r. ‘ . awn 3? max? . ‘ (2.2 kriau.’ n I ..‘ r35 i v.7? V ( , ML? . ur.‘ SA. It: :1... Huflvht ,. L. $u..,w..m : . .6 $3»: .uM...th_ Nb 8.! whiuhflhm if? lllllllllll\lllllllllllllll "lllllllllllllll LIBRARY Michigan State Unlversity This is to certify that the dissertation entitled Femtosecond Reaction Dynamics in the Gas Phase presented by Una Marvet has been accepted towards fulfillment of the requirements for Ph . D . degree in Physical Chemistry salsa Major professor Date l1‘ "l" 98 MSU is an Affirmative Action/Equal Opportunity Institution 0- 12771 PLACE IN RETURN Box to remove this checkout from your record. TO AVOID FINES retum on or before date due. MAY BE RECAUJ-ZD with earlier due date if requested. DATE DUE DATE DUE DATE DUE um. W' 1/98 chIFICID‘oOuopes-p.“ FEMTOSECOND REACTION DYNAMICS IN THE GAS PHASE By Una Marvet A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1998 FE T; :5me Di. S mflb“md Yifill of pm :15 Tris is; E E: gaining in ;: Lien ed b} 213 of mo ‘rs .. - "Midi“, l i k :31 mml' «Attics usiri cw . w l v} sew ’1. .' v- a “110 be 261 3:; ted In S(' ABSTRACT FEMTOSECOND REACTION DYNAMICS IN THE GAS PHASE By Una Marvet The advent of short pulsed laser sources has allowed time-resolved methods to be developed by which molecular dynamics can be studied directly. This facilitates the observation of processes that may not be amenable to study by frequency-resolved techniques. This is particularly so in the case of reaction dynamics, where many changes may be occurring in a short period of time and the transition state is too short-lived to be readily observed by continuous wave (cw) methods. The work described here involves the study of two such processes in the gas phase by femtosecond pump-probe SpCCtl'OSCOpy. The first involves photoinduced molecular detachment of halogens from gem- dihaloalkanes using a 312 nm femtosecond pulse. The progress of the reaction is monitored by selective detection of fluorescence from the halogen product. The reaction was found to be general to a number of dihaloalkanes, and in every case to produce the appropriate molecular halogen product in the D' state. Molecular dynamics were probed by fluorescence depletion using a femtosecond pulse at 624 nm. Vibrational coherence was observed in some halogen products, indicating a concerted reaction mechanism. Analysis of the spectroscopic and dynamic data was performed; it was determined that V 4 I II. 6;." . ‘3 :1“ .s¥“‘ . . W. ,. .‘n‘ .-’5 Militiilnb‘“ I". .H a h ' (“find C‘Tr I 17153. p315 0: “c; n hum-est: :C‘tj. 1n the l Intent. Tm “Vin ' t - ‘ ‘ 9‘ ,) ) -:—-~ :{irwl qu for one molecular detachment channel the reaction proceeds by an asynchronous concerted mechanism. The second experiment is a real-time study of an unrestricted bimolecular reaction. In this process, pairs of gas phase mercury atoms are photoassociated to an electronically excited state using a femtosecond pulse. The dynamics of the resulting molecules are probed by fluorescence depletion using a second pulse. Analysis of the rotational anisotropy in the nascent dimers conclusively confirms that dimer formation is photoassociative. The degree of rotational excitation in the nascent molecules indicates the impact parameter selectivity of the photoassociation process. for Jon, with love iv V the course of 2::iaclpcd me in Si [would panicul. :1.“ goal-humot :mmimmxx $.20 Zhang app zisisscrlptinn. a 2:1.“le “mm d. as: mll hours. lWit also li‘m . Q ». r'Illr ACKNOWLEDGMENTS In the course of my graduate career I have encountered a lot of people, most of whom have helped me in some way. I would particularly like to thank Pedro Cid-Aguero, who has a remarkable ability to remain good-humoured under all sorts of aggravation. Peter Gross is a truly practical theoretician, with whom discussions were invariably stimulating, no matter the subject. Qingguo Zhang applies an unparalleled attention for detail to every problem. Igor Pastirk defies description, and Emily Brown is one of the hardest-working people I have ever met. Mark Waner deserves a medal for his willingness to help produce posters into the wee small hours. I would also like to thank some of the non-academic staff at Michigan State, most notably the graduate secretary Lisa Dillingham, Scott and Manfred in the glass shop and Dick, Russ and Sam in the machine shop. And finally to Marcos, my advisor. It hasn’t always been smooth, but it was rarely boring. Thank you. Lhtol w“ I .u Lhtol I Lhtol 7"” l 39..) lfi-qu li 1.1m1m 1* 11111 a. aa i hi. Chapi l‘lbfi‘w 4 1... 3; ‘~ 3,. ‘ u “| ‘\~ Chap 8 8 3 ..l1- it 5 \ .. Sta \1. ‘UI l‘1 I‘. H‘. “IQ §\i- - n . I - ‘lfi “. ‘\..» 5‘. 8‘. 1\.. \\. 1‘. NJ ‘\. \‘v a.) TABLE OF CONTENTS Page viii List of Tables ix List of Figures xviii List of Symbols Chapter 1. Introduction 1 1.1 Frequency Resolved Spectroscopy and Reaction Dynamics 2 1.2 Time-Resolved Spectroscopy 2 1 .2. 1 Introduction 2 1.2.2 Preparation of the Wavepacket 4 1.2.3 Dynamics and Probing 9 A. Vibrational Dynamics 10 B. Rotational Dynamics 16 C. Dissociation 20 D. Bimolecular Reactions 22 1 .2.4 Detection 22 1 .2.5 Advantages Chapter 2. Laser System 24 2.1 The Oscillator 25 2.2 The Amplifier 33 2.3 Pulsewidth 37 2.4 Experimental Setup and Detection Chapter 3. Photoinduced Molecular Detachment 3 8 3. 1 Introduction 38 3.1.1 Photoinduced Molecular Detachment 38 3.1.2 Concerted Reactions 40 3 .1 .3 Methylene Iodide 42 3.2 Experimental 43 3.3 Results and Discussion 43 3 .3. 1 Methylene Iodide 47 A. The 300-350 nm Region; D'—-)A' 64 B The 250-290 nm Region 77 3.3.2 Other Compounds vi LI) 'J —‘ 'J) Li) 'JJ ‘JJ 1.. Chapti Appen Refere 92 3.4 Discussion 92 3 .4. l Spectroscopy 92 A. The Parent Molecule 94 B. The Products 96 3.4.2 Energy Partitioning 98 3.4.3 Mechanism Chapter 4. Photoassociation l 12 4. 1 Introduction 112 4.1.1 Bimolecular Reactions 1 13 4.1 .2 Photoassociation 116 4.1.3 The Mercury Dimer 1 17 4.2 Experimental 121 4.3 Results and Discussion 121 4.3.1 Spectroscopy 123 4.3.2 Dynamic Behaviour 126 4.3.3 Other Processes 128 4.3.4 Magnitude of the Signal 132 Chapter 5. Summary and Conclusions Appendices 137 A Mathematical Formulation for Fitting Time Zero Data 140 B Classical Mechanical Simulation of Dissociation Dynamics 143 References vii Photodissi Themed} X = H or a Energetics the minim produce C . energies 21: Compariso II. III. IV. LIST OF TABLES Photodissociation reaction pathways of CH212.'3° Thermodynamics of the dissociation reaction CXzYZ—> CX2( )~( ) + YZ(D’), where X = H or a halogen and Y and Z are halogens. Energetics for several dissociation channels of CH212.'30"50"55"56 The table gives the minimum energies required to dissociate a ground state CHZIZ molecule to produce CH2 and 12 fragments in several possible electronic states. The available energies are calculated based on a three photon transition at 312 nm. Comparison of theoretical and experimental CH2]; vibrational energies in cm". viii Schematic 0 1.11:3 PUISC ‘ mtil‘fl‘nic I propagates i lhf poignllai pulSE month 1 DefinitiOrlS heltlt‘t’ll lhi‘ pump and l“ are manit‘csl transition tli pump and l parallel to tl areat'eragec Clocking fig I2! Potentials ll ulmhon pt t’atelengths V: transitiot closel} reset ill Transients 0 resonant “it ecays rapit coupled real approached; ”I Schematic 0: ”nonic of LIST OF FIGURES 1.1 Schematic of time resolved pump-probe spectroscopy. (a) The pulse causes a vertical transition to the excited electronic state. Several rovibronic levels are accessed, producing a phase coherent wavepacket which propagates in time as shown. As the wavepacket propagates, it spreads out along the potential energy surface (PES). Subsequent probing by absorption of a second pulse monitors the progress of the wavepacket evolution along the PES. (b) Periodic modulation in absorption efficiency of the probe pulse as a function of pump-probe delay time. 1.2 Definitions of the polarisation and transition dipole vectors and the angles between them. The space—fixed vectors 5, and £2 denote unit vectors along the pump and probe electric polarisation directions, respectively. Rotational dynamics are manifested as the time dependence of the angle (1)2 between the molecule-fixed transition dipoles 111(0) and [12(1). The quantity 6 denotes the angle between the pump and probe pulse polarisation; 6 = 0 when the probe pulse is polarised parallel to the pump and 6 = n/2 when it is perpendicular. The remaining angles are averaged out in the derivation of the time dependent rotational anisotropy. 1.3 Clocking figure. (a) Potentials involved in clocking experiments. Excitation from V0 to V1 by an ultrashort pulse produces a wavepacket on V1. As the probe is tuned to shorter wavelengths, the wavepacket traverses the optically coupled region for the V1 -—) V2 transition at greater pump-probe time delays and the transition state more closely resembles the products. (b) Transients obtained at a range of probe frequencies. When the probe is tuned to be resonant with the transition state immediately after time zero, the signal forms and decays rapidly. As the time taken for the wavepacket to reach the optically coupled region increases, the resonance condition for the asymptotic products is approached and the signal no longer falls to zero. 2.1 Schematic of the amplifier. Four dye cells are transversely pumped by the second harmonic of the Nd:YAG laser. Telescopes are used to expand both the pump and amplified beams. ix ‘l !-I 9 ‘1 h Sketch 0ft Detail of ti Experimen XszAG l; teed to s reeompres: and a seat linearly rec as fluoresc hing sent Schematic Typical Fl posititely llli lT-‘tJm a Dispersed G“; at 3 it aSSlgnc detected a Fwdueed l llOl been Ci DlSPCrsed PhOloindm mlilllphou. H01 COUCH {if Speqmm 1 1c: Ambimt l: .Excimlitn 2.2 2.3 2.4 2.5 2.6 3.1 3.2 Sketch of the amplification mechanism. Detail of the Bethune cells. Experimental setup. A pulse from the CPM is collected by a photodiode. The Nd:YAG laser is triggered by the amplified pulse from the diode; an SM-l unit is used to synchronise the pulses. After amplification, the CPM beam is recompressed and steered to a Mach-Zehnder interferometer having a fixed arm and a scanning arm. One arm is frequency doubled, and the two beams are linearly recombined before being focussed into the sample cell. Signal is collected as fluorescence by a monochromator and PMT then averaged in a boxcar before being sent to the computer. The boxcar is also triggered by the CPM. Schematic of the frequency-resolved optical gating (FROG) system. Typical FROG traces, showing (a) negatively chirped, (b) unchirped and (c) positively chirped pulses. The chirp is altered by translating the prism P2 across the beam as shown. Dispersed fluorescence spectrum of 12, produced by multiphoton dissociation of CH2I2 at 312 nm. The dominant fluorescence is between 290 and 350 nm and can be assigned to the 12 D’ —> A' transition. A small amount of laser scatter is detected at 312 nm (shaded). The region marked (i) indicates fluorescence produced by other ion-pair states of 12 (see text). The fluorescence intensity has not been corrected for detection efficiency of the spectrometer. Dispersed fluorescence spectra of the D' state of 12. The spectra were produced by photoinduced molecular detachment of 12 from CH2I2 in a static cell by multiphoton excitation at 312 nm. The spectra are normalised and calibrated, but not corrected for detection efficiency of the spectrometer. (a) Spectrum recorded at 0 °C. (b) Ambient (room) temperature spectrum at 1 Torr. (c) Ambient temperature spectrum in the presence of 80 Torr of Ar. 3.3 Excitation scheme and corresponding time-resolved (pump-probe) data for neat iodine vapour, showing how the observed transient is generated. 1 A 624 nm um pulse c msitiuns tluttreseen '7' At negrtix reached an leeomes r positive lit 31 Excitation shutting h to the ioni u Initially. 1} Pulse. lhi Undergo“ '5' Ab-‘Ol'pllm D' state. D b." detectit mat not b W from 1 fluttrescen remains 31 enhmcm‘ will. AI l Willation 0f Vlbllillt “flepach time Cone Sarnp1e p0. jib Time‘rtsm H‘Sitite m ”Mined V l'ihrgiiflna] 3.4 3.5 3.6 (a) A 624 nm (pump) pulse excites 12 to the B state; subsequent absorption of a 312 nm pulse causes transition to the E and f ion-pair states. These have strong, bright transitions to the valence states A and B. The detected signal is f -) B fluorescence at 340 nm. (b) At negative times (probe pulse arriving before pump), neither the E nor f state is reached and no signal is observed. As the pulses become overlapped in time, it becomes possible to access the f state and molecular fluorescence is obtained. At positive times, vibrational coherence characteristic of 12(B) is observed.33 Excitation scheme and corresponding time-resolved (pump-probe) data for CH2I2, showing how the observed time-dependent fluorescence is generated. (I. P. refers to the ionisation potential of the molecule). (a) Initially, the molecule undergoes multiphoton absorption of the 312 nm (pump) pulse. This causes it to dissociate, producing I2 in the D'(31'123) state, which undergoes a fluorescent transition to A' (3112,.) , detectable at 340 nm. (b) Absorption of a 624 nm (probe) pulse by the iodine depletes the population of the D' state. Depletion efficiency tracks the progress of the reaction and is monitored by detecting the D'—) A' fluorescence at 340 nm. Note that the probe transition may not be as represented; there are a number of optically accessible 12 states 2 eV from the D' statelw’148 At negative times (probe pulse arriving first), the fluorescence produced by the D' —) A' transition is unaffected by the probe, and remains at a constant level. As the pulses begin to overlap in time, an intense enhancement is observed; this is due to a cooperative multiphoton effect (see text). At positive times, absorption of the 624 nm (probe) pulse depletes the population of the D' state, and the fluorescence intensity decreases. Observation of vibrational modulation in the depletion signal indicates that a coherent wavepacket is generated in the D' state of 12. Note that for the 12 transient, positive time corresponds to the 624 nm pulse arriving at the cell first; for the CH2I2 sample positive time is when the 312 nm pulse arrives first. Time-resolved data and vibrational fit to the D' —-) A' fluorescence at 340 nm and positive times. The data was collected with the probe laser polarised parallel to the pump and fit to a function A+Be"/ tcos(wt+¢). The fit displayed was obtained with an oscillation frequency a) of 92.2 cm", corresponding to a vibrational period of 362 fs. The dephasing time rwas ~ 1 ps. Possible excitation schemes to produce time zero fluorescence enhancement. The threshold indicated is the observed excitation threshold for production of CH2 and xi Wu. _,.._. lgiD'l. ThL corresponc .3, One plitlli) 634 (probe photon of 313 nm 15 (B; 1 state An initial requiring r equixalent unknonn. o A three-p.L pa’hvtay 0 pump and molecular ini‘estigatit Killt’llC mi compfi Std ‘3‘ Depletion CH21: wiri- dissociates PUlSfi probe ib’l lime Zero CH21: to a excited pa: Obsencd b‘ lip. I2(D'). The upper line on the figure corresponds to 12 eV, the excitation energy corresponding to a three-photon pump transition. (a) One photon excitation with the 312 nm (pump) pulse requires three photons of 624 (probe) nm light to reach the threshold for production of I2(D'). An additional photon of the probe produces an excitation of 12 eV. Single-photon absorption at 312 nm is equivalent to an excitation of 4 eV, which is sufficient to reach the A (IBI) state of CH2I2 (marked (i) in the Figure). (b) An initial absorption of two pump photons corresponds to an excitation of 8 eV, requiring one photon of 624 nm light to reach the threshold and two to be equivalent to an excitation of 12 eV. The pump-excited state, marked (ii), is unknown. (c) A three-photon pump corresponds to an initial excitation of 12 eV. This is the pathway of the most interest to us because the dynamics observed between the pump and probe pulses correspond to the transition state of the photoinduced molecular detachment reaction. The state (iii) is the dissociative state under investigation. 3.7 Kinetic model for the dissociation of CH2I2. The model assumes that the signal is comprised of two contributions: (a) Depletion signal, produced by the molecular detachment process. Excitation of CH2I2 with three photons of 312 nm light produces an excited molecule, which dissociates into CH2 and I2(D'). Depletion of the D' fluorescence with a 624 nm pulse probes the dynamics of formation of I2(D'). (b) Time zero signal. When the pump and probe pulses coincide, it is possible for CH2I2 to absorb probe photons prior to dissociation, which produces a highly excited parent molecule. This increases the amount of D' —> A' fluorescence observed because it opens another pathway for production of I2(D'). The statistical lifetime 1 of the pump-excited state determines for how long afier the initial excitation the molecule can absorb the probe. (c) The overall signal is a weighted sum of these two contributions, each of which is convoluted with a Gaussian to simulate the pulsewidth. 3.8 Time-resolved data of the molecular photodetachment of 12 from CH2I2 and n- C4Hgl2. The difference in dissociation time between the two molecules can be accounted for by the difference in mass of the alkyl fragment. The relatively poor fit to the C4Hgl2 dynamics at positive times is due to the presence of a vibrational oscillation at early times. xii F." lime-resolt and perpcn polarisation intensin' of The anisotr population . "CC. Pump-profit 385 nm (at probe beam Hotteter. tl trarsient do lime-result primed p. the mo trar both the ra,r remediateli - Purely isotr tn Figure 3, ‘3‘ The pure ; anisotropx' , ‘D' The Pure V1 The lthltcr midlittna] Ct. Si'mmetr}; 4." ' . 3.9 3.10 3.11 3.12 3.13 3.14 Time-resolved data of the CH2I2 dissociation obtained at 340 nm with parallel (a) and perpendicular (b) configurations; ‘parallel’ and ‘perpendicular’ refer to the polarisation of the probe beam relative to the pump. Note the much smaller intensity of the time zero feature in the perpendicular polarisation configuration. The anisotropy data is ambiguous; no reliable conclusions about the rotational population of the products can be drawn from analysis of this data. Pump-probe data obtained by selective detection of the I2 fluorescence signal at 285 nm (a) and at 272 nm (b). Both transients were obtained with the pump and probe beams polarised parallel to each other. Both exhibit vibrational coherence. However, the 285 nm transient exhibits a large time zero spike and the 272 nm transient does not. Time-resolved data at 272 nm of the CH2I2 dissociation, obtained with the probe polarised parallel (a) and perpendicular (b) to the probe. The difference between the two transients clearly indicates rotational anisotropy in the 12 product. Notice both the rapid anisotropy decay time and the fact that depletion is more efficient immediately after time zero in the perpendicular polarisation configuration. Purely isotropic and anisotropic components of the time-resolved data presented in Figure 3.11. (a) The pure rotational contribution as given by the time dependent rotational anisotropy r(t). (b) The pure vibrational contribution as given by the isotropic signal I“ + 21b The thicker lines show least—squares fits to the pure vibrational and pure rotational contributions. Model of the CH2I2 molecule in the centre of mass frame, showing the principal (X, Y and Z) and rotational (a, b and c) axes and their transformation under C2v symmetry. Fit to the dispersed I2 D'—-> A' fluorescence spectrum produced from the dissociation of CH2I2. (a) Fit obtained using only D'—) A' fluorescence. (b) The f -—> B fluorescence spectrum obtained from excitation of neat I2 vapour. xiii g; r" .- - BiF‘JOC Will fii'li.‘ (0) Fit to the observed fluorescence in the 300-350 nm range, taking into account the possibility of contribution from the f —+ B transition. The spectrum shown in (b) was scaled by a factor determined by optimisation and incorporated into the fit. 3.15 Fits to the vibrational coherences in the 12 D'—> A' fluorescence at positive pump- probe delay times. (a) Original, exponentially damped sinusoidal fit shown above (Figure 3.5). (b) Bimodal Gaussian fit. One mode has an oscillation frequency of 96.5 cm‘1 and a F WHM of 7. The second mode has an oscillation frequency of 104 cm'l and a F WHM equivalent to a single D' vibrational level. 3.16 Dispersed fluorescence spectra of X2(D') produced by multiphoton excitation at 312 nm. (a) From CH2Br2 at 0 °C. (b) From CH2C12 at 0 °C. The increasing signal level at longer wavelengths is due to laser scatter. 3.17 Transient data of photoinduced molecular detachment of X2(D') from dihaloalkanes. Both sets of data were recorded from static cells, with the polarisation vectors of pump and probe pulses parallel to each other. (a) From CH2Br2 at 287 nm. (b) From CH2Cl2 at 254 nm. The increased signalznoise ratio in this data, as in the spectrum in Figure 3.16 (b), is due to low signal levels. 3.18 Time resolved data from the multiphoton dissociation of CH2Br2 using 312 nm femtosecond pulses. The transients were obtained at 287 nm, with the polarisation vector of the probe laser aligned parallel (a) and perpendicular (b) to the pump. 3.19 Anisotropic (a) and isotropic (b) portions of the 287 nm data from the CH2Br2 cell. The fit to the r(t) derived from the data is also shown. To obtain the r(t), the data was properly normalised and a three-point smoothing applied. 3.20 Dispersed fluorescence spectra from multiphoton excitation at 312 nm of CH2Br2 (a), CBr2F2 (b) and CBr2Cl2 (c). All three are produced by the Br2 D' —> A' xiv mane hmeu huan pill". the aCHBn f [BEE 2 Dawn :C. Sho span hmmn Pumpp Wfdhn. i1 “thdt .‘1 Limp? Tifn'oj l . POICmSe til ihe PU: lam-Sq ill and g ml The rot transition. 3.21 Time zero data for the molecular detachment of halogens from CX2Br2. Fits to the data are shown as continuous lines. The time data was obtained consecutively, with the same laser intensity for each scan. (a) CH2Br2 at 0 °C. (b) CBr2F2 at -47 °C. (c) CBr2Cl2 at 0 °C. rm 3.22 Dispersed fluorescence spectra from the multiphoton dissociation of CH2IC1 at 0 ‘ °C, showing both the 320 - 400 and the 400 - 460 nm regions. The fluorescence spectra produced in these regions from a sample of pure I2 vapour are also shown for comparison. 3.23 Pump-probe data from the multiphoton dissociation of CH2IC1 at 312 nm. (a) Collected at 340 nm, corresponding to the G —> A transition. (b) Collected at 430 nm, corresponding to the D' —) A' transition. 3.24 Pump-probe data was collected from the CH2IC1 sample at 340 nm with the liquid reservoir maintained at 0 °C. Dynamics were studied with the probe laser polarised both parallel and perpendicular to the pump. (a) The purely anisotropic contribution r(t) to the 340 nm signal. Also shown are a least-squares fit obtained by assuming a Gaussian distribution of rotational levels (i) and a thermal (Boltzmann) distribution (ii). (b) The rotational populations P0) responsible for the fits shown in (a). The two results are very similar, and produce almost identical fits. 3.25 Pump-probe data collected from the CH2IC1 sample. Fits to the data obtained from the Fourier transform and from the exponential decay model (Equation 3.1) are also displayed. 3.26 Normal mode analysis of the ground state of CH2I2, plotted as a fimction of LI and CH2-I distance. Only the I-C-I bending (v4) and [-01 symmetric stretch (V3) XV I _ ‘3 KENS) M f Rmmnh X; from g then for a Smehron initiated ; forms bet trimmer i Annehro Camil'ht before lht Ii Classical large sphi moiety 1] tr sepam i 3' DC three int bond ‘dé‘ttmed I '— t. The lam 10 be 2.7 filmed modes contribute to the H2C-I2 distance. 3.27 Schematic of possible mechanisms for the photoinduced molecular detachment of X2 from gem-dihaloalkanes. Both proceed in a single kinetic step. The time scales given for these mechanisms are based on time-resolved measurements. (a) Synchronous concerted mechanism. Breaking of the two carbon-halogen bonds is initiated at the same time and proceeds at the same rate. An interhalogen bond forms before the carbon-halogen bonds are completely broken. This pathway has a symmetric transition state and preserves the C2v symmetry of the parent. (b) Asynchronous concerted mechanism. In this case, the rate at which the two carbon-halogen bonds break is different. Again, the interhalogen bond forms before the halogens are completely dissociated from the carbene. 3.28 Classical simulations of molecular detachment processes. In each snapshot, the large spheres represent the iodine atoms and the small sphere represents the CH2 moiety. In both mechanisms, the two C — I bond breaking events are assumed to be separated by 32 fs. (a) The three—step mechanism. The excess energy is estimated to be 1.8 eV for the first bond breaking event and 0.3 eV for the second. In this case, the I — 1 bond is assumed to form immediately after the second C — I bond breaks. (b) The asynchronous concerted (ylide) mechanism. The excess energy is estimated to be 2.7 eV for the first bond breakage and zero for the second. The I — I bond is assumed to form immediately after the first bond breaking event. 3.29 Dependence of I2 angular momentum on the time lag between the two bond breaking events. The two traces present the dependencies for the asynchronous concerted mechanism (a) and the three-step mechanism (b). The conditions are as stated for Figure 3.26. 4.1 Schematic of the potential energy surfaces relevant to the femtosecond photoassociation of mercury atoms. The corresponding atomic states at the asymptotic limits are indicated. 42 Dispersed fluorescence spectra resulting from the excitation of mercury vapor in a static cell at 160 °C. (a) Excitation at 266 nm with a nanosecond laser pulse. xvi 3. [sing a ( Compflet drierenet tom t\\ o Femtose; ran. Dat perpendit page ant molecule . Rotation; in best i Rti'ntton; rotationa ~ Sehemati impact p 0i collisi mum it Tilt Clllit 35 a fling mergieg that nm the th'COretic (b) Using a 60 fs laser pulse centred at 312 nm. The D —> X emission is red-shifted compared to the emission produced by 266 nm excitation because of the difference in excitation energy. The peak at 407.8 nm is an atomic line resulting from two-photon excitation to the 7'80 state. 