the long focal length lens used to reduce divergence of the
laser beam. GL (GIan-Laser polarizer) DFR (Double Fresnel Rhomb), and SFR
(Single Fresnel Rhomb) are the optics used to adjust the polarization state of the
laser beam. S is the sample that is housed in a cryostat and PD is the pyroelectric
photodetector. L2 and L3 are F/4 collection optics to couple the sample
fluorescence to the detector after passing through an appropriate filter (F). The
detector used depended on the molecule being studied as indicated in the text. The

( ------ ) box represents the sample chamber. .............................................................. 43

Figure 11.2. The dependence of idler and signal wavelengths on the BBQ crystal angle.
When the pump beam is normal to the crystal, the angle is 0°. The line is drawn at
710 nm which represents the degeneracy point, where the signal and idler
wavelengths are the same. ......................................................................................... 45

Figure 11.3. The variation of bandwidth with idler wavelength. Only the range from 800
— 2300 nm is shown. The bandwidth continues to rise to the blue, maximizing at

~1000 cm‘1 at 710 nm. .............................................................................................. 47

Figure 11.4. Comparison of the TPE spectrum taken with a (—)constant bandwidth
(~0.3cm'l) source and the ("0) Type I XPO. ............................................................ 48

Figure 11.5. The polarization state of the laser beam is experimentally determined as
shown here. Determination of circularly polarized light is shown in a.). The
horizontally polarized laser beam (H) passes through the Glan-laser polarizer (GL)
and its polarization is rotated by 90° to be vertically polarized (V) by the double
Fresnel rhomb (DFR). The vertically polarized light is converted to be circularly
polarized (C) by the single Fresnel rhomb (SFR). The laser beam is reflected by a
mirror (M), where the handedness of the circular polarization is changed (C’). The
polarization is ultimately changed to vertical after passing through the SF R and DFR
a second time. The vertically polarized light does not pass through the GL.
Vertically polarized light is determined by b.). The mirror is replaced by a Glan-
Thompson polarizer (GT) arranged to block vertically polarized light and the DF R is
rotated until no laser light is seen to pass through the GT. ....................................... 50

Figure 111.1. The effect of the twist angle (x) and overlap (S) on the electronic states of
the 5-manifold. .......................................................................................................... 56

Figure 111.2. a.) The energy of the 155* (hollow) and 355* (filled) states for

n
M02Cl4(P P)2 compounds. b.) The energy difference between the 155* and 355'”

states (solid) is essentially constant at 10500 cm". This corresponds to 2K, where K
is the two-electron exchange energy. The extinction coefficient (hollow) for the 1(5
-—) 5*) transition is also shown. The data was taken from Reference 26. ................ 60

xii

Figure 111.3. Absorption (—) and low temperature emission (0") spectra of
M02Cl4(S,S-dppb)2 in 3-methylpentane. The band in the absorption spectrum at 734

nm has been assigned as the 1(5 —> 5*) transition and the emission (925 nm) is
assigned as l(5*—-> 5). The emission spectrum was not corrected for the instrument
response. .................................................................................................................... 62

Figure 111.4. The absorption spectrum of 3-methylpentane (m) and two-photon
fluorescence excitation spectrum of M02C14(S,S-dppb)2 (——). The bands in the

solvent absorption spectrum at 1180 nm and 1380 — 1500 nm are manifested in the
two-photon excitation spectrum. ............................................................................... 63

Figure 111.5. The absorption (m) and two-photon fluorescence excitation (—) spectra of
MozCl4(S,S-dppb)2. When the artifacts due to solvent absorption are ignored, the

two-photon fluorescence excitation spectrum displays a maximum at 625 nm. ....... 65

Figure 111.6. a.) The polarization ratio (9) is plotted versus the wavelength and has a
value less than 1 across the entire band. b.) The power dependence, which is a plot
of the observed fluorescence intensity (lfl) versus relative laser intensity (power) has

a slope of 2.02. The line represents the best fit following a linear least squares
analysis. ..................................................................................................................... 66

Figure 111.7. Absorption (—) and low temperature emission (---) spectra of
M02C14(depe)2. The spectra were collected in 3-methylpentane solution. The

emission spectrum was collected at 77K. .................................................................. 68

Figure 111.8. The absorption spectrum of 1:1 CHzClz/toluene ("0) and two-photon
fluorescence excitation spectrum (—) of M02Cl4(depe)2 in this solvent. As with
M02C14(S,S-dppb)2, the most prominent bands can be attributed to artifacts due to

strong solvent absorption. If the artifacts are ignored, a band may be observed at
~1495 nm. .................................................................................................................. 69

Figure 111.9. The absorption spectrum (—) and the low temperature (120K) laser
induced fluorescence spectrum (m) of M02C14(dppe)2 in 3-methylpentane. ........... 71

Figure 111.10. Two-photon fluorescence excitation spectrum of M02C14(dppe)2 in 1:1
CHZCIZ/toluene at 120 K. The only bands seen can be attributed to artifacts due to

solvent absorption ...................................................................................................... 72

Figure 111.11. The absorption spectrum of M02C14(dmpm)2 in 3-methylpentane. ......... 73

xiii

Figure 111.12. The time dependent fluorescence of M02Cl4(dmpm)2 in 3-methylpentane
at 120 K when excited at 600 nm (top) and 950 nm (bottom). The one-photon
induced fluorescence has a lifetime of 83 ns. The two-photon induced fluorescence
was difficult to fit due to the low fluorescence but yielded a biexponential decay
values of ~10 ns and ~80 ns. The short component may be due to scattered laser
light. The fluorescence was detected at 675 nm. The one-photon induced
fluorescence signal represents the average of 50 laser shots, while the two-photon
induced fluorescence signal was collected with 5000 laser shots. Also, the slits on
the monochromator were much wider (8 mm) for the two-photon induced
fluorescence than for the one-photon induced fluorescence the slits were 0.1 mm. . 75

Figure 1V.1. The absorption spectrum of MozCl4(PMe3)4 in 3-methylpentane at room
temperature. The numbering scheme for the bands was developed in the literature.
As many as eleven bands can be seen in the spectra of M2X4L4 compounds,
depending on the sample conditions. ........................................................................ 79

Figure IV.2. The effect of halogen atom substitution on the metal-based orbitals of
M2X4(PH3)4 compounds. The left side of the figure is before the effect is “turned
on” and the metal-based orbitals are independent of the halogen. The right side of

the figure shows how the metal-based orbitals are affected by the halogen p orbitals.
................................................................................................................................... 83

Figure IV.3. Absorption spectra (in 3-methylpentane) of the M02X4(PMe3)4 series;
X = Cl (—), X = Br (- - -), X = I (m). As the halide becomes less electronegative,
the 1(5 -> 5*) transition red-shifts due to halide p electrons encroaching into the
metal-metal bonding orbitals. .................................................................................... 84

Figure 1V.4. The absorption spectrum (m) of M02C14(PMe3)4 in 3-methylpentane,

where the 1(1: —> 5*) transition has been expanded by a factor of 15 to show that it is
not coincident with the 1(52 -) 5*2) (—) transition. The emission spectrum (- - -) is
generated when the compound is excited with either one or two photons. The two-
photon excitation spectrum was generated by exciting in the near-infrared (/////).... 85

Figure 1V.5. Measurements from the two-photon fluorescence excitation spectrum of
M02C14(PMe3)4 in 3-methylpentane. a.) The power dependence when excited with
860 nm vertically polarized light. The line represents a best fit to a slope of 2.00.
b.) The polarization ratio is less than one across the 1(52 -—> 5*2) transition ............ 87

Figure IV.6. The absorption (- - -) and two-photon fluorescence excitation (—) spectra
of M02Br4(PMe3)4 in 3-methylpentane at room temperature. The 1(5 —> 5*)
transition has a maximum at 598 nm and the 1(52 -—) 5”) transition has a maximum
at 470 nm. The region in the near-infrared (/////) corresponds to the excitation
wavelength of the two-photon spectrum. .................................................................. 89

xiv

Figure 1V.7. Measurements from the two-photon fluorescence excitation spectrum of
MozBr4(PMe3)4 in 3-methylpentane. a.) The power dependence when excited with
950 nm vertically polarized light. The line represents a best fit to a slope of 1.93.
b.) The polarization ratio is less than one across the I(52 —-> 5”) transition. The rise
on the blue edge can be attributed to one-photon excitation of the red edge of the 1(5
-> 5*) transition ......................................................................................................... 90

Figure IV.8. The absorption (- - -) and two-photon fluorescence excitation (—) spectra
of M0214(PMe3)4 in 3-methylpentane at room temperature. The 1(5 —) 5*) transition
has a maximum at 636 nm and the 1(52 -) 5“) transition has a maximum at 505 nm.

The region in the near-infrared (/////) corresponds to the excitation wavelength for
the two-photon spectrum. .......................................................................................... 91

Figure 1V.9. Measurements from the two-photon excitation spectra of M0214(PMe3)4 in
3-methylpentane. a.) The power dependence when excited with 990 nm vertically
polarized light. The line represents a best fit to a slope of 1.92. b.) The polarization
ratio is less than one across the 1(52 -> 5”) transition. The rise on the blue edge can
be attributed to one-photon excitation of the red edge of the 1(5 -> 5*) transition... 92

Figure 1V.10. The absorption (- - -) and two-photon fluorescence excitation (—) spectra
of M02C14(PEt3)4 in 3-methylpentane at room temperature. The 1(5 —) 5*) transition
has a maximum at 591 nm and the 1(52 —> 5*2) transition has a maximtun at 474 nm.

The region in the near-infrared (/////) corresponds to the excitation wavelength for
the two-photon spectrum. .......................................................................................... 94

Figure 1V.11. Measurements from the two-photon excitation spectra of MozCl4(PEt3)4
in 3-methylpentane. a.) The power dependence when excited with 950 nm
vertically polarized light. The line represents a best fit to a slope of 1.99. b.) The
polarization ratio is less than one across the 1(52 —> 5*2) transition. The rise on the
blue edge can be attributed to one-photon excitation of the red edge of the 1(5 -) 5*)
transition. The rise on the red edge is likely due to noise. ....................................... 95

Figure 1V.12. The absorption (- - -), fluorescence (H), and two-photon fluorescence
excitation (——)spectra of M02C14(AsMe3)4 in 3-methylpentane. The 1(5 -> 5*)
transition has a maximum at 573 nm, the 1(5* -—> 5) has a maximum emission at 638
nm and the 1(52 —) 5”) has a maximum at 455 nm. The region in the near infrared
(/////) corresponds to the two-photon excitation wavelength. .................................... 96

XV

Figure 1V.13. Measurements from the two-photon excitation spectra of
M02C14(AsMe3)4 in 3-methylpentane. a.) The power dependence when excited at
910 nm with vertically polarized light. The line represents a best fit to a slope of
2.09. b.) The polarization ratio is less than one across the 1(52 —) 5*2)
band.polarization ratio is less than 1 across the observed band, again indicating that
the initial and final states have the same symmetry. ................................................. 97

Figure 1V.14. The absorption (- - -) and two-photon fluorescence excitation (—) spectra
of W2Cl4(PMe3)4 in 3-methylpentane. The 1(5 -—> 5*) transition has a maximum at
660 nm and the 1(52 -—> 5*2) transition maximizes at 520 nm. The hashed (/////) box
in the near infrared corresponds to the two-photon excitation wavelength region. .. 99

Figure 1V.15. Measurements from the two-photon excitation spectra of W2CI4(PMe3)4
in 3-methylpentane. a.) The power dependence of the fluorescence when excited at
1050 nm. The line represents a best fit with a slope of 1.93. b.) The polarization
ratio is less than across the 1(52 —> 5”) transition. The rise on the blue edge can be
attributed to excitation of the 1(5 —> 5*) transition. ................................................ 100

Figure 1V.16. The absorption (- - -) and two-photon fluorescence excitation (—-) spectra
of MoWCl4(PMe3)4 in 3-methylpentane. The 1(5 -> 5*) transition has a maximum

at 635 nm and the 1(52 —> 5*2) transition maximizes at 481 nm. The hashed (/////)

box in the near infrared corresponds to the two-photon excitation wavelength region.
................................................................................................................................. 101

Figure 1V.17. Measurements from the two-photon excitation spectra of
MoWCl4(PMe3)4 in 3-methylpentane. a.) The polarization ratio is less than across
the 1(52 —) 5*2) transition. The rise on the blue edge can be attributed to excitation
of the 1(5 —) 5*) transition, while the rise on the red edge is due to noise. b.) The

power dependence of the fluorescence when excited at 950 nm. The line represents
a best fit with a slope of 1.82 ................................................................................... 102

Figure IV .18. The absorption spectrum of cis-M02C12(mhp)2(PMe2Ph)2 in benzene at
room temperature. The spectrum is rather featureless and most of the bands do not
result in population of the emissive 155* state. ....................................................... 104

Figure 1V.19. The absorption (- - -), fluorescence (---) and two-photon fluorescence
excitation (——) spectra of cis-M02C12(mhp)2(PMe2Ph)2 in benzene. The 1(5 —) 5*)
transition has a maximum at 555 nm, the 1(5* —) 5) has a maximum at 615 nm and
the two-photon spectrum exhibits two maxirna, one at 390 nm and the other at 424
nm. The vertical black line is at 410 nm at represents the valley between the two
bands. The hashed box (/////) represents the two-photon excitation region ............ 105

xvi

Figure IV.20. Measurements from the two-photon excitation spectra of cis-
M02C12(mhp)2(PMe2Ph)2 in benzene. a.) The polarization ratio has a value of 1
from 360 - 410 nm and falls to be less than one from 410-460 nm. The vertical line
is at 410 nm where Q changes. b.) The power dependence of the fluorescence when
excited at 860 nm. The line represents a best fit with a slope of 2.02 .................... 106

Figure A1.1. Two extremes of orbital overlap in bond formation The nuclei are
represented by black dots. a.) The orbitals are overlapped very well and the CNDO
approximation is not valid. b.) The orbitals are not overlapped very well and the
CNDO approximation is valid ................................................................................. 120

xvii

Chapter 1

Introduction

At the heart of many natural processes is the ability to store multiple electrons in
one place; thereby providing a route to multielectron chemistry. A general scheme for
photoinitiated multielectron chemistry in naturally occurring systems is outlined in Figure
1.1. In this scheme, light is absorbed at the photon receptor and results in a series of
electron transfer reactions until the requisite number of electrons are stored at the
multielectron site. While this sounds like a fairly simple and straightforward process, it is
unique to natural systems.

The complexity of photoinduced multielectron chemistry in natural systems is
typified by the photosynthetic production of sugar and oxygen from carbon dioxide and
water. Photosynthesis in green plants occurs in the thylakoid membrane of chloroplasts
and is comprised of two reaction centers, Photosystems I and 11 (PSI and P811).1 The
reduction of NADP+ and ultimate production of six-carbon sugars occurs in PSI. The
multielectron oxidation of water occurs in PSII. While PSI and P811 are working

concomitantly, it is easiest to describe the process (shown in Figure 1.2) by starting with

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the absorption of a photon by chlorophyll P630 (680 refers to the km“ in the excitation
spectrum of this chlorophyll) or one of its antenna pigments in PSII. This 1m“ excitation
produces P680“ which is both a strong reductant and oxidant. P68O* reduces pheophytin
by rapidly transferring an electron to yield the P680“ — pheophytin‘ species. The
pheophytin’ reduces plastoquinone Q A by an electron transfer and ultimately the electron
is transferred to plastoquinone QB. Once two electrons have reduced QB, it gathers two
protons and leaves the binding site as QBHZ. When QBHZ leaves the binding site, it is
replaced by another plastoquinone from the quinone pool. The cytochrome b6/f complex
ultimately oxidizes QBHz leading to transmembrane proton transfer. Through the
cytochrome b6/f complex, the electron is transferred to the blue copper protein
plastocyanin and into PSI where it reduces the P700+ that was produced earlier by the
absorption of a photon and electron transfer to an electron accepting chlorophyll (A0).
The electron then moves through a series of acceptors, iron sulfur proteins, ferrodoxin
and ferrodoxin NADP+ reductase to reduce NADP" to NADPH. The cycle is completed
by the reduction of P680+ by the Yz tyrosine residue that is itself reduced by the Mn,
oxygen evolving complex (OEC). The OEC goes through five oxidation states So —> S4.
Once in the S4 oxidation state, water is oxidized to release 02 and produce the proton
necessary for the reduction of NADP+ to NADPH.

The current understanding of photosynthesis, summarized above in a paragraph, is
the culmination of centuries of work. While for much of that time the scientific
community did not possess the tools needed to study the kinetics, thermodynamics or
structure-functions relationships that are available today; they did have the insight to
perform simple yet brilliant experiments. Perhaps the earliest documented scientific
study of photosynthesis was reported by Joseph Priestley.2 His experiment was simple -
a piece of mint was placed in a sealed jar. After several days, the environment within the
jar was able to support both flame and life and he concluded that oxygen must be the

product of light driven reaction that occurred in the plant.

