UNDE RSTANDING AND CONTROLLING LASER - MATTER INTERACTION S : FROM SOLVATED DYE MOLECULES TO POLYATOMIC MOLECULES IN GAS PHASE By Arkaprabha Konar A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Chemistry Doctor of Philosophy 2015 ABSTRACT UNDE RSTANDING AND CONTROLLING LASER - MATTER INTERACTION: FROM SOLVATED DYE MOLECULES TO POLYATOMIC MOLECULES IN GAS PHASE By Arkaprabha Konar The goal of my research is to obtain a better under standing of the various processes that o ccur during and following laser - matter interaction s from both the physical and chemical point of view. In particular I focused my research on understanding two very important aspects of laser - matter interaction; 1) Intense laser - matter interactions for polyatomic molecules in the gas phase in order to determine to what extent processes like excitation, ionization and fragmentation can be controlled by modifying the phase and amplitude of the laser field according to t he timescales for electronic, vibrational and rotational energy transfer. 2) Developing pulse shaping based single beam methods aimed at studying solvated molecules in order to elucidate processes like inhomogeneous broadening, solvatochromic shift and t o determine the electronic coherence lifetimes of solvated molecules. The effect of the chirped femtosecond pulses on fluorescence and stimulated emission from solvated dye molecules was studied and it was observed that the overall effect depends quadratic ally on pulse energy, even where excitation probabilities range from 0.02 to 5%, in the so - independent of the energy of the pulse. It was found that the chirp dependence re veals dynamics related to solvent rearrangement following excitation and also depends on electronic relaxation of the chromophore. Furthermore , the chirped pulses were found to be extremely sensitive to solvent environment and that the comple mentary phases having the opposite sign provide information about the electronic coherence lifetimes. Similar to chirped pulses, the effects of a phase step on the excitation spectrum and the corresponding changes to the stimulated emission spectrum were also studied an d it was found that the coherent feature on the spectrum is sensitive to the dephasing time of the system. Therefore a single phase scanning method can provide the fundamental information regarding solvated species which could be eventually used to interro gate single molecules under a microscope. I also investigated the dynamics and control of large aromatic molecules following ionization with an intense laser pulse in order to understand the mechanism of ionization and further excitation to cationic excit ed states. T he strong - field photofragmentation of a large family of substituted aromatic ketone molecules was explored . The results are consistent with single electron tunnel - ionization leaving the cation with little internal energy in the remaining laser field. In the presence of electronic resonance with the excitation field, subsequent fragmentation takes place. A dvanced ab initio electronic calculations confirm our observations that similarly consider the initial point to involve a molecule in its groun d state configuration that suddenly loses an electron. This study serves to provide a model for the behavior of polyatomic molecules the field as it promp tly leaves the molecule. I also investigated the dynamic behavior of a symmetric organic molecule known to undergo reverse Diels Alder reaction following strong field ionization and found that the molecular ion has signatures of vibrational coherence that correspond s to a C - C Raman stretching mode in the neutral connecting the two rings. These kinds of studies could help us to understand the electron delocalization in a complex gas phase molecule following excitation and devise novel control schemes for stu dying important reactions under strong fields . iv To my family and teachers To Science v ACKNOWLEDGEMENTS Looking back in time and hoping that I could relive these fantastic six years spent in this quaint college town of East Lansin g and the outstanding Dantus research group, I am pretty sure I could not have asked for a better graduate school experience. As I write these final words of my thesis, I am overcome by nostalgia and want to dearly hold on to my life here at MSU. A number of people are responsible for making this journey a wonderful and memorable one and for keeping me sane during trying times of my graduate life . I would like to start by thanking my advisor Prof. Marcos Dantus for providing me the opportunity to work in a world class research lab . I am grateful for his unwavering support for the last six years and for encouraging me in each and every step of this joyous journey and for making it a splendid experience. His optimism has helped overcome frustrating days in the lab and his simple insights has helped improve setups and saved me a great deal of time. He is a great teacher and a fantastic scientist and I still have a lot to learn from him. In addition to all the science I have learned from him, his courage to pursu e unique and some of the most challenging problems through elegant experiments has made the most impression on me. remember his words thank him for instilling in me t he art of creative thinking and for teaching me the techniques of scientific communication . I would like to thank Dr. Vadim V. Lozovoy , whom I admire for his breadth and depth of knowledge regarding anything related to the physics and chemistry of the ultr afast. He has taught each and every one of the Dantus group members to approach critical problems from the very basics in an ab initio fashion. He was no less than an advisor to me in many ways. I would like to vi thank him for being a part of all the researc h projects presented in this thesis and for the many insightful suggestions. The past and present Dantus group members have been extremely helpful and made the Dantus Lab a fun place to work in. The infinite interactions and discussions in and out of lab a nd during group meetings has helped solve numerous problems small and big. I would treasure this learning experience forever. I would like to thank Dr Dmitry Pestov and Dr Paul Wrzesinski for showing me the ropes of the laser lab during the early days. I w ould like to thank Dr Xin Zhu and Dr Yves Coello for teaching me the basics of mass spectrometry. Dr Marshall B remer and Dr Bai Nie were great coworkers and I learnt a lot about optics and lasers in general from both of them. Ant on, Ilyas and Gennady, I wi ll always be grateful to all of you for sharing ideas and helping solve problems. I hope that all of you get your dream jobs. To the newer members of the Dantus group, Muath it was a pleasure working with you and helping you start your own project. Dr. Rac hel Glenn, it was a pleasure collaborating with you on the phase step project and I have learnt a lot from you in this small amount of time. Dr. Richa Mittal and Adam, thank you for your friendship . I would like to acknowledge the fantastic collaboration w e had with Prof. Ben Levine, Prof James E. Jackson and Yinan Shu during the Strong Field project. Your relentless dedication and perseverance has resulted in this beautiful work being published as a cover article. I would like to acknowledge members of my guidance committee including Profs . James E. Jackson , Pior Piecuch , Chong - Yu Ruan and Gavin Reid . I would like to express my sincerest gratitude to all my committee members for the helpful discussions and support throughout the entire journey in the Gradua te school. vii I would like to take this opportunity to express my gratitude to the present and past Chemistry support