4.3 F emtosecond pump-probe transients from the photoassociation of mercury at 312 nm. Data was collected with the probe laser polarised parallel (a) and perpendicular (b) to the binding laser. Note that bond formation occurs during the pulse and that the data is clearly anisotropic, indicating alignment of the nascent molecules. 4.4 (a) Rotational anisotropy r(t) obtained from the experimental data. The heavy line is the best fit to the experimental data (plotted as points), as described in the text. (b) Rotational population of the photoassociated product, obtained from the fit to the rotational anisotropy. 4.5 Schematic of a bimolecular collision process, illustrating the definition of the impact parameter b. The equations show the relation between the relative energy of collision ER and the energy E 2 along the direction of the interatomic axis as a function of the impact parameter. 4.6 The differential photoassociation cross section dam/db from Equation 4.9, plotted as a function of binding wavelength. Note that as the wavelength is tuned to lower energies the reaction requires smaller impact parameters and the products are formed with a narrower, lower energy distribution of rotational excitation. At 290 nm the photoassociation process is not very restrictive and approaches the" theoretical limit P(b) = 1 (see text). xvii LlSl Symbol A 115 ps mll‘ LIST OF SYMBOLS AND ABBREVIATIONS Symbol A IR mJ HS [)8 fs mW Meaning Angstrom, 10’10 metre Speed of light in vacuum Planck’s constant h/21r Infrared Joule millijoule, 10‘31 Boltzmann’s constant metre nanometre, 10'9 m second nanosecond, 10'9 s picosecond, 10'I2 s femtosecond, 10'15 5 Watt milliwatt, 10'3 w xviii Lllrequency F mend-re: "at. . , ., ti. sourtt - wi p O. ) -..e to deter 3:.t In the c “uh a a; . . .~ . r J PFO‘SC: b in 4’, . ‘ ll fithlliillfl 4.. l U 1. I x w ,3 M ' “‘l lL ) \a r. ‘ldfi‘t . l“‘lkh- a . lt SOlt 1. INTRODUCTION 1.1 Frequency Resolved Spectroscopy and Reaction Dynamics Frequency-resolved spectroscopy involves the excitation of matter using a narrow bandwidth source. By this method, single quantum states of materials can be interrogated in order to determine energy level spacing and the shape of potential energy surfaces (PES’s). In the case where excitation leads to a chemical reaction, the observation of changes in the spectroscopy of a sample as a reaction evolves can provide information about the progress of the reaction. An alternative approach is to use crossed molecular beam techniques, which allow the increasingly sensitive selection of reactant states, thereby facilitating state-to-state scattering experiments."2 This method relies on asymptotic properties, for example the translational excitation and spatial distribution of the products, to yield information about the characteristics of the potential energy surface along which a reaction occurs. These are statistical measurements, 1'. e. they reveal the kinetic behaviour of a thermally averaged ensemble of molecules. To probe microscopic chemical reaction dynamics, changes in the PES can be studied by analysis of phenomena such as line-broadening.3”4 These methods rely on the fact that the dynamic behaviour of a system is representable as the Fourier transform of the frequency-resolved spectrum. However, it can be difficult to interpret diffuse spectra, 23.1.91} in p -«r of sta 2.10:1 state re r; tor. lit‘etim 3:133. Slime-Rest Ill lntroducti The dfl ell); .r..‘ ‘1'“ ~-._‘,,( OS} for i . 2' :ion K 1 particularly in polyatomic molecules, because a number of other factors such as congestion of states may also contribute to the appearance of the spectrum. Short-lived transition state regions also tend to be difficult to examine in this way because they have very short lifetimes and therefore low spectra] intensity compared to reactant and product species. 1.2 Time-Resolved Spectroscopy 1.2.1 Introduction The development of ultrashort pulse technologys'7 has allowed an alternative methodology for the study of chemical reaction processes. This involves excitation using very short (< 10'‘3 s) pulses. The uncertainty principle dictates that pulses of short temporal duration have a broad bandwidth. The effect of this bandwidth is that a number of quantum levels are populated, which creates a phase coherent superposition of states. The resulting wavepacket will evolve in time, allowing the reaction dynamics to be probed directly. 1.2.2 Preparation of the Wavepacket Excitation with an ultrashort pulse may or may not be resonant with an electronic transition of the material irradiated. In the absence of resonances, impulsive stimulated scattering occurs.8 This produces a phase coherent wavepacket in the ground electronic state of a molecule and has been exploited in transient grating experiments, for examples’ to . . . . Multlphoton absorption of IR pulses can also be used to selectively excrte certain . ___‘-“ l_“ c- ‘ a. . ‘ jifzftllomh l "Liston ol the 2 1:35:20 a ten attrition V: 0' r: a, are the c a: rate will in p :ztazero for mt rein energ} St for. short tin 353%». ., ......ation. l' to to. first- vibrational modes in the ground electronic state.8"°‘12 The electronic resonance case is however of more relevance to this study. Absorption of a photon of the appropriate frequency allows a system in the ground electronic state V0 to undergo a vertical transition to an excited surface potential V1. This produces a wavefunction rm on V1 such that WFZ%%» an "=0 where an are the coefficients of the excited state eigenfunctions (pn. The value of a for each state will in part depend on the intensity of the pulse at the transition frequency. If a is non-zero for more than one value of n, W) is not a stationary state of the excited state potential energy surface (PBS) and a wavepacket will be produced. To examine the effect of using short time duration pulses, consider a system within the Born-Oppenheimer approximation. Under excitation with a Gaussian pulse of FWHM r and central frequency a), first-order perturbation theory yields an expression for the coefficients an as follows: ‘3 (1.2) 2 2 a. = C(91). | i110 )eXPl- (0)" w) at l, 4 where r/Io is the ground-state wavefunction of the system, a)" = (E, — E0)/h is the Bohr frequency and a and C are constants. In the limit of a pulse of long time duration (1' —> an = C<¢n ill/0 >5(wn —C()) ' (1'3) . .~ § '13 :lfl Jr. 1. . l ' ,-; *."‘Cf hlill ..'~ A“ ‘ haul: in it they 5pm 9:: are or graistertt nit} :rizion of reach. speet correlation 1 fair. produ Lisa; in the. Trim yield: . ‘. h I‘», ~‘.._.‘. e“ tthcn button of t ‘E‘teaetet din; ‘ii “‘“Dlnamics the the \\ a ‘t fit : ndentf l l I In this case, an is non-zero only when a) = (on, and a single eigenstate of V1 is populated. On the other hand, in the limit of very short pulses r-—) O and we get from (1.1) and (1.2) wt =CX(¢. n=0 v10 ho. . (1.4) This result indicates that excitation with an ultrashort pulse, i. e. one possessing a broad frequency spread relative to the energy level spacing of the system, reproduces the ground state wavefunction, multiplied by a scaling factor, on the excited state PES. This is consistent with the semiclassical method advanced by Heller and coworkers""'6 for the elucidation of spectra of complicated systems. In this inherently time-dependent approach, spectra are calculated from the Fourier transform of the appropriate autocorrelation firnction (of Wt(0) with (111(1)). The first step is to assume that a vertical transition produces the ground state wavefunction, multiplied by the transition dipole moment, in the excited state.14 This wavepacket can then be propagated and the Fourier transform yields the absorption spectrum. Both Heller’s model and equation (1.4) are applicable whenever the density of states of a system is high compared to the frequency distribution of the excitation and are used as the basis for many theoretical models of wavepacket dynamics. '2’ ' 7 1.2.3 Dynamics and Probing Once the wavepacket has been created it will begin to evolve in time according to the time-dependent Schrédinger equation: MM : Hw,(t). (1.5) at . H; . {axe-MIST.” L‘mL 5; "-fl"fi”q,c I égstlxlh“u‘ .A . :ezclnsrea harder to r fie pulse tt . .l l - . NECK (LN) qztées oi the i: he initial 5.3, .1 let the ”: the mole: .‘t_. a. ‘hn "'-4g’3l Equ Subsequent time evolution of the wavepacket on V1 can then be described by selection of the appropriate Hamiltonian. This may be done in a full quantum-mechanical calculation, but semiclassical methods have proved efl‘ective, particularly at early times.”’""’22 In order to monitor the progress of the wavepacket experimentally, we use a second (probe) pulse to cause a transition from V; to some final state V2. If we monitor an observable associated with the transition from V. to V2 we can directly determine the dynamics of the system along V1. A schematic is shown in Figure 1.1 (a). At some time t after the initial excitation, the system is irradiated with the probe pulse, which will be absorbed by the excited molecules if the central frequency a) of the pulse corresponds to the resonance condition Zia) = V2(q) — V.(q), where Vn(q) is the coordinate-dependent energy of potential surface Vn. To model the time-dependent behaviour of the system, a three-level model can be applied.23 The time-dependent Hamiltonian of the system can be considered to be a sum of contributions from the (unperturbed) molecular Hamiltonian F!“ and the effects Hp" and Hp, of the pump and probe interactions respectively: H(t)=HM +Hpu+Hp,, (1.6) where the molecular Hamiltonian A HM = 1510 0)(0| + f1,|1><1| + fi,|2>(2 , (1.7) and 19,, indicates the Hamiltonian of the system in state it. The time-dependent Schrodinger equation (1.5) can be written'7 inc ray i - I 'I «I. I. 'd c I U a I — ‘ iigre 1.1 5 tr The pul: I'llitl'OlllC l (a) (b) A , Potential Energy I r > 0 1: Pump-Probe Time Delay Probe Transition Probability V Figure 1.1 Schematic of time resolved pump-probe spectroscopy. (a) The pulse causes a vertical transition to the excited electronic state. Several rovibronic levels are accessed, producing a phase coherent wavepacket which propagates in time as shown. As the wavepacket propagates, it spreads out along the potential energy surface (PES). Subsequent probing by absorption of a second pulse monitors the progress of the wavepacket evolution along the PES. (b) Periodic modulation in absorption efficiency of the probe pulse as a function of pump-probe delay time. two) It. 17;.(0 17.20) Ill/0(1)) 171— III/1(0) = V100) hl V120) Ill/1(0) - (1-8) lV’zU» V200) V210) ha Ill/2(0) The solution of (1.8) is complex, but can be simplified by making certain assumptions. Firstly, we assume no direct coupling between the ground and probe states, ‘39. 1702(1) = 1720(1) z 0. The electric field is assumed to be classical and the dipole and 1mating wave approximations applied. For a pump pulse centred at t = 0 and a probe pulse occurring some time 2' later, where r is larger than the pulse duration, we can Write24 smebflm Knaann hanmll nnnhne ‘3'? H1 is ll‘lt ?eanfV ‘- l . 22:», waOHh' t 1 C mm = % clexptifizrmn expt—ifirmtoatow (1.9) (a) 114(1) = CXP(-iHiT)V/t (b) i °° .A .e W = ; Iexp(1H]t)y0|exp(—1Hot)r//0El(t)dt , (c) where EU) and E2(t) represent the electric field strengths of the pump and probe pulses respectively and ,u indicates the dipole moment of the appropriate transition. Equations (1.9) show that by separating the pump and probe pulses in time, we treat the pump-probe process as a sequential excitation. Equations (1.9) (b) and (c) describe the behaviour of the wavepacket on V], the state of interest. If we combine (1 .1) and (1 .9) (b), we can write v.0) =Za. (0,.6XP(-'i1:1.’) (1.10) 1:20 where H, is the Hamiltonian for motion on the potential surface V1 and (on are the eigenstates of VI. Applying the time-independent Schrodinger equation to (1.10) yields (assuming H, has no explicit time dependence) w.=2a.¢,.exp(—iE,.r/h>. (1.11) "=0 where E" is the energy of eigenstate go". If there is a well-defined phase relationship between the states (pa, we can expect to observe periodic behaviour in the wavepacket on V1 and therefore in the probability of the transition to V2. This can be understood quantum mechanically as a consequence of the interference between the populated states; 553:. surface. it desert abit region 01 m0 7' exile the t til at. We c; ration i.e. ti aiiis a lunet I ‘ ‘ \ v ~. . - " I:\‘..".’..:'tlt)ll. 21f “falls! we can also visualise a wavepacket as a classical-type particle oscillating on the potential energy surface. An observable related to the transition efficiency from V. to V2 will depend on the population of molecules in state V2, 1'. e. 1(1) = I.,-’ (b) where (1)2 is the angle between the molecular dipole direction 1120) and the probe polarisation direction at the time of absorption, see Figure 1.2. Substituting 1.20 (a) and (b) into 1.18 gives rise to the well—known formulation for the rotational anisotropy,32’36‘38 r(t) =1i0(1+3cos2¢2 (0)}. (1.21) From this expression it can be seen that the time-dependent rotational anisotropy signal can be described very simply by the orientation of the molecules relative to the polarisation of the probe. To average over the angular momentum j in the above expression, we begin by assuming that the molecule is a symmetric top with axes 5c, )3 and 2. The top motion is a Composite of two different types of rotation: the mutation of the figure axis about j at a rate (on = j/ii and the rotation of the top about its figure axis at a rate (0, = jcosO(1/ill - 1H1)» where ill and ii denote respectively the moments of inertia of 1116 molecule about its top axis and about any axis perpendicular to it.39 If x0 is the angle of rotation about the figure axis of the top at time zero and we define an angle 9 between 14 27:: i‘ -‘0 1‘9.“ ' \551 .- -La' .1153.“ _‘ '_ ‘?'~-3~.'H) the figure axis and the angular momentum j of the molecule, the equations of motion for the unit vectors along the top axes are as follows:21 £(t) = [cos(10 + a),t)cos(a),,t)— cos (9 sin(10 + a),t)sin(a),,t )1)? + [COS()[0 + a),t)sin(a),,t)+ cos 6 sin(xo + m,t)cos(a)nt)]}7 (1 .22)(a) +sin 63in( 10 +w,t)2 j/(t) = [— sing/0 +a),t)cos(a)nt)--c0319005(10 +a),t)sin(a)nt)]/\" + [— sin(10 + 0),! )sin(a),,t)+ cos (9 cos(10 + 0),! )cos(a),,t )1}; (b) + sin 19 cos( 10 + 0),!)2 2(t) = sinflsin(w,,t)X -sin19cos(w,,t)F + Z c0319. (0) Knowing the time evolution of the unit vectors along the top axes, the time evolution of an arbitrary vector can be predicted so long as its resolution in terms of the top unit vectors 56 , )2 and 2 is known. We can therefore use Equations (1.22) to evaluate the expressions in Equations (1.20). We need to consider two simple cases. First, (II, M) denotes the case where the dipole of both the pump and probe transitions are parallel to the figure axis (2 axis) of the molecule at time zero. The second case is where the pump and probe dipoles are perpendicular to each other at time zero and one of them is parallel to the figure axis; this will be denoted by (H, .L). For the (II, N) case, 111(0): 2(0) and 112(1) = 2(1). Similarly, in the (n, .L) case Mo) = 2(0) and 11,0) = 2(1). This gives” cos¢2(ll.ll) = cos(w.t) cos ¢2 (ll, .1.) = — cos(10 +w,t)sin(w,,t) (1'23) Combining these results with (1.21) yields”37 15 . s . .1 ' ‘0: vex " VII-n.e . U D f'i‘ fl (1“ ., ,1 K . ‘ 7‘: I]: :1 '3‘ cl '1 .1 -‘ 35 0.111 .’._ ‘1 r \ ‘rtnucukc 0 “"51"?“ m 1 . .- ‘IVIT 8:.qu n 102 . . " Mariano . l' ‘8‘ Fan'u “f‘LHk‘ ‘5. _r 'n. ., _ ‘ am 031 s... ..1' :5 1.) :“ —\h\mILai Ff. . 1 L 1.9.10 r”), (t ) = $0 + 3cos(2w,,t)) Zficos(21w.ot) (1.24) =— 1 3 j 10 + 2P.- .1 7 and3 ()> 1 Z P] 005(2jwr10t) (1.25) =—— 1+3 " 20 ZR. ,1 1.0.1 The quantity Pj denotes the rotational distribution of the species probed and the average over x0 is assumed to be uniformly weighted. Since cunt depends on j but not on G or m, only the j average is explicitly carried out in the last step. After such averaging, c0320“) + am), the only x0 dependent factor in (1.25), becomes 0.5. To explicitly show the dependence on j, 60,, has been replaced by jcono, where (one = 41tBj. Notice that the anisotropy in (1.25) is exactly —1/2 times that in (1.24). Similar j averages can be carried out for other more complicated cases. C. Dissociation When V1 is repulsive, the pump transition initiates a photodissociation reaction. It is for this application, termed femtosecond transition state spectroscopy (FTS), that pump- PTObe spectroscopy is particularly useful.4 As the name implies, the use of F TS to study a photochemical reaction allows one to directly monitor the progress of the reaction as it Proceeds through the transition state to products. 16 FOR In t 5—3“... F. _.....,. 1 . .'.-‘5 35:13:11 2 $5510 C“ ,,.. ‘.l :‘J 01 .111 $331101] 1 :24} 1111.): Figure 1.3 (a) illustrates the process. As discussed already for bound states, the pump is absorbed and produces a wavepacket on the excited potential surface V1, which then begins to evolve in time. In this case, instead of returning to the Franck-Condon region, some or all of the excited molecules will dissociate. As the reaction proceeds, the resonance condition It‘w = V2(R) —- V1(R) for the probe pulse will change; we can take advantage of this to determine the reaction dynamics. Classical mechanical methods”‘40 have been found to be quite effective in explaining dissociation dynamics as observed by F TS.”42 In this approach, the repulsive surface is usually modelled as a simple exponential V.(R) = A.+V.(R.)exp[—5:[:15'—] (1.26) where V, (R) is the potential energy of V1 when the dissociating fragments are a distance R apart along the reaction coordinate and R, is the internuclear separation at the moment of excitation by the pump. The parameter L1 is a measure of the steepness of the potential, i. e. how rapidly the molecule proceeds towards dissociation. To determine the motion of the molecule along V, as a function of time, a simple impulsive classical model is used. Assuming that the change of potential energy during the reaction is a consequence of conversion to kinetic energy of the dissociating fragments 1 dR 2 = _ ._ .27 E V,(R)+2,u( d!) , (1 ) 17 v vk (3) >3 OD t— D :2 SJ '23 '33 r: 0) H 0 On hc/l, (b) Figure 1.3 Clocking figure. (a) Potentials involved in clocking experiments. Excitation from V0 to V1 by an ultrashort pulse produces a wavepacket on V1. As the probe is tuned to shorter wavelengths, the wavepacket traverses the Optically coupled region for the V. —> V2 transition at greater pump-probe time delays and the transition state more closely resembles the products. (b) Transients obtained at a range of probe frequencies. When the probe is tuned to be resonant with the transition state immediately after time zero, the signal forms and decays rapidly. As the time taken for the wavepacket to reach the Optically coupled region increases, the resonance condition for the asymptotic products is approached and the signal no longer falls to zero. 18 .q o 37". u n- 1 o 1 F n ".9 ti U Lu'\ J .- - 5”,)! $.41.»- 55... \‘.. 1") \‘ .‘Ml‘u a [45‘ “k“. v ‘w. . "‘ ‘1—5 s, . I’ 'Ltk I. .‘ a. -. . . 4‘ 1 . ‘A “‘51“ 1‘ where ,u is the molecular reduced mass and V(0) = E. We can relate the terminal velocity v, of the fragments to the change in potential energy during the reaction, since v, = \f(2E/,u). Separation of variables and substitution for V1 (R) from Equation 1.26 therefore . . . 4 gives, afier integration 3 R(t) = R, — L, ln[sech2 2113]. (1.28) which allows us to determine V1(t):30 V,(t)= Esech2[2v’l: J. (1.29) If we select the frequency of the probe laser to correspond to the resonance condition at some arbitrary internuclear separation R > R), the time-dependent signal intensity I(t) affords a direct measure of the reaction dynamics. Figure 1.3 (b) shows typical transients for several values of a) (and therefore R). The signal will initially be zero, then rise to a maximum when the wavepacket traverses the optically coupled region for the probe frequency, falling off again as the molecules proceed to dissociation. If the probe frequency selected is at the asymptotic limit, i. e. a) = a)(oo), see Figure 1.3 (a), the resonance will correspond to absorption by one of the fragments; the time taken for the Signal to build will therefore yield a dissociation time for the reaction. At intermediate frequencies, the time required to reach each resonance point is determined by the slope of the potential to that point; a series of ‘off-resonance’ (with the fragments) experiments can therefore be used to map the shape of V1. If there is a crossing on the potential, a 19 ~Jq’)‘ .. .. -. J 15“»).9 v".'-.>“".’;' 1 d".......- .. v 5.131 film I a]. n. j barrier may be formed as in the case of NaI dissociation, for example;3 0‘41““ in this case, the wavepacket will oscillate in the bound portion of the potential with some molecules proceeding to dissociation each time the crossing region is traversed. The effect of this kind of process would be to produce oscillatory behaviour of the type shown in Figure 1.1 (b), superimposed on the clocking transient. By this method, information about the time required for the reaction to occur, as well as the shape of the reactive PES can be obtained.3°““’42’44’4649 Direct probing of the transition state (the ‘off-resonance’ probing) is of particular significance because it is extremely difiicult to examine the processes occurring during a reaction by any other method. D. Bimolecular Reactions Equation (1.14) can equally be applied to any of the cases we have discussed by application of the right wavefunction WM) and judicious selection of the form of the potential surface. In principle, bimolecular reactions can be investigated by pump-probe spectroscopy in the same way as any other process. In practice, however, they are more difficult to describe and study. This is because in order for a bimolecular reaction to occur, there has to be an interaction between the reacting species. We cannot then simply define ‘time zero’, the initiation time of the reaction, as the moment at which the pump pulse is absorbed, because there may be a delay between excitation and the time when the molecules come into contact with one another. One approach that has been used to overcome this is to begin with dissociation of a precursor to produce one of the reactants, 20 I ‘ . _ 5 oh) , I ' P 3.11 1 i_._ .. '. .. L ' 1:131. I: _; imp-pr T: T1“. M - ‘- ..-.. L41 \ I II p ‘1‘“:- ‘;‘~r “13111 which then immediately undergoes a reaction with another part of the precursor to form the product of interest.48‘50‘58 Laser-assisted reactions of this type have the advantage of defining both the time zero and geometry of the reactants within a limited range. However, the presence of another species in the complex influences the reaction 59-61 dynamics, and the presence of a bond in the initial complex means that the reaction is not truly bimolecular. It has been known for some time that two species in close proximity can collectively absorb radiation and both be excited by a single photonf’“37 Photoassociation occurs if a bond is formed by this process.2’65'7O Bimolecular reactions can therefore be studied by the pump-probe method if the pump pulse causes photoassociation. In this case, because the bond can only be formed in the presence of the exciting radiation, the initiation time could be defined very precisely without restricting the course of the reaction. This not only allows the observation of dynamics in the resulting product(s) but also enables us to directly measure the time taken for bond formation. There is however a drawback in using ultrashort pulses to study this type of reaction, which is that we are restricted to those reactive pairs that are close enough to each other during the pulse to form a bond. In the case of a pulse having a very short time duration, this means that the number of possible associating pairs could be prohibitively small. In a photoassociation reaction, the ground state potential surface V0 is repulsive or weakly binding and can be approximated by a Morse potential with a very shallow well. The difference between this and the excitation of a bound state is that the ground state 21 er 113.16. E ..— ;#-n sOlk‘) ‘;“-luttt 2:3: bet 11.4 Detecti it"; 1"}. ,x ’ blush ~'.-- ~ . git I: LbCI may. '_ ' ‘ «affailt C1 and 10 $3.25 on a S M1011. L 3; ‘1 2;, .1 . Mammy: 11, “‘3 .idl'am “if? :11: 5‘3in w wavefunction is a thermal ensemble of scattering states rather than a single eigenfunction of the potential energy surface. Calculation of Franck-Condon factors for the transition from the ground to the first excited state is performed semiclassically.l2’69’7O Once this has been done, Equations 1.1 and 1.5 can be applied to determine ”11(0), the time-dependent wavefunction on the first excited state V1. The same methods as in the bound-bound case can then be used to model subsequent dynamics. 1.2.4 Detection Any detection technique that allows one to observe the efficiency of absorption of the probe is useful. The choice of detection method can therefore be made depending on the characteristics of the system under investigation and the dynamic properties one wishes 41,45,47 71-74 to investigate. Common methods include fluorescence, absorption, molecular ”'78 and ion photodetachment.49 Each of these methods beam and ionisation methods relies on a signal intensity that depends on the population of the probe state V2. In addition, there are scattering-type techniques that do not require absorption of a photon; impulsive stimulated scattering or degenerate four-wave mixing are examples of these.8'10 1.2.5 Advantages There are many advantages to this type of spectroscopy. The high peak intensities associated with short pulses allow multiphoton excitation and other nonlinear optical Processes to occur relatively easily, which makes reaction pathways available which might not be accessible otherwise. Microscopic, state-resolved dynamics are probed directly, Which circumvents difficulties and the associated errors in converting from PBS 22 SLIILCPS 10 «i 1" 111.1" J ti . ‘ ‘ I 72.21: ~12>01 1:21:11} t] :Lspredxk timedcpcn r: spied \c‘ I»). 1.1.1.81 all I Lice-rent 1‘1".) 