I.A Zwitterionic Excited States

To circumvent some of the complexities associated with studying natural systems,
a different approach can be taken — use a system with no intermediates (Figure 1.3).
While this is a conceptually simple idea and has the merit of being relatively easy to
study, the difficulty arises when trying to find such a system.

The greatest challenge in finding a new system and thus a new route to
photoinduced multielectron chemistry is finding a system with the proper characteristics.
The most significant characteristic is accessibility of a photoinduced excited state that
possesses more than one electron that is available to do chemistry. This property is
revealed in the quantum mechanical description of the hydrogen molecule (see Appendix
I for a detailed derivation).3"l’5 Figure I.4(top) shows the molecular orbital diagram for
B; that results from the overlap of two atomic ls orbitals. The a bonding orbital is
formed by the constructive overlap of the two atomic ls orbitals, while the 6* orbital is
formed by the destructive overlap. Since the molecule possesses only one electron, the
orbital energies are the same as the state energies and in the context of this dissertation,
the energetic separation of the 0' and 0* molecular orbitals will be defined as AW, the
“one electron” energy.

When a second electron is added to the molecule it can be placed in either the 0’
or 6* orbital. Because of this, there are four nondegenerate states that must be
considered (Figure I.4(bottom)). The lowest energy state, 02, results when both electrons
are placed in the lowest energy (0) molecular orbital. The highest energy state, 0"”, is
produced when both electrons are placed in the highest energy molecular orbital. To a
simple approximation, the energy separating the 0'2 and 6*2 states is 2AW. It is also
possible to have one electron in each of the 0' and 0* orbitals. With this configuration,

the spin of the electrons must be considered. Obeying Hund’s Rule, the lowest energy of

.020 00800—0208 08 00 08000 0.0008000 00800—0208 000 0000000..
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n 0

 

00000001

 

 

 

 

2 2
— AW+K

 

 

2 electron mix

Figure 1.4. (top) The molecular orbital diagram for Hf that results when one electron is
placed in the molecular orbitals formed by the overlap of hydrogens’ atomic ls orbitals.
AW is the one-electron energy. (bottom) The four electronic states that arise when two
electrons are placed in the molecular orbitals of hydrogen. On the lefi side of the
diagram, the Is orbital of the hydrogen atom represents 0 on the energy scale. AW is the
one electron energy, and K is the two-electron exchange energy. Since 0'2 and 6*2 are
the same symmetry they mix together and gain some two-electron character. The energy

separating the state then becomes le AW2 + K2

these two 60* states is the 306* state, and the highest energy is 160*. The energy
separating these two states is 2K, where K is the two electron exchange energy. It is
simply the energy required to move an electron from one side of the molecule to the other
and in the limit of infinite separation corresponds to the electron affinity and ionization
potential of atomic hydrogen. Since 02 and 6*2 both have the same symmetry, the two
states mix together, giving rise to off-diagonal elements in the Hamiltonian matrix.‘5 This
results in a certain amount of two electron character being present, and leads to the states
being repelled from one another. Their separation becomes 2" AW2 + K2 as shown in
Figure I.4b.

From these definitions and the more complete potential energy diagram for the
hydrogen molecule (Figure 1.5) some interesting observations and conclusions can be
made. The hydrogen molecule is at its equilibrium geometry at the potential energy
minimum of the 0’2 ground state potential energy curve. The two ls orbitals overlap and
the strongly coupled electrons form the 0' bond. As the molecule is pulled apart,
however, the situation changes quite dramatically. Ultimately, the 0 bond is ruptured
leaving two hydrogen atoms (or radicals). Therefore, as the bond is stretched the
wavefunction describing the electrons begins to acquire a great deal of diradical
character. The Pauli Principle dictates that electrons with the same quantum numbers
cannot occupy the same orbital. Thus, a molecule on the 30'0" potential curve must also
dissociate to a diradical.

Consider the molecule on the 0'2 potential energy curve at a point where the bond
has not fully ruptured, but is far removed from the equilibrium geometry. If a molecule
at this point of the potential energy curve absorbs energy and is promoted to either 160'"
or ‘0”, the electron must be transferred from one side of the “molecule” to the other in
order to maintain its singlet spin configuration. Therefore, these two highest energy

states are described as being zwitterionic.

  

Energy

 
 

 

 

 

AW>>K AW=0

Figure 1.5. The potential energy diagram for the hydrogen molecule, showing the
behavior of the states as the bond is stretched. In the strongly coupled limit AW (which is
much greater than K) dominates the energy of the electronic states. In the weakly
coupled limit, AW ~ 0 and K determines the energy of the states.

The disposition of the potential energy curves can also provide some insight about
the relative characteristics of each of the electronic states. In the region where the
electrons are strongly coupled there is a relatively large energy gap separating 0'2 and
360*. This is followed by a small energetic separation of the 0'0"" states and then another
large gap separating 100"" and 0"”. This ordering of states is common. It stems from the
fact that AW is the dominant term in the energies of these states and that the two electron
terms, which arise largely from the effect of correlated electron motion, are relatively
small.

When the electrons are weakly coupled there is very little overlap of the parent
atomic orbitals and the situation is markedly different. The gap separating 0'2 and 366* is
small because the only energy required is to flip the spin of an electron that is at best
weakly coupled to the other electron (when the bond is fully ruptured, neither electron is
influenced by the other electron). The gap between the 06" states is relatively large
because moving from 366* to 166* requires placing two electrons into a volume that is
essentially the size of a Is atomic orbital. The gap between the 166* and 16"2 states
again is small because these states are simply the symmetric and antisymmetric linear
combinations of having two electrons on one half of the molecule. Of course, the gaps
separating the diradical and zwitterionic pairs of states coalesce to degeneracy when the
parent atomic orbitals are completely decoupled. At this point, these “molecular” states
correspond to the electron transfer reaction 2H -) H” + H’. Thus, the relative energetic
displacement of the states provides a great deal of qualitative information about the
character of the states.

Perhaps the most interesting aspect about the preceding description of the
hydrogen molecule is that while the overall description was postulated in the earliest days
of molecular quantum mechanics, and it has ofien been invoked in describing reaction
pathways, it has never been experimentally confirmed. Other than the work being

reported here, there have been some recent studies on derivatives of ethylene that have

10

provided experimental evidence for the character of the states of a two-center, two-
electron bond. 7'8

As ethylene is twisted about its sigma bond (Figure 1.6) a scenario quite
analogous to stretching molecular hydrogen develops. At the ethylene equilibrium
geometry the electrons that form the 1t bond are very highly coupled and the bond is
strong. However, as one half of the molecule is twisted with respect to the other, the
bond weakens until it is ultimately annihilated at a twist angle of 90 degrees. Along this
journey, the electrons became less and less coupled. Mulliken originally indicated that as
twisting occurs, the manifold of four states ultimately is reduced to two states when the
bond is broken, a diradical ground state and a zwitterionic excited state.9 Ohno, in a
more recent treatment, confirmed the ideas postulated by Mulliken and applied them to
more complicated 1: systems.10 As the twist is carried to 180 degrees, the bond is
reformed and the typical four-state manifold is reestablished. This evolution of states has
been invoked from both theoretical11 and experimental12 points of view to explain
product distributions and solvent dependencies of organic photoreactions involving cis-
trans isomerizations and photocyclizations. However, the diradical and zwitterionic
states eluded detection and were named the “phantom states”.l3 Recently, however,
some spectroscopic studies have revealed the true nature and disposition of these
states."*8

The most complete picture of these states is found in quadruply bonded metal
dimers (M-i— M). These dimers possess four bonds and the shortest metal-metal
distance in inorganic chemistry. In the cases of hydrogen and ethylene the two electrons
that form 0' and 1t bonds respectively are strongly coupled to one another due to the good
overlap of the parent 0 and 1: atomic orbitals. Because of this, the diradical and
zwitterionic character of the states only manifests itself as the electrons become weakly

coupled when the bond breaks. As shown in the molecular orbital diagram (Figure 1.7)

11

 

 

 

 

 

Figure 1.6. The electronics states of ethylene as it is twisted about the C—C internuclear
axis.

12

 

 

 

Figure 1.7. Molecular orbital diagram (D4,1 symmetry) showing the metal-metal bonding
in quadruply bonded dimers when two ML4 (D4h) fragments are brought together.

13

for (M-i- M) complexes, the six electrons that pair-wise form the o and 2 1: bonds are
strongly coupled due to the good overlap of the parent dzz, and (dwdyz) atomic orbitals
respectively. Because of the good overlap, these bonds are expected to display the
diradical and zwitterionic states only as the metals are pulled apart. The fourth bond, the
5 bond, is different however. Since the 6 bond is formed by the poor face-to-face overlap
of two dxy atomic orbitals, the electrons that reside in it are weakly coupled. Thus, the 5
bond can be thought of as lying in the nether world between a strong covalent bond and
two free metal fragments. The 8-bond has been cast into the theoretical form of hydrogen
and ethylene.14 The electronic states of the 8—manifold are shown Figure 1.8. It can be
seen from this diagram that, even in the equilibrium geometry, the energetic disposition
of states is consistent with weakly coupled electrons. The energy gap that separates the
low energy diradical states is small; there is a large gap between the 88* states and then a
small gap between the zwitterionic states. A significant feature of the fi-manifold is the
symmetry displayed. The energy gap between the diradical states is equal to the energy
gap between the zwitterionic states. Because of the weak coupling of the electrons that
form the S-bond, quadruply bonded metal dimers provide a unique opportunity to study a
weak two-center, two-electron bond.

One particularly interesting feature of (ML M) complexes is that as one half of
the molecule is rotated with respect to the other, only the 5 bond is broken. The 0' bond,
due to its cylindrical symmetry about the internuclear axis is unaffected by rotation. The
lobes of the orthogonal 1t orbitals are rotated into each other as the molecule is twisted
and there is no net change in the energy of these bonds since as they are being broken
they are also being reformed. Proper choice of the ligand set then allows for series of
molecules to be made with varied coupling of the parent (dxy) atomic orbitals. 1n affect,

this provides a means to “break” the B-bond in a step-wise fashion.15

14

 

1A1g 1(8*2) gg + g—g
20 ‘-

 

Energy / 10000 cm'1

 

5 _ 3A2u 3(85*)

 

 

1A19 1(52)

Figure 1.8. The 8—manifold of electronic states that results when two electrons are placed
in the 5 orbitals.

15

1.A.1. History of the Delta Bond

When Cotton et al prepared KzRezClg-HZO in 1964, the bond between the Re
centers was predicted to have the electronic configuration of 021:452 that implied one o-,
two 1t- and one 8-bond.16 The crystal structure supported this configuration. The
internuclear separation was small (~2.2A), and implied that there could be some overlap
of the dxy orbitals to form a 6-type bond. Furthermore, the Cl' ligands were eclipsed. If
the molecule was only triply bonded, the cylindrical symmetry of the o and two 1!: bonds
would allow for rotation about the internuclear axis and lead to a staggered disposition of
the ligands to relieve some steric strain. Lastly, the compound was observed to be
diarnagnetic, which indicated that all of the electrons were paired.

Cowman and Gray undertook an exhaustive study of the spectroscopy of this
compound in order to learn more about the electronic structure of quadruply bonded
metal dimers.17 From spectroscopic measurements on single crystals, they were able to
unambiguously assign the lowest energy transition observed in the UV/vis spectrum as
188* <— 52 (1(5 —) 5*)). The transition was observed to be polarized preferentially along
the internuclear (z) axis and progressed with an excited state frequency of 248 cm“. This
was consistent with a ground state metal-metal stretching frequency of 274 cm‘1 reported
in an earlier Raman study. 18 The spectroscopy of this compound also served to reveal the
weakness of the 8 bond.19 Although the 1(5 -—) 5*) transition is dipole and spin allowed,
it is very weak (amax = 1530 M"cm“). The analogous l(11: —-) 1r*) transition in an organic
compound could have an extinction that could be several orders of magnitude higher.
Mulliken showed that the intensity of electronic transitions is very dependent on the
coupling of the parent atomic orbitals. The oscillator strength (which is intimately related

to the extinction coefficient) can be related to the orbital overlap:20

f= 1.096x1011V82r2 (1.1)

16

where V is the transition energy in cm“, r is the internuclear separation in cm, and S is
the overlap of the parent atomic orbitals. Using the observed oscillator strength of the
1(5 -> 5*) transition (f = 0.02321), the overlap was determined to be 0.08.

Not surprisingly, the 5 bond was also of great interest to theoretical chemists. The
computational techniques of the time had proven useful for o and 1: bonds, and the 5
bond represented a new challenge. However, the 5 bond defied the techniques.
Calculations carried out by Benard on RezClgz' predicted a staggered geometry.22 Also,
the calculations indicated that the ground state would be a paramagnetic triplet instead of
the observed diamagnetic singlet. Computational techniques advanced as computers
became more powerful. This allowed for expanded basis sets to be used and thus made it
possible to account for higher order effects such as electron correlation and relativity. In
1982, Hay, took advantage of the computational power of Cray computers to perform
calculations on RezClsz' at a level that provided qualitative agreement with experimental

observations.23

1.A.2. Electronic States of the 5-Manifold

The electronic state diagram for the 5-manifold is shown in Figure 1.8. The
ground state was essentially discovered with the synthesis of RezClgz‘. Since the
molecule is diamagnetic the ground state is a singlet. The next highest energy state is
355*. By twisting the molecule about the internuclear axis, the 5-bond can be weakened
to a point that the triplet state is thermally accessible (Figure 1.9).24 Gray and coworkers
took advantage of this property and performed SQUID measurements on a rotamer of
MozCl4(PMe3)4.25 Later, Cotton and coworkers undertook a more complete study that
utilized temperature the dependence of the 31P{1H} NMR spectra.26 Their study fully
revealed the character and energetic disposition of the 355* state. As mentioned earlier,

the 155* state was first investigated by Cowman and Gray.17 The remaining state, 15“,

l7

 

 

 

 

\
155* ‘

E

,3, 2(AVV2 + K2)"2 2K

 

 

I 1 I 1 l n J
0 1 5 30 45

5-bond twist angle (20

Figure 1.9. The dependence of the electronic states of the 5-manifold on internuclear
twist angle (1). The 5-bond is broken at x = 45°. There is a mirror image of the manifold
from 45° — 90° that is not shown here.

18

is the purview of this dissertation. Elucidation of this state and its properties will allow
the first complete characterization of a two-center, two-electron bond.

Further inspection of the 5-manifold, however, reveals some challenges in finding
the 15'"2 state. First, the symmetry of the state is Alg’ the same as the ground state.
Conventional spectroscopic selection rules dictate that g <——> g transitions are forbidden.
A second and perhaps more substantial difficulty arises due to the fact that the transition
corresponds to moving two electrons from the 5 bonding orbital to the 5* antibonding
orbital. Two electron transitions are highly forbidden in conventional spectroscopy.
Therefore, in order to access the 15’“2 state then, it will be necessary to use an

unconventional spectroscopic technique.

1.B. Nonlinear Spectroscopy

Nonlinear spectroscopy will be discussed by two approaches. The first will be
largely phenomenological and consider the interaction of light and matter. The second

will involve a more mathematical description of both linear and nonlinear spectroscopy.

I.B.l Phenomenological Aspects of Spectroscopy”

A good place to begin this treatment of spectroscopy is to first consider the
interplay between light and matter. If plane-polarized blue light is incident on a clear
glass window, blue plane-polarized light is seen on the other side—apparently nothing
has happened. However, if the window itself is considered, a great deal has happened.

The window is essentially a huge collection of nuclei and electrons where the
Coulomb force holds the electrons to the nuclei. Together, the nuclei and electrons can
be thought of as a collection of dipoles. The light is an oscillating electric and magnetic
field that are orthogonal to one another. When the dipoles and electric field (the
magnetic field is going to be ignored) are combined there is a substantial interaction. The

electric field of the light causes the positively charged nuclei to move with the electric

19

field (though this motion is small due to the mass of the nuclei) and it causes the
electrons to move against the electric field. Therefore, as the light passes through the
window, it causes the dipoles to oscillate along with it. The light leaving the window
therefore is significantly different than the light that was incident.

Once a dipole starts to oscillate the light that emanates from it can go in any
direction. The electric field generated from a single dipole is shaped like a torus that
expands at the speed of light (Figure 1.10). No light, however, is seen to exit the sides of
the window. This can be explained by Figure 1.11, which shows a collection of three
dipoles (looking along the dipole’s axes). Dipole 1 (red) is the first to start oscillating,
then 2 (green), and finally 3 (blue). Dipole 1’s electric field will have the largest
diameter by the time dipole 3 starts to oscillate. By superimposing all of the electric
fields from each of the dipoles, it becomes apparent that the only constructive
interference occurs in the forward (relative to the incident light) direction. When the
electric fields constructively interfere, a new wavefront is produced known as the
secondary wave. Since the dipoles are oscillating in phase with the primary wave
(incident light), their velocity is also in phase. However, since radiation is only generated
when an electron is accelerating (at the turning point of its oscillation) the secondary
wavefront is 90 degrees out of phase relative to the primary wavefront. When the
secondary and primary waves are superimposed, they yield the refracted wave. This is
represented in Figure 1.12. The cumulative phase lag (90 degrees due to the secondary
wave, plus an amount linked to the intensities of primary and secondary waves) present
in the refracted wave can be translated directly into a reduced velocity of the wavefront
and this is observed as the refractive index of the material. If the clear window is
replaced with an orange colored window, the blue light will not pass through. From the
perspective of refractive index, absorption is the most extreme example of cumulative

phase lag in the refiacted wave; the light gets slowed down to a point where it no longer

20

0r" ‘ifi- “s
I‘.“" '

.4?“
fits?»