staff for helping out with the non - science issues of graduate career. I would also like to thank Glenn Wesley from the Chemistry Machine Shop for doing an excellent job every time I went to him with a machining project. I would like thank my wonderful friends at MSU, for being there during good and bad times and for being a close knit group that made this adventure as a Spartan truly enjoyable. Thank you all for the great journey. I would like to take this opportunity to thank my parents. I fall short of words in expressing my gratitude for the unwavering support and unconditional love that they have shown and for all that they have given up in ensuring that I never fall have made this far without both of you. Thank you for believing in my dreams. I would like to thank my sister for her love and support and for looking after our parents. Special thanks go out to my in laws and my extended family for their best wishes. Lastly I wou ld like to thank my best friend and wife, Kamalika for her unconditional love, constant dedication and rock solid support. She is the source of my inner peace and a tre mendous source of encouragement . She has been with me through many testing moments and has shared the occasional moments of success during this eventful journey. viii TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ .......................... x LIST OF FIGURES ................................ ................................ ................................ ...................... xi KEY TO ABBREVIATIONS ................................ ................................ ................................ ... xviii Chapter 1 Introduc tion ................................ ................................ ................................ ..................... 1 1.1 Motivation ................................ ................................ ................................ ....................... 4 1.2 Nonlinear Optical Properties of Matter ................................ ................................ ........... 8 1.3 Strong Field Laser - Matter Interaction ................................ ................................ ........... 11 1.4 Techniques ................................ ................................ ................................ ..................... 14 1.4.1 Ultrafast Laser System ................................ ................................ ................................ 14 1.4.2 Pulse Shaper and Pulse Compression ................................ ................................ .......... 17 1.4.3 Time of Flight Mass Spectrometry ................................ ................................ .............. 24 R EFERENCES ................................ ................................ ................................ ............... 27 Chapter 2 Stokes Shift Dynamics using Chirped Femtosecond Pulses ................................ .......... 31 2.1 Introduction and Background ................................ ................................ ........................ 32 2.2 Chirped Femtosecond Pulses ................................ ................................ ......................... 35 2.3 Experimental Methods ................................ ................................ ................................ ... 37 2.4 Results and Discussion ................................ ................................ ................................ .. 38 2.4 .1 Experimental Results ................................ ................................ ................................ ... 38 2.4.2 Theoretical Simulations ................................ ................................ ............................... 46 2.5 Conclusion ................................ ................................ ................................ ..................... 51 REFERENCES ................................ ................................ ................................ ............... 52 Chapter 3 Solvent Environment Revealed by Positively Chirped Pulses ................................ ....... 55 3 .1 Introduction ................................ ................................ ................................ .................... 56 3 .2 Experimental Methods ................................ ................................ ................................ ... 58 3 .3 Experimen tal Results ................................ ................................ ................................ ..... 59 3.4 Discussion ................................ ................................ ................................ ...................... 62 3.5 Conclusion ................................ ................................ ................................ ..................... 64 REFERENCES ................................ ................................ ................................ ............... 65 Chapter 4 Coherent Q u a n t u m Control of Stimulated Emi ssion ................................ ...................... 69 4 .1 Introduction ................................ ................................ ................................ .................... 70 4 .2 Experimental Methods ................................ ................................ ................................ ... 72 4 .3 Results and Discussion ................................ ................................ ................................ .. 75 4.3.1 Experimental Results ................................ ................................ ................................ ... 75 4 .3.2 Theoretical Simulations ................................ ................................ ............................... 78 ix 4.4 Conclusion ................................ ................................ ................................ ................... 82 REFERENCES ................................ ................................ ................................ ............. 83 Chapter 5 Polyatomic Molecules under Intense Femtosecond L a s e r Irradiation ......................... 86 5 .1 Introductio n ................................ ................................ ................................ .................. 87 5 .2 Experimental Methods ................................ ................................ ............................... 102 5 .3 Quantum Chemical Calculations ................................ ................................ ............... 105 5 .4 Results ................................ ................................ ................................ ........................ 107 5 .4.1 Mass Spectra ................................ ................................ ................................ ....... 107 5 .4.2 Preliminaries ................................ ................................ ................................ ....... 116 5 .4.3 Carbonyl Group Substituents and Locked Compounds ................................ ..... 119 5 .4.4 Functional Groups and Positional Isomerism ................................ .................... 123 5 .5 Discussion ................................ ................................ ................................ .................. 134 5 .6 Conclusion ................................ ................................ ................................ ................. 140 R EFERENCES ................................ ................................ ................................ ........... 14 2 Chapter 6 Reverse Diels Alder Reaction following Strong Field Ionization .............................. 149 6 .1 Introduction ................................ ................................ ................................ ................ 