1;). . " : ‘ NHL": \ J ‘9‘“2‘10 ‘. ‘ ~15 list “I calculations to dynamic information.12 In a similar vein, it is intuitively more logical to think of dynamics in a time-dependent framework than as the Fourier transform of frequency-resolved results. Theoretical modelling of pump-probe experiments is further simplified by the fact that in many cases the wavepacket behaves as a classical particle, as first predicted by Schrodinger79 and Ehrenfest.80 It thus becomes possible to describe the time-dependent behaviour of the wavepacket using semiclassical methods; this has been applied very successfully.”"6"8‘22 Another area of much interest is the control of photochemical reactions; there are - 12,81-91 - 11.92-97 - many theoretical and expenmental studies of the problem. Ultrashort pulses are potentially very useful for this purpose for a number of reasons. The short temporal duration is faster than the time scale of most molecular motion, allowing the possibility of reaching a particular state or mode before intramolecular vibrational redistribution (IVR) can occur. Sequences of pulses can thus be used to control the exit channel of a particular reaction.8’”’82'85 This method becomes even more powerful when combined with the ‘tailoring’ of pulses by control of phase,92‘93 temporal and/or frequency 11,85,87-89 88,97,98 components and chirp. 23 :1IheOsc Th»: laser u .112." lac: if i... 514 nm .1 '1 .1 qrfm, ‘ r35 327112011013 7156.22 1111016 1131*: are her Li‘ZIlEUOUS inn relati ax a salt 3.3-ditl5}l(1xa “it absort T512011 satur 2:" nd ea: 3311135111 9,, ~ K «n 1", .an will rises a 3181 r in) collidi. fih mp 1m 2. LASER SYSTEM 2.1 The Oscillator The laser used to generate femtosecond pulses is a home-built colliding pulse mode- locked laser (CPM). The heart of this system is a gain dye jet which is optically pumped by the 514 nm line of a continuous wave (cw) Ar+ laser; broad-band fluorescence from the dye propagates in both directions around a ring cavity. The dye used is rhodamine 6G tetrafluoroborate, a xanthene-type dye which absorbs light between 450 and 550 nm to produce fluorescence over the visible region of the spectrum. Typical Ar+ pumping powers are between 5.0 and 7.0 W over all lines. The light that is produced in this manner is continuous wave and multimode, each longitudinal mode having a phase that is arbitrary relative to the others. Pulse formation is caused by the second jet, which contains a saturable absorber. This is a dye that has an intensity-dependent absorption; 3,3'-diethyloxadicarbocyanine iodide (DODCI) is used. Light of relatively low intensities will be absorbed, but as the intensity of the incident light increases, the absorption transition saturates and allows some of the light to be transmitted. This is amplified at the gainjet and easily saturates the absorber at the next round trip; the process continues until the gain is saturated. Once this occurs, all the modes allowed by the cavity in both directions will have a maximum in the saturable absorber jet, at the same time. This produces a system of counter-propagating pulses which coincide in time and space, hence the term colliding pulse. The saturable absorber will absorb the leading edge of the pulses on each trip until the dye becomes saturated by the more intense portions of the pulse. 24 712 2311 "T" ‘1 1. 1 . ' “"*~“i ‘ iiiiitni v, ‘ "r “1 01 . V" . Hill-"W The trailing edge will be chopped at the gain jet, which is also saturated by the intense portions of the pulse; the trailing edge will consequently not be amplified. The net result is a shortening of the temporal width of the pulse and a concomitant spread in the spectrum. Stable operation of the mode-locked laser requires that the intensity at which the gain dye saturates is higher than the intensity required to bleach the saturable absorber. The optimal arrangement is thus to allow the pulses to coincide in the saturable absorber and to be as far away from each other as possible at the gain dye jet. This can be achieved by ensuring that the saturable absorber and gain dye jets are 1/4 of the cavity length away from each other. The cavity length of the CPM used for these experiments is 3.3 m, which produces a repetition rate of 100 MHz. The light produced by the CPM oscillator is centred at 624 nm and has an average power of 20 mW, which corresponds to 240 p] per pulse. In order to do spectroscopy, we need higher pulse energies. This requires amplification of the pulses. 2.2 The Amplifier T0 amplify the output from the CPM, a dye-based amplifier was constructed; a schematic is shown in Figure 2.1. Light from the CPM passes through four dye cells, Which are transversely pumped using light at 532 nm produced by frequency-doubling the OUIPUt of a Nd:YAG laser. The amplification mechanism is sketched in Figure 2.2. Absorption (a) of a nanosecond pulse at 532 nm excites the gain dye to the 81 electronic 25 Pd-fil- flIwR- 1:9.— --Uu-.—e—T.-:-u-dm- LIV. I. F.‘ n-Ah T.»- Fl 1‘ I . n“ a. 1 ~ MU a II PS to 1"“ Raw cut .1. PLUM. .miv .2 ...1 V U C) M N a _ B e e O Q U) 5 .D {U a .. F '5. 05'": sing/1.858 _ N Egsfiea N EmAEc/JQ 3 N v-s U (I) <0 :IQ 21:45:09 3 N _ N =-_‘ U 3D g E m. U 2, m I E. /[ 72 LL. F igm‘ e 2.1 Schematic of the amplifier. Four dye cells are transversely pumped by the Second harmonic of the Nd:YAG laser. Telescopes are used to expand both the pump and amplified beams. 26 .u‘“ 1 .uk. i,» .7353 i ,_ ,._ state; a number of rovibronic levels are excited, which undergo collisional relaxation (b) to lower energy rovibronic levels. Stimulated emission (c) from this state to excited vibrational levels of the ground state amplifies the CPM beam at 624 nm. Because the dye is in solution and has such a large molecular structure. a large number of rovibronic states are accessible to the CPM beam. This is important to ensure that the bandwidth of the amplified beam is not limited by the gain dye. Following stimulated emission, dye molecules eventually relax back down to the ground state. The Nd:YAG laser is run at 30 Hz and z 10.5 W with 5-7 ns pulses; this corresponds to an average pulse energy of 300 m]. The flow through the dye cells is such that the dye is completely replaced thirty times a second, so that each pulse of the YAG laser excites a fresh portion of dye. This reduces thermal distortion resulting from heating of the solution Figure 2.2 Sketch of the amplification mechanism by the pumping laser. The dye cells are of the Bethune prism type.99 This is a standard 45° right angle fused 27 silica prism with a hole drilled / through it to allow the dye to ,"’:~" ‘, I D circulate, see Figure 2.3. The Ox’/ — L; geometry of these cells is such that light incident on the front (plane) Figure 2.3 Detail of the Bethune cells. face of the prism is reflected internally so that dye inside the channel is illuminated evenly from all sides. This is advantageous because it minimises distortion in the amplified beam caused by uneven excitation of the gain dye; it also renders the amplifier less sensitive to imperfections in the mode of the pumping laser. The output beam profile is also improved by the use of spatial filters. Two diamond pinholes are used for this purpose; one between the first and second and the other between the third and fourth stages of the amplifier. Diffraction rings from the pinholes are used to help in properly aligning the input beam through the dye cells. Cylindrical lenses are used for all stages except the third to focus the NszAG beam to a line at the dye cells. The gain dyes used in the amplifier were Kiton red in the first stage and sulforhodamine 590 in the remaining three; in every case, the solvent is water containing 15% Ammonyx LO (lauryldimethylarnine oxide). Kiton red is chosen for the first stage because it has a lower absorption at 624 nm than sulforhodamine, which is more suitable for the later dye stages because it minimises distortion due to wavelength-dependent gain,'°°s'01 Dye concentrations are chosen to give the maximum possible gain at each Stage With as little absorption of the femtosecond pulses as possible. If or is the absorption 28 coefficient in mJ/mm2 for the pump light and Zr the diameter in mm of the beampath through the dye cell, it was found that a concentration which gives err = 1 is - 99,102 optimum. Spontaneous emission from the dye molecules occurs in the cells; this fluorescence can also be amplified, to produce amplified spontaneous emission (ASE). Because this is not a coherent process, it produces noise in the output of the amplifier and limits the gain. ASE is reduced by ensuring that r « L, where L is the pathlength of the CPM beam through the dye cell,'00"03 and by the use of a saturable absorber jet after the second stage. The saturable absorber acts as a temporal filter in a similar way to the DODCI jet used in the CPM. Malachite green dissolved in ethylene glycol is used, because it has a picosecond absorption recovery time104 and thus discriminates against the ASE, which has a nanosecond pulsewidth, relative to the femtosecond pulses. Correct synchronisation between the femtosecond and amplifying lasers is necessary to ensure amplification, and is achieved by the use of a photodiode to detect the femtosecond pulses from the CPM. The electronic signal from the photodiode is amplified and used to trigger the Q-switch impulse of the YAG (see Figure 2.4). The time delay between the pulse arriving at the photodiode and the triggering of the Q-switch on the YAG is manually adjusted using a commercial SM-l unit. The velocity with which light will propagate through a medium is determined by the fre(lufifllcy-dependent refractive index n(a)) of the medium. The difference between this velocity and the speed of light in vacuum can be expressed in terms of a phase shift ¢(w): 29 Figure 2.4 Experimental setup. A pulse from the CPM is collected by a photodiode. The Nd:YAG laser is triggered by the amplified pulse from the diode; an SM-l unit is used to synchronise the pulses. After amplification, the CPM beam is recompressed and steered to a Mach-Zehnder interferometer having a fixed arm and a scanning arm. One arm is frequency doubled, and the two beams are linearly recombined before being focussed into the sample cell. Signal is collected as fluorescence by a monochromator and PMT then averaged in a boxcar before being sent to the computer. The boxcar is also triggered by the CPM. 30 é—zn— A— ,li tuba-d FF— v f _1 l A (V .uduUXn vi - "aim—4% Ba 538QO 0583mm Hum. ENC N 35:58am _ . . J 00m...— ,/ J r.— I g H A ‘ K / Figure 2.4 humawu w<> 31 .1; be 2 fl ate-'5'- (his 1, such [ha (3,1) mfil' 1611i“ C" Eight from dGVD.C FMSIBIU phenomen' (1116 signi :hplilier. lowers the in the am; diet amp. pulses to l he compc Can introd At the atw)=—fwn(w). (2.1) where L is the pathlength of the light through the medium and c the velocity of light in vacuum.43 ’105 As the amount of material through which the pulse travels increases, there will be a frequency-dependent phase shift in each frequency component relative to the others; this is termed group velocity dispersion or GVD. If we define the group velocity vg such that v8 = fi— , where (15(0)) = [gig—j , GVD is produced by non-zero ¢”(a)). a) a) ,1 GVD may be either positive or negative; in general most transparent media exhibit positive GVD for visible light, in which the phase shift increases with frequency. As the light from the CPM travels through the amplifier, it will experience a substantial degree of GVD, or chirp, as a result of the large amount of glass and water through which it passesfl"OOJOZ’IO‘“O6 The effect of GVD is to temporally broaden the pulse.'06 The Phenomenon becomes more important as the spectral width of the pulses increases and is Quite significant for femtosecond pulses, which have a substantial bandwidth. Inside the amplifier, this is actually an advantage because it temporally broadens the pulses and thus l()W'ers the peak intensity, which reduces problems due to high intensity nonlinear effects in the amplifier media. However, a compression stage is necessary to regain short pulses afiel‘ amplification. A double-pass prism pair arrangement is used, which allows the PUISes to be recompressed by introducing negative GVD. However, only linear chirp can be cOlripensated for in this way, so care should be taken to ensure that processes which can introduce nonlinear chirp into the pulses are minimised. At the high peak intensities inherent with a femtosecond pulse, nonlinear optical 32 {(25563 b "at to dist risiiour O 7.971: balanc “iié'dblc diam u 9;; To redu M5 the Ifi-‘raxirttzitt 3105mm d J m) st. for Whip}. ““65”" a: k a pn idle bum liii‘nsities ( 235%: is Sclt‘ 3153516131 2‘3 Pillset processes become significant. This can be a problem because many of these processes lead to distortion of the beam profile and can affect both the temporal and spectral behaviour of the laser.43 ’99'104’mé‘107 Thus in the design of the amplifier one must strike the right balance between amplification of the pulses and limiting those processes which are undesirable. To reduce intensity-dependent distortion effects, the amplified beam is expanded as it passes through successive stages of the amplifier. The beam from the CPM has an approximate diameter of 0.75 mm; this is expanded by a factor of 12 in total, resulting in an output diameter of 9 mm. Relatively low intensities of pumping laser are incident on the early stages of the amplifier to reduce nonlinear frequency generation mechanisms, for example self-phase modulation (SPM), which also cause nonlinear chirp in the pulses.'°0"°4 This has the further advantage of reducing gain saturation in the dyes, which can be a problem because it limits the gain and distorts the pulse profile, through spectral hole burning for example.104 As the beam becomes larger in diameter, greater pump intensities can be used. In the last stage of the amplifier, the intensity of the pumping laser is selected so as to saturate the gain dye; this renders the intensity of the output Pulses relatively insensitive to fluctuations in the power of the Nd:YAG laser. 2-3 P ulsewidth The pulses produced from the amplifier typically have a power of 8 - 12 mW; at a repeti‘iion rate of 30 Hz, this corresponds to z 300 u] per pulse, an amplification factor of 33 11 This is 23163110 Literate 11 :mpress {3.0: a pri erasemen U “titre d is 1 1filtratels TO 61131 {mural an h is 3 me teamed W32 106. This is more than adequate for most spectroscopic measurements. There is another consideration, however; the temporal width of the pulses. GVD introduced by the dispersive media of the amplifier may broaden them to as much as 600 fs. In order to recompress the pulses we must compensate for this broadening by introducing negative GVD; a prism pair is used, in the arrangement shown in Figure 2.4. For this type of arrangement, the expression for (15" is as follows:'08 (tr—413 —dn'2+L 137—m” 1——1—-— (2 2) p 722:2 1+)?2 n2(l+n2) . where d is the distance between the prisms at the apices and L is the amount of glass the light travels through. To ensure proper recompression of the amplified pulses and to determine their temporal and spectral width, a frequency resolved optical gating (FROG) system is used; this is a method by which the spectral and temporal intensity profile of a pulse can be determined in a single shot.'09‘”0 A Clark-MXR FRG-l system was purchased for this purpose. Frequency resolved optical gating takes advantage of the instantaneous response of a nonlinear optical medium to the intensity of light incident on it. The method works by dispersing an autocorrelation trace, thus producing a trace of intensity versus frequency and time: 2 l(w,r)= °]E(t)g(t—r) exp(—ia)t)dt , (2.3) 34 Figu titre £11) iW 11111: Wham mated by I 1111), an . mhmmi CCD Camera \ Beamsplitter Polariser C _ V Quartz plate P Spherical lens W 1/7/ n \e....,, Polariser \ '7 ‘ Spherical lens 1"" 1 . . : /. Cylmdncal lens 1 Variable delay Figure 2.5 Schematic of the frequency resolved optical gating (FROG) system. where E(t) is the electric field of the incident pulse and g(t-r) is a gate pulse with variable delay.'°9’”° The Clark system uses a polarisation grating effect; a schematic is shown in Figure 2.5. The beam is split into pump and probe pulses, with the pump being significantly more intense than the probe. The polarisation of the probe beam is rotated so as to be at 45° relative to the polarisation of the pump. Each beam is then focussed using a cylindrical lens and overlapped in a second-order nonlinear optical medium (a quartz plate is used). When the pulses coincide in space and time, an optical Kerr effect is Produced; the pump pulse produces an anisotropic change in the refractive index of the ”1 A second polariser in the path of the quartz, thus rotating the polarisation of the probe. Probe beam is crossed with the first so that only the portion of the light field that was 1‘ Otated by the quartz plate is transmitted. Because each beam is focussed to a line, there Will be an intensity autocorrelation across the medium produced by the delay between each position on the line. This encodes temporal pulse information horizontally. 35 Li‘r‘eqllfi :::;221C\' at to det: EEC-35 for I steam in I Subsequent dispersion of the autocorrelation trace produces a spectrogram with frequency information encoded vertically. The result is the FROG trace, which allows one to determine the time-dependent frequency profile of the input pulses. Typical FROG traces for Gaussian pulses which are unchirped and positively and negatively chirped are shown in Figure 2.6. l (a) (b) (c) Figure 2.6 Typical FROG traces, showing (a) negatively chirped, (b) unchirped and (c) positively Chirped pulses. The chirp is altered by translating the Prism P2 across the beam as shown. By this method, the degree of chirp remaining in the pulses after recompression can be monitored; linear chirp is compensated for by lateral translation of one of the compression prisms. A certain amount of nonlinear chirp may also be present; this cannot be compensated for in a simple fashion, but with a Properly adjusted oscillator and amplifier will be minimal. The pulses produced by our CP M and amplifier setup are typically approximately 60 fs in duration. 36 LiExp Arie: sfin‘n .‘Jr‘ 31.11.51. its is Edi 53PM 03.113311 1 ittiical l1 smog: iii! pm it deter 2.4 Experimental Setup and Detection After recompression, the beam is steered to a Mach-Zehnder interferometer arrangement (see Figure 2.4). A beamsplitter is used to divide the beam intensity; to allow variable pathlength, a portion of the light is sent to a retroreflector mounted on a moveable platform. The other beam traverses a fixed path and the two beams are then collinearly recombined. If necessary, one or both beams can be frequency doubled using a second harmonic generation (SHG) crystal. The overlapped beams are focused into a sample cell and the fluorescence produced is collected perpendicular to the path of the laser. Detection is performed by a monochromator and PMT and the signal collected by a boxcar linked to the computer. The spectrometer used is a SPEX 270M imaging spectrograph with two gratings, one with a blaze wavelength at 630 nm and the other at 250 nm. The appropriate grating is selected depending on the wavelength of the signal to be detected. 37 3.1 Int1 3.1.1 P111 Phdh fit fem: fafi‘dUCilt is. C l melted {if 1110 c; Elation 3. PHOTOINDUCED MOLECULAR DETACHMENT 3.1 Introduction 3.1.1 Photoinduced Molecular Detachment Photoinduced molecular detachment occurs when photolysis of a molecule results in the formation of another molecule as one of the fragments. Examples include the production of H2 from photolysis of CH3NH2,“2 H20 and HzCO molecules113 and lBr from CHZIBr.114 Unlike most photodissociation processes, where only one bond is involved, molecular detachment (also called concerted elimination) requires the breaking of two existing bonds in addition to the formation of a new one. Understanding of this type of process thus represents an interesting and challenging area of research. Since the l 5 ground-breaking work of Woodward and Hoffrnann on pericyclic reactions, 1 much attention has been focussed on these reactions, particularly the mechanisms by which they proceed.1 1642' 3.1.2 Concerted Reactions Multibond reactions can be divided into two categories; sequential (also called stepwise) and concerted. A reaction is defined as concerted if it proceeds via a single kinetic step, whether the bond breaking and formation processes are simultaneous or not. 1 15-117,119 However, since little is commonly known about the transition state region of the potential energy surface in many reactions, it is difficult to determine a priori whether 01‘ n0t more than one kinetic step is involved in a given reaction. The existence of a plateau or local minimum in potential energy along the reaction coordinate would 38 333m 111 L the re; a redistribt i111 c011 fCItil‘idlio; Casi] frag 331360 It halt bee The: 1 Exam and {10m however be expected to result in formation of a species intermediate in some respect between reactant(s) and product(s). For this reason, a reaction is defined as concerted if it proceeds without forming a stable intermediate. In general, reactions which have an experimentally observable intermediate are considered to be non-concerted, i. e. stepwise. This observation may be direct, the appearance of a transient fluorescence for example, or it may be indirect, as in the measurement of fragment scattering angles and momenta from molecular beam experiments. In order for a photodissociation reaction to be concerted, a number of conditions must obtain. The excitation must be in a restrictive Franck-Condon region to ensure that the parent molecules have a narrow spread along the reaction coordinate and move in phase as the reaction is initiated. The repulsive potential must be somewhat uncoupled from the rest of the molecule and the excitation energy sufficiently high above threshold to prevent redistribution of energy between other modes during dissociation. It is to be emphasised that concerted reactions are not necessarily simultaneous, i. e. bond breaking and/0r formation processes may not all progress at the same rate. The important factor is that each fragment proceeds along a potential energy surface that is purely repulsive with respect to the parent molecule. Although many reactions are thought to be concerted, few have been unequivocally demonstrated to be so.i The reaction of interest to this study is the molecular detachment of a halogen ' E:Xceptions include the elimination of molecular hydrogen from 1,4-cyclohexadiene'20 and from st.‘2‘ 39 "nation 1 1135101 ’I; fr: math} 3511611 6X mean 0 lite-med . 1.329. "77‘; .K~§! , Stud 2?, ; HI? possibl “315151121115 molecule from a dihaloalkane: RCHXY + hv—) RCH + XY, where X and Y are halogens. Molecular photodetachment of halogen molecules from dihaloalkanes has been investigated in several systems.”3 '“4’122'128 In general, molecule formation is observed only at high excitation energies and is usually a minor channel. Most of these studies have specifically examined the molecular photodetachment of 12 from methylene iodide (CH2I2).l ”"22"” We will begin with a discussion of this molecule and then examine its analogues. 3.1.3 Methylene Iodide The spectroscopy and photodissociation of CH2I2 have received a great deal of attention over the past two decades or so.7z"24"26"28"4' Most of these studies are concerned with the photodissociation dynamics of low—lying excited electronic states,72’129'I39 which dissociate to produce CH2I and I fragments with I in either its ground 2P3/2 state or its spin—orbit excited 2P1/2 state. The possible photolysis products of CH2I2 and corresponding energies are shown in Table I- Although it is thermodynamically possible to form 12 when CH2I2 is excited at any waVelength below 333 nm,'32"33"35 this product has only been observed for excitation wavelengths in the range 125 - 200 min-125,133 40 :15: 1. MN ’________ Channel lponh 31d [2. it ifQ‘Onit‘a tiered Ill”- Table I. Photodissociation reaction pathways of CH2I2,I30 Channel Products Energy Required (eV) cm'1 1 CH2I+ I (‘P3/2) 2.22 17,900 2 CH2I +1* (‘13.,2) 3.17 25,600 3 CH2( 52 3B.) + I (212m) + I (2P3/2) 4-94 39,800 4 CHzOZ 3B1) + 1 (2133/2) + 1* (2P1/2) 5'88 47,400 5 CH2 (5 'A.) + 12 (x ‘22,) 3.72 30,000 6 CH2(b lBt)+l2 (x 12g) 4.60 37,100 7 C1420? 31304.12 (A 31'1“) 4.84 39,000 8 CH2 (X 3B1) + 12 (B 3n“) 5.33 43,000 9 CH2 (Si 3B,) + 12 (D' 3mg) 8.4 67, 750 Upon high energy excitation, CH2I2 undergoes molecular detachment to yield CH2 and I2, i.e. CH2I2 —> CH2 + 13.122426 The iodine molecule produced is highly electronically excited and fluoresces in the 340 nm region of the spectrum. Black126 Showed that the 340 nm fluorescence, which is due to the 12 D' ——> A' transition, reaches its maximum intensity within 10 ns of excitation, which is considerably less than 50 us, the mean collision time under the experimental conditions. This suggests that 12 formation is a primary event. When CH2I2 was irradiated with a Kr resonance lamp (emitting at 116.5 nm and 123.6 nm), Okabe et al.124 observed weak fluorescence bands in the 180—240 nm (12 H—aX), 250—300 nm (12 F—>X) and 450—500 nm regions in addition to the dominant I2(D’ —-) A') fluorescence between 290 and 345 nm. The 41 — a" -,: ‘1)— .-5 " ~0“"J' .‘ _ _.1.. k ‘.:._l . H «with T‘s-r- o 1‘ Methyl U 3.1-Ext -\lr quantum yield for the strongest I2 fluorescence was measured to be less than 1%.‘24’126 The 250—300 nm and the 450—500 nm fluorescence systems were found to be at least another order of magnitude weaker than the 290—345 nm fluorescence, while the 180— 240 nm fluorescence is the weakest of all.‘24 12 fluorescence resulting from two—photon excitation of CH2I2 at 248 nm as obtained by Fotakis et al.‘25 revealed a completely different intensity pattern, with the F ——> X fluorescence being the strongest. The two photon absorption was thought to cause a two — electron excitation of CH2I2.'25 Fotakis er al. also observed extensive fragmentation of CH2I2, leading to the formation of CH and C fragments. The results of a study of the molecular detachment of a halogen molecule from dihaloalkanes will be presented. Femtosecond pump-probe methods were used in an attempt to elucidate the mechanism and dynamics of this reaction. 