«u I:

 

Figure 1.10. The toroidal shaped. electric field that is generated by an oscillating dipole.

—* E

Figure 1.11. View down the axes of three oscillating dipoles, along with the cross-
section of their emanating electric fields are shown. Constructive interference of the
electric fields only occurs in “forward” direction where the three electric fields overlap.

21

 

 

 

Figure 1.12. The primary wave ("0) is at the frequency of the incident light. The
secondary wave (- - -) that is generated when the oscillating dipoles are accelerating (at
their turning points) is 90° out of phase with the primary wave. The refracted wave (—)
is the superposition of the primary and secondary waves. Its phase relationship is
determined by the 90° phase lag due to the secondary wave, plus a component related to
the intensities of the primary and secondary waves.

22

moves forward at all. Quantum mechanically this corresponds to the orange glass having
an allowed electronic transition that is at the same frequency as the incident blue light.
The preceding description is based largely on the classical physics description of a
forced harmonic oscillator where the Coulomb force, which represents a spring, holds the
electron to the nucleus. Not surprisingly, this harmonic oscillator view is somewhat
flawed — it is assumed that no matter how intense the applied electric field, the electron
will respond in a linear fashion. At some electric field intensity, however, the electron
will be displaced far enough from the nucleus that it overcomes the Coulomb force that
holds (~3x10lo V/m).28 The harmonic oscillator model thus must be replaced with one
that allows for anharmonic behavior. This is accomplished by allowing the dipole to
become overdriven and oscillate at frequency multiples of the incident light. Therefore,
in cases of very intense electric fields, two colors of light can be seen exiting the material
(Figure 1.13). If the material is not transparent to the new color of light, the new light

will be absorbed.

l.B.2. Mathematical Aspects of Spectroscopy
The Beer-Lambert law represents a cornerstone in spectroscopy:29

If=10e’°‘b° (1.2)

it relates the intensity of radiation transmitted by the sample (If) to the intensity incident
upon the sample (10), where b and c are the sample thickness and concentration
respectively and or is the absorption coefficient and is related to the extinction coefficient

by:

e = — (1.3)

23

300000000 w8>t0 08 0055 00 0000 00005000 20000 08 .0002 000000000 w8>t0 08
00 00—00—08 00 000—0000 000 000 003.005 0080000 2000 0.0 .200 0500—0 :30 00> 0 00 0000000 00 2000 0 0003 .m: 0.5!..—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

24

It is 8 (or 0t) that carries the quantum mechanical information about the molecule being
studied through the oscillator strength (f):
l2

l0. (1.4)

 

4 1 10 2
f= meceozn [8(v)dv=8n mezv
NAe 3 he

where pf, is the transition dipole between the initial and final state ( W1 and tyf):
ufi=lwiwi ;u=er (1-5)

The preceding section demonstrated the importance of the refractive index. An
expression can be derived that relates Beer’s law to the refractive index.

The electric field of the radiation (E(z,t)) at a point far behind the sample (z>>b)
is given by:30

E(Z’t)=e{iu)(n—l)b/C}E0e{—im(t-z/c)} (1.6)

where z is the direction of propagation of the field, b is the sample thickness, c is the
speed of light, and 130 is the unperturbed electric field amplitude and (1) is the angular
frequency of the radiation ((1) = 21w). The first term is often referred to as the phase

factor and for n-l < 1 is expanded to give the expression:

E(z,t)=[1+ico(n — 1)b / c+....]aoe{““’(““ °>} (1.7)

Assuming as earlier that the material can be thought of as a collection of dipoles
where the Coulomb force holds the electron to the nucleus. The oscillating electric field
(Eoe'iw‘) causes the dipole to behave as a forced harmonic oscillator. The equation of

motion for the dipole in one dimension (x) is thenz3°~31

m5z+yx+kx=Boe"‘”‘ (1.8)

where m is the mass of the electron, y is the damping constant, and k is the restoring force
(k = mwoz, 000 is the angular frequency of the oscillator). The trajectory of the electron

x(t) is then:

25

 

/ -1(.01
.0. ((1,050? (.9)
030-0) —1010

All of the dipoles following this trajectory, then, reradiate electromagnetic energy
at frequency a) and have a strong resonance (absorption) at a) = (no. The total field —
which is the sum of unaffected electric field plus the field that is phase shifted — at some
distance away from the sample is then:30

bqsz

280cm ((03 —0)2 —i(nry)

 

E z,t =13 e““"“Z/°) 1+ (1.10)
0
where N is the number of dipoles and so is the permitivity of free space. Equating this

expression for the field with the one above (equation 1.7) allows n to be determined:
n=101(0),,;0)(0(2,-—02 +iwy) (1.11)
where A((00;(1)) = Nq2/2£:Om[(o)02-c02)2 + 7209]. This demonstrates that the refractive

index is a complex number where the real and imaginary parts are given by:

Re(n)=1+A(0o;0)(05—02) (1.12a)
Im<n>=1mA(a>0;w> (1.121.)

When this index of refraction is substituted into the phase shift term (equation 1.7) and
the resultant electric field is squared, the intensity at a point after the sample is given
by:32

1~:(z,t)‘1307,00:0 _

1(2) 2 2

 

If (1.13)

Using the same procedure, 10 can be determined from E0. If and 10 can be combined to
yield a different expression for Beer's law, that is dependent on the imaginary part of the

refractive index:

If =1(z)=10e"2‘°"“(“’b’° (1.14)

26

Therefore, the refractive index serves two roles; the real part imparts a phase shift onto
the incident beam, and the imaginary part serves to attenuate the beam.

A second way to look at refraction and absorption is through the relationship
between the average dipole moment density (P) that is induced in the sample by the

driving electromagnetic field (E):33

P=xE (1.15)

The incident electric field is attenuated and phase shified by x, the susceptibility of the

material. It has been shown that x is related to the refractive index:

n2=1+41rx (1.16)

x has both imaginary and real components just as the refractive index does, where the
real part retards the phase of the incident electric field and the imaginary part attenuates

the electric field. The real and imaginary components of x in terms of the refractive

 

 

index are:30
Re(n)2—1m(n)2—l
Re(x)= (1.17a)
41:
1m(x)=Re(“)Im(”) (1.17b)
21:
This allows Beer's law to be written in terms of the susceptibility:
If ___ 106-411:1m(x)b/cRe(n) (1.18)

To this point, the dipole has been assumed to behave linearly as a harmonic
oscillator responding to a harmonic driving force. However, as the driving force
becomes more intense, the dipole can no longer respond linearly (either the electron is
ejected, or the oscillator becomes overdriven), this results in a nonlinear response as the
dipole becomes anharmonic. The anharrnonicity can be treated by expanding the
susceptibility as a power series:

P=(x“)+x(2)E+x(3)E2+...)z (1.19)

27

These higher order susceptibilities give rise to nonlinear responses to the driving force.
These responses are well known in optics. Second harmonic generation, where two
frequencies are mixed to form a third frequency that is the sum of the original two
frequencies, arises from x0) (Figure 1.14a). Sum frequency generation and self-focusing
are common examples where three frequencies are mixed through x(3) to generate a
fourth frequency (Figure 1.14b). Besides these optical effects, nonlinear responses to
driving forces are also common in spectroscopy. Coherent anti-stokes Raman
spectroscopy (CARS) and two-photon absorption spectroscopy are only two examples of
four wave mixing through )6” in spectroscopy (Figure 1.15).

Two-photon spectroscopy has several characteristics that separate it from
conventional, linear spectroscopy. The first is the difference in selection rules. With
two-photon techniques it is possible to observe states that are forbidden to conventional
spectroscopy.34 The second characteristic is the quadratic dependence of the observed
signal on the incident electric field.34'35 The third characteristic, and perhaps the most
useful, is the dependence of the two-photon transition probability on the polarization of
the incident radiation.36 Taking advantage of this characteristic allows for symmetry

assignment of the excited states, depending on experimental arrangement.

I.B.2.a. Selection Rules

Orbital, vibronic, and spin selection rules govern the allowedness of a
spectroscopic transition. The one most important to distinguish between one- and two-
photon spectroscopy is the orbital or Laporte selection rule. The transition dipole, 115, for
a one-photon process is given by:37

#fi=(\l’r|llj|\l’1);ll=er (1.20)

where wf and W1 are wavefunctions representing the final and initial states respectively,
and 11]- is the dipole moment in the j direction. From group theory, for a transition to have

28

hV1 i A

hvz =hv1 + hv1 hv3 =hv1 + hv1 + hv1

hV1

hV1 ' A

 

 

Figure 1.14. a.) Second harmonic generation is an example where two frequencies (hvl)

are mixed through the second order susceptibility tensor, )6”, to yield a new frequency
(hvz), that is the sum of the incident frequencies. b.) In sum frequency generation, three

frequencies (hvl) are mixed through 1(2) to yield a new frequency (hv3) that is the smn of
the three incident frequencies.

29

 

 

 

 

 

 

 

F
V1 V1
V
A
V1 V2 V1 V5
V1 V1 *
A #

Figure 1.15. Two examples of nonlinear spectroscopy where a total of four frequencies
are mixed through 1(3). a.) Two-photon absorption (TPA), where two photons (v1)

populate the excited state that then relaxes to the ground state by two-photon emission.
b.) Coherent anti-Stokes Raman spectroscopy (CARS) is a more complex process, where
V] places the system in a virtual state that is driven down to a vibrationally excited state

by v2. This excited state interacts with a second photon v1 and ultimately the scattered
photon at frequency V5 is detected.

30

nonzero intensity, the product ‘l’rtlei must be an even function (must include the totally
symmetric irreducible representation). Since 111 is an odd function that transforms as x, y,
or z, the product of 11mm must also be an odd function. This results in g <—> u transitions
being allowed and g <—> g or u (—> u transitions being forbidden.

In two-photon spectroscopy, on the other hand, the allowedness of the transition is

given by the two-photon transition tensor ,Sz35a

0.x...

where Va is an intermediate state, and uj and 11, indicate that the dipole moments involved

(1)

s «- (11.11, ufz’lw.) (1.21)

 

 

in the transition are not necessarily the same. The effective two-photon operator is then
11qu. The product of the two dipole moment operators transforms as x2, yz, 22, xy, xz, or
yz, all of which are even filnctions. Therefore, g (-) g and u <—-> u transitions are allowed

in two-photon spectroscopy and g <—> u transitions are forbidden.

I. B. 2. b. Power Dependence

In one-photon spectroscopy, there is a linear relationship between If and 10 as
stated by Beer’s law. In two-photon spectroscopy, however, there is a nonlinear
dependence on 10. The probability for a two-photon transition can be determined from
time-dependent perturbation theory.353 When both photons involved in the transition are

from the same laser ((1)1 = 002 = (1),), the transition probability, w(2), is given by:

 

2
“1(2)ng Z<Wf|p|Wn>(Wnlplw1>l

(1.22)
n ABM—ha), I

where 10 is the intensity of the incident laser beam, wn is the virtual intermediate state and
W1 and “If are the initial and final states respectively. ARM is the energy of the virtual state
and (1)r is the frequency of the incident radiation. This shows that the transition
probability is proportional to the square of the intensity of the incident laser beam. In

general, for any n-photon transition, the probability is proportional to 1“. The quadratic

31

dependence is a powerful tool to determine if an observed transition results from a two-
photon absorption. Taking the logarithm of each side results in the more familiar
expression:

logW(2)=210g1+logC (1.23)

where the terms have the same meaning as before and C represents the terms in the

summation above (Equation 1.22) along with experimental variables.

[3. 2. c. Polarization Dependence

1n one-photon spectroscopy the symmetry of an excited state can only be
determined by using a rigidly oriented sample or working on a time-scale that is
sufficiently fast to “freeze” molecular motion. In two-photon spectroscopy, however, the
symmetry can be determined using a randomly oriented sample.”38 This attribute has
made two-photon spectroscopy a valuable tool to spectroscopists.

In one-photon spectroscopy the absorption cross-section, 0', for randomly oriented
molecules is related to the transition dipole (defined in Equation 1.20):
12

60c l). 11,-, (1.24)

where A is the unit polarization vector of the absorbed photon. Since 7132* = 1 there is no
polarization information contained in the observed transition.
In two-photon spectroscopy, however, the cross-section, (5) (more correctly, the

absorptivity), is given by:36

(5) =|x - sg" ~1c '2 (1.25)

where x and 2. are the polarization vectors of the two absorbed photons and 5:," , the two-

photon transition tensor is:

5 $1, :2 (w? | 141113 Xwfil ply?) + (WI HM X‘Viil 11W?) (1.26)
n (uni—(9K will —0.);‘

 

 

32

where (0111 is the energy of the intermediate state and (1)}- (j = K or 2.) is the energy of the
photon absorbed. The cross-section is most ofien written in terms of molecular

parameters and polarization (experimental) parameters:

(5)=5FF+SGG+5HH (1.27)

where, F, G, and H are functions of the polarization of the absorbed photons:

 

 

 

2 t 2
F=4|1-x|—1—|i-x (1.28a)
2 It 2
G=—|1-K|+4—|1-x (1.28b)
2 .. 2
H=—|x.x| —1+4|;.-x (1.28c)
and 5F, 55 and 5” are functions of molecular parameters:
6,02 2 sgasgb‘ (1.29a)
a b
50 «zzsgasga‘ (1.2%)
a b
afloczzsgasgb‘ (1.29c)
a b

where a and b represent the molecular axes and S? are the two-photon transition tensors
as before. If two photons of the same polarization are used then 56 = 5” (Sba = 88").
Since 5F is then the square of the trace of the tensor (which implies it is totally
symmetric), it is nonzero only if the excited state is of the same symmetry as the ground
state.

The values of F, G, and H have been calculated for the eight possible polarization
cases (using circularly and linearly polarized light) and are shown in Table 1.1. The
tensor patterns have also been determined for most symmetries and the relevant patterns

are shown in Table 1.2 along with their polarization ratio, Q, that is defined as:

0:90) (1.30)

(511.)

33

Table 1.1. Values for the polarization functions F, G, and H, depending on the eight
polarization cases. From References 34 and 36.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Case 1 2 3 4 5 6 7 8
TT T-r D) ()0 T) TO DC) 00

F 2 -1 -1 -1/4 1/2 1/2 -2 3
2 4 4 7/2 3 3 3 3

H 2 -1 -1 -1/4 1/2 1/2 3 -2

 

Polarization Cases:

(1)
(2)
(3)

(4)
(5)
(6)

(7)
(8)

Two linearly polarized photons with parallel polarization.
Two linearly polarized photons with perpendicular polarization.

One linear and one circular with the linear photon polarized such that it is
perpendicular with the plane of the circularly polarized photon.

Both circular with propagation opposite to each other.
Both linear, with 45° between their polarization vectors.

One linear and one circular with the linear photon polarized such that it is
parallel with the plane of the circularly polarized photon.

Two circularly polarized with polarization in the same sense.

Two circularly polarized with polarization in the opposite sense.

34

 

Table 1.2. Two-photon tensor patterns and the polarization ratio expected for each

transition in the DZd point group. From References 34, 36, and 38.

 

 

 

 

 

 

Tensor Pattern Transition Symmetry Polarization Ratio
operator (gs <——> es)’r Q
. 2 2
A1" “5'2 AIHA1;A2(—)A2; r2<1
SI 0 O
0 S] O BIHBI;BZHBZ
O 0 $2
. 2 __
31' x y: AIHBI 9:3/2
S3 0 0
O _ S3 0 A2 <-—) 82
O 0 0
B :
2 xy A1 H B2 S2 = 3/2
0 S4 0
_ S4 0 0 A2 (—) 81
0 0 O
E‘ xz’ ’2 A (—-) E n = 3/2
0 0 SS 1
0 0 — iss and E H E
86 —' iS6 O
0 0 s;
o 0 - is;

t . t
56 456 0

 

 

 

T gs = ground state symmetry; es = excited state symmetry.

35

 

where (501,) and (511:1) are the cross sections for using two circularly and two linearly

polarized photons respectively and are given by:

(5...)= F5F +(G + 11):;G =—25,.+65G (1.31a)
(61m): 135F +(G + 11):;G =+25p+450 (I.31b)

The polarization ratio is bounded by:

osns (1.32)

le

Therefore, by measuring the intensity of the transition when two circularly polarized
photons are used and comparing that to the intensity when two linearly polarized photons
are used, the symmetry of the states involved in the transition can be determined. As
indicated in Table 1.2, when two circularly and two linearly polarized photons are used

Q < 1 only occurs when the symmetry of the initial and final states is the same.