150 6 .2 Experimental Methods ................................ ................................ ............................... 152 6.3 Results ................................ ................................ ................................ ........................ 153 6.3 .1 Intensity Dependence of Mass Spectrum ................................ ........................... 153 6.3 .2 Pump - probe Tr ansients ................................ ................................ ....................... 156 6 . 4 Discussion ................................ ................................ ................................ .................. 161 6 . 5 Conclusion ................................ ................................ ................................ ................. 163 REFERENCES ................................ ................................ ................................ ........... 16 4 Chapter 7 Su mmary and Future Directions ................................ ................................ ................ 167 7.1 Single Beam Phase Shaped Pulses for Probing Solvated Molecules ......................... 168 7.2 Behavior and Dynamics of Polyatomic Molecule s under Strong Field ..................... 17 1 x LIST OF TABLES Table 5.1 Energy required to dissociate the acetophenone radical cation via various fragmentation channels. These values were calculated from the heats of formation of different species obtained from NIST. The values given for correspond to the number of photons that would be required given a photon energy of 1.55eV. ................................ ................................ . 113 Table 5.2 Fragment ion yield ratios with respect to benzoyl ion yield for most of the compounds. Unusual ratios have been highlighted in bold. ................................ ................................ ............ 116 Table 6.1 Fitting parameters for the ion yield modulations of the parent and fragment ions using the formula . ................................ ................................ ......................... 160 xi LIST OF FIGURES Figure 1.1 Jab lonski diagram illustrating one p hoton absorption, fluorescence, stimulated emission, excited state absorption, internal conversion, intersystem crossing, and phosphorescence. ................................ ................................ ................................ .......................... 10 Figure 1.2 Binding potential of an atom (light gray line), valence electron energy (~10 eV) (black dashed lin e), laser dressed binding potential in the tunneling ionization case (gray) and laser dressed binding potential in the over the barrier case. ................................ ......................... 11 Figure 1.3 Regenerative amplifier and CPA technique; (a) illustrates the temporal pulse shape evolution in CPA . (b), (c) and (d) illustrate the stretcher, regenerative amplifier and compressor, respectively. The combination of (a), (b) and (c) gives a full optical layout of a regenerative amplifier based on CPA. FI: Faraday isolator, Gl and G2: grating, CM: curved mirror, LM : long mirror, P: periscope, PC1 and PC2: Pockels cells, and /2: half - wave plate. .............................. 15 Figure 1 .4 Schematic of a 4f pulse shaper where a transform limited input pulse is transformed into an arbitrarily shaped pulse. ................................ ................................ ................................ .... 18 Figure 1 .5 Schematic of a folded 4f pulse shaper . CM is a gold curved mirror and M3 is the back m irror. M1 and M2 are mirrors. ................................ ................................ ................................ .... 19 Figure 1.6 LCOS chip structure ( www.hamamatsu.com ) . ................................ ........................... 21 Figure 1.7 Simulation of a MIIPS scan. Example of a sinusoidal phase scan for pulses having (a) flat phase, (b) 400 fs 2 second order dispersion and (c) 4000 fs 3 third order dispersion and chirp scan for pulses having (a) flat phase, (b) 400 fs 2 second order dispersion and (c) 4000 fs 3 third order dispersion. ................................ ................................ ................................ ............................ 23 Figure 1.8 Schematic of the time of flight (TOF) mass spectrometer. R epeller plate has a voltage of 2500 V, extractor plate has a voltage of 1600 V and the third plate is grounded. The field free drift region is 0.5 m long. The sample is introduced into the chamber via a manual valve. A focused laser beam is shown in red. ................................ ................................ ............................... 2 5 Figure 1.9 Simulation showing the dependence of power along the radius of a Gaussian beam (black) along with the radial probability of field ionization (red) and six - photon ionization of the molecules (blue). R 0 represents the distance at which the proba bility of field ionization is zero. Radial probability is the amount of molecules ionized within a cylinder of thickness dr at a distance r at the same intensity of I(r). In the above example, probability of ionization is 1 above threshold I th and zero bel ow the threshold. Maximum intensity of the pulse is double that of the threshold value. The shaded gray area represents the very small contribution of the multiphoton ionization in absence of field ionization. The relative contribution can be estimated to be only about 1% of the total amount. ................................ ................................ ................................ ....... 26 xii Figure 2.1 Simulation of spectral intensity (black) and phase (blue) (first column), temporal intensity (black) (second column) and spectrogram (third column) corresponding to a 15 fs pulse having (a) zero phase, (b) positive chirp and (c) negative chirp. ................................ .................. 36 Figure 2.2 Experimental setup. The amplified output beam is attenuated and sent to a Spatial Light Modulator ( SLM ) based folded 4 - f shaper. ................................ ................................ ......... 37 Figure 2.3 Absorption (black), spectra of the laser (red), fluore scence spectra (green), and coherence emission (blue). ................................ ................................ ................................ ............ 38 Figure 2.4 (a) Experimental interferometric frequency resolved optical grating ( xFROG ) trace for the transform limited 36 fs pulses. (b) Experimental data (black dots) for SHG Chirp scan along with the theoretically simulated curve (red line). Dependence of integrated intensity of fluorescence (c) and stimulated emission (d) as function of chirp at different intensities of the laser pulse. Difference between fluorescence measured at different chirp values normalized to transform limited ( TL ) pulse excitation as a function of chirp for (e) fluorescence and (f) stimulated emission. ................................ ................................ ................................ ...................... 41 Figure 2.5 Dependence of integrated intensity for (a) fluorescence and (b) stimulated emission as a function of avera ge laser power flux for the TL excitation. The value of chirp effect as a function of calculated probability of one photon excitation with TL pulse are shown for (c) fluorescence and (d) stimulated emission. The y - axis is the difference between the maximum and minimum of the value measured at different pulse energies. The red curves represent quadratic fits to the experimental data. ................................ ................................ ................................ ......... 