3.2 Experimental All experiments were performed on neat vapour (~ 0.1 — 10 Torr) of the relevant alkyl halide in a static quartz cell. The cell is comprised of a bulb, which is used as a reservoir for the condensed phase of the sample of interest, and a tube 2-4" in length, which has flat windows and acts as the laser interaction region. Afier samples have been loaded, the cell can be attached to a vacuum line for evacuation and then closed off using a Teflon- seaJed Kontes tap. When necessary, cold baths were used to lower the vapour pressure of the Sample. Copper or dehydrated sodium thiosulphate were used as scavengers to 42 prevent the accumulation of molecular halogens. The pump pulse for these experiments was the 312 nm second harmonic of the amplified CPM, which initiated the reaction by multiphoton excitation of the sample vapour. The dissociation products were detected by fluorescence. Spectra were recorded under excitation with 312 nm pulses only, and calibrated with Hg lamp emission. The 624 nm pulse at the fundamental of the CPM was used to deplete the population of halogen molecules in the fluorescent state. This acts as a probe of the temporal evolution of the reaction; sweeping the delay between pump and probe pulses thus allows a transient which reflects the time-resolved dynamics of the reaction to be collected. For each sample, the intensity of the probe beam was attenuated to the point at which no fluorescence could be detected when only the probe beam was incident. At each pump-probe time delay, signal is collected for ten laser shots; pulses that have an intensity greater than one standard deviation from the mean are discarded. Typical transients contain data from two hundred time delays and are averages of a hundred scans. 3.3 Results and Discussion 3.3.1 Methylene Iodide The dispersed fluorescence spectrum resulting from multiphoton excitation of CH2I2 at 312 nm is presented in Figure 3.1. Most of the spectral features can be assigned to fluorescence from nascent halogen molecules resulting from photodissociation of the parent. The principal fluorescent product is iodine in the D' state, which is an ion-pair state, i. e. it correlates to XI + X'.'42’m This is consistent with frequency-resolved studies 43 D' —> A' (12) Intensity (Arbitrary Units) 230 250 270 290 310 330 350 Wavelength (nm) Figure 3.1 Dispersed fluorescence spectrum of 12, produced by multiphoton dissociation of CH2l2 at 312 nm. The dominant fluorescence is between 290 and 350 nm and can be assigned to the 12 D' —> A' transition. A small amount of laser scatter is detected at 312 nm (shaded). The region marked (i) indicates fluorescence produced by other ion-pair states of 12 (see text). The fluorescence intensity has not been corrected for detection efficiency of the spectrometer. of photodissociation at high energiesm"25 The D' state of homonuclear halogens is optically inaccessible from the ground state, but the D' —> A' fluorescence is commonly observed when 12 is excited in the presence of buffer gasesm’m’I48 Under these circumstances the D' state is populated by collisional relaxation from other ion-pair states; this process is very efficient. However, for the current experiments the pressure in the reaction cell is ~ 1 Torr. This precludes the possibility of forming I2(D') by collisional relaxation, since the time between collisions at this pressure is z 130 us, which is much longer than the fluorescence lifetime of other ion-pair states (~ 10 ns).‘49 In addition, under experimental conditions a collisional formation process would produce a rise time 0n the order of 100 us. The observed signal had a very rapid (< 10 ns) rise time and was collected with a boxcar integrator having a 50 ns gate. 44 1“)! Q-.. a 5.2» Vet 0 l '1 ., F‘s" I C. no Qua; I fit"? 30 £03 4 ' l I—Jib'u 33.7: II 1' db Il‘f ‘. I‘. \\ in..- ‘90:“; ’,‘.‘ azimuth] Atnut- (xv shawl-nub an. nib-navtvlbt-Av-d-RI Figure 3.2 shows dispersed fluorescence spectra of the 12 D' —> A' transition; the spectra were all produced by photoinduced molecular detachment of 12 from CH2I2 in a static cell by multiphoton excitation at 312 nm. The 290 — 350 nm portion of the ambient temperature spectrum, as presented above (Figure 3.1), is displayed in Figure 3.2 (b). In order to verify that the observed vibrational distribution in the D' state is produced directly from the reaction and is not a consequence of collisional relaxation in the cell, the same spectrum was also recorded at 0 °C, and is shown in Figure 3.2 (a). To obtain this spectrum, the bulb containing liquid CH2I2 was kept in an ice bath but the laser interaction region was at ambient temperature, as before. The result of this is to lower the — (a) 0 C — (b) Ambient temperature - (c) 800 Torr Ar A A l A A 4“ k l 4 A h A A A A 1 A A A i A A A 290 300 310 320 330 340 350 Wavelength (nm) Figure 3.2 Dispersed fluorescence spectra of the D' state of 12. The spectra were produced by photoinduced molecular detachment of I2 from CH2I2 in a static cell by multiphoton excitation at 312 nm. The spectra are normalised and calibrated, but not corrected for detection efficiency of the spectrometer. Fluorescence Intensity (Arb.) (a) Spectrum recorded at 0 °C. (b) Ambient (room) temperature spectrum at 1 Torr. (c) Ambient temperature spectrum in the presence of 80 Torr of Ar. 45 "' ~. u .‘i ‘13) 21-0?» .,. an I .\ but r-unt u... {his 1‘! «o 1i AaU‘J-h ‘1“ A‘ I :11 I 3.7: PC It 762.58 i mix CH2I2 vapour pressure in the cell to z 0.2 Torr while retaining the same energetics of reaction. Comparison of Figure 3.2 (a) and (b) reveals that the spectra are very similar; we can therefore conclude that there is a negligible amount of collisionally induced vibrational relaxation in the 12 (D') molecules after formation. The D'—-> A' spectrum that would be produced by collisionally relaxed molecules was also recorded; Figure 3.2 (c) shows the dispersed fluorescence obtained from a sample of CH2I2 in 80 Torr of Ar at ambient temperature. The high pressure in this cell is expected to produce a Boltzmann population of vibrational states in the D' electronic state of 12. It is clear from Figure 3.2 (b) and (c) that the I2(D') population resulting from the photodissociation of CH2I2 can not be represented by a Boltzmann distribution, i. e. is non-statistical. This is important because it indicates that molecule formation is a primary process, rather than the result of secondary bond formation produced by (for example) collisions in the cell. The spectrum in Figure 3.1 also exhibits fluorescence bands between 250 and 290 nm; the integrated intensity of the fluorescence in this region relative to the 290 - 350 nm )’150 1:02;“) _) X('2+ ),150 08 region is approximately 10 %. The r(3ngg) —-) A(3l'I lu r(‘zgg) —> B(3ng),'5' g(0‘) —+ 3r1(0;,)'5° and (30,) —) A(1,,)'50 transitions of 12 8 fluoresce in this region. Okabe et al. also observed fluorescence between 250 and 300 nm 124 and tentatively assigned it to the F -—> X transition. The assignment of the states responsible for this signal will be discussed in detail later. 46 41.1] :\\ (I. . t ”1‘“ .. “'1‘ " K It:- h‘l ‘h . Time-resolved dynamics of the molecular photodetachment of 12 from CH2I2 have been recorded and analysed, both in the 290 - 350 nm region corresponding to the D' —-) A' fluorescence and in the 250 - 290 nm region. These results are discussed separately. A. The 300-350 nm Region; D'—>A' To confirm that the observed fluorescence does not originate from background 12 in the cell, time resolved data of the signal at 340 nm was recorded for two cells, each containing CH2I2 or 12. Figure 3.3 shows the situation for the I2 cell. When 12 absorbs a photon of energy 2 eV (provided by the 624 nm pulse), it is excited to the B state, as shown in Figure 3.3 (a). Absorption of an additional 4 eV from the 312 nm pulse causes excitation to the ion-pair states E and f (0;). These states have strongly fluorescent transitions to the A0,.) and B (0:) states; the transient obtained by detecting the 340 nm fluorescence from the f —) B transition is shown in Figure 3.3 (b). Because ground state I2 does not absorb at 4 eV, no fluorescence signal is observed from the iodine cell when the 312 nm pulse arrives first (negative time). As the pulses become overlapped in time (time zero), the ion pair states are populated and the fluorescence begins to appear. At positive times (624 nm pulse arriving first), modulation in the signal intensity can be seen as the pump-probe time delay is scanned. This is a F ranck-Condon effect caused by vibrational oscillation of the wavepacket prepared by the 624 nm pulse on the potential energy surface of the B state, as discussed in Chapter 1. 47 fjfi‘ Potential Energy (eV) l l . l . . l . l l 1 l . I n l I -500 0 1000 1500 Pump-Probe Time Delay (fs) I J \ r Fluorescence Intensity (Arb.) -1000 Figure 3.3 Excitation scheme and corresponding time-resolved (pump-probe) data for neat iodine vapour, showing how the observed transient is generated. (a) A 624 nm (pump) pulse excites 12 to the B state; subsequent absorption of a 312 nm pulse causes transition to the E and f ion-pair states. These have strong, bright transitions to the valence states A and B. The detected signal is f —) B fluorescence at 340 nm. (b) At negative times (probe pulse arriving before pump), neither the E nor f state is reached and no signal is observed. As the pulses become overlapped in time, it becomes possible to access the f state and molecular fluorescence is obtained. At positive times, vibrational coherence characteristic of I2(B) is observed.33 a P rub -2... J _. i.ul‘.".\ “it T: it'll ova-1w , -wh)I' , i123? ’j‘ 14bit i L 211,7), (D t 2'". q. o “ddii )\ . I Llii‘l‘n» I'L3bc By contrast, examine the transient produced from the CH2I2 cell, shown in Figure 3.4 (b). The pump pulse at 312 nm causes the parent molecule to dissociate, producing I2(D'), which is the source of the fluorescence signal. At negative times (624 nm pulse arriving first), 12 has not yet formed when the probe pulse arrives and a constant signal level is observed. At time zero, the signal from the CH2I2 sample shows significant enhancement _ in fluorescence intensity; this effect is not observed in the 12 cell. At positive times, the 624 nm (probe) pulse depletes the population of the D' state, causing a drop in signal intensity. Unlike the case of the iodine sample, however, the signal does not become zero when the 312 nm pulse arrives first; it is simply at a lower level. Figure 3.4 (b) also clearly shows vibrational coherence in the 12 fragment after photodissociation of CH2I2. Note that for the 12 vapour cell, vibrational modulation is observed only when the 624 nm pulse precedes the 312 nm pulse, while in the CH2I2 cell the opposite is the case. It is clear from the comparisons above that the 12 fluorescence signal being produced from the CH2I2 sample is a result of photoinduced molecular detachment of 12 molecules and not background iodine in the cell. The observation of modulations at positive times in the intensity of the D' —> A' fluorescence is very significant. The period of the oscillations is z 300 fs, which corresponds to a vibrational period of 12 in the D' state.'42"43 ‘152 This is important because it indicates that a vibrationally coherent wavepacket remains in the nascent iodine product afier dissociation; the observed modulations are due to oscillation of this wavepacket on the PES of the D' state. The initial coherence induced in the parent 49 Figure 3.4 Excitation scheme and corresponding time-resolved (pump-probe) data for CHziz. showing how the observed time-dependent fluorescence is generated. (I. P. refers to the ionisation potential of the molecule). (a) Initially, the molecule undergoes multiphoton absorption of the 312 nm (pump) pulse. This causes it to dissociate, producing 12 in the D' (31128) state, which undergoes a fluorescent transition to A' (3H2u) , detectable at 340 nm. (b) Absorption of a 624 nm (probe) pulse by the iodine depletes the population of the 13' state. Depletion efficiency tracks the progress of the reaction and is monitored by detecting the D'—) A' fluorescence at 340 nm. Note that the probe transition may not be as represented; there are a number of optically accessible 12 states 2 eV from the D' statelw’I48 At negative times (probe pulse arriving first), the fluorescence produced by the D' —> A' transition is unaffected by the probe, and remains at a constant level. As the pulses begin to overlap in time, an intense enhancement is observed; this is due to a cooperative multiphoton effect (see text). At positive times, absorption of the 624 nm (probe) pulse depletes the p0pulation of the D' state, and the fluorescence intensity decreases. Observation of vibrational modulation in the depletion signal indicates that a coherent wavepacket is generated in the D' state of 12. Note that for the 12 transient, positive time corresponds to the 624 nm pulse arriving at the cell first; for the CH2I2 sample positive time is when the 312 nm pulse arrives first. 50 CH212 12 (a) 12 — 11> — €10 - ¥ — 3 f t... 8 — (0+) 2 $ 7 H / _ 6 _ _ i=5 ’ D'(3I'I ) ‘3 4 — - 2g 9" 731(1B1) B(3H0u) 2 _ ~ _ X(1A ) ' 0 1 > A (3112“)fi‘ Reaction Coordinate Internuclear Distance )7 1 Fluorescence Intensity (Arb. -2000 -1000 0 (b) lllllllllllIllllullllllllllllllllllllll\ 1000 2000’ Time Delay (fs) Figure 3.4 molecule can only survive in this way if the nascent product molecules vibrate in phase, i.e. they must be formed within a short time of each other (the limit is a vibrational period) and on the same region of the reactive PES. Intermediate formation or redistribution of energy during the reaction would disrupt this coherence, preventing the observation of vibrational modulations in the signal. This phenomenon therefore indicates that the dissociation reaction is concerted. Figure 3.5 shows pump-probe data collected at 340 nm from the CH2I2 cell, along with a fit to the observed vibrational dynamics. The pump and probe lasers were polarised parallel to each other. The vibrational modulation dephases quickly and does not seem to recur (see Figure 3.3), so it was decided to fit the data using a damped sinusoidal function of the form: A + Be" / ’ cos(a)t +¢) (3.1) Where A and B are experimentally determined parameters, 1 is the dephasing time, a) the Vibrational frequency and (15 the phase. The exponential factor accounts for the effective dephasing of the vibrational coherence and the cosine factor describes the signature of the vibrational motion. The data shown in Figure 3.5 were fit using this model and were found to have an oscillation frequency of 92.2 cm", corresponding to a vibrational period Of 362 fs. This is the oscillation period of an iodine molecule in v = 28 of the D' state. Fourier transform analysis of the same data revealed a major contributing frequency at 97'7 Cm", less than 6 % from the fit result. The dephasing time from the sinusoidal fit w N . . . as “\- ] ps, whlch IS also corroborated by the Fourier transform. 52 E :5 —'—Datax10 —Fit E‘ m = 8 E 8 a 0 8 2 e a iiiiliiiiliiiilliiiiii1111111 -500 0 500 1000 1500 2000 2500 Time Delay (fs) Figure 3.5 Time-resolved data and vibrational fit to the D' —> A' fluorescence at 340 nm and positive times. The data was collected with the probe laser polarised parallel to the pump and fit to a function A+Be"’/ T cos(a)t+¢). The fit displayed was obtained with an oscillation frequency a) of 92.2 cm], corresponding to a vibrational period of 362 fs. The dephasing time rwas ~ 1 ps. The theoretical models of wavepacket propagation discussed in Chapter 1 (see Equations 1.9 particularly) apply only to the case where the probe pulse does not overlap the pump. They are unable to describe the processes that occur when pump and probe pulses coincide. The situation in this case is far more complicated and the simplifying assumptions used in Chapter 1 are not valid. When pump and probe pulses are incident on a System at the same time, coherence effects occur.8 Additionally, the intense radiation present in the time zero region causes a number of other nonlinear effects, such as coupling of electronic states by the electric field and cooperative multiphoton absorIDtion.153 These effects are only possible before the fragments have separated, so when they are observed they can be used to determine dissociation time. Figures 3.4 (b) and 3 -5 show that the 340 nm fluorescence signal from the CH2I2 cell shows a large e . . . . . . nharleement at t1me zero. This is of interest both because it can be used to yield 53 information about the electronic structure of the parent molecule and because it affords a measure of the lifetime of the transition state for the molecular photodetachment reaction. When pump and probe pulses coincide, the CH212 molecules absorb 312 nm photons and 624 nm photons simultaneously, which leads to an enhancement in the fluorescence signal if it opens up another reaction pathway for the production of 12(D'). We need to consider possible causes of the observed enhancement. Since the threshold for production of 12(D') from the photodissociation of CH212 is 9.4 eVm’m’ and the energy of a 312 nm photon is 4 eV, multiphoton absorption is required to produce the observed fluorescence signal. Reliable power dependence measurements for high order nonlinear processes of this type are inherently difficult because of the necessity for a wide dynamic detection range and because these types of processes can easily become saturated. However, absorption of two photons of 312 nm light is equivalent to an excitation of 8 eV, which is below the thermodynamic threshold for this reaction. Absorption of four photons, on the other hand, provides 16 eV of energy, which is well above the ionisation potential of this molecule. Three-photon excitation is therefore the most likely and the ensuing discussion is written assuming that this is the case . Figure 3.6 shows a schematic of the possible excitation schemes that can lead to enhancement of the time zero fluorescence signal. The decay time of the time zero fluorescent enhancement is directly related to the lifetime of the initial excited state of the parent molecule accessed by the pump transition (which we will call the pump-excited 54 state). The molecular dynamics are manifested as an asymmetry in the time zero peak; the decay time (on the positive side of time zero) is slower than the rise time. This allows us to determine an upper limit for the lifetime of the pump-excited state. It should be noted that the pump —- probe data at time zero measure the statistical lifetime of the pump- excited state, not the time taken to reach a particular region of the potential energy surface. This data thus contains no direct information about the exit channel dynamics, but can be used to measure an upper limit for the dissociation time of the molecules. In order to have the observed effect, the process responsible for the fluorescence enhancement must be of the general type shown in Figure 3.6, i. e. one or more 312 nm (pump) photons causes a transition to an excited electronic state. Subsequent absorption of 624 nm (probe) photons produces CH212 in a sufficiently high energy state to produce CH2 + I; (D'). There are a number of possibilities for this excitation scheme; the case When the transition state of the photoinduced molecular detachment reaction is accessed by a three-photon pump transition is shown in Figure 3.6.(c). However, other excitation processes are also possible at time zero. If the initial excitation is provided by absorption 0f one 312 nm photon, it requires three photons of 624 nm light to reach 10 eV, above the Observed threshold for production of I; in the D' state;124 four (plus the initial one photon at 3 1 2 nm) provides the same energy as three photons of 312 nm light. This is shown as SCheme (a). In either case, the state being probed is 4 eV above the ground state; observed molecular dynamics would give the statistical lifetime of this state. On the other hand, Figure 3.6 (b) shows the situation if the pump-excited state is reached by two pump 55 12 10 pump pump pump (a) (b) (C) Figure 3.6 Possible excitation schemes to produce time zero fluorescence enhancement. The threshold indicated is the observed excitation threshold for production of CH2 and 12(D'). The upper line on the figure corresponds to 12 eV, the excitation energy corresponding to a three-photon pump transition. G N «B Ox on I A ’ (a) One photon excitation with the 312 nm (pump) pulse requires three photons of 624 (probe) nm light to reach the threshold for production of I2(D'). An additional photon of the probe produces an excitation of 12 eV. Single-photon absorption at 312 nm is equivalent to an excitation of 4 eV, which is sufficient to reach the A (1B1) state of CPM; (marked (i) in the Figure). (b) An initial absorption of two pump photons corresponds to an excitation of 8 eV, requiring one photon of 624 nm light to reach the threshold and two to be equivalent to an excitation of 12 eV. The pump-excited state, marked (ii), is unknown. (e) A three-photon pump corresponds to an initial excitation of 12 eV. This is the pathway of the most interest to us because the dynamics observed between the pump and probe pulses correspond to the transition state of the photoinduced molecular detachment reaction. The state (iii) is the dissociative state under investigation. 56 photons. There are again two possibilities; a one-photon probe transition will exceed the threshold for production of 12 (D'); a two-photon probe transition accesses the same state that is reached by three photons at 312 nm. If this were the excitation scheme, the lifetime of the state 8 eV above the ground state would be reflected in the molecular dynamics. The scheme shown in Figure 3.6 (c) represents pump excitation to the state of CHzlz that we wish to examine. The lifetime of this state is probed by excitation by the 624 nm pulse to a higher energy state. We have observed a significant enhancement to the fluorescence at time zero even for quite low intensities of 624 nm pulses. This implies that the scheme shown in Figure 3.6 (a) is probably not a likely alternative, since it requires at least three 2 eV photons to be absorbed as the probe. Scheme (c) would allow the lifetime of the transition state to be determined; scheme (b) would yield molecular dynamic information characteristic of the lifetime of another electronic state than the one of interest. We cannot determine at this time which is more likely. However, it should be noted that because we are measuring an Upper limit for the dissociation time, the process that produces the depletion signal cannot be slower than the dissociation time measured using the transition state dynamics. In order to analyse the transition state dynamics of the reaction, a kinetic model was conStructed for the behaviour of the fluorescence signal as a function of delay time between the pump and probe pulses. Figure 3.7 illustrates the model. The observed tranSient can be modeled as the sum of two contributions. The molecular detachment Signal (a) will exhibit a step at time zero due to depletion by the 624 nm pulse. The time 57 zero fluorescent enhancement (b) can be represented as a Gaussian - type peak decaying exponentially at positive time. Figure 3.7 (a) illustrates the depletion signal. Three photons of 312 nm light are absorbed by CHzlz, which causes the molecule to dissociate, producing I; in the D' electronic state. Detection of fluorescence from the D' —> A' transition at 340 nm allows reaction dynamics to be probed by monitoring the amount of D' state population depleted by a second femtosecond pulse at 624 nm. When the 624 nm (probe) pulse arrives before the 312 nm (pump) pulse (negative time), it does not affect the intensity of the fluorescence. Since it is the nascent product that is being probed, depletion starts to become possible once the probe pulse arrives after the molecules have formed, in other words once the delay time between pump and probe pulses is sufficient for dissociation to have occurred in the meantime. We have assumed that this begins to happen at time zero, i. e. when the pulses are overlapped in time. Assuming a delta function pulse, if the molecular response were instantaneous the result would be a step function. To model the dissociation time, the step function is multiplied by an exponential decay. This produces a constant signal at negative times, followed by a gradual drop in signal level beginning at time zero as depletion becomes possible. To account for the temporal width of the Pluses, this function is convoluted with a Gaussian; the resulting curve is shown in Figure 58 Depletion signal (a) T probe _ \ T - l 12 (D') + CH2 x g(A5+CH2 I Csz 0 CH I * *4: . . 2 2 \ CHZIZ 'l' Time zero srgnal (b) _ _ 1' probe 12 (D!) + CH2 A ’ 5(A3+CH2 $t Total signal (c) —» k ‘ + t 0 Figure 3.7 Kinetic model for the dissociation of CHzlz. The model assumes that the signal is comprised of two contributions: (a) Depletion signal, produced by the molecular detachment process. Excitation of CHzlz with three photons of 312 nm light produces an excited molecule, which dissociates into CH2 and 12(D'). Depletion of the D' fluorescence with a 624 nm pulse probes the dynamics of formation of 12(D'). (b) Time zero signal. When the pump and probe pulses coincide, it is possible for CHZIZ to absorb probe photons prior to dissociation, which produces a highly excited parent molecule. This increases the amount of D' —) A' fluorescence observed because it opens another pathway for production of 12(D'). The statistical lifetime I of the pump-excited state determines for how long after the initial excitation the molecule can absorb the probe. (c) The overall signal is a weighted sum of these two contributions, each of which is convoluted with a Gaussian to simulate the pulsewidth. 