36

Chapter 11

Experimental Methods

There are two general classes of quadruply bonded compounds that have been
studied. The first to be reported have the general formula M2X4L4 (l) (where M2 = M02,
W2 or MoW; X = Cl, Br, or 1; and L = uncharged 0' donor ligand). The second class has
the general formula MozCl4(I§P)2 (2) where PP indicates a bridging diphosphine ligand

that induces a twist about the internuclear axis.

 

 

 

 

 

 

 

 

x 1 P P l b
N o
/
4'- [x :01 ’CI «Mo—7M0
.-" .-'“' Mo— p\\““ '60“? l
\‘ \“ .- ..-
1.\\“‘ )6‘“ c1“. ct“

 

 

 

 

(1) (2) (3)

37

11.A. Materials and Standard Instrumentation

Compounds with the general formula M2X4L4 were prepared by a number of
colleagues using literature methods. Dr. Carolyn Hsu provided ample quantities of
M02C14(PMe3)439 while Dr. Sara Helvoigt provided the Br,40 1,40 W241 and MoW42
derivatives that completed the series. Several unsuccessful attempts were made by Dr.
Ann McIntosh to synthesize the F analogue.43 Dr. McIntosh did, however, make
available the low symmetry (C2) compound cis-M02C12(mhp)2(PMe2Ph)2 (3) (where mhp
= 6-methyl-2-hydroxypyridine) that was very important in the earliest days of two-photon
investigations on quadruply bonded complexes.44

Dr. Sara Helvoigt prepared the twisted compound MozCl4(dmpm)2 (dmpm =
bis(dimethylphosphino)methane).45 The other twisted compounds studied
M02Cl4(depe)2, (depe = bis(diethylphosphino)ethane), M02Cl4(S,S-dppb)2 (S,S-dppb =
(28,3S)-bis(diphenylphosphino)butane), and M02C14(dppe)2 (dppe = bis(diphenyl-
phosphino)ethane) were prepared as outlined below. The twist angle of these compounds

is listed in Table 11.1

Table 11.1. The twist angle (x) for each of the compounds studied. The ligand
abbreviations are given in the text. MozCl4(PMe3)4 corresponds to a 90° twist. Values
taken from Reference 26b.

 

 

 

 

 

 

 

 

 

Compound Twist Angle (x)
MozCl4(dmpm)2 0
MozCl4(S,S-dppb)2 24.7
MozCl4(depe)2 41 .4
MozCl4(dppe)2 59.5
M02C14(PMe3)4 90

 

38

("N
II.A.l. Synthesis of MoZCl4(P P); compounds

All manipulations were carried out under an argon atmosphere provided by a
Schlenk line. The pertinent bridging phosphine ligands were purchased from Strem
Chemical and used as received. The K4M02C18 starting material had been previously
prepared by other group members using the literature method.46 The solvents used in
synthesis were dried by standard techniques and freshly distilled prior to their use. No
attempts were made to quantitate the yields of any of the syntheses. All NMR spectra
were collected with the sample dissolved in CDZCIZ and UV/visible spectra with the

sample dissolved in CHZCIZ.

HA. I .0. Synthesis of M02C14(S, S-dppb) 2" 7

K4M02C18 (85 mg) and S,S-dppb (120 mg) were placed in a 50 ml three-necked
round bottom flask that possessed a magnetic stirring bar. A reflux condenser was placed
on the flask and the two remaining necks were capped, one with a ground glass stopper,
the other with a septum. The apparatus was connected to a Schlenk line and repeatedly
evacuated and filled with dry argon. Freshly distilled methanol (~10 ml) was added by
syringe through the septum which was then replaced with a ground glass stopper. The
apparatus was then heated in an oil bath to reflux and was allowed to reflux for eight
hours. During the course of the reflux, the solution turned from red to yellow-green with
a yellow-green precipitate. The methanol was removed by vacuum and the yellow-green
powder lefi behind was washed several times with methanol. After several rinses, diethyl
ether was used to thoroughly dry the compound. The NMR spectrum of this material
indicated that there was no unreacted phosphine. Due to the sample’s significant triplet
character, the NMR spectrum was too broad to be interpreted. The UV/visible spectrum

had a 1(5 —) 5*) transition consistent with that reported in the literature.47

39

II.A.1.b. Synthesis of Mo 2C1 4(a'epe) 24 8

K4M02C18 (100 mg) was placed in a three-necked round bottom flask that
contained a stirring bar and was equipped with a reflux condenser, septum, and ground
glass stopper. Freshly distilled degassed methanol (~10 ml) was added by syringe
through the septum which was then removed and replaced with an addition funnel. The
addition funnel contained a 0.7 M solution of depe in toluene (1 ml). The depe solution
was added to the reaction mixture and the addition funnel was replaced with a ground
glass stopper. The solution was heated to reflux and changed from a red to red-brown
color. After 6 hours of reflux, the solution was allowed to cool and the red-brown solid
was removed by filtration. The product was washed first with water and then methanol.
An NMR spectrum was taken, but like the dppb derivative it was too broad to reveal
anything except that there was no unreacted phosphine in the mixture. The UV/vis

spectrum had a 1(5 —) 5*) transition that was consistent with the literature.48

II.A.1.c. Synthesis of M02C14(dppe) 249

The preparation of the dppe derivative was modified from the literature as
suggested by Dr. Sara Helvoigt. Rather than starting with M02(OZCCF3) and adding Cl'
with Me3SiCl, K4M02C18 was used as the starting material and the same preparation
procedure described for the depe compound was followed. The solution turned from red
to green to muddy-orange on reflux. According to the literature, the green stage
corresponds to the a-isomer of this compound.” The solution refluxed for 12 hours to
drive it as fully as possible to the B-isomer. The light-brown product was washed with

water and methanol; its UV/visible spectrum was consistent with the literature.49

40

II.A.2. Spectroscopic Solvents and Materials

All spectra, unless otherwise noted were measured for samples dissolved in Gold
Label 3-methylpentane(3-MP) purchased from Aldrich Chemicals. 3-MP was first dried
over activated 4A molecular sieves, then transferred via a high-vacuum manifold to a
high-vacuum pot containing sodium-potassium (N aK) alloy. The pot was sealed from the
atmosphere by a Kontes high-vacuum stopcock. The samples were placed in a slightly
modified high-vacuum cell.50 The modification consisted of having the cell attached to
manifold in such a way that it could be easily cut off in the glass shop. The cells had to
be removed from their manifolds so they could be loaded in an Air Products (Air
Products and Chemicals, Allentown, PA) crysostat to perform the two-photon
measurements. The crysostat was used to cool the samples to 60 — 120 K, depending on
the solvent and excitation wavelength. Cooling the samples resulted in a significantly
increased quantum yield as compared to room temperature. The low-temperature.
quantum yields were not measured, but it was readily apparent to the eye that the
quantum yield increased. Also, with all samples other than MozCl4(PMe3)4, the emissive
lifetime of the 55* state increased significantly when the sample was cooled. This
increase in lifetime also made it easier to detect the fluorescence. To maintain good
thermal contact with crysostat cell holder, the cells were wrapped in indium foil. Once
the cells were in place, the indium foil was cut away from the area of the cell where the
laser beam would pass through. It must be noted that all cells and optics were either
Pyrex or BK7 optical glass. Quartz was originally used; however, small amounts of
crystallinity remained even after the fusing process, which resulted in the optics and cells
producing very small amounts of doubled laser light. This frequency doubled light often-

times corresponded with allowed one-photon transitions and led to spurious data.

41

II.A.3. Standard Instrumentation.

The absorption spectra were recorded using either a Cary-17D spectrometer that
was retrofitted by OLIS to provide computerized data collection or a Perkin Elmer 3840
Diode Array UV/visible spectrometer. Emission spectra were recorded on a spectrometer
that was constructed at Michigan State University and recently modified to include
digitized fluorescence detection by means of a Stanford Research Systems SR 400 photon
counter.51 31P{1H} NMR spectra were recorded on a Varian Inova-300 MHz

spectrometer.

II.B. Two-Photon Fluorescence Excitation (TPE)

As indicated in Chapter I, two—photon spectroscopy is a very powerful tool.
However, as with most techniques, there are significant drawbacks. Perhaps the most
substantial weakness of TPE is its poor sensitivity owing to the extremely low cross-
sections (~10'50 cm4s'1molecule'1) that are encountered. The selection of a very sensitive
detection scheme can improve the sensitivity. Several schemes are available that provide
for detection against a so-called “dark” background. The one used in this study was

fluorescence excitation.

II.B.l. TPE Instrumentation

The instrumentation used in the two-photon investigation of quadruply bonded
compounds has evolved substantially over time. The first version has been reported
previously in the literature.52 The most current version of the instrument (Figure 11.1)
will be described here.

In order to obtain the high photon flux necessary to access two-photon states it is
necessary to use a pulsed laser. The heart of the instrument is a Coherent Infinity 40-100
Nd:YAG laser (Coherent Laser Group, Santa Clara, CA). The fundamental wavelength

of the laser is 1064 nm, emanated with a pulse width of approximately 3.5 ns. The pulse

42

0008000 20800 000
0000000000 080 Aiv 000. .0000 000 00 00000008 00 000080 w800 00000008 000 00 00000000 0000 00000000 000. .000 0000 00000000000
00 0w00000 w80000 0000 00000000 000 00 000000000000 20800 000 0.0000 00 00000 00000000 $0 000 m0 000 m0 0000000000000
0500000000 000 00 Q0 000 00000000 0 8 000000 00 0000 20800 000 00 m .8000 0000— 000 .00 00000 0000800000 000 0000.00 00 0000 00000 000
000 008000 300000 0389 00m 000 .008000 0000000 20009 .000 000000000 000000050 .06 .8000 0000— 000 .00 0000w00>00 000000
00 0000 000— 0&02 000.0 w00_ 000 00 3 0808080008 .000. 800.0000 00 0000 0000000800008 000 .00 80580 00080000 < .3— 0.00»:—

5

 

IIIIII-IIIIIIIIIIII-IIIIIIIIIIIIIII’

 

  

 

 

 

 

 

m on. 0 00 En 00m 0.. \ J
020202 . 0000802
s O
u n K x
m 0.. O m

n. H

V 1

00000000

 

 

43

energy can be varied from a few mJ/pulse up to 600 mJ/pulse and the repetition rate can
be adjusted from single-shot mode up to 100 Hz. The fundamental frequency can be
doubled (532 nm) and tripled (354.7 nm) using crystals supplied by Coherent. The
efficiency of doubling and tripling are 50% and 40%, respectively, of the incident
fundamental pulse energy. The three frequencies that are provided by the Nd:YAG laser
and its harmonics do not provide the tunability that is necessary to fully study the two-
photon spectroscopy of quadruply bonded dimers.

The tunability is accomplished by a Type 1 XPO that is also supplied by Coherent.
The XPO is an optical parametric oscillator (OPO). An OPO provides broad tunability
(420 — 710 nm signal frequencies, 710 nm — 2300 nm idler frequencies). The broad
tunability arises from the nonlinear optical parametric process. The optical parametric
process is essentially sum frequency generation (SFG) (refer to Figure 1.14b) in reverse.
One high energy pump photon (354.7 nm) is split into a visible (signal frequency) and
red/near-infrared (idler frequency) photon such that the energy constraint (Equation 2.1)

is met:53

Epump = Esignal + Eidler (2'1)

The optical parametric material in the XPO is B-BaBzO4 (B-barium borate
(BBO)). The signal and idler wavelengths are tuned by adjusting the angle of the crystal
as shown in Figure 11.2. Since both the signal and idler wavelengths are generated at the
same time it is necessary to use the appropriate optics in the XPO cavity to make the
cavity resonant in either the signal or idler frequency. If both are resonant, the energy
density within the cavity can get too high and lead to optical damage. For all of the
experiments reported here, the XPO was operated in the idler resonant mode. Some
residual signal energy is present with the idler beam and this is removed by passing the
XPO output beam through a Schott RG715 long-wave pass filter (also supplied by

Coherent). The XPO is not seeded; therefore, the bandwidth of the output is wavelength

44

.0800 000
000 0080000203 00000 000 00080 000 00003 .0800 000000030 08 0000000000 00003 80 00 n 00 03000 00 000 000. .00 00 0300 000 4000000
000 00 008000 00 8000 0800 000 0003 .0300 0000000 0mm 0.00 00 0£w0000>03 .0090 000 00—00 .00 0000000000 000. .~.= 000w:—

0.?< .0000 0200.00

 

 

 

o v N o N- v. o.
— u — - — u — - — 0 dl -
106
j
100.
.l u w
lm_. Mk
1 a
. rm.
low .M.
- w
10d
10.0

 

45

dependent as shown in Figure 11.3. In terms of idler wavelengths, the bandwidth varies
the most from 710-1200 nm. This was a concern, so an earlier experiment that used a
constant bandwidth (~0.3 cm'l) source was repeated. The result is shown in Figure 11.4.
There is a slight difference on the blue edge of the spectra; however the difference is
inconsequential since it does not affect the maximum of the transition.

In order to maintain the most consistent operation of the XPO it was necessary to
pump it at constant repetition rate and pulse energy (100 Hz and 170 mJ/pulse at 354.7
nm). While the high repetition rate was useful for shortened acquisition times and signal-
to-noise ratio concerns, the constant pump energy precluded doing measurements to
investigate the dependency of emission intensity on incident laser power. To circumvent
this limitation, a Newport (Newport Corporation, Irvine, CA) 935-10 High Energy Laser
Attenuator was used. This optic uses a series of quartz wedges to attenuate the beam.
The angle of the wedges is adjusted by means of a lead screw. Changing the angle
changes the amount of Fresnel reflection. The wedges are arranged so they rotate in
opposite directions thus minimizing beam walk. The use of this optic made it possible to
attenuate the intensity by as much as 27 dB with minimal walk.

After leaving the attenuator, the beam is passed through a long focal length (500
mm or 1000mm) lens to reduce its divergence. The polarization of the laser beam is
manipulated to be either circularly or linearly polarized by three optics. These optics are
a CVI (CVI Laser Corporation, Albuquerque, NM) CLPA-10.0-670-1064 Glan-Laser
polarizer (GL), a Newport PR-950 double Fresnel rhomb (DF R) and a CVI FR-4-C single
Fresnel rhomb (SF R). The GL is used to ensure constant horizontal polarization of the
laser beam before it reaches the next two optics. The BF R is placed in a rotatable mount
that can be rotated about the optical axis of the laser beam. When the DFR is rotated, the
plane of polarization of the laser beam is rotated with respect to the incoming laser beam.
This results in changing the plane of polarization of the laser beam with respect to the

optical axis of the SFR. The SFR produces either circularly polarized or linearly

46

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48

polarized light, depending on the plane of polarization of the incident laser beam. This is
accomplished by variably retarding either the magnetic field or electric field of the laser
beam. The degree of retardation is dependent upon the plane of polarization of light
incident upon the SFR.

The polarization state of the laser beam is experimentally determined as shown in
Figure 11.5. By placing a mirror in the beam path and rotating the DFR, a minimum is
observed in the reflected laser (using an IR viewer (Find-R-Scope, FJ W Optical Systems,
Inc., Palatine IL)) beam when the light is circularly polarized. Linearly polarized light is
determined by placing a Glam-Thompson (GT) polarizer in the beam path. By rotating
the DFR, a minimum is observed after the GT when the light is linearly polarized.

The laser beam then passes through the sample and onto a Molectron (Molectron,
Portland, OR) J8LP photodetector. This thermopile detector has an essentially constant
wavelength response from 200 nm to 10 um (i 2%). Because of the constant response,
no attempt was made to correct for slight variations. The photodetector was connected to
a 1M!) impedance signal input of a Stanford Research Systems (Stanford Research
Systems, Sunnyvale, CA) SR250 Gated Integrator/Boxcar Averager Module.

The fluorescence that is generated when the sample absorbs two near infrared
photons is detected in one of two ways, depending on the sample’s emission wavelength.
For compounds with the general formula M2X4L4 and MozCl4(dmpm)2 the emission is
centered in the red area of the spectrum. For these compounds, the emission was
dispersed by a SPEX (Instruments S. A. Inc., Edison, NJ) 1681 monochromator and
detected by a Hamamatsu (Hamamatsu Corporation, Bridgewater, NJ) R943-02
photomultiplier tube (PMT) that was operated at 2200 V while being cooled in a Products
for Research (Products for Research, Danvers, MA) TE-104 thermoelectrically cooled
PMT housing. The output current of the PMT was fed into the 50 (2 load of a Stanford
Research Systems SR400 Gated Photon Counter. The photon counting technique

provided a substantially improved signal-to-noise ratio over the previously used boxcar

49

a.)

Incident Laser Beam /l\ C
H KIAIN v K lfl
l/ N

l/

 

 

 

 

 

 

GL DFR

SFR c'
Reflected Laser Beam /l\ .
s. Mirror
v HAN H

 

 

 

 

 

 

 

 

 

b.)