43 Figure 2.6 [Max (Intensity of fluorescence) Min (intensity of fluorescence)] / (Intensity of fluorescence of TL pulse) p lotted as a function of the probability of excitation for IR 144. Red line is the linear fit to the data. ................................ ................................ ................................ ...... 44 Figure 2.7 Normalized fluorescence detected (red) and stimulated emission detected (blue) chirp effect for different laser intensities. ................................ ................................ .............................. 45 Figure 2.8 Schematic of the four level model used to simulate the experimental results . 0 represent the transition frequency, is carrier frequency of the pulse, V is the dipole interaction of transitions with light, is the relaxation rates in ground and exc ited states, are the dephasing rates, are elements of density matrixes representing the population and the coherences. ......... 46 Figure 2.9 Normalized plots of (a) experimentally determined and (b) theoretically simulated chirp dependence of fluorescence (re d) and stimulated emission (blue). Experimental curves are chirp effects averaged over inhomogeneous broadening of absorption and emission lines. ........ 48 Figure 2.10 Spectra of the states in the upper directly excited state (black) and second relaxed exited s tate (green) used in the model together with laser spectrum (red). The symmetry of positions of corresponding states are marked with arrows. ................................ .......................... 50 xiii Figure 3.1 Fluorescence and stimulated emission response to chirped pulses for IR125 (a) and (b) and for IR144 (c) and (d) respectively in ethylene glycol at three temperatures 278K (blue), 294K (black), and 323K (red). The plots have been normalized on the asymptotic value of the chirp effect. ................................ ................................ ................................ ................................ ... 60 Figure 3.2 Fluorescence (black) and stimulated emission (red) dete IR125 and IR144 dissolved in ethylene glycol at 323 K. Data were normalized to their minimum and maximum value s , to take into account differences in fluorescence quantum yield in the two solvents. ................................ ................................ ................................ ................................ ........ 63 Figure 4.1 (a) Experiment al Setup. The pulse shaper placed after the amplifier is used to perform the phase scans. The unfocussed beam is sent through the sample and stimulated emission is detected along the direction of propagation of laser via a compact spectrometer. (b) Spectru m 73 Figure 4.2 (a) Laser fundamental as a function of s across the spectrum. ................................ ............................... 74 Figure 4.3 - - s are scanned over the excitat ion spectrum. ................................ .............. 76 Figure 4.4 Experimental data obtained for IR125 solution in methanol. Sections at 795.09 nm (black), 800.12 nm (red), 805.11 nm (blue), 810.07 nm (magenta), 815.18 nm (olive), 820.05 nm (navy) and 825.08 nm (violet) showing the difference - ... 77 Figure 4.5 Energy level diagram consisting of one ground and a number of vibrational excited states used for simulating the nonlinear stimulated emission. and signify the first and third order density matrix elements and is the dephasing rate. The excitation spectrum (red) is shown along with the absorption spectrum for IR125. ................................ ..................... 79 Figure 4.6 Simulations. Stimulated emission signal fr om a solu tion of IR125 in methanol when s are scanned over the excitation spectrum. ................................ .... 80 Figure 4.7 Comparison of the experimental stimulated emission signal (black) with the simulated signal (red) for s applied at 805.6 nm on the excita tion spectrum. ................................ ................................ ................................ ................................ ....... 81 Figure 5.1 Four cases illustrate schematically the behavior of polyatomic molecules under strong field excitation. Case (a) in the case of sparse electronic states such as in hexatriene, the threshold for ionization is typically a three or four photon excitation to the first excited state, followed by resonant multiphoton ionization. Excitation is typically limited to the ground state of the cation, and double ionization is observed for very intense fields. Case (b) the intermediate case involves additional resonances that result in the opening of additional ionization and photodissociation channels, resulting in a wider variety of fragment ions such as in the case of xiv decatetraene. Case (c) reduction in the density of non - degenerate states is observed due to the introduction of symmetry in the molecule. Case (d) offers a denser electronic state distribution and leads to a very wide range of photoionization and photodissociation pathways, making it unlikely to find the intact molecular ion p - carotene. The energy levels have been roughly approximated using Kohn - Sham (KS) orbital energies obtained at the B3LYP/6 - 31++G** level of theory. Neutral excitation energies were approximated as orbital energy diffe rences, with the lowest excitation energy shifted to match the experimental first excitation energy. Occupied orbital energies have been shifted to the experimental IP to approximate the energies of the cationic states. Neutral energy levels (black) have b een cut - off at the experimental IP and the blue lines represent the cationic ground and excited states. The red arrow represents energy of 1.5 eV. ................................ ................................ ............................... 97 Figure 5.2 The chemical structures of the molecules being studied are shown and have been divided into fo ur groups according to various trends. The first group corresponds to alkyl phenyl ketones having different alkyl substituents. The second group corresponds to similar compounds where the alkyl group is chemically bonded to the phenyl ring such that the ke to group is in plane. The third group represents alkyl phenyl ketones with different substituents at different positions on the phenyl ring. The fourth group consists of a number of di - substituted methyl acetophenones. ................................ ................................ ................................ ............................ 101 Figure 5.3 Schematic of the expe rimental setup. The amplified beam is split into two parts and recombined using beam splitters (BS) before sending it through an optical delay line consisting of a corner cube (CC). The collinear pump and probe beams are focused into the time of flight (TO F) mass spectrometer. ................................ ................................ ................................ ........... 103 Figure 5.4 The intensity of acetophenone molecular ion, the most abundant photoproduct from acetophenone, drops to zero within a half second after closing the valve, which confirms the fast flow of our system. ................................ ................................ ................................ ..................... 104 Figure 5.5 Mas s spectra of (a) benzaldehyde, acetophenone and propiophenone, (b) o - methylacetophenone, m - methylacetophenone and p - methylacetophenone, (c) o - fluoroacetophenone, m - fluoroacetophenone and p - fluoroacetophenone and (d) 2,4 - dimethylacetophenone, 3,4 - dimethylac etophenone and 3,5 - dimethylacetop henone corresponding to the negative time delays when the probe pulse precedes the pump . ................................ ....... 