59 To model the intense time zero feature, a similar approach was used. In this case, there is no signal at negative times. When pump and probe pulses coincide, a cooperative (multiphoton) effect occurs and fluorescence is produced. As with the depletion process discussed above, we have assumed that this occurs at time zero and that the point at which signal levels reach their maximum value corresponds to time zero. As the time delay between pump and probe pulses increases, the molecules begin to dissociate and the multiphoton signal enhancement is no longer possible. Thus the time zero feature can be represented as a half exponential function; no signal at negative times, then a step to maximum signal levels at time zero, followed by an exponential decay. Again, this is convoluted with a Gaussian to account for the temporal pulsewidth; the result is shown in Figure 3.7 (b). The overall signal should then behave as a weighted sum of contributions from the depletion and time zero features as shown in Figure 3.7 (c). For simplicity, variations in the signal caused by rotational and vibrational motion of the nascent products were not included. The model does not take into account the possible presence of other states, but should provide a reliable upper limit on dissociation time for a given pulsewidth. The details of the mathematical formulation are included in Appendix A. In order to better understand the factors affecting dissociation time, pump-probe data were obtained to measure the dissociation time of methylene iodide CHzlz and 1,1- diiodobutane C3H7CH12. The results are shown in Figure 3.8. Both transients were taken With the polarisation vector of the probe laser aligned parallel to the pump. The data were fit using a non-linear least squares procedure and the model described above. The diSsociation time of C3H7CHI2 was found to be r S 87 i 5 fs, indicating that molecular 6O ’1‘ E ‘ Bur2 Data E — Fit 2 - Mel2 Data 3 — Fit = I-I 0 O E 0 8 o A 3 “atm- 3 Ln -400 -200 0 200 400 600 800 Time Delay (fs) Figure 3.8 Time-resolved data of the molecular photodetachment of 12 from CHzlz and n-C4Hglz. The difference in dissociation time between the two molecules can be accounted for by the difference in mass of the alkyl fragment. The relatively poor fit to the C4H312 dynamics at positive times is due to the presence of a vibrational oscillation at early times. detachment is prompt. Fitting of the CHzlz time zero transient using the same method produced a dissociation time ‘c S 47 i 3 fs. If there is some redistribution of energy occurring during the reaction, we would expect the effect to be substantially greater in the larger molecule, both because the larger reduced mass allows more time for any redistribution to occur and because there is a greater density of vibrational states in the molecule, allowing for more efficient intramolecular coupling. If we assume that the products of each reaction have the same amount of kinetic energy and that the difference in dissociation time is caused only by the difference in reduced mass p, we can use the following relationship to predict the expected difference in dissociation time: TAM, _ ”Mel, Tau], #814], (3.2) Based on the reduced mass of each molecule, this expression yields wen/131,12 = 0.538. The observed ratio obtained from the fit is 0.54 :t 0.08. Thus the difference in 61 dissociation time can be completely accounted for by the mass difference, i.e. there appears not to be a significant intramolecular redistribution of energy occurring during dissociation even for a system like gem-diiodobutane in which there is a moderately large density of states. To estimate the amount of available energy that is partitioned into center—of—mass translational motion of the fragments we use I as an upper limit for the dissociation time of each molecule. For the purposes of the model, we will assume I to be the time taken for the fragments to move a distance L apart, at which point dissociation will be considered to be complete. The amplitude of the C —I stretch is z 1 A, so it is reasonable to assume that the carbon-iodine bonds are completely broken once the fragments have moved more than 2 A away from the equilibrium distance. A simple impulsive model can then be employed to estimate the translational energy E of the fragments by assuming that they reach terminal velocity instantaneously: 1 L 2 where ,u is the reduced mass of the carbene and I2 moieties, assuming they form a pseudodiatomic (essentially the mass of the alkyl fragment). Using this expression and a length parameter of L = 2.0 A and a dissociation time T of 47 fs, the total kinetic energy of the fiagments produced by dissociation of CH2I2 is estimated to be 1.26 eV. Analysis of the rotational excitation in the nascent product molecules is also of value, both to determine the partitioning of energy in the fragments and to help elucidate 62 0.12 0.08 0.04 Fluorescence Intensity (Arb.) 0 1000 2000 3000 — Parallel h ' ‘ — Perpendicular -1000 0 1000 2000 3000 Time Delay (fs) Figure 3.9 Time-resolved data of the CH2I2 dissociation obtained at 340 nm with parallel (a) and perpendicular (b) configurations; ‘parallel’ and ‘perpendicular’ refer to the polarisation of the probe beam relative to the pump. Note the much smaller intensity of the time zero feature in the perpendicular polarisation configuration. The anisotropy data is ambiguous; no reliable conclusions about the rotational population of the products can be drawn from analysis of this data. the reaction mechanism. For this reason, the anisotropic contribution to the signal was extracted using the formula36 r(t): _ (3.4) where H and J. denote the polarisation of the probe laser relative to the pump and 1 represents the intensity of the fluorescence at each pump-probe time delay. Figure 3.9 Shows transients obtained from the CH2I2 cell when the probe laser was polarised parallel (a) and perpendicular (b) to the pump. The purely anisotropic contribution to the signal ’0‘) is shown as an inset. Unfortunately, the anisotropy signal is on the same scale as the nOise, so it isn’t possible to obtain reliable information about the rotational dephasing 63 time of the molecules from the extracted r(t). This may be because the rotational dephasing occurs very rapidly and is buried under the time zero feature, or there may be such a long, slow dephasing that it is difficult to observe. The fact that time zero enhancement is greater when the 624 nm pulse is polarised parallel to the 312 nm pulse than when it is perpendicular further confirms that this feature is due to a co-operative process. B. The 250 - 290 nm Region As with the D'—-)A' fluorescence, time resolved data was obtained in this region by multiphoton dissociation with femtosecond pulses at 312 nm to produce molecular iodine in a fluorescent ion-pair state. A probe pulse at 624 nm then allows the reaction and nascent product dynamics to be monitored by depletion of this state. Figure 3.10 shows transients recorded at two wavelengths in this region; 285 nm and 272 nm. The dynamic data collected at 340 nm indicated that the molecular halogen detachment from CH2I2 is extremely fast. Examination of the transients shown in Figure 3.10 also demonstrates the promptness of the dissociation process. The rapid onset of the depletion at 272 nm and of decay in the time zero signal at 285 run both show that the reaction is essentially instantaneous within the time resolution of the pulses (z 50 fs). Both transients exhibit fluorescence depletion and vibrational coherence at positive times, but whereas the 285 nm data has a large time zero enhancement, the 272 nm data does not. Additionally, there is no discernible anisotropy in the fluorescence detected at 285 nm but a substantial degree in the 272 nm channel (vide infia). These differences reveal that the fluorescence 64 (a) 285 nm (b) 272 nm Fluorescence Intensity (Arb.) l l r l l -500 O 500 1000 1500 2000 Pump Probe Time Delay (fs) Figure 3.10 Pump-probe data obtained by selective detection of the 12 fluorescence signal at 285 nm (a) and at 272 nm (b). Both transients were obtained with the pump and probe beams polarised parallel to each other. Both exhibit vibrational coherence. However, the 285 nm transient exhibits a large time zero spike and the 272 nm transient does not. 65 i1 between 250 and 290 nm originates from at least two electronic states of molecular iodine and is being formed by two distinct reaction pathways. In the section below, the time- dependent signal at 272 nm will be analysed. Figure 3.11 shows time-resolved data of the molecular detachment of 12 from CH2I2 detected at 272 nm. The data are recorded with the probe polarised parallel (a) and perpendicular (b) to the pump. As with the time-resolved data obtained at 340 nm, vibrational coherence can be seen in the data. Unlike the 340 nm data, howeVer, there is a substantial difference between the two transients. This is caused by alignment of the molecules in the gas phase. Those parent molecules that have a transition dipole aligned with the polarisation vector of the laser will undergo reaction, producing a nascent product population selectively aligned in a particular direction. The ability of the probe pulses to deplete the newly-prepared fluorescent state then depends on the orientation of its polarisation vector relative to that of the pump pulse. As the molecules rotate, the probability of the probe transition will therefore vary as a function of time delay between pump and probe. Figure 3.11 indicates that there is a large degree of anisotropy in the formation of the product molecules detected at 272 nm. The anisotropy decays very rapidly, within z 500 fs of time zero. Note also that the depletion efficiency immediately afier time zero is greater when the pump and probe pulses are polarised perpendicular to each other than when they are parallel. This is somewhat counterintuitive and indicates that the pump and probe transitions are perpendicular to each other. The fast decay implies a high degree of rotational excitation in the 12 fragment. 66 .6 h A a i: 'l‘m' l ’N ——- (a) Parallel 'g — (b) Perpendicular 0 E 0 O a 0 O 33 h e 3 EH 4 l r l r l 1 l r L r l -500 0 500 1000 1500 2000 Pump-Probe Time Delay (fs) Figure 3.11 Time-resolved data at 272 nm of the CH212 dissociation, obtained with the probe polarised parallel (a) and perpendicular (b) to the probe. The difference between the two transients clearly indicates rotational anisotropy in the 12 product. Notice both the rapid anisotropy decay time and the fact that depletion is more efficient immediately after time zero in the perpendicular polarisation configuration. The time-dependent rotational anisotropy is extracted from the data using the form of (3.4) above; the isotropic component of the signal is likewise extracted from the data using [isotropic = I“ + 211. (3-5) Isolation of the data in this way into isotropic and anisotropic contributions allows us to analyse the rotational and vibrational dynamics of the nascent molecules separately. Presented in Figure 3.12 (a) and (b) are respectively the purely anisotropic and isotropic contributions derived from the 272 nm transients shown in Figure 3.11. 67 .cos2wt mgr—It: 1_1.,I_’_"_ “0 0-3 I"+21_L 12 2p j j . . 2 0 2 _ e-(J'Jmax)/mj)2 jmax = 354 d: 38 A ' 41' \/7T Aj = 509 i 52. % —— 0.1 — 00 1 l n I i l l I Iisotropic = 1”+ 21-1- (b) zA e't h Cos((ot + 4)) r=501i82fs Isotropic Signal (Arb.) co = 98 :h 2 cm'1 (p = 513: 6° 1 I 1 I l l 1 l 0.0 0.5 1.0 1.5 2.0 Pump Probe Time Delay (ps) Figure 3.12 Purely isotropic and anisotropic components of the time-resolved data presented in Figure 3.11. (a) The pure rotational contribution as given by the time dependent rotational anisotropy r(t). (b) The pure vibrational contribution as given by the isotropic signal I" + 211- The thicker lines show least—squares fits to the pure vibrational and pure rotational contributions. 68 A quantitative analysis of the rotational dephasing in the 272 nm data can be performed on the purely anisotropic contribution presented in Figure 3.12 (a). A formulation of time—dependent rotational anisotropy for the case of one—photon pump and one—photon probe has been given by Baskin and Zewail2| for a (II, II) transition case. As discussed in the Introduction, extension of the formulation to the (H, .1.) case yields37 1 ZPjCOSZO)"t r(t)=—— 1+3 1 (3.6) 20 2P, ./ where r(t) is the anisotropic contribution to the signal at pump-probe time delay t and P] denotes the relative rotational population distribution, which is assumed to be a Gaussian function given by P1: elimi] (3.7) 1 AN; (AjY The j dependent nutational frequency a;- = 41:8,, where B is the rotational constant of the nascent molecular product in rotational quantum level j. However, analysis of the r(t) shown in Figure 3.12 (a) using this formulation failed to reproduce the experimental data. This is due to the multiphoton nature of the pump transition. A three—photon pump transition would be expected to produce a greater degree of alignment than is expected for a one—photon transition because it produces a c0569 distribution in the nascent Products rather than a c0528 distribution. This narrower initial alignment causes the dephasing of rotational anisotropy to appear faster than it really is. 69 In order to model time-dependent rotational anisotropy experiments in which the excitation is a multiphoton process, the existing treatment21 has been extended to apply to the current experiment, which was assumed to involve three-photon pump and single photon probe transitions. If all the pump transition dipoles are aligned parallel to each other, Equation (1.19) becomes: 1.0) = Arturo)- at fiz(’)'éz 2> (3.8) where A(t) contains the isotropic contribution to the signal. For this case, if the probe dipole is perpendicular to the pump dipole at time zero we find that the rotational - 54 anisotropy can be expressed as:1 1 Zchosant r(t)=—— 1+3 ’ , (3,9) 12 2?. j where the symbols are defined above. To obtain the experimental r(t) and lisouopic curves shown in Figure 3.12, the average fluorescence intensity at negative time delays (probe pulse absorbed before pump) was subtracted from each transient before perfonning proper normalisation to the asymptotic limits at long time delays. A least-squares fit of the observed r(t) data using the above formulae is also presented in Figure 3.12 (a). The fit corresponds a center jmax of the rotational distribution of the 12 fragment = 354 :t 38 and a l/e width of the distribution Aj = 509 i 52. 7O Figure 3.13 shows a model of CH212 in the centre-of-mass frame. Note that because of the large mass of the iodine ":i-i atoms compared to carbon and X(a),'B] Y(c);BZ hydrogen. the centre of mass of the molecule is very close to the midpoint between the iodine atoms. Because of this, upon dissociation into 12 and CH2, rotational motion of CH212 about the X Figure 3.13 Model of the CH212 molecule in the centre of mass frame, showing the axis will be manifested as translational principal (X, Y and Z) and rotational (a, b and c) axes and their transformation under motion of the CH2 fragment. Similarly, C2v symmetry. rotational motion about the Y (c) axis will be partitioned into 12 rotation and CH2 translation. On the other hand, most of the rotational energy of the parent about the Z (b) axis, the symmetry axis of CH2I2, remains as rotational energy of the 12 fragment because the moment of inertia of 12 is significantly larger than that of CH2. Thus the rotational motion of the parent molecule becomes translational motion of the CH2 fragment and rotational motion of the 12 fragment after dissociation. The CH2 fragment is therefore expected to have relatively high translational and vibrational excitation but low rotational excitation. A room temperature sample of CH212 would be expected to have a rotational population centred at j z 100, so the results above indicate a difference of about 250 h in angular momentum between the parent CH212 and the 12 fragment. Conservation of angular momentum demands that 71 Jam, = Jr'H, +JI, +119 (3-9) where J, is the angular momentum of the appropriate species and L indicates that portion of the angular momentum of the parent that is converted on dissociation to linear momentum in the fragments. Due to the large masses of the iodine atoms, the magnitude L of the ‘orbital’ angular momentum can be well approximated as that of the CH2 fragment only, L z mm) v(.,,2b (3.10) where mm: and v”,2 denote respectively the mass and velocity of the CH2 fragment and the “impact parameter” b represents the perpendicular distance between the velocity vector v”,2 and the center of mass of CH212. Since J”,2 is negligible, we find from (3.9) that L z 2501:. This, along with the broad spread of rotational population Aj, indicates a high degree of rotational excitation in the nascent 12 after dissociation. The isotropic transient shown in Figure 3.12 (b) clearly exhibits oscillations at positive time delays. As with the data collected at 340 nm, this indicates that the reaction mechanism responsible for formation of molecular iodine in this channel is concerted, i. e. happens in a single kinetic step. To obtain quantitative information about the vibrational coherence, the isotropic data were modelled using the same exponentially decaying cosine function (3.1) used for the D' —) A' fluorescence (vide supra). Least-squares fit of the experimental isotropic data in Figure 3.12 (b) using the functional form of (3.1) gives 72 rise to the following parameters: r= 501 i 82 fs. w= 98 i 2 cm’1 and ¢= 51 i 6°. The fitted result is shown in Figure 3.12 (b). Most ion—pair states of 12 have vibrational frequencies on the order of 100 cm”; the fitted value of 98 cm‘l therefore seems reasonable if the species being probed is the 12 fragment. Also, the fitted vibrational frequency should provide a lower bound to the nominal vibrational frequency of the fluorescent state, particularly so because anharmonicity tends to reduce the effective vibrational frequency of higher—lying vibrational levels. This allows us to eliminate as the source of the 272 nm fluorescence those 12 states that have vibrational frequencies smaller than 98 cm”. There are several known emission systems of 12 that fall into the 250—290 nm spectral region, notably the F0; —-) X02, f0; -—> A1,,f0; —> 3"], , f'O; —> 80;, Glg —> A1, and g0; —> 2431 3ngu'50"5"‘55~'5‘ transitions. Since the vibrational frequencies of both the F 0; (96.31 cm") and the f '0; (96.98 cm") states are smaller than the fitted vibrational frequency of 98 cm", they are quite unlikely to be responsible for the observed vibrational coherence based upon the above criterion, although similar [.124 and Fotakis et al.125 have been tentatively assigned to features observed by Okabe eta the F 0; —) X 0; fluorescence of the nascent I2 fragment. However, there is a sizeable uncertainty (2 cm”) in the present determination of the vibrational frequency, which does not permit the involvement of the F 0: and f ' 0; states to be unequivocally eliminated. 73 The remaining three upper states have quite similar vibrational frequencies, 1'. e. —l + —l —l - - - 104.14 cm for fog, 106.60 cm for Glg and 105.70 cm for gOg. Taking into consideration the anharmonicity constants of 0.2113 cm”, 0.2134 cm"1 and 0.4900 cm-1 for the f, G and g states respectively, we can estimate that a vibrational frequency of 98 1 cm' corresponds to vibrational levels 14, 19 and 7 respectively in these states. If the f (3 Hag) state is responsible for the vibrational coherence at 272 nm, the f -+ B fluorescence would be expected to contribute to the coherences observed in the 340 nm region. This will have two effects; the dispersed fluorescence spectrum in this region will be comprised of contributions from both transitions, and the observed dephasing would be due in part to the additional contribution to the time-resolved signal. First, a least-squares fit to the fluorescence in the 290 - 350 nm region of the spectrum was attempted, taking into account the possible contribution to signal in this region of fluorescence from the f —> B transition. Figure 3.14 shows the results, along with the fit obtained without accounting for the f —> B fluorescence, for comparison. The fit shown in Figure 3.14 (a) was determined by assuming that all the fluorescence in this region was produced by the 12 (D' ——> A') transition. Figure 3.14 (b) shows the 12 f—-) B fluorescence in the same region, produced by excitation of neat I2 vapour at 612 nm. In Figure 3.14 (c), the same data as in (a) are fit again, this time incorporating z 30 % (optimized for fit) of f —) B fluorescence. The fits were both obtained by using a least- squares routine and by assuming a Gaussian distribution of vibrational levels in the D' 74 ’ Data (a) _ Fit 9,: A A L l A k A L l 4; A A #1 A J A L l L 1 A L l L A A L l A A L I l A A L Fluorescence Intensity (Arbitrary Units) 310 315 320 325 330 335 340 345 350 Wavelength (nm) Figure 3.14 Fit to the dispersed 12 D’—) A' fluorescence spectrum produced from the dissociation of CH212. (a) Fit obtained using only D'—) A' fluorescence. (b) The f —> B fluorescence spectrum obtained from excitation of neat I2 vapour. (c) Fit to the observed fluorescence in the 300-350 nm range, taking into account the possibility of contribution from the f —) B transition. The spectrum shown in (b) was scaled by a factor determined by optimisation and incorporated into the fit. 75 state; the observed fits correspond to a central vibrational level vmax = 8 in Figure 3.14 (a) and 7 in Figure 3.14 (c). To assess the possibility of a contribution from the f ——) B transition to the time- resolved data collected at 340 nm, the vibrational dynamics shown in Figure 3.5 were fit using a bimodal-type model. Figure 3.15 shows the results of this fit, along with the original damped cosine fit for comparison. The displayed fit was obtained by assuming a bimodal Gaussian distribution of vibrational levels. One mode is centred at v' = 18 in the D' state with a FWHM of 7. This corresponds to a vibrational spacing of 96.5 cm", which é“ ["t ,f‘ 2 1 1 \ ‘\ I ‘ \- ’\ 1‘“ r ' —‘— Data — Original Fit — Bimodal Fit Fluorescence Intensity (Arb.) l l 1 1 l 1 1 1 l l 4 l l l l l 1 l l l 1 i 1 l 0 500 1000 1500 2000 2500 Time Delay (fs) Figure 3.15 Fits to the vibrational coherences in the 12 D'—) A' fluorescence at positive pump-probe delay times. (a) Original, exponentially damped sinusoidal fit shown above (Figure 3.5). (b) Bimodal Gaussian fit. One mode has an oscillation frequency of 96.5 cm"1 and a FWHM of 7. The second mode has an oscillation frequency of 104 cm'1 and a FWHM equivalent to a single D' vibrational level. 76 reflects an oscillation period of 346 fs and is close to the result from the damped sinusoidal model discussed above (vide supra). The second mode has an oscillation frequency of 104 cm'I and a FWHM equivalent to a single D' vibrational level. This mode appears to be contributing approximately 15 % of the time-dependent signal at 340 nm, which is consistent with the intensity of the f —> B fluorescence expected in this region. Clearly, there is a discrepancy between the apparent vibrational population of the D' state obtained from fitting the dynamic data (v' = 18) and dispersed fluorescence spectrum (v' = 8), even when the possibility of another contributing process is accounted for. The reason for this is not clear. 3.3.2 Other Compounds In addition to methylene iodide, photoinduced molecular detachment experiments were performed on other gem-dihaloalkanes. Figure 3.16 shows dispersed fluorescence spectra produced by multiphoton dissociation of CH2Br2 and CH2Cl2 at 312 nm. Both spectra were obtained from static cells. In both cases, fluorescence characteristic of the d.’45”47”57 These results indicate that the reaction is X2 D' —> A' transition was observe general, 1'. e. the observation of molecular halogens in the D' state as a product of photoinduced molecular detachment from dihaloalkanes is not restricted to methylene iOdide. Because of the elevated vapour pressures of CH2Br2 and CH2C12 at room temperature, it was necessary to reduce the pressure in the cells. This was done by 77 (a) (b) Fluorescence Intensity (Arb.) l l l l l 200 220 240 260 280 300 320 Wavelength (nm) Figure 3.16 Dispersed fluorescence spectra of X2(D') produced by multiphoton excitation at 312 nm. (a) From CH2Br2 at 0 °C. (b) From CH2C12 at 0 °C. The increasing signal level at longer wavelengths is due to laser scatter. maintaining the liquid reservoir of each cell in a cold bath; the CH2Br2 cell was kept at 0 °C in an ice bath and the CH2C12 cell at —41 °C in a mixture of dry ice and acetonitrile. As with methylene iodide, time-resolved data of this reaction were obtained from each cell by multiphoton excitation by a 312 nm femtosecond pulse, followed by probing with a second pulse at 624 nm. Figure 3.17 shows the resulting transients for CH2Br2 and CH2Cl2. Each set of data was obtained at 0 °C. Signal was collected at the position of maximum intensity for the D' —) A' fluorescence, corresponding to 287 nm for the CH2Br2 cell and 254 nm for the CH2Cl2 cell. A number of similarities can be seen with 78 '5 a CH Br 5; ( ’ 2 "' E” m r: 8 AA. - V— vAv— 4—:— E 1 r l L 1 L l 3 5 (b) CH2C12 a 2 e E Ii -5 00 0 500 1000 1500 2000 Pump-Probe Delay Time (fs) Figure 3.17 Transient data of photoinduced molecular detachment of X2(D') from dihaloalkanes. Both sets of data were recorded from static cells, with the polarisation vectors of pump and probe pulses parallel to each other. (a) From CH2Br2 at 287 nm. (b) From CH2Cl2 at 254 nm. The increased signal:noise ratio in this data, as in the spectrum in Figure 3.16 (b), is due to low signal levels. the time-resolved data of the reaction to produce 12 in the D' state (Figure 3.4), most notably that the fluorescence intensity in each case shows a substantial enhancement at time zero and depletion at positive times. As with the spectral data displayed in Figure 3.16, the signal level from the CH2C12 cell is comparatively low, resulting in a greater signal to noise ratio than was observed from the other systems. Pump-probe data were obtained from the CH2Br2 cell at 287 nm with parallel and perpendicular polarisation vectors. The results are shown in Figure 3.18. Using the same methods already discussed, the isotropic and anisotropic portions of the signal at positive 79 (a) Parallel — (b) Perpendicular Intensity (Arb.) l -1000 0 1000 2000 3000 4000 5000 Time delay (fs) Figure 3.18 Time resolved data from the multiphoton dissociation of CH2Br2 using 312 nm femtosecond pulses. The transients were obtained at 287 nm, with the polarisation vector of the probe laser aligned parallel (a) and perpendicular (b) to the pump. pump-probe delay times were extracted and are shown in Figure 3.19 (a) and (b). The rotational dephasing of the molecules was determined by fitting the anisotropic portion of the signal using Equation (3.8). The fit was obtained using a Gaussian distribution of rotational level population, centered at jmax = 76 i 7, with a FWHM A, of 170 i 20. A Br2 molecule with j = 76 populated has 250 cm"1 of rotational energy. This indicates considerably less rotational excitation than was observed in the 12 fragment at 272 nm (direct comparison with the 12 D' rotational excitation isn’t possible because the r(t) data at 340 nm could not be reliably analysed). Similarly, molecular parameters of Br2(D') were used to obtain a fit to the isotropic portion of the signal. Unlike the data collected from the CH212 cell, vibrational modulation at positive times can not be clearly seen in this data. There does however appear to be a single vibrational oscillation in the perpendicular data, which is probably 80 (a) Isotropic Intensity (arb.) 1 J l l l l l l l (b) Anisotropic : 0_03 :E : 0.04 : 0 -0.04 0 1000 2000 3000 4000 5000 Time delay (fs) Figure 3.19 Anisotropic (a) and isotropic (b) portions of the 287 nm data from the CH2Br2 cell. The fit to the r(t) derived from the data is also shown. To obtain the r(t), the data was properly normalised and a three-point smoothing applied. hidden underneath time zero when pump and probe are polarised parallel to each other. Fourier transfonn analysis of the isotropic portion of the data yields contributing frequencies at 33, 104 and 222 cm", corresponding to oscillation periods of 1000, 320 and 150 fs respectively. The fundamental frequency of Br2 in the D' state is 150.86 cm", so there is no apparent correspondence between this frequency and the results of the Fourier transform analysis. Analysis of several scans collected with the pump and probe lasers polarised parallel was also not able to yield consistent results, either by Fourier transform or by modelling the vibrations as described previously for the CH212 data. Multiphoton excitation of CBr2F2 and CBr2Cl2 at 312 nm is also found to produce Br2 in the D' state, see Figure 3.20 (b) and (0). Observation of spectra from CBr2F2 and CH2Br2 recorded at 0 °C seems to indicate a difference in vibrational population.154 81 A L l l (c) CBr2C12 Fluorescence Intensity (arb.) AIALJAJAJLA 1A4. LA 220 240 260 280 300 Wavelength (nm) Figure 3.20 Dispersed fluorescence spectra from multiphoton excitation at 312 nm of CH2Br2 (a), CBr2F2 (b) and CBr2Cl2 (c). All three are produced by the Br2 D' —-) A' transition. However, the vapour pressure of CBr2F2 is 314 Torr at 0 °C,158 which produces a gas phase collision frequency of 2.45 x 109 s". This is sufficient to cause vibrational relaxation in the observed fluorescence spectrum. The spectra shown in Figure 3.20 (a) and (b) were recorded at 0 and -61 °C respectively; the two molecules have comparable 158 vapour pressure at these temperatures (11.5 Torr for CH2Br2 and z 12 Torr for CBr2F2.ii Examination of Figure 3.20 indicates that in fact the vibrational temperature in the D' state of Br2 is similar whether the parent molecule was CH2Br2 or CBr2F 2. A comparison of the dissociation times of CBr2F2, CH2Br2 and CBr2Cl2 was also ” Calculated using data from Reference 158 and a modified Clausius-Clapeyron of the 82 made, see Figure 3.21. The scans were collected consecutively, with the laser intensity kept constant as far as possible to avoid apparent differences in dissociation time caused by saturation of the transitions. Analysis of the time zero data using Equation (A3) and assuming the same pulsewidth for all three scans yielded dissociation times of 58.6 i 1.4 fs for CH2Br2, 80.6 i 4 fs for CBr2Cl2 and 29.7 i 0.6 fs for CBr2F2, as shown in Figure (3.21). The dissociation time of CBr2F2 is significantly faster than either of the other two molecules. The relative masses of CH2Br2 and CBr2F2 might lead one to expect that the latter molecule would dissociate more slowly, so this result is slightly surprising. The enthalpies of reactions (ii) and (iv) (see Table II) are quite similar, so the difference in dissociation time also apparently can’t be explained by the thermodynamics of the systems involved. Since the ground states of CCl2 and CF2 are singlets,"’0”"l the energies required to produce these fragments in the first excited (triplet) states were calculated and are also displayed in Table II. In this case however, the enthalpy of reaction (v) is substantially higher than the enthalpy of reaction (iii), which makes the result shown in Figure 3.21 even more difficult to explain. The most probable cause of the anomalous dissociation time is therefore almost certainly the high electron density of the fluorine atoms, which is expected to significantly affect the electronic states of the parent molecule. For this reason, the CBr2F2 data will not be compared with results from its analogues. - 0.2185A T form log,o(p)= +8 '59. 