 

 

 

 

 

 

H KI/im 4s Klfi—V
l/ \J l/

GL DFR SFR GT

 

 

 

Figure 11.5. The polarization state of the laser beam is experimentally determined as
shown here. Determination of circularly polarized light is shown in a.). The horizontally
polarized laser beam (H) passes through the Glam-laser polarizer (GL) and its polarization
is rotated by 90° to be vertically polarized (V) by the double Fresnel rhomb (DFR). The
vertically polarized light is converted to be circularly polarized (C) by the single Fresnel
rhomb (SFR). The laser beam is reflected by a mirror (M), where the handedness of the
circular polarization is changed (C’). The polarization is ultimately changed to vertical
after passing through the SFR and DFR a second time. The vertically polarized light
does not pass through the GL. Vertically polarized light is determined by b.). The mirror
is replaced by a Glan-Thompson polarizer (GT) arranged to block vertically polarized
light and the DFR is rotated until no laser light is seen to pass through the GT.

50

averager method.52 The discriminator level of the photon counter was adjusted to
minimize the number of spurious photons detected that were the result of thermionic
emission from the various dynode stages of the PMT. The discriminator level was
usually set to -40 mV. The gate width was determined by measuring the fluorescence
lifetime (1') of the sample. Usually the gate width was set to 51.

For the twisted compounds, M02C14(PP)2, with the exception of MozCl4(dmpm)2,
the emission was too far in the near infrared to be detected by the R943-02 PMT.
Therefore, a CCD detector was used instead. The emission was dispersed by a SPEX
270M spectrograph and a SPEX SpectrumOne CCD detector measured the fluorescence.
This arrangement was not used for all of the compounds for several reasons. Since a
CCD can not be gated and maintain its near infra-red sensitivity, there was no way to
time resolve the emission. Thus, the CCD was collecting light for a continuous period of
several minutes (even though the samples were emitting for only about 1 millisecond
total when the laser was operated at 100 Hz) whereas the photon counter can operate only
when the sample was emitting light. This gave rise to a substantial CCD background
spectrum even when the sample was enclosed in a light tight compartment and the room
lights were off. Also, a benefit of the lack of sensitivity in the near infrared by the PMT
was advantageous in terms of reducing the amount of scattered laser light detected by the
PMT. Due to the CCD’s sensitivity in the near infrared, even a small amount of scattered
laser light in the 800-1100 nm range could saturate the detector. With the twisted
compounds, the laser excitation was much further into the NIR (1150-1600 nm) where

the CCD is not sensitive to scattered laser light.

11. B. 1. a. T PE Measurment

Regardless of the detection method that was used, the laser and detector were
interfaced using LabView. For both detection schemes, the Molectron detector that was

fed into the Stanford Research Systems SR250 Boxcar Averager was used to measure the

51

relative laser intensity. LabView then communicated with the boxcar via the SR245
computer interface module with GPIB commands. When the PMT/photon counter
detection scheme was used, the communication was also performed using GPIB
commands between LabView and the SR400. For the CCD detection scheme, LabView
virtual instrument drivers provided by SPEX were used to gain low-level access to the
CCD detector. LabView communicated with the XPO using dynamic data exchange
(DDE) to facilitate tuning the laser.

The data collection was routine. The maximum of the 52 —-) 5*2 transition was
estimated based on the maximum of the 1(5 —> 8*) transition. The laser was tuned to this
wavelength and the fluorescence was detected accordingly. When the PMT/photon
counter was used to detect the fluorescence it was desirable to attain approximately 400
counts/ 100 laser shots; too high a count rate oftentimes resulted in saturation of the PMT
for the first several nanoseconds after the laser pulse. Since the photon counter literally
counts pulses, it would only count once for the saturation, despite the fact that the
saturation was actually due to several photons striking the photocathode at nearly the
same time. The slits on the monochromator were adjusted to yield the desired signal
level. When the CCD detected the fluorescence, the CCD integration time was adjusted
such that the signal after the background spectrum was subtracted had at its maximum
600 counts. Once the detection parameters were determined, LabView was launched and
it took over data acquisition. The laser was tuned to its starting frequency and if the CCD
was being used, LabView would prompt for a beam stop to be placed in the beam for
acquisition of a background spectrum. If the PMT/photon counter was being used, it was
not necessary to take a background due to the phase-sensitive nature of the gated
detection and low dark current of the PMT used. The next step involved determining the
fluorescence intensity and laser intensity. Once this was done LabView would determine

the signal by dividing the fluorescence intensity by the square of the laser intensity and

52

then advance to the next wavelength. This would be repeated until the full spectral

region of interest was covered.

11. B. [.b. Power Dependence Measurement

As indicated in Section I.B.2.b, the signal intensity of a two-photon transition is
proportional to the square of the incident laser intensity. Measurement of this
dependence provides a useful check to be certain that the data being gathered are in fact
due to a two-photon process.

The power dependence measurements were also straightforward. LabView was
again utilized to gather the data. The laser was tuned to the desired wavelength and the
fluorescence intensity and relative laser intensity were measured. LabView would then
prompt to adjust the laser energy using the attenuator while the laser energy was being
constantly updated on the computer monitor. The laser energy would be decreased in
approximately 10% steps until the fluorescence intensity was too low to be accurately
measured. If smaller step sizes were used, the error in the energy measurement (~i2%)
would be almost as large as the step size.

For the M2X4L4 compounds and M02C14(dmpm)2 the signal intensity was high
enough that meaningfirl power dependence measurements (those comprised of more than
5 different energies) could be made at many different wavelengths across the spectrum.
For the other MozCl4(Rl’)2 compounds this was not the case and consequently the power

dependence was measured only at one or two wavelengths.

II. B. 2. c. Polarization Dependence Measurement

The polarization dependence was measured in a manner very similar to the
process described for the TPE measurement, the only differences being that the signal
was measured once with vertical polarization and once with circular polarization. Also,

for the polarization dependence the step size between points was usually larger and the

53

number of times the signal intensity was measured was increased with respect to the TPE
measurement. The signal intensity observed when circularly polarized light was used
was divided by the intensity when linearly polarized light was used to yield 9, the

polarization ratio.

54

Chapter 111

n
Two-Photon Spectroscopy of M02C|4(P P); Complexes

n
III.A. Experimental Background of M2X4(P P)2

The opportunity to study a bond as it is systematically broken is provided by this
class of compounds. The breaking of the S-component of the metal-metal quadruple
bond is accomplished by twisting one half of the molecule with respect to the other. The
twist is introduced by the bridging diphosphine (PP) ligands. The effect of the twist (x)
on the electronic states of the 5-manifold is shown in Figure III. 1. This figure also shows
the dependence on the coupling (S)of the parent dxy orbitals. Cotton and coworkers have
demonstrated that the strength of the 5-bond follows a cos2x dependence.15 Ultimately,
the energy gap that separates the diradical states gets small enough that the triplet state

can be thermally populated.

55

 

‘\

 

 

Energy

2(AVV2 + K2)1/2 2K

 

 

 

V/

 

—— a-bond twist angle (x) —>

<—— overlap (S)

 

Figure 111.1. The effect of the twist angle (x) and overlap (S) on the electronic states of
the 5-manifold.

56

As mentioned in chapter I, both Gray and Cotton have taken advantage of this
feature of the S-bond. Gray et. al. used a SQUID to measure the magnetic susceptibility
of B-MozCl4(dmpe)2 where dmpe is bis(dimethylphosphino)ethane, which has a twist
angle of approximately 40°25 (50° as measured by Cotton et a126). The 358* state energy
was measured to be in the 400 - 500 cm'1 range. From this single point, the separation
was extrapolated based on the cost dependence, to a 90° (and therefore 0°) twist angle.
It was determined that the triplet state energy for a fully formed 6—bond was
approximately 5200 cm".

The magnetic susceptibility measurements required a great deal of high purity
compound to be available. Cotton et al performed similar measurements using
temperature dependent 31P{1H} NMR spectroscopy.26 With this technique, as the
temperature is raised there is more triplet character present, which leads to an upfield
chemical shift and paramagnetically broadened peaks in the NMR spectra. From the
measured shifts and peak widths, the triplet state energy of a number of M02C14(I§P)2
compounds with twist angles that ranged from 24.7° to 64.9° was determined.
Compounds with twist angles outside of this range could not be studied with this
technique since the 385* states are too high in energy to be thermally populated without
sample decomposition. However, when the data were extrapolated based on the cost
dependence the 358* state energy at 0° and 90° was estimated to be 4840 cm". At 45°,
where the 8-bond is formally annihilated, the 358* state was estimated to be 1230 cm‘1
above the ground state. Derivatives where iodide and bromide replaced chloride were
also studied. The 385* state energy for these compounds was also estimated to be 4840
cm‘l. Since there was only one sample studied for each of the different halides, as
compared to seven for chloride, the conclusion is more speculative. Two W2 derivatives
were also studied, and their estimated 355* state energy at 0° (and 90°) was less than

4500 cm‘l.

57

In addition to the aforementioned studies on the 385* state, the 155* state of these
compounds has also been studied. The 1(8 —> 8*) transition energy and extinction
coefficients (a) for those molecules investigated by NMR are reported in Table III.l,
along with their respective triplet state energies and twist angles (x).

The model developed in Chapter I is strictly adhered to by this class of
compounds. As can be seen in Figure III.2a, which is a graphical representation of the
data in Table 111.], both (5 —) 5*) transitions red shift as the B-bond is broken and blue
shift as it is reformed. Furthermore, as shown in Figure III.2b, the intensity of the 1(5 —>
5*) optical transition is observed to decrease as the 5-bond is broken and increase as it is
reformed. This is expected since the parent dxy orbitals are becoming less coupled as the
bond is broken. Mulliken demonstrated the linear dependence of oscillator strength on the
square of the coupling (Equation 1.1). A last point to be considered is that the energy
difference between the 88* states (Figure III.2b) remains essentially constant as the 8-
bond is twisted, which is also predicted by the model. The energy difference is 2K,
where K is the two-electron exchange energy.

Only the 6*2 state remains to be observed in this class of compounds. If this state
can be identified, all of the electronic states available to a two-center, two-electron bond

will be spectroscopically determined.

n
[11.8. Two-Photon SpectroscOpic Results for MozCl4(P P); Compounds.

The molecules investigated are listed in Table 11.1 and represent only a subset of
the molecules studied by Cotton. Sadly, only B-MozCl4(S,S-dppb)2 was able to provide
interpretable spectra. The other complexes, MozCl4(dmpm)2, MozCl4(depe)2, and
MozCl4(dppe)2, either did not display sufficiently strong emission, or the two-photon

excitation spectrum was obscured by strong solvent absorption bands in the near infrared

58

m
Table [11.1. Spectroscopic and structural data for M02C14(P P)2 compounds. 1(8 —> 8*)

is the transition energy in cm'l, 8 is the extinction coefficient for the 1(8 -> 8*) transition
at the maximum in M'lcm", 3(8 -> 8*) is the transition energy in cm'1 and x is the twist
angle in degrees. NM not measurable. Except as noted, the data was taken from
Reference 26.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Compound 1(8 —> 8*) e 3(8 -> 8*) x
MozCl4(dmpm)2 15556 1730 NM 0
M02C14(S,S-dppb)2 12513 1500 2240 24.7
M02C14(depe)2 11690 NR 1320 41.4
M02C14(dmpe)2 11484 21025 1290 50
M02C14(dppe)2 12123 1030 1650 59.5
MozCl4(dppee)2 12812 2500 2250 64.5
M02C14(dppp)2 13706 2680 2980 69.4
M02Cl4(PMe3)4 17150 31 10 NM 90

 

59

 

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region. All of the complexes did display some emission when excited in the predicted

region (based on Cotton’s observations).

III.B.l. MozCl4(S,S,-dppb)2

The absorption spectrum and low temperature emission spectrum of MozCl4(S,S-
dppb)2 are shown in Figure 111.3. The lowest energy band in the absorption spectrum has
been assigned as the 1(8 —> 8*) transition. The emission spectrum has not been
previously reported for this compound, but since it is nearly a mirror image of the
absorption spectrum and reasonable Stokes shifted it will be assigned to 1(8* -> 8). The
emission is observed only at reduced temperature (here at 77K) and is difficult to detect
with a PMT since it lies in the near infrared region of the spectrum.

The two-photon fluorescence excitation spectrum and the solvent (3-
methylpentane) absorption spectrum are shown in Figure 111.4. The wavelength on the x-
axis is the actual excitation wavelength and has not been divided by two to reflect the
energy of the two-photon transition. The sharp band at 1180 nm and the series of bands
from 1380 — 1500 nm are present in both the two-photon fluorescence excitation and
absorption spectra. The sharp bands in the two-photon excitation spectrum are artifacts
of solvent absorption and are the primary reason why the spectra of MozCl4(depe)2 and
MozCl4(dppe)2 could not be readily interpreted.

The appearance of the bands in the two-photon excitation spectrum can be
justified by considering the instrumental layout depicted in Figure 11.1. The laser energy
is measured by the photodetector afier the laser beam has passed through the sample;
therefore, if the solvent (or the sample for that matter) absorbs a significant amount of the
laser light, the energy measured is lower than the actual energy in the sample. The
appearance of the bands can be explained by considering the most extreme example.
When the laser beam first enters the sample, fluorescence is excited that is detected by

the CCD. As the excitation beam passes through the sample the energy is reduced by

61

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solvent absorption to a level that cannot be measured by the photodetector. This scenario
would lead to an infinite two-photon fluorescence excitation signal, since the signal is
determined by dividing the fluorescence intensity by the square of the laser energy. An
experiment was attempted where the laser beam was split before the sample, with a small
portion (~ 10%) sent to the photodetector and the rest passing through the sample. This
experiment failed because it was not possible to pick off enough of the laser beam for the
energy measurement and still have enough lefl to provide adequate excitation of the
fluorescence. Also, with this arrangement, sharp dips in the spectrum would be predicted
since the measured energy would be greater than the energy in the sample.

Figure 111.5 shows the absorption and two-photon excitation spectra of
M02C14(S,S-dppb)2 where the two-photon spectrum has been plotted versus the
wavelength that represents the energy of the transition (i.e. excitation wavelength/2). If
one ignores the bands due to solvent absorption (590 nm and 690 - 750 nm) another
broad band is seen with a maximum at 625 nm (16000 cm"). The polarization ratio
across this band and power dependence of the emission intensity excited at 1250 nm are
shown in Figure 111.6 a and b respectively. The polarization ratio is less than 1 across the
entire band (including the artifact peaks) and the power dependence displays a slope of
2.02. The polarization ratio below 1 indicates that the symmetry of the excited state is
the same as the ground state, which is A for this molecule of nominally D2 symmetry
(Table 1.2). The power dependence indicates that two photons are involved in the

fluorescence excitation.

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b.)

Figure 111.6. a.) The polarization ratio (Q) is plotted versus the wavelength and has a
value less than 1 across the entire band. b.) The power dependence, which is a plot of
the observed fluorescence intensity (Ifl) versus relative laser intensity (power) has a slope

of 2.02. The line represents the best fit following a linear least squares analysis.

(9)

1.0

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III.B.2. MozCl4(depe)2

The absorption and emission spectra for MozCl4(depe)2 are shown in Figure 111.7.
The extinction coefficient for this compound has not been measured, but since its twist
angle (41 .4°) is close to a broken 8-bond, it may be assumed that its extinction coefficient
is very similar to MozCl4(dppe)2 (50°) which is 210 M'lcm’l. Because of the low
absorptivity the molecule does not display a strong luminescence relative MozCl4(S,S-
dppb)2. The weak emission, coupled with strong solvent absorption, made it impossible
for the two-photon spectrum to be unambiguously interpreted. This compound was
studied in two solvent systems. The first was 3-methylpentane, which worked well for
MoZCl4(S,S-dppb); in this solvent, it was impossible to obtain a two-photon fluorescence
excitation spectrum since the emission was very weak due to limited solubility. A one-
to-one mixture of CH2C12 and toluene was then used with hopes of increasing the
solubility and therefore the emission. With this solvent combination a spectrum was
obtained that is shown along with the absorption spectrum of a CHZCIZ/toluene solution
in Figure 111.8. Again, the solvent has strong absorbances that are manifested in the two-
photon spectrum. If the obvious artifacts are ignored, a maximum can be seen at 1495
nm (747.5 nm when the energy of the transition is considered). It cannot be determined
whether this is a true maximum or another artifact. Despite the increased solubility in the
mixed solvent relative to 3-methylpentane, the fluorescence detected from this compound
is significantly less than that for MozCl4(S,S-dppb)2. When MozCl4(S,S-dppb)2 was
excited at its 37m (1250nm) it yielded a fluorescence intensity of approximately 1000
counts at its observed emission maximum when the CCD was exposed to the
fluorescence for 30 seconds (3000 laser shots). For MozCl4(depe)2, the CCD detector
was exposed for 100 seconds (10000 laser shots) and only approximately 100 counts
were registered at its emission maximum. This extremely low signal, coupled with the

fact that the observed maximum in the two-photon spectrum is quite different from that

67

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69

predicted from Cotton’s data (~1450 nm) leads to guarded interpretation. Furthermore,
the low emission intensity precluded the measurement of either the power dependence or
the polarization ratio. It should be noted that when the polarization of the laser beam was
circular, there was no emission observed from the sample whereas when the laser beam is
linearly polarized there is some emission This observation indicates that the polarization

ratio might be less than 1.