109 Figure 5.6 Mass spectra of (a) benzaldehyde, (b) acetophenone (c) propiophenone, (d) o - methylacetophenone, (e) m - methylacetopheno ne and (f) p - methylacetophenone, obtained using 70 eV electron ionization. (Source: webbook.nist.gov) ................................ .............................. 110 Figure 5.7 Mass spectra of (a) 2 - fluoroacetophenone, (b) 3 - fluoroacetophenone (c) 4 - fluoroacetophenone, (d) 2,5 - dimethylacetophenone and (e) 3,4 - dime thylacetophenone obtained using 70 eV electron ionization. (Source: webbook.nist.gov) ................................ .................... 111 xv Figure 5.8 Mass spectrum of acetophenone corresponding to W/cm 2 35 fs pulses showing limited fragmentation and the formation of lower mass fragments. Note that molecular and benzoyl ions have similar yield. ................................ ................................ ........................... 112 Figure 5.9 Resonance structures of the b enzoyl cation. ................................ ............................. 114 Figure 5.10 Mass spectra of (a) m - cyanoacetophenone and (b) p - cyanoacetophenone. ............ 115 Figure 5.11 Schematic illustrating t he strong - field ionization pump followed by the weaker probe laser pulse and fragmentation pathways for acetophenone. Strong - field ionization to the ground ionic state leads to twisting to a lower energy configuration. Subsequent excitation by the probe to higher excited ion states depletes the ion and leads to formation of products. The twist angle refers to the torsional motion of the acetyl group relative to the benzene ring. ................ 118 Figure 5.12 Normalized transients corresponding to the acetophenone molecu lar ion (black squares) along with the products, benzoyl (blue triangles) and phenyl (red circles) ions. The transients have been color coded according to the fragments and normalized to unity at negative time delays. ................................ ................................ ................................ ................................ . 119 Figure 5.13 Normalized molecular ion yields (black dots) as a function of delay of the probe pulse for the molecular ions from (a) Benzaldehyde, (b) Acetophenone, (c) Propiophenone and (d) Benzophenone along with the fit to the damped oscillations (red line). The plots have been normalize d to unity at negative time delays. ................................ ................................ .............. 120 Figure 5.14 The D 0 energy of benzaldehyde (red circles) and acetophenone (black squares) as a function of the twist angle is shown. ................................ ................................ .......................... 122 Figure 5.15 The D 0 , D 1 , D 2 , D 3 , D 4 , D 5 and D 6 state energies of acetophenone a nd benzaldehyde as a function of the twist angle of the acetyl group are shown in (a) and (b) respectively. Arrows indicate the positions of the S 0 minimum structures. ................................ ................................ .. 122 Figure 5.16 Normalized ion yields (black dots) as a function of delay of the probe pulse for the molecular ions (a) Indanone and (b) Fluorenone. The plots have been normalized to unity at negative time delays. ................................ ................................ ................................ ................... 123 Figure 5.17 Normalized ion yields (black dots) as a function of delay of the probe pulse for the molecular ions of (a) o - met hylacetophenone, (b) m - methylacetophenone, (c) p - methylacetophenone, (d) 2,4 - dimethylacetophenone, (e) 3,4 - dimethylacetophenone and (f) 3,5 - dimethylacetophenone along with the fit to the damped oscillations (red line). The plots have been normalized to the corresponding yield at negative time delays. ................................ ........ 125 Figure 5.18 (a) The D 0 energies of ortho - , meta - , and para - methylacetophenone as a function of the twist angle of the acetyl group are shown in black, red, and blue, respectively. Arrows indicate the posi tions on each curve corresponding to the S 0 minimum structures. Yellow lines superimposed on the geometric insets mark the four atoms which define the O - C1 - C2 - C3 xvi dihedral angle. (b) Singly occupied molecular orbitals of the D 0 state of para - , meta - , and o rtho - methylacetophenone cations at the neutral minimum energy geometries. ................................ . 126 Figure 5.19 The D 0 , D 1 , D 2 , D 3 state energies of ortho - , meta - and para - methylacetophenone as a function of the twist angle of the acetyl group are shown in (a), (b) and (c), re spectively. ....... 127 Figure 5.20 The D 0 , D 1 and D 2 energies of para - methylacetophenone cation as a function of the twist angle of the acetyl group. ................................ ................................ ................................ ... 128 Figure 5.21 SOMOs of the three lowest - energy cation states (D 0 , D 1 , and D 2 ) of para - methylacetophenone in t he planar - constrained S 0 minimum energy structure (left) and 35º twisted structure (right). Top and side views of each orbital are provided. ................................ 130 Figure 5.22 Normalized ion yields (black dots) as a function of delay of the probe pulse for the molecular ion s of (a) o - fluoroacetophenone, (b) m - fluoroacetophenone and (c) p - fluoroacetophenone. The plots have been normalized to unity at negative time delays. ............ 131 Figure 5.23 The D 0 energies of ortho - , meta - , and para - fluoroacetophenone as a function of the twist angle of the acetyl group are shown in black, red, and blue, respectively. Arrows indicate the locations of the S 0 minimum structures on each curve. ................................ ........................ 132 Figure 5.24 Normalized ion yields (black dots) as a function of delay of the probe pulse for the mol ecular ions of (a) m - cyanoacetophenone and (b) p - cyanoacetophenone. The plots have been normalized to unity at negative time delays. ................................ ................................ .............. 133 Figure 5.25 The D 0 energies of meta - , and para - cyanoacetophenone as a function of the twist angle of the acetyl group are shown in red and blue respectively. ................................ .............. 134 Figure 5.26 Time of flight mass spectra of acetophenone corresponding to different peak intensities corresponding to a 1 ps pulse. Absence of any molecular ion peak points towards the fact that fragmentation is p ulse duration dependent. ................................ ................................ .. 138 Figure 6.1 Photofragmentation scheme of dicyclopentadiene into two cyclopentadiene moieties under laser irradiation. The bonds marked in yellow break and rearrange to form the cyclopentadiene molecules. ................................ ................................ ................................ ........ 154 Figure 6.2 Mass sp ectrum o f d icyclopentadiene obtained with pulses having an average power of 7 µJ/pulse. At these low excitation powers CPD + yield is comparable to that of the DCPD + ion yield. ................................ ................................ ................................ ................................ ............ 156 Figure 6.3 (a) Normalized ion yield of DCPD + (black squares) and CPD + (red circles) as a function of laser power. (b) Ratio of CPD + and DCPD + ion yields (black circles) along with the linear fit. ................................ ................................ ................................ ................................ ...... 