83 ° Data (a) CH2Br2 _ Fit t=58.6i1.4fs l l l l J Fluorescence Intensity (Arbitrary Units) 1: =80.6 i 4 fs l l l l l -600 -400 -200 0 200 400 600 Pump-Probe Time Delay (fs) Figure 3.21 Time zero data for the molecular detachment of halogens from CX2Br2. Fits to the data are shown as continuous lines. The time data was obtained consecutively, with the same laser intensity for each scan. (a) CH2Br2 at 0 °C. (b) CBr2F2 at ~47 °C. (C) CBT2C12 at 0 °C. 84 Assuming that Equation 3.2 applies, the ratio of the dissociation times of CBr2Cl2 and CH2Br2 is expected to be e 2, not 1.4 as measured experimentally. The reason for the difference could possibly be explained by the fact that the enthalpy required to form CC12 and Br2(D') from CBr2Cl2 is lower than is needed to produce CH2 and Br2(D') from the dissociation of CH2Br2, as shown in Table II. This could have the effect of making less energy available for partitioning into fragment recoil in the latter reaction. This is somewhat speculative, however; the electronics of both reactants and products are also expected to play a role. Additionally, the assumption that the dissociation can be treated as a pseudodiatomic separation with no redistribution of energy during the reaction is rather na'r‘ve in the case of CBr2CI2, where the mass of the two fragments is comparable and the C-Br and C-Cl vibrational frequencies similar. Table II. Thermodynamics of the dissociation reaction CX2YZ —-> CX2( X) + YZ(D'), where X = H or a halogen and Y and Z are halogens."l Reaction Enthalpy (cm’l) eV (i) CH2Br2 —+ CH2( 52 ) + Br2(D') 85047 10.5 (ii) CBr2Cl2 —> CC12(’)Z)+ Br2(D') 70735 8.8 (iii) CBr2Cl2 —+ CC12(A ) + Br2(D') 79042 9.8 (iv) CBr2F 2 —) CF 20? ) + Br2(D') 68557 8.5 (v) (213121:2 —2 CF2( .3; ) + Br2(D') 88398 11.0 ”‘ Enthalpies of formation of reactants were taken from References 162 and 163 and of the products from Reference 162. The value of Te for the D' state of Br2 was taken from Reference 148; singlet-triplet splittings for the carbene fragments from References 160 and 161. 85 All the molecules discussed thus far have one thing in common; their C2v symmetry. In the interest of observing the effects of breaking this symmetry, experiments were also conducted on gas-phase CH2lCl. Time-dependent data were observed from this cell at two wavelengths; 340 nm and 430 nm. The fluorescence spectra in these two regions are shown in Figure 3.22. The 430 nm fluorescence is probably due to the D' —> A' transition, which is known to occur at this wavelength)“'65 Fluorescence between 325 and 340 am has been assigned to the G(3 P 1) —> A(3I'I.) transition of 1C1;166 it is possible that the observed fluorescence at 340 nm originates from this transition. However, it is known that [Cl decomposes readily to produce I2;"’7 for this reason, the spectra from the CH2ICl sample were compared with the dispersed fluorescence spectrum obtained from neat l2 vapour. This is also shown in Figure 3.22. Comparison of the spectra from each source indicates that the fluorescence observed at 340 nm from the CH2IC1 sample may well include a contribution from the f —> B transition of 12, but that the 430 nm signal probably contains no contribution from 12 fluorescence. Figure 3.23 shows pump-probe data collected at each of these wavelengths from the CH2IC1 cell at 0 °C. Both sets of data exhibit intense time zero enhancement in the signal and depletion at positive pump-probe delay times. Although it is possible that the fluorescence detected at 340 nm is contaminated by a contribution from ambient I2 (vide supra), this is not expected to significantly affect the measured dissociation time. The 86 -— From 12 vapour (neat) From CH21C1 320 340 360 380 400 l I 400 410 420 430 440 450 460 Wavelength (nm) Figure 3.22 Dispersed fluorescence spectra from the multiphoton dissociation of CH2IC1 at 0 °C, showing both the 320 - 400 and the 400 - 460 nm regions. The fluorescence spectra produced in these regions from a sample of pure I2 vapour are also shown for comparison. reason for this supposition is that the time-resolved behaviour of 12 f —> B fluorescence under excitation with 612 and 324 nm pulses is quite different to what is observed in Figure 3.23 (see Figure 3.3). For this system, there is no intense feature at time zero such as the one shown in Figure 3.23 (a). Additionally, for I2(f —> B) the 624 nm pulse is the pump and the 312 nm pulse the probe; time-resolved data would then be observed in the region marked as negative time in Figure 3.23. The following analysis is therefore made assuming that the observed pump-probe transient is due only to the G —-> A transition of 1C1. 87 (a) 340 nm T=71i4fs T=48ilfs l l 1 l I -600 -400 -200 0 200 400 600 Time Delay (fs) Figure 3.23 Pump-probe data from the multiphoton dissociation of CH2IC1 at 312 nm. (a) Collected at 340 nm, corresponding to the G —> A transition. (b) Collected at 430 nm, corresponding to the D' —-) A' transition. The displayed fits are produced by modelling the dissociation time using the same method described above for CH212. The observed fits yielded l/e times of 71 i 4 fs for dissociation to the G state and 48 i 1 fs for dissociation to the D' state. Assuming the excitation process and energy partitioning in CH2IC1 to be the same as in CH212, the latter value is in agreement with the dissociation time that would be predicted by reduced mass considerations. Using Equation (3.3), again with a length parameter of 2 A, to calculate the kinetic energy of the fragments from the dissociation time yields a translational energy of 4278 cm'1 (0.53 eV) when the product is ICl(G) and 9361 cm'l (1.16 eV) when 88 the product is ICl(D'). This represents a difference in translational energy of 5083 cm", or 0.63 eV. The energy separation between the G and D' states of CH2IC1 is 6491 cm", or 0.8 eV.”8 It therefore appears that z 0.6 eV of the excess energy available when the halogen product is ICl(D') is partitioned into kinetic energy and the remaining 0.2 eV into internal energy of the fragments. The dynamics of molecular photodetachment of ICl(G) from CH2ICl were studied with the probe laser polarised both parallel and perpendicular to the pump. A certain degree of rotational anisotropy was observed. The r(t) obtained from the data, along with a least-squares fit, is presented in Figure 3.24 (a). As before, the fit was determined by assuming a Gaussian population of rotational j levels and fitting for the position and F WHM of the Gaussian. Because the observed rotational population so closely resembles a Boltzmann distribution, see Figure 3.24 (b), the r(t) was also fit to a thermal distribution of rotational levels. The fit is shown in Figure 3.24 (a) and the resulting rotational population in Figure 3.24 (b). In both cases, the rotational population of [Cl molecules was found to be centered at approximately j = 10, which corresponds to a rotational temperature in the Boltzmann case of 169 K and a rotational energy of 6 cm". This is very much lower than was observed in the X2 fragments, and indicates that CH2ICl is undergoing a different photodissociation mechanism than was observed in the CH2X2 molecules. This result, and the apparently lower excitation energy (vide supra), are not unexpected because the CH2IC1 molecule carries none of the transition restrictions arising from the C2v symmetry of the other molecules studied. 89 Data (a) —- (i) Gaussian fit — (ii) Thermal fit r(t) 0 2000 4000 6000 8000 10000 Time Delay (fs) ’1? g 0.06 - (b) a r — (i) Gaussian population ’2" 0.04 — (ii) Thermal population fl :8 g 0.02 :1 n. e 0 10 20 30 40 50 Rotational Level j Figure 3.24. Pump-probe data was collected from the CH2IC1 sample at 340 nm with the liquid reservoir maintained at 0 °C. Dynamics were studied with the probe laser polarised both parallel and perpendicular to the pump. (a) The purely anisotropic contribution r(t) to the 340 nm signal. Also shown are a least-squares fit obtained by assuming a Gaussian distribution of rotational levels (i) and a thermal (Boltzmann) distribution (ii). (b) The rotational populations P(]') responsible for the fits shown in (a). The two results are very similar, and produce almost identical fits. 90 « q".l"ll“ll. :1 1 IIII.‘ There were no discernible vibrational oscillations in the time-resolved fluorescence data collected at 340 nm from the CH2IC1 cell. The 430 nm data, however, does exhibit some modulation in the intensity as a function of pump-probe time delay: this data is shown in Figure 3.25. Pump-probe data were collected with the pump and probe lasers polarised parallel to each other and the liquid reservoir maintained at 0 °C. Fits were obtained using the exponential decay model described above and also by fast Fourier transform (FFT); the fits are also shown in Figure 3.25, along with the resulting parameters. The FFT ‘fit’ was obtained by taking a Fourier transform of the transient data. Two major contributing frequencies were identified from the FFT results and the (a) — Data — From FFT m- Decay Fit Fluorescence Intensity 1 0 500 1000 1500 2000 2500 3000 3500 4000 Pump-Probe Time Delay (fs) Figure 3.25 Pump-probe data collected from the CH2ICl sample. Fits to the data obtained from the Fourier transform and from the exponential decay model (Equation 3.1) are also displayed. 91 time behaviour arising as a result of these frequencies simulated. To do this, a crude model was constructed in which the time-dependent behaviour is produced by addition of cosines of the contributing frequencies. The data were fit using a bimodal Gaussian distribution, with the centre of each mode fixed at the frequency yielded by the FFT results and the width and relative intensity of each mode allowed to vary. It can be seen from Figure 3.25 that a fairly good fit to the data can be obtained by this method. The central frequencies used to obtain this fit were 78 cm‘1 for the decay fit and 78 and 107.4 cm”’ for the Fourier fit, which were the frequencies yielded by the FFT. Two sets of data are shown in Figure 3.25; (a) and (b) were recorded separately but were both fit using the same frequency parameters. The observed frequencies therefore seem to be quite reproducible. A beat frequency of 78 cm"1 corresponds to v z 23 in the A state of ICU“'69 v a 86 of 1c1(1)'),'48 or v a 78 of 101(0).“56 Similarly, an oscillation of 107.4 cm“' indicates occupation ofv = 17-18 in ICl(A),"’8""9 v = 60 in 10(0)148 or v = 56 - 57 in ICl(G)."’" 3.4 Discussion 3.4.1 Spectroscopy A. The Parent Molecule For all the molecules studied, photoinduced molecular detachment was found to occur very rapidly (usually < 100 fs). Within this time, the molecules are not expected to have rotated to any significant degree, which makes it likely that all the dipoles of the 92 multiphoton pump transition are parallel, since this is the most favourable situation for absorption. This is particularly so in the case of the pathway responsible for the 12 product that fluoresces at 272 nm. Figures 3.11 and 3.12 clearly show that there is a high degree of anisotropy in this pathway. If each of the transition dipoles corresponding to the three— photon pump transition had different orientations, one would not expect the anisotropy to be so clear. Thus, the three transition dipoles are likely to be parallel to each other; in the absence of evidence to the contrary it is reasonable to assume that they are so. Few studies of the spectroscopy of CH212 at high energies have been conducted, and the large size of the iodine atoms makes the molecule difficult to model using theoretical methods. As a consequence, the excited state which is being accessed by the excitation is unknown. In an effort to elucidate the nature of the parent electronic state that correlates to dihalogen products, Okabe et al. compared the absorption spectrum of CH212 in the vacuum ultraviolet region with the fluorescence excitation spectrum in the same region (342 nm detection).'24 The absorption and fluorescence excitation spectra both showed broad continua, which were ascribed to C — 1 0' —-) 0* transitions. Although features assignable to Rydberg transitions appeared in the absorption spectrum, their absence from the fluorescence excitation spectrum seems to exclude the involvement of Rydberg state excitation in the 12 photodetachment process. Since molecular Rydberg states have very long lifetimes, particularly at high excitation energies (from z 100 fs for low N to ~ us for high N), the rapid rise-time of the signal in these experiments also indicates that Rydberg states are not involved in the molecular detachment process. 93 It is possible to reach a relatively low energy excited state of CH212 by absorption of a single 312 nm photon. One therefore expects resonance enhancement in the three photon process if the first transition is to this state, which has Bi symmetry.’29"30’132 If this is the case, the dissociative state reached is expected to be a B; electronic state at about 12 eV above the ground state. A B. transition in this molecule is aligned along the I — 1 direction. Although it has been argued that an orbital with B. symmetry has a node between the iodine atoms and therefore cannot be responsible for the production of 12, the total (1'. e. many electron) wavefunction may nevertheless have electron density between the two iodine atoms. Two-photon resonant enhancement at 312 nm allows access to B2 (perpendicular to the CH2 plane) and A .(parallel to the Z axis) dissociative states; there are no symmetry restrictions on forming a bond between the iodine atoms via transitions having either symmetry. B. The Products No evidence of molecular halogen products in any of the lower (valence) states was observed. However, valence states of halogens tend not to be very strongly bound; for example, 12 has a dissociation energy of 1.54 eV in its ground state, 0.54 eV in its B state and z 0.3 eV in its A and A' states.I70 Molecular product in any of these states would dissociate rapidly under the experimental conditions because the available energy is very high. An ion-pair state, which correlates to Xir + X', would be a good candidate for a dissociation product because these states are strongly bound and have long range attractive forces. For homonuclear halogens there are eighteen of these, corresponding to the 3P, ’D and lS terms ofthe X+ ion. 94 First tier ion-pair states of 12 have equilibrium energies within 0.16 eV of each other.”’ The two other ion-pair families are found approximately 0.9 and 1.5 eV higher.I70 Three photon excitation with 312 nm is equivalent to 12 eV, which translates into an excess energy of z 3 eV above the observed barrier to molecular photodetachment at 9.4 eV. This brings all the ion-pair states within energetic reach. The observed data for CH212 photodissociation indicates that only a small percentage (10%, not corrected for fluorescence yield or detection efficiency) of fluorescence occurs at wavelengths between 250 and 290 nm. These wavelengths correspond to the second tier of ion-pair states, which correlate with X+(3Po) + X'(’S).I50 (In the case of CH2Br2 and CH2Cl2 dissociation, second and third tier ion-pair states fluoresce too far in the UV to be detectable in air.) The observed predominance of the D' state strongly suggests that electronic excitation directly correlates to this state. It may also be the case that dissociation to the D' state is brought about by two-photon resonance enhancement, producing a dissociative state of A1 or B2 symmetry as discussed above, but that the f state is a product of the single photon enhancement through 13; symmetry. One would expect this pathway to produce less 12 product because formation of an interhalogen bond would not be favoured in this case. However, it is also possible that high-energy excitation of the parent molecule yields a halogen molecule in another ion-pair state while it is still close to the carbene fragment, and that under these circumstances relaxation to the D' state occurs. For example, the dissociation process itself may act as a half-collision. It is known that single collisions of most 12 ion-pair states with buffer gases are highly efficient in causing non- radiative transitions to the D' state;’46 it is possible that the half-collision represented by 95 the dissociation may be efficient enough to produce a similar effect. If this were the case, it would explain the observed discrepancy between fits to the dispersed fluorescence spectrum and the vibrational dynamics in the 340 nm region. Halogen molecules in the D' state produced by collisional association would contribute to the observed fluorescence spectrum, but would not necessarily be in phase with those molecules that dissociated directly into the D' state. 3.4.2 Energy Partitioning If a 12 eV excitation produces 12 in the D', f, g or G states, only the three lowest electronic states of CH2, i.e. 32 (3B,) (To = 0.0 eV), '5('A1) (T0 = 0.39 eV), and '13 (‘13.) (To = 1.27 eV),”2 are energetically feasible products of the photodissociation process. Table 111 lists possible combinations of the 12 and CH2 states, each of which represents a distinct photodissociation channel of CH212. For each channel, Table III also gives the minimum energy required for the dissociation process and the remaining energy available for internal and kinetic energy of the photofragrnents. From fitting the observed rotational anisotropy data at 272 nm, the 12 rotational distribution has been found to be centered around jmax = 350, which corresponds to an average rotational energy in the product 12 molecules of approximately 0.3 eV. From fitting the experimentally observed vibrational coherence data, the 12 fragment has been found to contain only moderate vibrational excitation with an average vibrational quantum number of v z 14 for 12 in the f state, or v z 19 for 12 in the D' state. With vibrational frequencies on the order of 100 cm"’, we can therefore estimate that the 96 Table III. Energetics for several dissociation channels of CH2I2.l30"50"55"56 The table gives the minimum energies required to dissociate a ground state CH212 molecule to produce CH2 and 12 fragments in several possible electronic states. The available energies are calculated based on a three photon transition at 312 nm. 12 States CH2 States Energy Required (eV) Available Energy (eV) ~ 3Bl 8.38 3.62 D' (3mg) 5' , 8.77 3.23 5 '31 9.65 2.35 ~ 33‘ 9.20 2.80 113113,) a'A, 9.59 2.41 5'3] 10.47 1.53 )7 3 1 10.2 1.8 g (’20g+) [i'Al 10.6 1.43 5'3] 11.5 0.55 X33] 9.27 2.65 G(1g ) 2:24, 9.66 2.26 5‘3, 10.54 1.38 97 energy partitioned into vibrational excitation of the 12 fragment is approximately 0.2 eV in both cases. The small vibrational energy in the 12 fragment can be attributed to the fact that the I — 1 distance in CH212 is 3.57 A, very similar to that of 12 ion—pair 4 0 813168;] 1,15 ,155, ’56 little vibrational excitation is then expected. The fragments therefore contain at least 1.8 eV of translational and internal energies. With the assumption of a three—photon excitation and of 12 in one of its second tier ion— pair states f, g or G, the formation of CH2 (5) can be ruled out because there is not enough energy available (see Table 111). If this is the case, we are lefi with a limited number of choices, i. e. CH2 (if) + 12 (f, g, G) and CH2 ('5') + 12 (f, g, G). Which of these channels is responsible for photodissociation of CH212 to yield 12 fluorescence at 272 nm remains to be investigated. Because the HCH angle in ground state CH212 differs significantly from the bond angle of CH2 in the )~( and b states,l4l vibrational excitation should be expected in the CH2 photofragment if it is produced in either of these states. This could represent a significant amount of energy, especially when one considers the high vibrational frequencies of CH2. 3.4.3 Mechanism Femtosecond studies of the reaction dynamics of Rydberg states of methyl iodide showed a substantial difference in reaction time for the photodissociation of CH3I and CD31.” The explanation proposed for this observation was that vibrational modes in the 98 alkyl fragment are involved in the predissociation process, thus making the isotope effect for the dissociation substantial. Photodissociation studies of alkyl iodides at 304 nm excitation energy also revealed that the partitioning of available energy into IVR increased from 19% for methyl iodide to 70% in n-butyl iodide, an energy difference of 1 eV.’73”74 Both findings contrast directly with our results, which indicate no apparent increase in IVR in the alkyl fragment on going from diiodomethane to gem-diiodobutane (vide supra). Furthermore, within experimental resolution the dissociation time for CH212 and CD212 was found to be the same. Reduced mass considerations alone predict that CD212 will dissociate z 3 fs slower than CH2I2, which is well within the experimental resolution. This is strong evidence that vibrational modes in the alkyl fragment are not involved in the dissociation. The short time photodissociation dynamics for breaking of a single C — 1 bond of CH212 have been studied recently by many groups using both femtosecond time—resolved 72,136 134,135,137,138 It was techniques and resonance Raman spectroscopic measurements. found that the dissociation process takes place in less than 120 fs72”36 and that the I—C — I symmetric stretching mode is initially activated, which leads to breaking of one of the two C — 1 bonds by coupling to the l—C — I antisymmetric stretching mode.""”'3 5’13“” In order to investigate the possible contribution of various vibrational modes of the parent molecule to the molecular detachment process, a frequency analysis of the ground- State equilibrium geometry of CH212 was performed using GAUSSIAN 94.175'177 Table IV Compares the normal mode frequencies of the calculated gas phase values to the 99 experimental liquidI78 and solution phase values.137 Despite the fact that the calculated and experimental values are determined for different phases, it can be seen that the calculated frequencies are close to the experimentally observed ones (0.1 - 9% deviation). The larger errors occur for those modes involving mostly iodine atom motion. This is not unexpected, because ab initio calculations on molecules containing many-electron atoms like iodine are inherently less precise. Table IV. Comparison of theoretical and experimental CH212 vibrational energies in cm". Calculated Experimental Mode Description Gas phase Liquid CH212 Liquid CH212 Solution (Raman) (Infrared) (Raman) v4 I-C-I bend l 17 121 134 v3 I-C-I symmetric stretch 454 486 486 493 v9 I-C-I asymmetric stretch 552 567 573 581 v7 CH2 rock 716 714 717 714 V5 CH2 twist 1056 1028 1028 v3 CH2 wag 1148 1104 1106 v2 H-C-H bend 1374 1350 1351 1369 v1 H-C-H symmetric stretch 2958 2968 2967 2968 V6 H-C-H asymmetric stretch 3043 3049 3049 3049 Figure 3.26 shows the results of the normal mode analysis, plotted as a function of I - I and CH2-I2 distance. For each mode, the amplitude of the motion corresponds to one 100 quantum of excitation in that mode. It is apparent that only the I-C-I bending and I-C-I symmetric stretching modes, v4 and v3 respectively, contribute to the I - I interatomic distance. The other normal modes produce little or no change in the distance between the iodine atoms, which is further evidence that these modes are not involved in the molecular photodetachment process. The I-C-I bending v4 contributes significantly to the H2C l2 coordinate. Because this is the lowest energy mode, it is expected to be significantly populated at room temperature; at 294 K approximately 10 % of the molecules have four quanta in this mode. A reaction coordinate that mimics the motion the molecule undergoes when M, is excited is therefore a reasonable candidate for the photodetachment mechanism. The two mechanisms shown in Figure 3.27 are both concerted; in other words, breaking of the two C — 1 bonds and formation of the I — I bond happen in a single kinetic step. The difference between the two is that one preserves the C2v symmetry of the parent molecule CH2I2, while the other proceeds through a bent geometry and does not. In this situation, one of the C — I bonds breaks earlier, or to be more precise, faster than the other. The synchronous concerted mechanism shown in Figure 3.27 (a) conserves the C2,, symmetry of CH212. According to this mechanism, CH2 flies away along the symmetry axis, which passes through the center of mass of CH212. The impact parameter b would in this case be zero, and no rotational excitation is expected in the halogen fragment. On the other hand, the asynchronous concerted mechanism shown in Figure 3.27 (b) does yield a nonzero orbital angular momentum because in this case b is finite. 