“1.8.3. M02Cl4(dppe)2.

This compound was the most difficult to study. Its absorption spectrum is shown
in Figure 111.9. It did not display an detectable emission when excited with the Xe lamp
in the emission instrument. However, when excited with the pulsed laser at 770 nm
M02Cl4(dppe)2 did emit (Figure 111.9). Also, when the compound was excited in the
near infrared at 1450 nm (as predicted from Cotton’s data) emission was detected with
the CCD detector. However, the emission was extremely weak, only 20 counts when the
fluorescence was integrated for 100 seconds (10000 laser shots). A two-photon
excitation spectrum was attempted (several times) and the results are shown in Figure
111.10. The features that are displayed in the spectrum can be attributed solely to artifacts

due to solvent (CHzClz/toluene) absorption.

III.B.4. M02Cl4(dmpm)z.

For this compound, it was not possible to use the CCD detector since the CCD is
very sensitive to the two-photon excitation wavelengths (800 — 1000 nm) that were used.
A small amount of scattered laser light would inevitably reach the CCD and cause it to
saturate. Therefore, the double monochromator and PMT configuration depicted in
Figure 11.1 was used. The absorption spectrum of M02C14(dmpm)2 is shown in Figure
III.11. Like M02C14(dppe)2, this compound did not display detectable fluorescence when

excited with the Xe lamp. The sample did display sufficient fluorescence when excited

70

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73

in the near infrared (950 nm, as predicted) that the lifetime of the emission could be
measured as shown in Figure 111.12. However, when the laser was scanned from 800 —
1100 run, it was not possible to obtain a spectrum due to very low (4 counts/ 100 laser

shots) fluorescence intensity.

III.C. Discussion

The only compound in this series to yield a two-photon fluorescence excitation
spectrum that can be readily observed and quantitated is MozCl4(S,S-dppb)2. The energy
difference between the 1(5 -> 8*) kmax (734 nm) and the 1(52 —9 6'”) 21m (625 nm) is
2375 cm", which corresponds to the energy gap between the zwitterionic states. Cotton
measured the triplet state energy, which can be equated to the energy gap between the
diradical states, to be 2240 cm‘1 for this compound. The similarity of the energy gaps in
consistent with the model developed in Chapter I and displayed in Figure [11.1. This
demonstrates that the 8—bond can be quite accurately described by the age-old model
developed originally for the hydrogen molecule. Most importantly, the 5-bond provides
the first opportunity to spectroscopically investigate all of the electronic states available
to weakly coupled electrons in a two-center, two-electron bond.

Although the spectra of the other compounds in the series could not be readily
interpreted, the fact that they all emit when excited at the predicted wavelengths provides
hope that they can in the future, be studied by two-photon fluorescence excitation. For
this to be accomplished, two different avenues could be pursued. The first would involve
modifications to the instrument. If a longer path length cell was used, more molecules
could be exposed to the laser beam and higher fluorescence should result. To properly
image a longer path length cell on the entrance slits of the monochromator it would be
necessary to either use cylindrical lenses to effectively rotate the fluorescence image by

90° or to literally rotate the monochromator by 90°. This option would be most effective

74

 

 

Intensity
1

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l I l l l I l I l I I L l I l l l
-300 -200 -100 0 100 200 300 400 500 600

time/ns

 

Figure 111.12. The time dependent fluorescence of M02C14(dmpm)2 in 3-methylpentane

at 120 K when excited at 600 nm (top) and 950 nm (bottom). The one-photon induced
fluorescence has a lifetime of 83 us. The two-photon induced fluorescence was difficult
to fit due to the low fluorescence but yielded a biexponential decay values of ~10 ns and
~80 ns. The short component may be due to scattered laser light. The fluorescence was
detected at 675 nm. The one-photon induced fluorescence signal represents the average
of 50 laser shots, while the two-photon induced fluorescence signal was collected with
5000 laser shots. Also, the slits on the monochromator were much wider (8 mm) for the
two-photon induced fluorescence than for the one-photon induced fluorescence the slits
were 0.1 mm.

75

for M02Cl4(dmpm)2 since its two-photon fluorescence excitation spectrum is not
expected to be strongly affected by solvent absorption. The solvent bands that conceal
the spectra of MozCl4(depe)2 and M02Cl4(dppe)2 are likely due to overtones of C-H
stretches. By dissolving these compounds in perfluorinated solvents it should be possible
to move the OH stretches around, or possibly avoid them all together. Another
possibility is to avoid solvent altogether, either by isolating the molecules in a rare gas
matrix or placing a concentrated solution on a sapphire window and allowing the solvent
to evaporate. These last two possibilities must be approached with caution since high
laser energies (~5 mJ/pulse) are used to excite the fluorescence, which is very likely to

damage the sample.

76

Chapter IV

Two-Photon Spectroscopy of M2X4L4 Complexes

IV.A. Spectroscopic Background for M2X4L4 Compounds‘o's“

The M2X4L4 class of compounds is the most heavily studied class of quadruply
bonded complexes. This stems from the systematic perturbations that can be performed
due to the variety of ligands that are available. Also, most of the complexes are readily
crystallized and thus provide important structural information to help interpret
spectroscopic observations.

A great deal of the spectroscopy of these compounds was performed under the
direction of Harry Gray. Measurements were made under a variety of conditions that
included alkane solutions at room temperature and 77K, single crystal studies at room
temperature and 10K, emission from samples under all conditions and also fluorescence
excitation. A numbering scheme for the bands in the UV/visible spectra of these
compounds was developed in the literature and will be adhered to here to maintain

consistency with previously published work. The UV/visible spectrum of

77

MozCl4(PMe3)4 is shown in Figure IV.1. This spectrum is representative of the M2X4L4
class of compounds. The bands are labeled as indicated in the literature.

The most heavily studied transition is 55* <— 52 ('(5 —> 5*)) metal-to-metal
charge transfer (MMCT), due to its uniqueness to quadruply bonded complexes. This
transition produces the lowest energy band (Band I) observed in the UV/visible spectrum
of this class of compounds. The wavelength maximum (711,“) and extinction coefficient
(8) of this band is reported in Table IV.1 for each of the relevant compounds in alkane
solution at room temperature. The assignment of Band 1 to the 1(5 —) 5*) transition is
based on a number of spectroscopic observations. The band is polarized almost
exclusively along the internuclear axis and progresses with a frequency (320 — 340 cm'1
for M02X4(PMe3)4 series) consistent with a metal-metal stretch. Also, excitation of this
band gives rise to prompt luminescence that is a mirror image of the absorption band.

The next lowest energy band (Band III) observed in the UV/visible spectrum has
been assigned as 55* (— 1t4 (1(1t —> 5*)) MMCT transition. This band progresses with a
metal-metal stretching frequency that is somewhat lower energy than observed for the 1(5
—-> 5*) transition. The lower energy progression is expected since this transition
corresponds to moving a more strongly bonding 1t electron to the 5* orbital. This
transition is polarized perpendicular to the internuclear axis, also consistent with a ‘(n ->
5*) transition. The band is quite weak (Table IV.1) since it corresponds to a symmetry
forbidden transition in the D4,, point group.

Band II is the next that is clearly observable in the spectra of these compounds.
This is the most intense band seen in near-UV/visible region of the spectra and has been
assigned as the ligand-to-metal charge-transfer (LMCT) transition 55* (— 6(MP)
(1(O'(MP) —> 5*), where MP indicates that the origin lies in the metal-phosphine bond.
The assignment is based on the fact that the band is more intense than the MMCT
transitions. LMCT transitions are expected to be more intense due to the higher

absorption cross-sections of their chromophores. MMCT transitions, on the other hand,

78

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Table IV.1. The entries are in the form of nm (M'lcm"). a reference 54a, ” reference 40,
and c reference 54b d reference 54c. lThis band was only reported in the fluorescence

spectrum and the extinction coefficient was not measured.

 

 

 

 

 

 

 

 

 

Compound Band I Band 11 Band 111
MozCl4(PMe3)4 585 (3110)” 324 (3720)” 441 (210)c
MozBr4(PMe3)4 598 (4060)“ 345 (6650)” 457 (310)c

M0214(PMC3)4 636 (5250)“ 395 (11850)” 495 (460)0
MozCl4(AsMe3)4 574 (2970)b 323 (3630)” 423d (NR)*

MozCl4(PEt3)4

W2Cl4(PMe3)4 660 (4170)” 293 (9090)” 493 (460)°
MoWCl4(PMe3)4

 

 

 

 

80

 

are based on metal d-d transitions that have notoriously low cross-sections. Furthermore,
the transition exhibits a strong blue-shift when W is substituted for Mo. Bands 1 and 111
both exhibit a red-shift with this substitution. The blue-shift is consistent with the
decreased electronegativity of W, which leads to a larger energetic splitting of the 0’ and
5* orbitals. Due to the significant red-shifl that is observed as X is changed from C1 < Br
< 1, it is speculated that there is also a significant amount of halide character present in
Band II.

To the blue of Band 11 there are two to five intense bands, plus some weaker
bands that reveal themselves depending on the sample conditions labeled Band VII to
Band XI. Since these bands are all energetically close to one another, a great deal of
mixing occurs; thus, the assignments are more speculative than those for Bands 1, II, and
111. All of these bands show a strong dependence on the nature of the halide and have
been assigned as halide-to-metal type LMCT transitions.

Fluorescence excitation spectra of these compounds show that all of the observed
transitions lead to 155'“ luminescence. With the exception of the deep-ultraviolet bands
of some compounds, the relative intensities of the bands in the fluorescence excitation

spectra are the same as the relative intensities observed in the absorption spectra.

IV.B. Theoretical Observations on M2X4L4 Compounds.

While no calculations performed on quadruply bonded dimers match the work
done by Hay on Re2C132'23 there have been a number of studies that provide useful albeit
qualitative information on the M2X4L4 class of compounds. One important observation
made by Hay and supported by ab inito calculations on M2X4(PH3)4 complexes is that
the 5 and 5* orbitals have a significant amount of halide character mixed into them.55.

Cotton and Feng have also performed ab initio calculations on M02C14(PH3)4.56 They

81

 

determined the 355’“ state to lie 5890 cm'1 above the ground state; in excellent agreement
with experiment?”

Perhaps the most useful calculation, with respect to this dissertation, reported to
date deals in particular with the halide dependence of the molecular orbitals of
M2X4(PH3)4 compounds.57 The results of these calculations are summarized pictorially
in Figure IV.2. It was demonstrated that as the halogen is made less electronegative, the
lone-pair electrons move into the metal-based orbitals involved in metal-metal bonding in
general and the 5/5* orbitals in particular. When Cl is the halide, its 3p electrons are
energetically below even the orbitals involved in metal-metal 0' bonding. Because of
this, there is little mixing of halide character into the metal-metal orbitals. The Br 4p
electrons are energetically located between the metal orbitals involved in 0' and 1!:
bonding and those of 1 fall between 1t and 5 bonding metal-metal orbitals. Due to the
increased mixing of the halogen orbitals, the 55* transition is seen to red shift upon
substitution by a less electronegative halogen atom (Figure IV .3).

Further evidence for mixing of halide character into the 5-bond comes from
resonance Raman data.40 When polycrystalline samples of M02X4(PMe3)4 were excited
with a laser line corresponding to their respective 1(5 —> 5*) transitions a band was
'observed that was attributed to the Mo-X stretch. While the intensities of the observed
bands were not quantitated past the observation of “m” (moderate intensity), their
presence in the resonance Raman spectra indicated that some metal-halide character is

present in the 5 manifold.

IV.C. Two-Photon Spectroscopic Results of M2X4L4 complexes.

IV.C. l . M02C14(PMC3)4

MozCl4(PMe3)4 was the first compound to be studied and reported in the

literature.52 The traces shown in Figure IV.4 show the conventional absorption spectrum,

82

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85

the emission induced by one- and two-photon excitation, and the two-photon
fluorescence excitation spectrum (that is represented as excitation wavelength/2). The
hashed box in the near-infrared represents the wavelength of light that was used for two-
photon excitation. The two-photon fluorescence excitation spectrum was collected using
vertically polarized light and displays a maximum at 467 nm (21415 cm“). The rise on
the blue edge of the spectrum is due to one-photon excitation of the red edge of the 1(5 —-)
5*) transition. Band III in the absorption spectrum has been expanded by a factor of
fifieen to show that it is not coincident with the two-photon band.

The power dependence and polarization ratio of the two-photon fluorescence
excitation are shown in Figure IV.5a and b respectively. The power dependence shown
in the figure was collected at 860 nm using vertically polarized light and is just one of
many measurements taken at approximately 5 nm increments in both circularly and
linearly polarized light. The power dependence at this particular wavelength was chosen
because it demonstrates that the quadratic dependence is maintained for more than an
order of magnitude change in fluorescence intensity. While this broad dynamic range
was not observed for each of the power dependence measurements made, all of them
displayed slopes of 2.00 i 0.05. The polarization ratio (Q) is less than 1 across the
observed band. As indicated in section I.B.2.c, this implies that the excited state has the
same symmetry as the ground state, namely A].

The aforementioned observations led to the assignment of the band as the
5’”2 <— 52 (1(52 —> 5*2)) transition.52 Gray’s and Cotton’s values for the diradical energy
gap of 5200 cm'1 and 4840 cm'1 respectively, are in good agreement with the zwitterionic
energy gap (as determined from the observed maxima of the transitions) of 4325 cm'1

measured from the two-photon spectrum.

86

 

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Figure IV.5. Measurements from the two-photon fluorescence excitation spectrum of
M02C14(PMe3)4 in 3-methylpentane. a.) The power dependence when excited with 860

nm vertically polarized light. The line represents a best fit to a slope of 2.00. b.) The
polarization ratio is less than one across the 1(82 —> 8”) transition.

87

IV.C.2. MozBr4(PM€3)4

The absorption and two-photon fluorescence excitation spectra of MoZBr4(PMe3)4
are shown in Figure IV.6. The 1(8 —> 8*) transition in the absorption spectrum displays a
maximum at 598 nm (16720 cm") and the 1(52 —> 5’”) spectrum has a maximum at 470
nm (21275 cm!) The power dependence and polarization ratio are displayed in Figure
IV.7 a and b respectively. The power dependence (collected at 950 nm with vertical
polarization) has a slope of 1.93. The power dependence was measured at several
different wavelengths in both polarizations and yielded slopes that were similar (1.95 :1:
0.05). This particular wavelength was chosen since it was measured near the maximum
of the two-photon transition and displays a very broad range of fluorescence intensities.
The polarization ratio is less than one across the 1(52 —-) 5”) band, which indicates that
the excited state symmetry is the same as the ground state symmetry. It is seen to rise on

the blue edge. This is likely due to excitation of the red edge of the 1(5 —> 6*) transition.

IV.C.3. Mozl4(PMe3)4

The absorption and two-photon fluorescence excitation spectra of Mozl4(PMe3)4
are shown in Figure IV.8. The 1(5 -9 5*) transition in the absorption spectrum displays a
maximum at 636 nm (15723 cm'l) and the 1(82 —) 8*2) spectrum has a maximum at 505
nm (19800 cm"). The power dependence and polarization ratio are displayed in Figure
IV.9 a and b respectively. The power dependence (collected at 990 nm with vertical
polarization) has a slope of 1.92. Power dependence was measured at several difl‘erent
wavelengths in both polarizations with slopes that were 1.94 :t 0.07. This depicted
example was chosen since it was measured near the maximum of the two-photon
transition and displays a very broad range of fluorescence intensities. The polarization

ratio is less than one across the 1(52 —> 5’”) band, which indicates that the excited state

88

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MozBr4(PMe3)4 in 3-methylpentane. a.) The power dependence when excited with 950
nm vertically polarized light. The line represents a best fit to a slope of 1.93. b.) The
polarization ratio is less than one across the 1(62 —> 5’”) transition. The rise on the blue
edge can be attributed to one-photon excitation of the red edge of the 1(8 -) 5*)
transition.

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3-methylpentane. a.) The power dependence when excited with 990 nm vertically
polarized light. The line represents a best fit to a slope of 1.92. b.) The polarization
ratio is less than one across the 1(52 —) 8“) transition. The rise on the blue edge can be
attributed to one-photon excitation of the red edge of the 1(5 —-> 5*) transition.

92

symmetry is the same as the ground state symmetry. It is seen to rise on the blue edge.

This is likely due to excitation of the red edge of the 1(5 —-) 5*) transition.