157 Figure 6.4 Double logarithmic plot of ion yield as a function of peak intensity for (a) DCPD + and (b) CPD + along with the linear f its (red line). The slope of the fit provide s information about xvii the number of photons involved to reach an intermediate neutral excited state during the ionization process. Slopes of 2 and 3 for DCPD and CPD respectively point to a two and three photon pro cess. ................................ ................................ ................................ ........................... 158 Figure 6.5 Normalized molecular ion yields (black dots) as a function of delay of the probe pulse for (a) C 10 H 12 + , (b) C 5 H 6 + , (c) C 4 H 4 + and (d) C 3 H 3 + and (e) C 2 H 2 + ions. Plots (e) - (j) show the fast oscillations along with the fits (red) for the parent and fragment ions. The left plots have been normalized to unity at negative time delays and the right plots were constructed by subtracting the slow decaying envelope from the raw data in order to extract the relatively fast oscillations. ................................ ................................ ................................ ................................ . 159 Figur e 6.6 Schematic illustration of the mechanism behind quantum coherent control of dicyclopentadiene fragmentation. Each red arrow corresponds to one 1.55 eV photon from the near - IR laser. ................................ ................................ ................................ ............................... 162 xviii KEY TO ABBREVIATIONS 3PEPS Three Pulse P hoton Echo Peak Shift ADK Ammosov Delone Kraniov ATI Above Threshold Ionization CARS Coherent Anti - Stokes Raman Scattering CPA Chirped Pulse Amplification CPD Cyclopentadiene CRATI Channel Resolved Above Threshold Ionization DCPD Dicyclopentadiene FW HM Full Width at Half Maximum HHG High Harmonic Generation HOMO Highest Occupied Molecular Orbital IP - EOM - CC Ionization Potential Equation of Motion Coupled Cluster IVR Intramol ecular Vibrational Relaxation i - XFROG interferometric Cross Frequency Resolve d Optical Grating LC Liquid Crystal LCOS Liquid Crystal on Silicon LUMO Lowest Unoccupied Molecular Orbital MCP Micro Channel Plate MIIPS Multiphoton Intrapulse Interference Phase Scan MO - ADK Molecular Orbital Ammosov Delone Kraniov MP2 Moller - Plesse t Second Order Perturbation Theory xix MRCI Multi Reference Configuration Interaction MS Mass Spectrometry MSAE Molecular Single Active Electron NLO Nonlinear Optical NME Nonadiabatic Multielectron Theory PES Potential Energy Surface SAE Single Active E lectron SFI Strong Field Ionization SLM Spatial Light Modulator SOMO Singly Occupied Molecular Orbital STIRAP Stimulated Raman Adiabatic Process TD - RIS Time Dependent Resolution in Ionic States TL Transform Limited TOF Time of Flight WPI Wave Packet Interferometry 1 Chapter 1 Introduction This thesis deals wit h understanding ultrafast laser - matter interactions using shaped femtosecond pulses for systems ranging from dye molecules in solution to polyatomic molecules in the gas phase. Experimental resu lts along with theoretical simulations and ab initio calculations have been presented. Study and control of solvated dye molecules elucidate processe s like inhomogeneous broadening and solvatochromic shift and to determine the electronic coherence lifetime s of solvated molecules using phase shaping based single beam methods . On the other hand , investigation of polyatomic molecules in the gas phase using strong fields provides an understanding of ionization and fragmentation mechanism and sheds light on the dynamical behavior of these molecules in the cationic ground and excited states . The rest of the thesis is organized as follows: Chapter 1 starts with a brief motivation behind carrying out the studies presented in this thesis followed by a short excursion into the nonlinear optical properties of matter and an introduction to strong field laser - matter interaction. T he tools and techniques employed and associated principles are then described in detail . In particular, the ultrafast amplified laser system , pu lse shaper used to compress and shape the ultrafast pulses and the homebuilt time of flight mass spectrometer are described. Chapter 2 is focuses on understanding the effect of chirped femtosecond pulses on solvated dye molecules. The effect is studied vi a monitoring the fluorescence and stimulated emission signal from the molecules. The magnitude of the overall chirp effect on fluore scence and stimulated emission wa s found to depend quadratically on pulse energy, even for very low excitation probabilities . Also , the shape of the chirp effect curve was found to be independent o f 2 pulse energy and was found to depend on the electronic relaxation and solvent rearrangement following excitation. Chapter 3 builds on the important outcomes of interaction of chirpe d pulses with solvated dye molecules and discusses how these pulses can be used as a tool to probe inter - and intra - molecular dynamics. In particular the behavior of two different dye molecules in ethylene glycol was studied as a function of solvent viscos ity. It was found that positively chirped pulses are an efficient tool that can detect changes in solvent environment , while negatively chirped pulses , being similar to a pump - probe kind of sequencing , are sensitive to the internal dynamics and coherence d ephasing of the dye molecules. Chapter 4 explores the use of a different kind of phase shaped pulse in elucidating the behavior of these solvated dye molecules using a single beam approach. To that end the effect that a phase step on the excitation spectru m has on the stimulated emission signal was investigated. It was found that the high frequency components were absorbed and a sharp narrow - band enhanced emission of the low frequency components was observed at the step position . A /2 step was found to cau ses greater enhancement than a step. Interestingly, the negative /2 step was found to induce absorption instead of emission. These features in the stimulated emission spectrum are found to be sensitive to the molecular properties from the theoretical si mulations. Chapter 5 deals with the investigations of the behavior of polyatomic molecules under strong laser fields. A set of experiments along with theoretical calculations exploring the dynamical behavior of a large collection of aryl alkyl ketones was investigated . In particular , it was considered to what extent molecules retain their molecular identity and properties under strong laser fields 3 was found that following ionizati on a relatively cold molecular ion is left behind and further fragmentation is contingent on the presence of resonant cationic excited states. Chapter 6 explores the behavior of dicyclopentadiene under strong field excitation via time resolved mass spectro metry. Dicyclopentadiene is capable of undergoing a reverse Diels Alder type of reaction to produce two cyclopentadiene molecules upon excitation . It was found that the molecular ion shows modulations in ion yield which are different from the ion yield mod ulations observed for other fragment ions. The modulations in the dicyclopentadiene molecule yield are assigned to the C - C stretching frequency of the bonds connecting the two rings for the neutral molecule. The entire research work presented in this thes is is summarized in Chapter 7 and future directions are discussed. 