101 4.5 4.3 e '_' v2 v3 4.1 ’— 2 3.9 — 3 5 jg 3.7 — a _ .i 3.5 ~— 3.3 *— 3.1 e 2 9 1 J l L 0.7 0.9 1.1 1.3 1.5 1.7 CH2 I2 Distance (A) Figure 3.26 Normal mode analysis of the ground state of CH2I2, plotted as a function of [-1 and CH2-I distance. Only the I-C-I bending (v4) and I-C-I symmetric stretch (V3) modes contribute to the H2C-I2 distance. 102 The data collected from the CH212 cell at 272 nm exhibits a high degree of rotational excitation in the nascent 12. In this case, based on an estimated 1.26 eV of translational energy and the 250 h of angular momentum determined from the rotational anisotropy, the impact parameter b can be estimated to be approximately 2.7 A. This clearly indicates that the molecular detachment process which produces the 12 molecules that fluoresce at 272 nm happens according to the asynchronous concerted mechanism. It was however not possible to reliably analyse the rotational excitation in the [2 fragment detected at 340 nm. For this reason, we cannot with any degree of confidence assign a mechanism to the reaction CH212 —) CH2 + I2(D'), at least not based on the analysis of the rotational anisotropy of the 12 fragment. A Huckel frontier molecular orbital study of the dissociation of CX2Y2’2" at lower energies indicated that the ‘least-motion’ path (in which C2v symmetry is retained) is a high-energy pathway and that when the carbene moiety is allowed to slip off-centre from the halogen-halogen axis, the reaction path is considerably stabilized.128 This corresponds to a pathway for the concerted elimination of the general type shown in Figure 3.27 (b). Because the carbene radical is arnbiphilic, i. e. the lone pair at the front of the radical behaves as a nucleophile and the empty pTC orbital is electrophilic, an asynchronous concerted mechanism would tend to produce charge separation in the halogen fragmentm This is consistent with the fact that only ion-pair states of halogen molecules have been observed on the photodetachment of halogens from dihaloalkanes. In this case, an ylide-type transition state would be stabilised by the charge distribution of the carbene 103 (a) Synchronous concerted Figure 3.27 Schematic of possible mechanisms for the photoinduced molecular detachment of X2 from gem-dihaloalkanes. Both proceed in a single kinetic step. The time scales given for these mechanisms are based on time-resolved measurements. (a) Synchronous concerted mechanism. Breaking of the two carbon-halogen bonds is initiated at the same time and proceeds at the same rate. An interhalogen bond forms before the carbon-halogen bonds are completely broken. This pathway has a symmetric transition state and preserves the C2, symmetry of the parent. (b) Asynchronous concerted mechanism. In this case, the rate at which the two carbon-halogen bonds break is different. Again, the interhalogen bond forms before the halogens are completely dissociated from the carbene. 104 fragment. ISO-diiodomethane, H2-C — I - I, has been observed in gas matrices at low energies;179 in calculations of this system, it was found that less than 2 eV of excitation energy is required to produce this species. This is less energy than is needed to form CH2I + 1’40 However, the bonding between the iodine atoms in this species is significantly weaker than in 12 or 12', which may explain why CH2 + 21 are the more common reaction products. The iodine atoms in this molecule are described as a contact ion pair in which the charges are mostly concentrated on the iodine atoms; there is little redistribution of charge on the carbon atom. ’40 This is also consistent with a charge-transfer mechanism. One would expect a direct recoil pathway to allow relatively efficient coupling between the a— carbon and the internal modes of the alkyl fragment, in which case a significant difference in IVR rate would be observed between methylene and butylene iodide. This may however be defeated in RCHI2 both by the very rapid rate of reaction and by the large difference in vibrational frequency between modes involving primarily the C-1 and C-C or C-H bonds. Cain et al. also found that the barrier height for CX2 + Y2 —+ CX2Y2 (where Y denotes a halogen atom) or the reverse process depends on the HOMO—LUMO gap of the halogen molecule Y2.’28 The lower the gap, the lower the barrier. Since the HOMO- LUMO gap decreases from F2 to 12, they concluded that the barrier decreases from CX2F2 to CX2I2, resulting in a corresponding decrease in rotational excitation. This leads to the prediction that there will be an increase in rotational excitation on traversing the series from CH212 through CH2Br2 to CH2Cl2. Unfortunately, it wasn’t possible to analyse the 105 anisotropic data from the D' state of either 12 or C12, so this prediction can not currently be tested. The possibility of a third mechanism has also been investigated. If we assume that it requires one 312 nm photon to dissociate one of the C — 1 bonds and a second to dissociate the other C — 1 bond, the third photon could then be said to cause photoassociation between the two iodine atoms thus produced. This will be called a three—step mechanism. The difference between this mechanism and the asynchronous concerted mechanism has to be emphasised. In the asynchronous concerted mechanism, absorption of the three photons happens simultaneously and instantaneously. The bond breaking and bond formation events then take place after absorption of the three photons. Since the photodissociation processes happen within the time duration of the pulse, we can not directly distinguish the two possibilities experimentally unless much shorter laser pulses are used. Therefore, in order to distinguish between them, the dynamics resulting from each mechanism were simulated as described in Appendix B. As far as the photoinduced molecular detachment processes in this study are concerned, the penta—atomic molecule CH212 can be treated as a triatomic with the CH2 moiety being viewed as a pseudo atom. In Appendix B it is assumed that the bonds are rigid and that there is no translation or rotation of the system as a whole. Excess energy deposited to dissociate a bond is assumed to be manifested as a force acting along the direction of the bond (i.e. axial recoil). Therefore, it is sufficient to consider only the motion of the atoms on the triatomic plane. 106 Figure 3.28 Classical simulations of molecular detachment processes. In each snapshot, the large spheres represent the iodine atoms and the small sphere represents the CH2 moiety. In both mechanisms, the two C -— 1 bond breaking events are assumed to be separated by 32 fs. (a) The three—step mechanism. The excess energy is estimated to be 1. 8 eV for the first bond breaking event and 0.3 eV for the second. In this case, the I — 1 bond is assumed to form immediately after the second C — 1 bond breaks. (b) The asynchronous concerted (ylide) mechanism. The excess energy is estimated to be 2.7 eV for the first bond breakage and zero for the second. The I — 1 bond is assumed to form immediately after the first bond breaking event. 107 1' r! 1W N man: ecm m.— cm an em mkGV a an muev 33:28: can» so Emu-282 53.1.9.5. A5 Figure 3.28 108 Figures 3.28 (a) and (b) present the simulated results for the two mechanisms. To obtain the simulation shown in Figure 3.28 (a), we have assumed that the molecular detachment process proceeds according to the following three steps: KCH,], (2?)+hv(312nm) —> CH,](X)+](2P,,) + 1.8ev att=0 1CH,1()'?)+hv(312nm) —> CH,(]?)+](2P,) + 0.3eV att=32fi (3.11) ](P ,1+] (P ,1+hv( 312nm) —> ],(f) + 0.6ev where the excess energies are obtained based on the data given by Baughcum et al.130 The first C — I bond is assumed to break with an excess energy of 1.8 eV to produce I atom in the ground state 2P372. The second C — 1 bond is assumed to break at 32 fs later37 and with an excess energy of 0.3 eV. In this step, excited 1 atom (2P1/2) is assumed to be formed. The third step involves the photoassociation"8 of the two iodine atoms to form 12 in the f excited state. The possibility of two ground I products has not been considered because photoassociation in the third step to produce 12 (f) from two ground state iodine atoms is not energetically possible with a 312 nm photon. An alternative bond breaking and formation sequence for the three-step mechanism was also investigated, in which, instead of producing ground I in the first step and excited I in the second step as shown in (3.11), the first and second photons break both carbon- iodine bonds and form one electronically excited and one ground state iodine atom. The results from a simulation of this mechanism and of the pathway shown in (3.11) both predict an 12 angular momentum that is inconsistent with experimental observations (vide infia). Because of this, only the pathway described in (3.11) will be considered in the following discussion. 109 The energetics shown in the following equation have been used for the simulation of the asynchronous concerted mechanism in Figure 3.27 (b). CH212 + 3hv(312 run) -> CH2 + I2(f) + 2.7 eV. (3.12) Here the excess energy is taken from Table III. The first C — 1 bond is assumed to break with an excess energy of 2.7 eV. At 32 fs later, the second C — 1 bond is assumed to break with no excess energy. Each snapshot in Figures 3.28 (a) and (b) depicts the spatial arrangement of individual atoms (the CH2 moiety is treated as a pseudo atom) and their bonding configuration at a particular instance. Here, notice that the time reference is chosen to be the instance when the first bond breaks and it may not coincide with the experimental time zero, which is the instance when the pump transition takes place. Aside from facilitating visualisation of the molecular detachment process, a more important purpose of the simulation is to obtain a quantitative estimate of the orbital angular momentum L. This then allows one to compare the estimated L with that obtained from analysis of the experimental data. Since the three (pseudo) atoms in CH212 are assumed to be motionless before the first bond breaking in this simulation, the triatomic system contains no total angular momentum and will continue not to do so because of conservation of angular momentum. Thus the orbital angular momentum L is the same as the 12 angular momentum in magnitude but opposite in sign. With a time lag of 32 fs between the two bond breaking events, an 12 angular momentum of 85 h is predicted 110 -100 - -200 '- — (a) Three-step mechanism — (b) Asynchronous concerted mechanism 1 l l l 0 10 20 30 40 50 Time of the Second C-I Bond Breakage (fs) -300 '- Angular Momentum of the 12 Fragment I Figure 3.29 Dependence of 12 angular momentum on the time lag between the two bond breaking events. The two traces present the dependencies for the asynchronous concerted mechanism (a) and the three—step mechanism (b). The conditions are as stated for Figure 3.26. from the three—step mechanism, Figure 3.28 (a) and 248 h from the asynchronous concerted mechanism, Figure 3.28 (b). Figure 3.29 examines how the time lag affects the angular momentum of the 12 fragment. This figure and Figure 3.27 clearly show that the asynchronous concerted mechanism predicts an 12 angular momentum that is more in agreement with experimental observations. 111 4. PHOTOASSOCIATION 4.1 Introduction 4.1.1 Bimolecular Reactions Many spectroscopic studies on the dynamics of chemical reactions examine the photodissociation process, in which the molecule of interest undergoes a unimolecular decomposition. Of more general interest however are bimolecular, or full-collision, reactions in which two or more free, unbound reactants form a collision complex, undergo structural, energetic and electronic changes as a result of the interaction between them, and separate into fragments. Bimolecular reaction dynamics have typically been investigated by molecular beam techniques, in which the states of reacting species can be quite carefully controlled and the nature of the products accurately measured. However, as discussed in the Introduction, this approach allows only the asymptotic properties of the system to be examined. While this certainly yields some information about the nature of the transition state region, it is vital to a proper understanding of reaction processes to determine what happens while the reactive species are interacting with each other. Because the collision complex (hereafter called transition state complex) is typically short-lived, the processes occurring during its lifetime are difficult to measure directly, but they are vital to the progress of the reaction. A bimolecular reaction can be thought of as a sequence of half-collisions; the reactants first combine with each other to form a collision complex which then undergoes 112 the requisite changes before dissociating to form products. In principle, either or both of these processes may be investigated spectroscopically. To interrogate the second ‘half’ of the full-collision reaction, it is possible to use photodissociation, which is a very common, and useful, method of studying what occurs when a species undergoes fragmentation to form products. The analogous technique for examination of the first process discussed above is photoassociation, which is considerably less extensively applied. It is photoassociation which is of interest to this study. 4.1.2 Photoassociation Photoassociation occurs when the absorption of a photon by a collision pair induces bond formation between them."6’”’0""3 The process can be described as truly bimolecular when the reactants are free and unbound prior to initiation of the reaction. Photoassociation is distinct from other types of photoinduced reaction because the reacting species absorb the light cooperatively; a sequential process in which one body is excited and subsequently reacts with the other is described as a laser-assisted or photoinduced rather than photoassociation reaction. To avoid ambiguity, it is therefore important to ensure that neither of the reacting species absorbs the light independently of the other; excitation and bond formation are cooperative and concurrent. For this reason, the frequency of the light is carefully chosen so as to be resonant with a transition of the transition state complex but not with either of the reactants.2 This condition ensures that the transition state complex is excited directly. The efficiency of product formation and the nature of the products should then be sensitive to the form of the reactive potential energy surface. Monitoring the properties of the reaction products as the photoassociation 113 energy is tuned therefore provides a sensitive probe of the transition state region for the bimolecular reaction. Photoassociation spectroscopy has been used for a number of purposes, for example to study the electronic excited states of species having repulsive ground states."""188 A number of frequency-resolved photoassociation studies exist on the long-range interactions between ultracold atoms as a means to elucidate details about the ground- state potential of alkali metal dimers near the dissociation limit.’8’"193 ‘Collision-induced absorption’ is a consequence of photoassociation, and has been described in some 194-197 198,199 detail."‘~"63 The gas-phase reactions of metal atoms with H2 and on salt surfaces have been studied by this method. Additionally, the possibility exists to use excimers which undergo a radiative transition to the ground state as lasing media; several investigations have therefore been conducted on these types of systems.65’2"0'202 Photoassociation has obvious potential in directing the outcome of chemical reactions, and a number of theoretical studies exist on the possibility of using it for this application.6”"’7’2(’3’204 Experimental results have been demonstrated in the frequency- 205,206 for resolved regime for the Penning ionisation of Li"4 and for energy transfer, example. Unlike photodissociation, which is generally amenable to study by time-resolved methods, real-time observation of photoassociation reactions presents difficulties. There are several reasons for this. Because the irradiation time is short, the number of collision pairs which can be associated within the pulse essentially depends on the spatial 114 distribution and relative momenta of the atoms at the moment when the pulse is switched on. In a gas phase sample this number may be prohibitively small. A more fundamental problem arises as a result of the nature of the ground state, which is composed of a thermal ensemble of continuum states and will therefore contain a broad distribution of positions and momenta. As a result of this, it may not be possible to prepare a well- defined wavepacket on the excited state potential energy surface. The ‘time zero’ or initiation time of a bimolecular reaction is also ambiguous because the species are undergoing random motion, which introduces a spread in both the energy and timing of the reaction. These drawbacks have to some extent been circumvented by the use of precursors.55‘57’5‘”207 These are generally van der Waal's complexes which undergo a full collision reaction upon liberation of one of the reactants from the complex, or following photoactivation of an atom.56 In this way, the collision geometry and initiation time of the reaction are clearly defined. A number of such harpooning or laser-assisted reactions have been studied experimentally.2'48’57‘207'210 While this approach overcomes many of the drawbacks to studying bond formation processes by time-resolved methods, it involves absorption of light by a precursor before the reaction can occur, not direct excitation of the transition state complex. Reactions of this type are therefore not photoassociative. A number of theoretical studies exist on the possibility of directly probing photoassociation dynamics in real time."7‘2’ "2'2 These however deal with the ground state as a coherent superposition of states, which is not likely to be valid in the case of a thermal gas sample at ambient temperature. 115 When a pulse of sufficiently short time duration excites a molecule, a coherent superposition of eigenstates or wavepacket is produced. In the case of a free —) bound (photoassociation) transition, where the initial excitation is from a set of continuum states, well localised wavepackets can be formed on the excited state surface as long as there is a large enough difference in the slope between the upper and lower electronic states. The Franck-Condon factors of the transition dictate that photoassociation probability is greatest when the laser wavelength is resonant with the energy difference between the ground and excited state energies, which imposes a spatial and energetic restriction on the reaction. Tuning of the wavelength of the binding pulse can thus be used to select a range of reactive impact parameters. Temporal resolution is afforded by the binding pulse, and is limited only by the pulse duration. Molecular dynamics following photoassociation can thus be probed using the same techniques that have been used for bound —) free or bound —) bound transitions.“213 Results are presented below on the application of this method to the formation of Hg2*. In this work, experimental observations of photoassociation investigated by time- resolved pump-probe spectroscopy are presented. The system selected for these studies was gas-phase mercury atoms, which have the potential to form electronically excited molecular dimers. 4.1.3 The Mercury Dimer The spectroscopy of Hg2 has been extensively studied, both experimentallym’zoz'z'4'228 and by computational methods.200'229‘23°. The ground X(0;) state is almost purely 116 repulsive, having a well depth of 370 cm", representing the formation of Van der Waal’s dimers at an internuclear separation of 3.63 A."”6“"“"222 The first ungerade molecular state 216,218,2 - . 22 which correlates wrth accessible from the ground state is the D1u(32:) state, Hg('So) + Hg(3P0).22’ The D1u state is characterised by a broad, intense fluorescence centred at 335 nm (29,850 cm"), which has been observed by nanosecond excitation of mercury vapour in a molecular beamm'216 The second harmonic of our CPM is at 312 nm, which corresponds to 32,050 cm". This is resonant with the X( 0;) —) D1u transition in Hg2; it should therefore be energetically possible to cause photoassociation to produce Hg2 using 312 run pulses. The molecular product would be easily detectable by observation of fluorescence at 335 nm, and the repulsive ground state prevents the accumulation of molecular products, allowing the use of a static cell. The relatively high vapour pressure of mercury also avoids the necessity to use prohibitively high experimental temperatures. For these reasons, mercury vapour was considered to be a suitable system for a study of photoassociation on the femtosecond time scale. 4.2 Experimental For these experiments, a sample cell very similar to the one described previously for the photoinduced molecular detachment reactions was used. However, it is particularly important in these experiments to exclude gaseous impurities, particularly air, to avoid 231,232 problems associated with spurious fluorescences and quenching of Hg2 emission. Because there are no problems associated with buildup of molecular product for this 117 _J ‘I .m.J.fl~ ‘\ -‘. ’3': r system it was therefore decided to prepare a permanently sealed cell for these experiments. The mercury sample, triply vacutun distilled and certified to contain a total of less than one part per million impurities (Bethlehem Apparatus Co.), was introduced to a thoroughly cleaned and vacuum baked glass line by injection over an argon atmosphere. The injection port was then sealed and the sample pumped to 10'5 Torr. Mercury was transferred to the sample cell by distillation under vacuum, until an amount substantial enough to be able to form a reservoir was collected. The portion of the line containing the quartz cell and a 'U' trap was then closed to the rest of the pumping station and immersed in liquid nitrogen to achieve cryopumping while the cell was sealed off. The purity of the sample was checked by LIF in the 190 to 850 nm region at high laser intensity. Fluorescence from the cell showed some atomic mercury lines (resulting from multiphoton excitation); no spectral evidence of contamination in the sample was found. In order to raise the vapour pressure of the sample, the cell was wrapped in heating tape and maintained at a constant temperature throughout the experiment. The cell temperature was monitored externally by thermocouples placed in two positions; the first beside the liquid reservoir, to get a measure of the vapour pressure inside the cell, and the second as close as possible to the laser interaction region in order to determine the energetics of the reaction. Raising the cell temperature has the additional advantage of imparting sufficient thermal energy to the unbound ground-state mercury atoms to raise 118 8 l 1 I l 7 - 1g — 61S0+61P1 6 - - mu 5 _ )‘probe - 6130+63P1 4 - _ I I I 3 - 1 - LIFE I 2 "' I a 1 Mind 1 i '" 1 I X(%_ 0 _ ”WWW,” ‘ _ 6lso+6lsO -1 I l 1 l 2 3 4 5 6 Internuclear Distance R (A) Figure 4.1 Schematic of the potential energy surfaces relevant to the femtosecond photoassociation of mercury atoms. The corresponding atomic states at the asymptotic limits are indicated. 119 them above the shallow well in the molecular X state. Most of the results were obtained at 160° C, which corresponds to a mercury vapor pressure of 4.2 Torr.233 A schematic of the potential energy surfaces involved in the Hg-Hg photoassociation process is shown in Figure 4.1. Because the ground state of Hg2 is repulsive, molecules in this state exist as separated atoms. Pairs of atoms will then be located on the ground state potential energy surface according to their separation distance and the amount of thermal energy they possess; for convenience these can be termed collision pairs. There will be a finite Franck-Condon factor for excitation from the appropriate region of the ground state to the D1u state of Hg2. It is expected therefore that collision pairs with the appropriate internuclear distance and combined thermal energy to be located in the optically coupled region of the 312 nm pulse can be photoassociated to the molecular D1u state. This can be verified by observation of the characteristic D —) X fluorescence at 335 nm. Also shown (inset) is the region AR, of most probable excitation based on the average thermal energy kT of the atoms and on the spectrum of the binding pulse. Notice that the narrow range of interatomic distances captured by the excitation process is in the repulsive part of the ground state potential, above the dissociation energy of the dimer. Once the Hg2* excimers are formed, molecular dynamics can be probed by fluorescence depletion using a second femtosecond pulse at 624 nm. There is a high density of electronic states in Hg2 at energies above 32,000 cm", which means there is a good chance that the probe pulse energy will correspond with a resonance from the D1u state to some higher-lying molecular state. The state represented in the figure corresponds 120 to the 1g state of Hg2, which has been observed z 2 eV above the D1u statez‘m’234 and has the correct parity for a single-photon transition from this state. 