IV.C.4. MozCI4(PEt3)4

The spectra obtained for MozCl4(PEt3)4 in 3-methylpentane are shown in Figure
IV.10. The 1(8 ——) 8*) transition in the absorption spectrum displays a maximum at
591 nm (16920 cm‘l) and the 1(52 —) 5*2) spectrum has a maximum at 474 nm (21100
cm'l). The power dependence and polarization ratio are displayed in Figure NJ] 3 and
b respectively. The power dependence (collected at 950 nm with vertical polarization)
has a slope of 1.99. The various power dependence measurements for this compound
displayed slopes of 2.00 d: 0.05. The polarization ratio is less than one across the
1(62 —> 5”) band, which indicates that the excited state symmetry is the same as the
ground state symmetry. Like the M02X4(PMe3)4 compounds, the rise on the blue edge is
likely attributable to one-photon excitation of the 1(5 —-> 8*) transition. The polarization
ratio also rises on the red edge; however, due to the noise it is difficult to tell if this is an

artifact.

IV.C.S. M02C14(ASMC3)4

The two-photon fluorescence excitation, power dependence and polarization ratio
measurements of MoZCl4(AsMe3)4 in 3-methylpentane were made with the first version
of the instrumentation.52 The absorption, emission and two-photon fluorescence
excitation spectra are shown in Figure 1V.12. The 1(6 —> 5*) transition exhibits a
maximum at 573 nm (17450 cm“), the l(5"‘—> 6) at 638 nm and 1(62 -—> 6”) at 455 nm
(21980 cm"). The power dependence and polarization ratio are shown in Figure IV.13a
and b respectively. The power dependence was collected at 910 nm using vertically
polarized light. The polarization ratio was collected point-by-point across the observed

1(52 -> 8”) band in 5 nm increments. The power dependence has a slope of 2.09. The

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in 3-methylpentane. a.) The power dependence when excited with 950 nm vertically
polarized light. The line represents a best fit to a slope of 1.99. b.) The polarization
ratio is less than one across the 1(82 —9 5”) transition. The rise on the blue edge can be
attributed to one-photon excitation of the red edge of the 1(5 —> 8*) transition. The rise
on the red edge is likely due to noise.

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M02Cl4(AsMe3)4 in 3-methylpentane. a.) The power dependence when excited at 910

nm with vertically polarized light. The line represents a best fit to a slope of 2.09. b.)
The polarization ratio is less than one across the 1(52 -> 5'”) band.polarization ratio is
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the same symmetry.

97

IV.C.6. WZCI4(PMC3)4

The absorption and two-photon fluorescence excitation spectra of W2Cl4(PMe3)4
in 3-methylpentane are shown in Figure 1V.14. The 1(6 —-> 6*) transition in the
absorption spectrum displays a maximum at 660 nm (15150 cm‘l) and the 1(62 —) 6*2)
spectrum has a maximum at 520 nm (19230 cm“). The power dependence and
polarization ratio are displayed in Figure IV.15a and b respectively. The power
dependence (collected at 1050 nm with vertical polarization) has a slope of 1.93. The
other power dependence measurements had slopes of 1.94 :L- 0.08. The polarization ratio
is less than one across the 1(62 —) 6’”) band, which indicates that the excited state
symmetry is the same as the ground state symmetry; it too displays a rise on the blue

edge.

IV.C.7. MoWCl4(PMe3)4

The absorption and two-photon fluorescence excitation spectra of
MoWCl4(PMe3)4 in 3-methylpentane are shown in Figure IV.16. The 1(6 —) 6*)
transition exhibits a maximum at 635 nm (15750 cm") and the 1(62 —> 6'”) transition has
its maximum at 481 nm (20790 cm“). The 1(62 —-> 6'”) transition does not return to the
base-line on the blue edge of the spectrum; rather it rises quickly just to the blue of the
maximum. The polarization ratio (Figure IV.17a) also rises quite sharply on the blue
edge of the spectrum. This is likely due to the 1(6 —> 6*) transition being broader (full-
width-half-maximum (FWHM) = 74 nm) than that of M02Cl4(PMe3)4 (FWHM = 59 nm).
Presumably, the F WHM of the 1(62 —> 6“) transition is also broader thus creating a more
substantial overlap of the red edge of the 1(6 —-> 6*) transition and the blue edge of the
1(62 —> 6”) transition. The red edge of the polarization ratio also appears to rise;
however, owing to the very low fluorescence intensity (5-10 counts/ 100 laser shots) this
is best attributed to noise. The power dependence (950 nm, vertical polarization) shown

in Figure IV.17b has a slope of 1.82. The power dependence measurements had a

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0.0 l 1 I 1 L L
450 500 550

wavelength / nm

Figure 1V.15. Measurements from the two-photon excitation spectra of W2Cl4(PMe3)4

in 3-methylpentane. a.) The power dependence of the fluorescence when excited at 1050
nm. The line represents a best fit with a slope of 1.93. b.) The polarization ratio is less
than across the 1(62 —> 6”) transition. The rise on the blue edge can be attributed to

excitation of the 1(6 —> 6*) transition.

100

 

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2.0

 

1.5 -

 

 

 

1.0 —

(Q)

 

 

 

0.0I1IIIIIIIII1I
460 480 500 520 540 560 580

 

 

 

 

wavelength / nm
b.)
2.0
1.5 —
3
1.0 —
0.5 l l L l l l l
-0.8 -0.6 -0.4 -0.2 0.0
log (power)

Figure IV.17. Measurements from the two-photon excitation spectra of
MoWCl4(PMe3)4 in 3-methylpentane. a.) The polarization ratio is less than across the
1(62 —> 6*2) transition. The rise on the blue edge can be attributed to excitation of the 1(6
—> 6*) transition, while the rise on the red edge is due to noise. b.) The power
dependence of the fluorescence when excited at 950 nm. The line represents a best fit
with a slope of 1.82.

102

broader distribution (1.85 i 0.1) than those for the other compounds, due to the generally

lower fluorescence intensity observed.

IV.C.8. CiS'MOzCl2(mhp)2(PM02Ph)2

The absorption spectrum for this compound is shown in Figure IV.18 and is largely
uninforrnative. Most of the bands observed in the absorption spectrum do not result in a
charge transfer to the 6* orbital and therefore do not produce 1(6* —-) 6) fluorescence. To
better see the transitions that do result in a charge transfer to the d* orbital, the one-
photon fluorescence excitation spectrum is shown along with the fluorescence spectrum
and the two-photon fluorescence excitation spectrum in Figure 1V.19. Although cis-
M02C12(mhp)2(PMe2Ph)2 is listed as the last in the series, it was actually the second
studied. This compound is the only one to yield a multi-band two-photon spectrum. The
1(6 —) 6*) transition in the one-photon excitation spectrum has a maximum at 555 nm
(18020 cm'l) and the two-photon fluorescence excitation spectrum has two bands with
maxima at 390 (25640 cm'l) and 424 nm (23585 cm'l). The valley between the two
bands is at approximately 410 nm. The polarization ratio measurements (Figure IV.20a)
reveal their utility in the assignment of the low energy band as 1(62 —-) 6*2). The
polarization ratio has a value of approximately one from 360 — 410 nm and falls to less
than one for 410 — 460 nm. The power dependence (860 nm, vertical polarization) is
shown in Figure IV.20b and has a slope 0f 2.02. The high energy band (390 nm) in the
two-photon fluorescence excitation spectrum is difficult to assign due to the low
symmetry (C2) of the molecule. It obviously involves a charge transfer to the 6* orbital
since it produces ‘(6* —) 6) emission, but it is impossible to whether it originates from a

ligand based orbital or a metal based orbital.

103

 

 

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1.5
1.0 —

9 ’III.
0.5 —
0.0lllllllllll

360 380 400 420 440 460
wavelength/nm
b.)
2.0 L
1.5 -
3 1.0 —
0.5 -
J 1 l L
2.0 2.5 3.0
'09 (power)

Figure IV.20. Measurements from the two-photon excitation spectra of cis-
M02C12(mhp)2(PMe2Ph)2 in benzene. a.) The polarization ratio has a value of 1 from

360 — 410 nm and falls to be less than one from 410-460 nm. The vertical line is at 410
nm where 9 changes. b.) The power dependence of the fluorescence when excited at 860
run. The line represents a best fit with a slope of 2.02.

106

IV.D. Discussion

The data for the 1(52 —) 5“) transition energies, along with the 1(5 —> 5*)
transition energies and the energy gap (AE) (as determined from the band maxima)
between the 85* and 8*2 states are collected in Table IV.2. From the values of these two
transition energies, the values of the one— (AW) and two-electron (K) energies that were
defined in Chapter I (and Appendix I) can be determined. The energy of the 186* state is
K +\/K2 + AW2 and the energy of the 15*2 state is 2 K2 + AW2 . The values
calculated for AW and K, along with the overlap (S) (as determined from the oscillator
strength) of the parent dxy orbitals and metal-metal bond length (where known) are shown
in Table IV.3.

IV.D.l. Effect of Halogen Substitution on the 8-manifold.

With respect to the M02X4(PMe3)4 series of compounds, the data presented in the
preceding tables reveal some startling inconsistencies. The data in Table IV.2 indicate
that both the 1(5 —) 5*) and 1(52 —> 8'”) transitions red-shift as the halogen is changed
from C1 to Br to I. In the context of the model that was developed in Chapter I, and
affirmed by the data in Chapter III, the observed red-shifi would correspond to a
weakening of the 5-bond by reducing the overlap of the parent d,‘y orbitals. However, the
metal-metal bond length (Table IV.3), remains essentially constant across the entire
halogen series. This constant bond length suggests that the dxy orbitals are remaining the
same distance apart and therefore maintaining a constant overlap. A second point of
consternation arises when the intensity of the 1(5 —> 8*) transition is considered. The
band gets more intense as the halogen is changed from C1 to Br to I. As was shown in
Chapter III, as the 5«bond is broken the red-shifi observed is coupled with a decreased

intensity of the 1(5 -> 6*) transition.

107

Table IV.2. Summary of data for the 1(8 —) 6*) and 1(52 —) 5”) transition energies and
the energy gap (AE) separating the 58* and 8*2 states as determined from the band

maxima. The energies are in cm“.

 

 

 

 

 

 

 

 

 

 

 

 

 

Compound 1(5 —-> 8*) 1(82 —> 5”) AB
MozCl4(PMe3)4 17090 21415 4325
MozBr4(PM€3)4 16720 21275 4555

M0214(PM33)4 15723 19800 4077
MozCl4(AsMe3)4 17450 21980 4530
MozCl4(PEt3)4 16920 21 100 4180
W2Cl4(PMe3)4 15150 19230 4080
MoWCl4(PMe3)4 15750 20790 5040
cis-MozC12(mhp)2(PMe2Ph)2 18020 23585 5565

 

108

 

Table IV.3. The metal-metal bond distance (in A), overlap (S) of parent clxy orbitals and

one- (AW) and two-electron (K) energies in cm’l. * S was determined from the
oscillator strengths using Mulliken’s relationship (Equation 1.1), the references are for the
oscillator strengths. NM not measured. ** This value is for cis-M02C12(mhp)2(PEt3)2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Compound M-M S404: AW K
M62C14(PMe3)4 2.13058 .16 8597.3 6382.5
MOZBI‘4(PMC3)4 2.12540 .19 8726.9 6082.5

M0214(PMC3)4 2.12940 .22 8006.4 5823
MozCl4(AsMe3)4 NM .16 8890.9 6460
MozCl4(PEt3)4 2.14159 8409.9 6370
W2Cl4(PMe3)4 2.262 .18 7862.1 5535
MoWCl4(PMe3)4 2.209428 8909.5 5355
cis-M02C12(mhp)2(PMe2Ph)2 2.10360" 10014.1 6227.5

 

109

 

 

The reason for these inconsistencies is the over-simplified nature of the model
that has been used. While the model is appealing because of its simplicity, it is applied as
if the 5-bond is isolated from the remainder of the molecule, and this is obviously
incorrect. As was demonstrated by the calculations reported by Milletti, there is a
substantial interaction between the nonbonding halogen p-orbitals and the 5 and 5*
orbitals.” This was further supported by the Mo-X stretches that were observed in the
resonance Raman spectra by Gray et. 01.40 Furthermore, Cotton demonstrated a strong
correlation between the LMCT (Band II) transition and the 1(6 —> 8*) transition for the
M02X4(PMe3)4 series of compounds.43 Also, both Gray‘“*40 and Cotton43 have proposed
that the 1(5 —) 6*) transition steals a great deal of its intensity from Band II. With this
wealth of evidence that the halide has a profound effect on the 1(8 —> 8*) transition it is
reasonable to assume a similar halide effect on the 1(62 —) 5”) transition. The red shift
that is observed in both transitions is consistent with n-backbonding from the 5*
molecular orbital to the nonbonding p orbitals of the halogen. In this scenario, electron
density is removed from the (Ixy orbitals to facilitate the p-backbonding, this in turn
weakens the 5—bond. This is manifested as a general reduction in AW. The red shift
observed in K can also be justified in the context of this picture. Due to the mixing of
halogen nonbonding p orbitals into the 8* molecular orbital, the volume of the 5* orbital
is increased. This increased volume translates into a reduced K because K is solely
dependent on the distance between the electrons (1/r12) as shown in Appendix I.

It is interesting to note that while the 1(5 -> 8*) and 1(52 —-> 5”) transitions are
red shifting on the order of 1500 cm“1 as Cl is replaced by I, the energy gap (AB) is only
moving ~ 300 cm'l. This is appealing in the context of the model. Recall that it is the
energy gap and not the transition energies that determines where on the potential energy
curve a molecule lies. Since the energy gap is very similar for this series they all are

equally weak bonds. What this implies, in the context of the model, is that perpendicular

110

to the axis describing the coupling of the orbitals, there is another axis that describes the
mixing of halogen character into the S-manifold.

Some recent work reported by Hopkins demonstrates conclusively that both AW
and K red shift as the halogen is changed from C1 to Br to 1.61 His experiments involved
isolating both the cations (one-electron oxidized) and anions (one-electron reduced) of
the parent M02X4(PMe3)4 compounds. When an electron is either removed or added to
the 8-bond, the two-electron term vanishes. The 2(5 —) 5*) transition then is a direct
measure of the energy that separates the 8 and 8* molecular orbitals. Hopkins measured
the 2(8 —) 5*) transition for each of the oxidized and reduced species. The results of

these measurements, along with his values calculated for K are recorded in Table IV .4.

Table IV.4. The 2(8 —> 5*) transition energies for the Mo2X4(PMe3)4+/‘ series of
compounds. From Reference 61.

 

 

 

 

 

2(5 —> 8*) MozCl4(PMe3)4 MozBr4(PMe3)4 Mozl4(PMe3)4
Cation (oxidized) (AW) 6350 6200 5850
Anion (reduced) (AW) 7850 7850 7750

K 6200 6050 5600

 

 

 

 

 

The data for the cations displays a definite red shift, whereas the shifts for the
anions are not as pronounced. This is likely due to the expansion of the orbitals when an
extra electron is placed in them, leading to better overlap. Better orbital overlap is also
consistent with the one-electron energies being higher for the anions as compared to the
cations. Hopkins’ values of AW are consistently lower than those determined from this
study; however, the 8-bond typically stretches by 0.05 A when an electron is added or
removed.62 This lengthening of the 8-bond would be accompanied by a decrease in

overlap of the parent orbitals and therefore a general decrease in the energy.

111

 

IV.D.2. Effect of o-donating ligand on the S-manifold.

The spectra of MozCl4(PMe3)4 and MozCl4(PBt3)4 are very similar. Both the 1(8
—-> 5*) and 1(52 ——) 8”) transitions red shifi by ~ 6 nm (1(6 -> 5*) 170 cm“; 1(82 -) 5‘”)
315 cm‘l) when PEt3 is substituted for PMe3. Other PR3 compounds have 1(5 —> 5*)
transitions that can be superimposed with PMe3. This behavior is largely expected since it
is the phosphorous atom that is directly bound to the metal-metal core. Furthermore, the
metal-metal bond (Table IV.3) is slightly longer for the PBt3 derivative which would lead
to red shift of the transitions. A blue shift of both transitions by 12 nm ('(5 —> 8*) 360
cm‘l; (1(82 —-) 8'”) 565 cm") is observed when AsMe3 is substituted for PMe3. The
crystal structure for MozCl4(AsMe3)4 has not been determined. It is suggested by the
similarity of the metal-metal stretching frequencies (AsMe3 = 356 cm'l; PMe3 = 355 cm‘
1) that metal-metal bond length is similar. One possible explanation for the observed
blue shift is based on a synergism between c-donating and n-accepting done by the L
ligands. The L ligands are bound to the metal through the dx2,y2 orbital. PMe3 is a
stronger o-donating ligand than AsMe3; as it pushes electron density into the electron-
rich metal-metal core, it also removes electron density through a n-backbonding
arrangement with the dxy orbital. This would result in a smaller “effective” overlap of the
d,‘y orbitals and therefore a smaller AW as observed. This argument is also supported by
data from resonance Raman measurements. Mo-L stretches are observed in the
resonance Raman scattering which indicates that there is some mixing of the MoL
orbitals with the 5 and 5* orbitals. Furthermore, the Mo-As stretch (217 cm‘l) is lower in
energy than the Mo-P stretch (235 cm'1 for X = Cl and Br; 248 cm“1 for X = I).40 AsMe3,
which is a better viz-acceptor than PMe3 is not as good a o-donor. This coupled with the
weaker Mo-As bond makes the argument of synergism between o-donating and 1t-

accepting more valid.