4 1.1 Motivation Chemical bonds are responsible for holding together the atoms in a molecule that constitute the entire matter known to mankind. Chemists and physicists all over t he world are striving to understand how these bonds are formed and/or broken during chemical reactions and trying to exert control on these processes . T he nature of the chemical bond 1 and the ensuing molecular dynamics (usually in the range of a few femtoseconds (10 - 15 s) to hundreds of picoseconds (10 - 12 s)) will be determined by the electromagnetic forces between the nuclei and their valence electrons . The in vention of the laser in 1960 2 , followed several years later by the first pulsed laser, opened up a large number of new avenues for research in physics and chemistry and biology . It allowed high resolution spectr oscopy to unravel the rotational, vibrational and electronic energy structure of molecules with unprecedented spectral precision. 3 - 5 The average power that a femtosecond laser beam carries is actually concentrated in the femtosecond time duration of the pulses constitu ting the pulse train. As a consequence, femtosecond laser pulses give rise to extremely high peak powers, which typically fall in the range 10 4 - 10 6 W /cm 2 for a non - amplified system. When such a laser beam is focused, peak power densities of 10 10 W/cm 2 are obtained at the focal plane. These peak power densities are high enough to generate nonlinear optical (NLO) processes that are useful for many applications, includi ng biological imaging. Chirped pul se amplification (CPA) 6 w as a major advance that allowed the increase of maximum intensity of produced pulses. Pulses shorter than about 100 fs, that are routinely produced in the infrared range of wavelengths using CPA, reach a peak intensity that is comparable to the scale of at omic electric fi eld (10 11 V/m), su ffi cient to ionize electrons from atoms and molecules. 7 In addition to the peak intensities they provide, ultrafast lasers enabl e 5 time - resolved measurements to be performed on molecular systems, where a pump laser initiates dynamics that can subsequently be probed by another ultrafast laser pulse. This combination of fi eld strength and time - resolution makes ultrafast lasers an esse ntial and unique tool for studying the dynamics and structure of atoms and molecules and cations , since they can both initiate and probe nuclear and electronic dynamics. For many decades physicists and chemists have employed various spectroscopic methods to carefully observe quantum systems on the atomic and molecular scale. The desire to go a step further and exert control over the quantum systems gave birth to the field of quantum control. 8 , 9 Having explored the perturbative reg ime, it was soon realized that strong electric fields on the order of magnitude of molecular field strength were necessary for breaking the chemical bonds. 8 Laser fields in particular can be chosen stron g enough to modify the potential energy surfaces which govern the molecular dynamics. 10 This goal appears increasingly within reach due to rapid development in femtosecond (fs) laser and pulse shaping technologies which permit the production of very high power, well - characterized yet variabl e coherent optical wave forms. The role of q uantum interference in optical control of molecular systems was identified by Brumer and Shapiro 11 wherein they proposed using two monochromatic laser beams with commensurate frequencies and tunable intensities and phase for creating quantum interference between two rea ction pathways. Tannor and Rice 12 proposed the method of pump - dump for selectively controlling the intra - molecular reaction by using two successive femtosecond laser pulses with a tunable time delay. Several other techn iques like sti mulated Raman adiabatic passage 13 (STIRAP) and wave packet interferometry 14 (WPI) were also exploited. All the above methods employ the phenomenon of quantum inter ference at the fundamental level where the phase difference between the two laser fields is the controlling parameter. 6 With the development of pulse shaping technologies scientists began to modify femtosecond laser pulses by adding linear chirp, first to control wave packet motion, 15 and then to control th e yield of chemical reactions. 16 It was also used in the selective excitation of vibrational modes in coherent anti - Stokes Raman scattering (CARS). The combination of shaped femtosecond pulses with mass spectrometry (MS) has proven to b e the most promising technology for laser control of chemical reactions. O nly a few groups have conducted these types of experiments and succeeded in understanding the physical phenomena and rationale behind the observed control results . A systematic and t horough search for laser control of fragmentation using known phase functions was performed by our group and found that linear chirping of the pulses was sufficient to cause changes by almost two orders of magnitude. 17 To gain a better understanding of the control phenomena, it is extremely important to discern the basic processes which play significant role during strong field ionization. A variety of strong field effects are observed when molecules are subject to intense femtosecond and picoseconds laser pulses. 18 These effects include field tunneling a nd barr ier - suppression ionization, 19 - 21 above - threshold ionization, 22 , 23 generation of highe r - order harmonic emissions, 24 , 25 field - induced resonant enhancement of ele ctronic absorption, 26 , 2 7 and nonadiabatic multi electron excitation. 28 , 29 All of these processes generally res ult in the generation of ch arged ions, photoelectrons and photons. It will be extremely important to determine to what extent these processes can be controlled by modifying the temporal shape of the laser field according to the molecular timescales for electronic (<50 fs), vibration al (10 - 1000 fs), and rotational (1 - 100 ps) coherence, and the rates at which these different coherent oscillations dephases. The issue of coherence and dephasing is not only important for understanding the processes under strong fields but is also very im portant for photochemical processes occurring in 7 nature under perturbative excitation . Advances in optical spectroscopic methods are allowing us to investigate quantum molecular models associat ed with the early time dynamics of these processes . The most im portant is the quantum coherence in photochemistry for harnessing solar energy. The relevant timescales regarding photo - excitation in solution are determined by the inter - and intra - molecular interactions and their corresponding energy fluctuations, which occur in the 10 - 100fs regime. 30 - 32 I nteraction of light with the system takes place coherently through absorption and stimulated emission, and incoherently through fluo rescence. In order to ascertain the role of coherence in photochemical reactions, it is pertinent to determine the timescale over which phase coherence is maintained by the system and thus understanding and controlling the interactions at the microscopic l evel is a very important challenge. The study of laser - matter interactions thus leads to a fundamental understanding of the structure and properties of the matter and also of the behavior of atoms and molecules in response to electromagnetic radiation in t he perturbative and extreme regimes. 8 1.2 Nonlinear Optical Properties of Matter Recent developments in femtosecond lasers have enabled the production of high peak powers pulses . These p ulses can induce interesting phenomena in the system during laser matter interaction . The time varying polarization of a molecule due to the interaction with a time varying electric field leads to the creation of a new electromagnetic field. This process can be described mathematically using the wave equation ( 0 . 