4.3 Results and Discussion 4.3.1 Spectroscopy Presented in Figure 4.2 (a) is the dispersed fluorescence spectrum obtained from the mercury cell by excitation with the fourth harmonic of the Nd:YAG laser at 266 nm. Light at this wavelength is resonant with the 6 ’So -) 6 3Po transition of mercury atoms, and will cause excitation of some of the mercury in the vapour. Three-body collisions with other atoms and with the walls should then produce excimers in the D1u state. The reason for collecting this spectrum in addition to the one obtained under 312 nm excitation is to compare the appearance of the spectra and thereby confirm whether or not the D1u state of Hg2 is producing the fluorescence. The 266 nm pulses are e 5 ns in duration and should produce a significant population of Hg(6 3P0) and consequently Hg2(D1u). The spectrum shown in Figure 4.2 (a) is characteristic of Hg2 D —-> X fluorescence.2""2"’ The spectrum produced by excitation of the mercury cell with a 60 fs pulse at 312 nm is presented in Figure 4.2 (b). This is also a characteristic D —> X spectrum; the lower signal:noise in the second spectrum is a consequence of lower fluorescence intensity. The population of Hg2(Dlu) producing the spectrum in Figure 4.2 (b) is somewhat red-shifted relative to the spectrum produced by excitation at 266 nm, which is not unexpected given the difference in excitation energy. Power dependence measurements indicated that there is a linear dependence of fluorescence on the intensity 121 ”at? w.- 11.11" .i l ‘.' ‘2 b bind laser 312 nm, 60 fs >5 J‘: m E G) H = 1"1 1 D—>X Emission M Q 250 300 350 400 450 c.) ..............,,, 5 C bind laser 266 nm, ns 0 m ca 8.. O 2 FE J D—>X Emission 250 ’ 300” 350 "400 “ 450 Wavelength (nm) Figure 4.2 Dispersed fluorescence spectra resulting from the excitation of mercury vapor in a static cell at 160 °C. (a) Excitation at 266 nm with a nanosecond laser pulse. (b) Using a 60 fs laser pulse centred at 312 nm. The D —> X emission is red- shifted compared to the emission produced by 266 nm excitation because of the difference in excitation energy. The peak at 407.8 nm is an atomic line resulting from two-photon excitation to the 7’So state. 122 of the 312 nm pulse. It is apparent by comparison of Figures 4.2 (a) and (b) that excitation of atomic mercury vapour with a 312 nm femtosecond pulse produces Hg2. It remains to verify the mechanism of this process. 4.3.2 Dynamic Behaviour To determine the dynamics of the Hg2 formation process and the molecular dynamics of the nascent product, pump-probe experiments were performed with 312 nm pulses as the pump and 624 nm pulses acting as the probe. Fluorescence data were collected at 340 nm with the probe laser polarised both parallel and perpendicular to the pump. The results are shown in Figure 4. 3. The data were normalised to the same level at negative times, since the fluorescence intensity when the probe pulse precedes the pump should be insensitive to the polarisation of the lasers relative to one another. At negative times, the fluorescence signal produced by photoassociation into the Dlu state is unaffected by the depletion (probe) pulse, which precedes it. As time zero is approached, depletion of the molecular fluorescence begins to be apparent as molecules in the D1u state absorb the 624 nm pulse and are excited into a higher energy electronic state. Figure 4.3 indicates that the possibility for depletion persists for at least five picoseconds. Two aspects of the figure are worthy of particular attention. First, it should be noted that the onset time of the depletion is very rapid, being completed within z 200 fs. This observation implies that the process responsible for the portion of the fluorescence being depleted also takes place on a femtosecond time scale. As discussed above for the case of 12 formation from CH212 (vide supra), the time of onset of the depletion can be used to 123 obtain a direct measure of the bond formation time. Fitting to the isotropic portion of the data revealed that the molecule formation time is within the pulse. J (a) Parallel polarisation — (b) Perpendicular polarisation Fluorescence Intansity (Arb.) W 1 0 1000 2000 3000 4000 5000 Time delay (fs) Figure 4.3 Femtosecond pinup-probe transients from the photoassociation of mercury at 312 nm. Data was collected with the probe laser polarised parallel (a) and perpendicular (b) to the binding laser. Note that bond formation occurs during the pulse and that the data is clearly anisotropic, indicating alignment of the nascent molecules. The second point is the observed anisotropy in the data. If photoassociation is occurring, the pump pulse would produce Hg2 molecules selectively aligned according to a cosine squared distribution about its polarisation direction (assuming a parallel transition). The probability for absorption of the probe pulse and consequent fluorescence depletion would then be greater when the probe pulse was polarised parallel to the pump than when it was perpendicular. For the case of parallel polarisation direction, the depletion probability would be expected to be at a maximum immediately after time zero, when the molecules still retained their initial alignment, and would gradually decrease in 124 time as they rotate away from the position of maximum alignment with the laser field direction. The data shown in Figure 4.3 has a dephasing time 1:c of z 1.1 ps. The observed anisotropy and time evolution of the data clearly indicate rotational coherence in the nascent Hg2 molecules. The rotational anisotropy r(t) of the transients can be extracted using the weighted - 36 difference 11’]: rt =———; () [n+2], (4.1) the result is shown in Figure 4.4. The observed dephasing of rotational anisotropy can be analysed using a simple model which treats the rotational population 1’} as a Gaussian: r0) = 241.013,, (4.2) J=0 where 1 41 2 ' ' 2 P,=— “ exp —4ln2 L1]— (4.3) ' A», it A, and r(i,t) = 0.1 + 0.3C03(2(0jt) (4.4) where A,- = 4 7rBj is the molecular rotational frequency.” Least-squares fitting to the data indicates that the rotational excitation can be modeled with a rotational distribution centred at jmax z 30 of Hg2(Dlu) and a FWHM Aj of z 90, as shown in Figure 4.4 (b). This is equivalent to z 17 cm‘l of rotational excitation at the position of maximum population (the spread is 0 - 103 cm”). 125 0.25 " ' ‘ - (b) Population of gigggginal 0'010 Rotational Levels 0.2 ‘ 0.008 0.006 0.15 * 0.004 0.1 * 4 . 0.002 005 1 1 1 1 r O J r 0 2 4 6 50 100 150 Pump-Probe Time Rotational Quantum Delay (ps) Number j Figure 4.4 (a) Rotational anisotropy r(t) obtained from the experimental data. The heavy line is the best fit to the experimental data (plotted as points), as described in the text. (b) Rotational population of the photoassociated product, obtained from the fit to the rotational anisotropy. 4.3.3 Other Processes In order to verify that the observed dimer fluorescence and molecular dynamics are a result of photoassociation, we need to consider other processes that might produce the same results. There are several alternatives, including excitation of an existing (van der Waal’s) dimer population, photolysis of an equilibrium population of Hg molecules and multiphoton excitation of atoms followed by collisional association to form the excimer. The ratio of dimers to monomers under the experimental conditions is estimated to be z 3.5 X 10'5."' In addition, the relative displacement of the two states makes the Franck- "’ Calculated by statistical thermodynamic methods using the procedure outlined in Reference 235. 126 Condon factors for transition between the ground state well and the D1u state very small (< 10"").2’6’222 Also, it requires z 300 cm"1 more energy than a 312 nm photon possesses to excite molecules by a vertical transition from the bottom of the ground state to the D1,l state. These factors combine to make bound -—> bound transitions highly improbable. At the temperature and pressure conditions of the experiments, the trimer concentration in the cell is estimated to be less than one in 10’s. The observed fluorescence intensity is quite substantial; it seems most unlikely that a femtosecond 3 in a narrow focal pulse acting on less than 1:10I5 of a total number density of 1017 cm' area could produce a measurable amount of fluorescence, particularly if that signal was then depleted. The formation of short-lived (r < 50 ns) Hg2* excimers by collisional association of ground and excited state atoms has been shown to occur.236 This is probably the origin of the ‘background level’ of fluorescence; the amount of depletion observed represented only about 10 % of the total undepleted signal. However, collisional association of excited atoms requires three-body collisions. At 160 °C the mean time between two-body collisions is 125 ns;" the rise time of any signal associated with three-body collisions would therefore have to be on the order of several hundred nanoseconds. The gate on the boxcar was set to z 50 ns for collection of data, which discriminates against slower processes. Also, femtosecond depletion of a nanosecond signal should not produce any v Assuming ideal gas behaviour. Pressure-temperature data obtained from Reference 159, p. 6-113. 127 visible change in intensity because the timescale of the probe laser is so short. Most importantly, collisional association of atoms is an inherently isotropic process and could not result in molecular products exhibiting rotational anisotropy as was observed in the time-resolved data collected from the cell at 335 nm (see Figure 4.3). The presence in the cell of excimers formed by collisional association is therefore not expected to interfere with observation of the photoassociation data. 4.3.4 Magnitude of the Signal The magnitude of the photoassociation signal depends critically on the number of atoms that have a neighbour within the binding distance ARx = Rmax - ngn at the instant that the binding pulse is applied. To determine this quantity, a radial distribution function P(r) is used to calculate the probability that a shell of radius r and thickness dr centred on a single atom contains a neighbouring atom: P(r) = Tpg(r)47rr‘dr (4.5) R min where p is the number density of atoms in the vapour and g(r) is the radial distribution function.235 As a first approximation, we used we] a... r = ex — g( ) p[ H where V(r) is the potential energy describing the interaction between the atoms and P(r) is the fraction of atoms having a neighbour within the volume described by ARX. Using parameters for the ground state potential from Koperski et al.2’6 yields P(r) z 7 X 10'7. Rmin and Rmax were estimated based on the spectrum of the 312 nm pulse, the available 128 kinetic energy and the vertical transition energy between the X 0; and D1u states. impact parameter Figure 4.5 Schematic of a bimolecular collision process, illustrating the definition of the impact parameter b. The equations show the relation between the relative energy of collision ER and the energy E, along the direction of the interatomic axis as a function of the impact parameter. In order for photoassociation to occur, the relative collision energy of an atom pair with a given impact parameter b (as defined in Figure 4.5) should satisfy the condition V.(R') m121_(b/Ry)2 ’ (4'7) where V1(R') is the potential energy of the ground state and R' the internuclear distance at which the laser is resonant with the transition from the ground to the upper electronic state.69 An expression can be derived for the differential photoassociation cross section dam/db using the well-known expression for the scattering cross section: do“ = 2an(6) (4.8) db ’ 129 where P(b) is the opacity function.’ Integration over the Boltzmann population of scattering states, taking into account the energetic restriction in Equation (4.7), results in mm 1 (49) Pa” __. “‘1‘ [1 — (b / R')2]k,,T Figure 4.6 shows plots of dam/db for three values of binding wavelength. Note that at 350 nm, only those collision pairs with very small impact parameters are photoassociated. As the binding laser is tuned to shorter wavelengths, the position of highest photoassociation probability shifts to larger impact parameters and the selectivity is lost. The opacity function in Equation (4.9) reaches a limiting value P(b) = 1 at high excitation energies, when V.(R’) approaches zero. This behaviour is also shown in Figure 4.5 for comparison. The restrictions on impact parameter imposed by Equation (4.9) are reflected in the rotational quantum numbers of the product molecules. The conversion from impact parameter to angular momentum is obtained by using the quantum-to-classical conversion jh = uvb, where v is the relative velocity of the atoms at the moment when they are photoassociated. Figure 4.6 was plotted using the mean relative velocity V. Under experimental conditions (Chino = 312 nm, R' = 2.82 A), it can be seen that the predicted parameters are jmax z 50 and Aj z 65. A number of assumptions inherent in the model may be responsible for the discrepancy between the experimental and theoretical rotational distribution, see Figure 4.4 (b). The larger Aj in the experimental data may be due to the use of a single average value for the relative velocity of the atoms rather than 130 Rotational Quantum Number, j 20 40 60 80 1 00 1 20 140 1.2» i 1:350 nm 1 . in : _ _ 3 0.8: L312 nm P(b)— SE 0.6:, 1:2/90 nm '8 : 0.4} 0.2} 1.5 2 ' 2.5 3 oslmpadt Parameter, b (A) Figure 4.6 The differential photoassociation cross section dam/db from Equation 4.9, plotted as a function of binding wavelength. Note that as the wavelength is tuned to lower energies the reaction requires smaller impact parameters and the products are formed with a narrower. lower energy distribution of rotational excitation. At 290 nm the photoassociation process is not very restrictive and approaches the theoretical limit P(b) = 1 (see text). the thermal distribution. A slight saturation of the photoassociation transition by the laser may also make the rotational distribution appear to be broader than it actually is. Quantum mechanical simulations of this work indicate that it is also possible to 9.70.2 7 6 3 However, the observe vibrational coherence in the photoassociated molecules. modulation depth of these coherences is not large and we have to date been unable to unambiguously identify vibrations in the pump-probe data. 131 5. SUMMARY AND CONCLUSIONS Time-resolved spectroscopy using ultrashort pulses is a complementary technique to more conventional, frequency-resolved, spectroscopic methods. The advantage of using ultrashort laser pulses to study molecular processes is that dynamic behaviour can be observed directly, which avoids ambiguities that may arise in the analysis of spectral linewidths, for example. Additionally, the fast nature of the excitation can be used to favour the detection of short-lived species over asymptotic products. In many cases, particularly where reactions are occurring, this allows the observation and analysis of processes that may not be observable by frequency-resolved methods. Two experiments have been performed in which this principle is demonstrated. Results have been presented of a femtosecond pump-probe experiment on a photoinduced molecular detachment process. Dissociation of gem-dihaloalkanes using multiphoton excitation with a femtosecond pulse was found to produce molecular halogens in ion pair states as a product. The reaction has been shown to be quite general, occurring for a number of dihalogenated molecules and always producing the appropriate halogen in the D' state. The reaction is prompt, and appears to occur without a significant amount of IVR. When iodine was the molecular product, a simple impulsive model was found to reproduce the relative dissociation time for alkane fragments having different masses; this model broke down however with other halogen products. In the case of molecular detachment of iodine from methylene iodide, vibrational 132 coherence in the molecular product was observed, indicating that the reaction is concerted. This is a significant result because it demonstrates that a phase coherent wavepacket created in a molecule can persist even after dissociation into products. At least two other ion-pair states of iodine were observed as products of this reaction. For one of these pathways, rotational anisotropy was observed in the pump-probe data, indicating a high degree of rotational excitation in the molecular product. It was concluded that the observed reaction dynamics and product excitation can best be explained by an asynchronous concerted reaction mechanism, in which one of the carbon-halogen bonds breaks more rapidly than the other. It was not possible to determine the degree of rotational excitation in the I2(D') product, but analysis of the molecular detachment of Br2 from CH2Br2 indicated a rotational population centred at j z 76, which is considerably less than was observed for the iodine product in a more highly excited ion-pair state (1' as 350). The majority of dihaloalkanes studied were of C2, symmetry. Experiments conducted on CH2IC1 showed that for this molecule, the halogen in the D' state was again produced and that the dissociation was very rapid. Analysis of the anisotropy observed in the time data revealed that there was very little rotational excitation in the molecular product, being approximately equal to a thermal distribution centred at j z 10. This is very different to the results from the rest of the study, in which significant rotational excitation was observed in the products, and indicates a different reaction pathway. This is not unexpected in light of a possible symmetry barrier in molecules of C2, symmetry to the 133 formation of an interhalogen bond. A barrier of this type would tend to favour an asynchronous concerted mechanism of the type proposed for highly excited ion-pair states of 12, in which the symmetry of the molecule is broken during dissociation. No such restriction exists in the case of CH2ICl, so that there is no barrier to a ‘direct dissociation’ mechanism of the type shown in Figure 3.28 (a). The asynchronous concerted mechanism would be expected to produce a high degree of rotational excitation in the products; an impulsive dissociation retaining the geometry of the parent molecule would not. It seems reasonable therefore that the asynchronous concerted mechanism is the pathway when the parent molecule has C2, symmetry but that the reaction proceeds by the synchronous concerted mechanism when it does not. In order to determine more about the mechanism of the photoinduced molecular detachment mechanism, it would be very useful to be able to measure the energetics of the alkane fragments. If these experiments were performed in a molecular beam apparatus, time-of flight detection could be used to do this. A reliable description of the excited state of the parent molecule from which the dissociation occurs would also be very useful; theoretical work is underway to allow this. Results have also been presented of an experiment in which a femtosecond pulse was used to cause an unrestricted bimolecular (photoassociation) reaction. In this case, excitation of unbound mercury atoms in a thermally populated set of continuum states to a bound electronically excited state produces electronically excited dimers (excimers). The restrictive Franck-Condon factor for the excitation process produces phase coherent 134 wavepackets on the upper state. This allows the molecular dynamics of the reaction and of the nascent products to be studied in real time by fluorescence depletion probing. It was determined that under the conditions of the experiment, the rotational excitation in the mercury excimers can be fit to a Gaussian distribution having a maximum at jmax z 30 and a FWHM Aj of z 90. The rotational excitation in the product reflects the energy restrictions imposed on the photoassociating molecules by the resonance condition with the binding pulse. The effect of this restriction on reactive impact parameters has been analysed. Observation of vibrational coherence in the nascent dimers would allow a more complete analysis of the energetics, and a fuller understanding of the bond formation process. To date it has not proved possible to unambiguously identify vibrational oscillations in the time resolved data. Part of the difficulty may be the fact that a depletion experiment is inherently more subject to noise variations in the signal. A background-free detection method could help tremendously in elucidating more information about the photoassociation reaction studied here. Additionally, it would be of great interest to study photoassociation reactions between an atom and a diatomic molecule, for example, in which orientation and alignment would also play a role. 135 APPENDICES 136 APPENDIX A Mathematical Formulation for Fitting Time Zero Data In order to simulate the transition state dynamics of the molecular detachment reaction, the signal is treated as a sum of two contributions so that 1,013.0) = Idcplctionfi) + Itimczema), as shown in Figure 3.7. To model the depletion dynamics, we will use a function of the form shown in Figure 3.7 (a). This can be represented mathematically by 77(t){e"“—1 }, where 77(1) is a step function and t represents the decay time of the transition state, which we will assume decays as an exponential. This function will be convoluted with a Gaussian to simulate the effects of the temporal width of the pulse: n(t{exp[—-:—1—l:1® x1” exp(-%1 where x = a and 0' is the FWHM of the ulse. Integrating this expression over t ‘14an p produces the dynamic model for depletion of the molecules: 137 x . 6 _ x l . 6 6 x 2r 11srgn[; $1 -2—x[1 +srgn(;1erf [1:111 (A2) 2 Lexp (i1 *9: 1+erf 6 2x 2r 1 where 6 indicates the time delay between the pump and probe pulses. In order to model time zero, we need the convolution of a delta function with a Gaussian. This has already been solved; it is the second term in (A1). Thus the complete solution for the molecular dynamics of the molecules at time zero can be represented as shown: ’2 1 exp(——1 ® (t)ex (—L1+C x5 x2 77 P T A 1 _ I; [_ :1 _ xs/Tr— exp£ x2] (8 n(t)[exp 1 11 + B = A exp(a2 — ,b’)[l + sign(y — a)erf(|y - 01)] + Bsign(y)erf(|71) + C, (A3) where a=§-, ,6 = 6/rand 7= 6/5c. r A, B and C are experimentally determined fitting parameters, since we cannot predict a priori the amount which each component will contribute to the overall signal. A number of assumptions and approximations were made in this model. First of all, in the interest of simplicity, the changes in signal caused by rotational dephasing and vibrational coherence have not been accounted for. Also, the intensity profile of the pulse in the depletion model is in fact a convolution of the three 312 nm pulses causing the initial excitation with the 624 nm (probe) pulse. For the model, the temporal width of the probe pulse as measured by frequency-resolved optical gating (FROG) was used. This introduces little error because the three-photon excitation will have a considerably narrower temporal width than the 624 nm pulse; the cross-correlation will therefore have 138 a width very similar to that of the probe. We have also assumed that the convoluted FWHM of the pulses producing the time zero feature is the same as that used for the depletion; the assumption is necessary because the exact excitation process at time zero is not known. 139 APPENDIX B Classical Mechanical Simulation of Dissociation Dynamics To illustrate the general idea of the treatment, we will consider a specific bonding arrangement, 1'. e. atom l is initially bonded to atom 2 and atom 2 to atom 3 (e. g. the CH2 pseudo atom to the two 1 atoms of CH212). Let mi, (xi, yr) and (vxi, vyi) be the mass, current position and velocity of atom 1' respectively. At an infinitesimal time 8! later, changes of the atomic positions can be determined trivially using 5x, = vxlbt , etc. The changes in the atomic velocities, on the other hand, can be determined by the following set of simultaneous equations: 5px : mlsvxl + m25v.r2 + m35Vx3 = 0 (B1) (a) 51’, = ml5v“ + m,6v_,, + m38vy3 = 0 (b) 6.!: = m,(x,8v,, — y18v,,)+ m,(x,8v,, - y,6vx,) + m3(x35V,3 ’y35Vx3)=0 (C) l 557": ml(v,,8v,l + v,15v_,,)+ m,(v,,6v,2 + v,,5v_,,)+ (d) m3(v,35V,3 + Vy35Vy3) = 0 d 2 g 7.11.. - v.12 +0.. Warts” o) (xl—x,)(5V,,—5V,2)+(}’1‘J’2)(5v.vI—5vy2)=0 d 2 gag—316.. -) +0.2 -va)’]6t+ (0 (x, ‘x3X5Vx2 ‘5Vx3)+(y2 ‘y3X3Vy2 '5Vy3)=0 140 where equations Bl (a) -— (d) are essentially the conservation laws of momentum, angular momentum and kinetic energy. Equations B1 (c) and (f) are imposed by the rigid bonds between atoms 1 and 2 and between atoms 2 and 3 respectively. These equations govern the free propagation of the triatomic system. Now consider the situation of a bond breaking event, specifically breaking of the 1—2 bond with an excess energy E. Assuming that the bond breaking event is instantaneous, there is no change in the position of each atom before and after the breaking. But there will be abrupt changes in the velocities of the atoms, which can be obtained by solving the following simultaneous equations: 5P, = m,6v_,, + m,25v_,2 + m38v,3 = 0 (BZ) (a) 5P, 2 mISV,l + m,5vy, + m38v,3 = 0 (b) 6.1, = m,(x,25v,l — y15v,,)+ m,(x,5v,, — y25vx21+ (C) m_,(x,t’>v,3 — y36v,,) = 0 1 2ST = ml(v,,5v,, + Vy15Vy1) + m,(v,,5v,2 + v,,5v,,) + (d) m_,(v,36v,3 + v_,35v,31= E / 2 5V“ = x1 “x2 (6) 5V,“ yi - .V2 1 dr,‘3 ‘2‘8 dt = (x2 - x3X5Vx2 ‘5Vx3)+(y2 _ Y3X5Vy2 " 8"'13): 0 (l) where Equations B2 (a) — (c) are identical to those in B1. Equation B2 (e) reflects the restriction that bond breaking results in axial recoil. 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