112

 

IV.D.3. Effect of Metal Substitution on the 5-manifold.

When W is compared to Mo two important factors must be considered; the size of
the dxy orbitals and the metal-metal distance. While W’s orbitals are larger than Mo’s the
metal-metal bond in the resultant quadruply bonded species is also longer. Because the
l(5 —-) 5*) (and the 1(52 —> 5”» transition for W2Cl4(PMe3)4 is red shified relative to
MozCl4(PMe3)4 it is apparent that the increased bond length is not sufficiently
compensated by the increased orbital size and a net decrease in the coupling of the dxy
orbitals is observed. A weakened W2 quadruple bond is also manifested in the general
reactivity of W2 and M02 analogs.63 The red shift observed in AW is due to the weaker
coupling of the dxy orbitals and the red shift in K can be attributed to the increased
volume of W’s orbitals relative to Mo’s. When the metal-metal core is heterobimetallic
(MoW) both 1(5 —> 5*) and 1(52 —> 5”) transitions are seen to fall in between the M02
and W2 transitions. The values of AW and K for this species appear to be out of line with
those observed for Mo and W. This is due to the model used to determine AW and K. In
the model, the energy of the dxy orbitals is set to zero and AW represents the energy
difference of the 5 and 5* molecular orbitals (AW = 5* - 5). For the MoW species the
two dxy orbitals are not at the same energy and therefore AW (and K) have little meaning

for this species.

IV.D.4. cis-MozCl2(mhp)2(PMe2Ph)2

Due to the substantially different ligand set and reduced symmetry of this
molecule relative to M02C14(PMe3)4, perhaps the only meaningful comparison that can be
made is between metal-metal distance and AW. For cis-M02C12(mhp)2(PMe2Ph)2 the
metal-metal distance is shorter which implies a better overlap of the dxy orbitals as

compared to MozCl4(PMe3)4. This is manifested in the blue shift of AW.

113

 

IV.E. Zwitterionic Character of the 55* and 5"2 States.

From the values for AW and K derived from the transition energies, it is possible
to determine the extent of mixing of the 52 (pure diradical) and 5"'2 (pure zwitterionic)
states of the 5-manifold (see Figure 1.4 in Chapter I). The details of this calculation,
performed only on the M2X4(PMe3)4 series of compounds, are presented in Appendix II.
The extent of mixing is highly dependent on the overlap (S) of the parent d,‘y orbitals.
The overlap was determined using Mulliken’s relationship (Equation 1.1) and is related to
the intensity of the 1(5 —> 5*) transition. Because the intensity of the 1(5 —) 5*) transition
is strongly influenced by the halogen the calculation was performed twice. The first
calculation represents a very naive approach, where S was determined from the 1(5 —) 5“)
transition. In the second calculation, S was held constant at the value for M02C14(PMe3)4
(S = 0.16) for the M02X4(PMe3)4 series. The results of both calculations are shown in
Table IV.5. The same value of S was used for both calculations performed on
W2C14(PMe3)4.

Table IV.5. Results of calculation to determine the percentage of zwitterionic character
of the excited state.

 

 

 

 

 

 

 

 

Compound %Z (varying S) %Z (constant S)
Mo2C14(PMe3)4 81.33 81.33
MozBr4(PMe3)4 80.69 80.09

Mozl4(PMe3)4 82.43 80.97
W2Cl4(PMe3)4 80.70 80.70

 

The calculations demonstrate that the 5*2 state is very ionic. Since the 155* and
5*2 states are the antisymmetric and symmetric linear combinations of having two-
electrons “trapped” on one side of the molecule (“M—i- M': :t :‘M—4— M +), ‘55" is

equally zwitterionic. The same conclusion was drawn from ultrafast-time-resolved-

114

 

 

emission experiments performed by Winkler and co-workers.64 Using a streak-camera,
they were able to monitor the fluorescence of MozCl4(PMe3)4 on the time-scale of
solvent motion. When a polar solvent was used, the emission was observed to red shifi as
the solvent moved to accommodate the newly introduced dipolar excited state. Based on
these data, it was calculated that the 155* excited state possessed a dipole moment of 4.0
Debye.

In terms of the original goal of this dissertation — to locate and characterize a
discrete excited state capable of multielectron of multielectron chemistry this research is
a resounding success. Moreover, multielectron chemistry has been observed from

quadruply bonded dimers by other students that have been involved in this project.

115

 

Appendix I

The 0' and 6* molecular orbitals will be defined as the symmetric and
antisymmetric linear combination of 3 type atomic orbitals of hydrogen on nuclei A and
B:

0' ___ s( A) + s(B)

AI.1
JZ+ZS ( a)
6* =S(_A);i3_) (AI.1b)

JZ—ZS

where S is the overlap of the atomic orbitals (S = (s(A)|s(B)) ). The terms in the
denominators serve to normalize the wavefunction.
When two electrons (labeled (1) and (2)) are placed in the two orbitals four non-

degenerate states may be formed. The lowest energy state is when both electrons occupy

 

the 0' orbital (02):
0’2 = o(1)o(2) (AI.2a)
= 2 1 (s(A)(1>s(A)(2)+s(A)(1)s(B)(2)
+ ZS
+s(B)(1)s(A)(2)+s(B)(1)s(B)(2)) (AI.2b)
= 2:15 (A(1)A(2) + A(1)B(2) + B(1)A(2) + B(1)B(2)) (AI.2c)

 

_ 1 1
_ __2 + 28 (A(1)A(2) + B(1)B(2))+ 2 + 28 (A(1)B(2) + B(1)A(2))(AI.2d)

An important point of the linear combination of atomic orbitals is that it neglects the
affect of correlated electron motion. This is exemplified in the last equation (AI.2d)
where the term on the left describes a purely ionic situation where both electrons are
associated with either nuclei A or B. The term on the right has one electron associated
with nuclei A and the other with nuclei B and this term can be regarded as being a

diradical.

116

 

The highest energy state occurs when both electrons occupy the highest energy

molecular orbital 6* (6”):

*2 _ 1 ———l
0' _ 2 _ 2S (A(1)A(2) + B(1)B(2)) 2 _ 2s (A(1)B(2) + B(1)A(2))(AI.3)

At intermediate energy there are two states where one electron occupies each of
the 6 and 6* molecular orbitals. Following Hund’s rule, the triplet state (366*) is the
lowest energy of the 66* states. Since its spin function is symmetric (011132 + B1002), the
spatial component of the wavefunction must be the antisymmetric combination of one

electron in each of the 6 and 6* molecular orbitals:

3 66* = % (6(1)6 * (2) — 6 * (1)6(2)) (AI.4a)
= 5'? (A(1)B(2) — B(2)A(1)) (AI.4b)

The 366* state is a purely diradical state with one electron on nuclei A and the other on
nuclei B. This is the basis of the Pauli Principle that states that two electrons with
identical quantum numbers cannot occupy the same region of space.

The 166* is then the symmetric linear combination of having one electron in each

of the 6 and 6* orbitals:

166* = 2/1—5 (6(1)O' * (2) + 0' * (1)6(2)) (AI.5a)
= % (A(1)A(2) — B(1)B(2)) (AI.5b)

The 166* state is a purely ionic state, with both electrons associated with either nuclei A
or nuclei B.

The Hamoltinian for the total energy of the system (H) consists of a Hamiltonian
for each of the electrons (11(1) and hm) and a l/rlz operator that describes the interaction

(electron correlation) between the two electrons:

117

 

H = h“) + 11(2) +—1— (AI.6a)
r12

where h“) take the form of a typical one electron Hamiltonian:

_ 2
110) = {le2 + v (AI.6b)

2me /

The 62 and 6*2 states are of the same symmetry (12;), and therefore can mix
together. The energy of the states is determined by considering the two-dimensional
Hamiltonian matrix:

(0’ |H|02> (6’ 1H
(6*2 H|62> (6*2 H

 

6*2>

(AI.7)

 

 

 

The matrix elements on the diagonal represent the energies of the “pure” 62 and 6*2
states, while the off-diagonal elements determine how much the energy is perturbed by
mixing the two states together. This matrix will be called upon in Appendix II to
determine the extent of mixing of the states.
Each of the four matrix elements will be determined as follows:
2 2 2 1 2 2 2 2 2 1 2
<6 |H|6 >=<G ’h‘ )lo >+<G lh‘ )Io >+<G IEIO > (AI.8a)
=(6(1)O’(2)|h(l)|0'(2)0'(1)>+(6(1)6(2)|h(2)l0’(2)6(l)>
+<O’(I)O’(2)I$|O’(2)O’(l)> (AI.8b)

where the first term is the energy of electron (1) in the 6 molecular orbital, the second
term is the energy of electron (2) in 6, and the last term accounts for the Coulomb
repulsion of the two electrons in the same orbital. The energy of electrons (l) and (2)
will be denoted as W1(1) and W1(2) and the Coulomb repulsion will be I 11- Using this

notation, the energy of the pure 62 state is then:

<02 |H|62> = WI (1) + w,(2) + 11 , (1,2) = 2w1+ Jll (AI.9)

118

 

where the notation has been even further reduced by assuming W1(l) is equal to W1(2)
and the electron labels have been lefi off.
The energy of the pure 6*2 state is determined in an analogous fashion and the
subscripts on W and I refer to the electrons being in the 6* molecular orbital:
<.,..

H 0*2>=2W2 +122 (AI.10)

 

 

The energy of the off-diagonal elements is given by:

6244004621")«wan-9«wag;

 

 

6*2>(AI.11)

 

The first two terms are zero, since 62 and 6*2 are orthogonal, the last term, however is
nonzero. This term is similar to the Coulomb repulsion (Iii), but now considers the effect
of having two-electrons in the 6 (or 6*) orbital and moving them to the 6 (or 6*) orbital.
Since this term involves moving the electrons between the orbitals, it has been named the

“exchange” energy. The energy of the states is then given by the secular determinant:

E— 2W1+JH "A. K12 J

= 0 (AI.12)
K12 2W2+122 '-

Some substitutions can be made that further simplify the secular determinant.
The first is to effectively set the energy of a hydrogen ls orbital to zero. This is
accomplished by setting the average energy of the 6 and 6* molecular orbitals to zero
('/2{W1 + W2} = 0) and defining AW as the energy difference between the 62 and 6*2
molecular orbitals (AW = W2 - W1). The J ii terms are effectively removed by making the
CNDO (complete neglect of differential overlap) approximation. This is justified in
Figure A.1. Two extremes of bonding (atomic orbital overlap) are depicted in this figure.
In Figure A.1a, the 6 molecular orbital is formed by the extensive constructive overlap of
hydrogen’s ls orbitals. The electron density is concentrated in the region between the
two hydrogen nuclei. The 6* antibonding orbital is formed by the extensive destructive

overlap of the atomic orbitals. The electron density in the 6* molecular orbital is pushed

119

 

 

 

 

b.)

 

 

 

Figure AI.1. Two extremes of orbital overlap in bond formation The nuclei are
represented by black dots. a.) The orbitals are overlapped very well and the CNDO
approximation is not valid. b.) The orbitals are not overlapped very well and the CNDO
approximation is valid.

120

 

out to the ends of the molecule. Since the Coulomb energy (Iii) is solely dependent on
the distance between the electrons (1/r12), it is going to be very different for two electrons
in the 6 orbital as compared to two electrons in 6* (J 11 at J22). At this extreme of bond
formation then, the CNDO approximation is not applicable. However, in the other
extreme where the Is atomic orbitals are only weakly overlapped (Figure A.1b) the
CNDO approximation is very valid. The 6 molecular orbital is effectively just two
hydrogen ls orbitals barely touching one another and the electron density is concentrated
around the nuclei. The 6* molecular orbital’s electron density is also concentrated about
the nuclei. Because of this, the Coulomb repulsion energy is very similar when there are
two electrons in 6 as compared to 6*. Since the Coulomb repulsions are similar, they
can be neglected as a constant offset in energy (I 11 = J22 = 0). When these

simplifications and assumptions are made, the secular determinant is reduced to:

-—AW—7. K12 _0
K12 AW— _

(AI.13)

 

The energy of the 66* states can be determined in exactly the same fashion; the
only new bracket that is encountered is a Coulomb repulsion between the electrons in

different orbitals:

(6(1)6* (2)|;L|O'(2)O’* (1)) = 1202) (A114)
12

This Coulomb repulsion can also be ignored based on the CNDO approximation.
The energies of the four electronic states of the hydrogen molecule, when the

bond is nearly broken, are then:

 

_ _ 2 2

1362 _ \[Kn +AW (AI.15a)
E300, = —K12 (AI.15b)
E'OO’ = +K12 (ALISC)

_ 2 2
130,2 _ “/8.12 + AW (AI.15d)

 

where the energies of the 62 and 6"‘2 states were determined by solving the secular

determinant (Equation A. l 3).

122

 

Appendix II

The 62 and 6*2 states are of the same symmetry (12; ), the two states can mix
together:
11 2; = c162 + €26 *2 (AII.la)

2'2; =c16*2 +C20'2 (AII.1b)

112; is the ground state of the molecule and 2'2; is the highest energy state. The
energies and coefficients (which give the extent of mixing) of the states are obtained as F":-

the solution to the eigenvalue problem:

 

 

 

 

W = 911 (AII.2a) ‘2'
62 H 62 62 H 0*2
(3.1.112) (14'...) 911-21»
111 = [C‘ J (AII 2c)
c2 '

The energies of the states were determined in Appendix I and Equation AII.2b is the

same as Equation A17 The energies, with a more convenient labeling scheme are:

1362 == -,/ K122 + sz = e_ (AII.3a)
130,,2 = +«lK122 + sz = e, (AII.3b)

The coefficients are determined from:

 

 

 

(H —s, )(c)= 0 (AII.4a)

E 2 — 8:1: K Cl
0 = 0 (A1146)

[ K EG*2 - 8i 1C2 ]
(1362 - a, )+ K[-°-Z- = 0 (AII.4c)
c1
— E

9.2. = ___(€* 9’ ) _—_ 1+ (AII.4d)

Cl K -

123

where e_ and L are associated with the ground state. The coefficient (cl)of the “pure” 62
state is fixed by normalization such that the wavefunction for either state (depending on

choice of e or 71.) can be written as:

 

 

2 .2
)1! = 6 + ”$6 (AII.5a)
J] + A:
= (102 + [36 *2 (AII.5b)
where a and B are given by:
a = 1 15 = 60., (A116)

1/1+7~2: ,

With these relationships, the wavefunction can be written in terms of pure diradical and
pure zwitterionic character (recall that 62 and 6*2 are both mixtures of diradical and
zwitterionic character). This is essentially the transition from a molecular orbital picture

to a valence bond picture:

 

~11: (A(1)A(2)+B(1)B(2)(zf 23 2 st)

 

+(A(1)B(2)+B(1)A(2){Zf 2s— 2 328) (A117)

There are two extremes that must be considered. The first is when the nuclei are
far apart, in this extreme, A = i1 and S = 0. The two wavefunction are then purely
diradical (R) and purely zwitterionic (Z):

A(1)B(2) + B(1)A(2)
J 2 + 282

 

R(1,2) = : doubly occupied ground state (AII.8a)

Z(l, 2)- — A(1)A(2) + B(1)13(‘7'):double occupied excited state (AII.8b)
2 + 282

 

However, as the nuclei come together, the wavefunctions mix together:

(2| R) : (A(1)A(2) + B(1)B(2)| A(1)B(2) + B(1)A(2)) : 28
2 + 252 1 + s2

 

(A119)

124

The last step was performed using Bquations AI.1 and AI.3 plus the relationship
s = (A| B) .

Ultimately, the wavefunction for the two states (depending on whether 8_ or 8+ is
chosen) is:

‘1’ = cZZ(1,2) + cRR(l,2) (AII.10)
where CZ and CR represent the coefficients of the zwitterionic and diradical wavefunctions
respectively.
I‘I’Zdv(l,2) = c§Z(1,2)2 + cf.R(1,2)2 + 2ch R2(1,2)R(1,2) (AII.11)

Since, (Z(l,2)|R(1,2))¢0, the mixing of the states is not simply the square of the

coefficients:

cg +cf. .41 (A1112)

The mixing of the states is instead determined by:

6% + of. + 2cch(Z(l,2)| R(1,2)) =1 (A1113)

where the fraction of zwitterionic character is given by:

6;, + c Zc,.(2(1,2)| R(1,2)) (A1114)

where CZ and CR, in terms of spectroscopically measured parameters are:

cZ=\/2+2S2[ a kn-t-Ai) (AII.lSa)
/

 

2(1— S)

 

cR=J2+2sz[ 0‘ 101—1,) (A11156)
/

2(1 - S)

where Otis given in Equation A116 and n = E—z.

125

.- ' I' A?
...1

 

10.
ll.

12.

13.

14.

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