1 ) where n is the linear refractive index and c is the speed of light in vacuum. This expression can be interpreted as an inhomogeneous wave equation where t he second order term of the nonlinear polarization describes the acceleration of charges due to the presence of an electric field. In order to und erstand the nonlinear properties of matter it is important to understand how the dipole moment per unit volume or polarization P(t) depends on the electric field strength E(t) of an applied field. In the linear domain of interaction this is mathematically described by, ( 0 . 2 ) where the constant of proportionality is known as the linear susceptibility and is the permittivity of free space. However in the presence of high enough fields this relationship and the equation for linear response must be generalized for nonlinear response. This is done by expressing the polarization as a power series in the field strength as ( 0 . 3 ) The quantities and are known as the second and third order non - linear optical susceptibilities, respectively. In media having inversi on symmetry, such as isotropic media, the 9 even - order susceptibilities vanish. This is since the polarization must change its sign when the optical electric fields are reversed. Therefore, for most media the lowest order nonlinearity is the 3 rd - order nonlin earity. The macroscopic polarization originating from the media is given by the expectation value of the dipole operator µ as . For a two level system, ( 0 . 4 ) and ( 0 . 5 ) Therefore we see that the off diagonal elements of the density matrix give rise to a macroscopic polarization and emit a light field. The linear macroscopic polarization, is g enerated due to the absorption of a photon and this in turn generates an electric field with a 90 0 phase lag and can be represented as .This is called a free induction decay signal. A third order polarization is generated from the sample when the field interacts more than once with the sample. In a typical pump - probe experiment the pump pulse interacts twice with the sample and the probe pulse once. The resulting coherence emits an electric field that is heterodyne detected with th e probe. For the experiments presented in chapters 2, 3 and 4 , a single beam approach was taken and the transmitted nonlinear signal which is heterodyned with the excitation field was detected along the direction of propagation. The detected signal is . A Jablonski diagram illustrating the electronic processes associated with the molecule is shown in Fig. 1.1. 10 Figure 1.1 Jablonski diagram illustrating one photon absorption, fluorescence, stimulated emission, excited state absorp tion, internal conversion, intersystem crossing, and phosphorescence. 11 1.3 Strong Field Laser - Matter Interaction Laser - matter interaction s in the weak field can be described perturbatively, where the unperturbed Hamiltonian is the atomic or mo le cular Hamiltonian, while the fi eld is treated as a small perturbation. How ever, when the electromagnetic fi eld is very strong, p erturbation theory fails and the interactions lead to processes such as ionization and high harmonic generation . The two regimes in whi ch laser - driven strong - fi eld ionization (SFI) can occur that are relevant for the work presented in this thesis, are the quasi - static tunneling regime and the multiphoton regime. Figure 1. 2 illustrates these regimes for the Coulombic binding potenti al of an atom. The binding potential of a molecule is more complicated, with structure refle cting the multiple nuclei present and advanced ab initio calculations need to be performed in order to predict the potential surface along a reaction coordinate as discussed in Chapter 5 . Figure 1.2 Binding potential of an atom (light gray line), valence electron energy (~10 eV) (black dashed line), laser dressed binding potential in the tunneling ionization case (gray) and laser dressed binding potential in the ov er the barrier case. 12 When the laser frequency is suffi ciently small, atoms and molecules ionize via tunneling through a barrier arising from the shape of the laser - dressed binding potential. In the multiphoton regime, the ionization occurs through the ab sorption of multiple photons needed for the bound electron to gain enough energy to reach one of the continuum states. The two ionization regimes are commonly characterized by the Keldysh adiabaticity parameter , where ( 0 . 6 ) Here I P is the ionization potential and U P is the ponderomotive energy or the average energy of the electron oscillation in the laser field, is the central frequency of the laser and is the field amplitude. The field amplitude or strength is related to the peak intensity of the laser as , where Z 0 is the resistivity of I is the peak intensity of the laser pulse. Peak intensities of the order of 10 13 W/cm 2 , produce an electric field strength that is comparable to that of valence electrons in molecules (~1 V/Å). The condition of is referred to as quasi static tunneling , while multiphoton ionization corr esponds to . T unneling time is an important concept that needs to be defined ; it is the time it would take the electron to cross the barrie r moving in a n uniform electric fi eld, if the process were classically allowed. For this process (setting electron mass m e =1, and electron charge e =1), the velocity of the electron as a function of time is given by . Here and for tunn eling , results in an electron produced in the continuum with zero energy i.e, . This leads to a tunneling time of . When the Keldysh parameter is expressed in terms of laser frequency , the tunneling frequency which is defined as leads to . 13 The quasi - static tunneling regime is characterized by . So the shape of th e barrier does not change sig nifi cantly during the tunneling process . 33 It is an interplay of laser frequency , ionization potential and fi eld strength that leads to quasi - static tunneling being the dominant eff ect in an ionization process. The fi eld strength has to be high enough to tilt the potential suffi ciently to give rise to a fi nite barrier, while the frequency has to be low enough that t he condition from equation is satisfi ed for tunneling to take place on a sub - cycle timescale. It should be noted that a tunneling component is present in the multiphoton regime as well. This tunneling di ff ers from the quasi - static one, in that the barrier shape changes during the tunneling process. The multiphoton nature of ionization by intense, high - frequency laser fi elds is particularly clear in the photoelectron spectra taken at intensities high enough that more photons than required for ionization are absorbed. The photoelectron spectra show a periodic structure, where the spacing between features corresponds to the photon energy. 34 Chapters 5 and 6 of this thesis deal with processe s occurring follow ing strong fi e l d ionization where a new model of behavior of polyatomic molecules under strong fields has been proposed and the vibrational coherence in the dissociation of dicyclopentadiene under strong field has been studied. 14 1.4 Techniques 1.4.1 Ultrafast Laser System All the experimental results presented in this thesis were carried out using a n ultrafast Ti: Sapphire regenerative amplifier (Spectra - Physics, Spitfire) . The amplifier is seeded by an oscillator (KM labs) pumped by the second harmon ic of a Nd:YVO4 laser (Millennia - Spectra Physics), resulting in femtosecond pulses centered around 800nm and with a spectral bandwidth of 40nm full width at half maximum( FWHM ) at 86MHz and an average power of 380mW. For t he experiments presented in chapter s 2 and 5, the output ultrash ort pulses from the oscillator we re shaped with a phase only pulse shaper having a 640 pixel Spatial Light Modulator (MIIPS Box, B iophotonic S olutions I nc. ). The SLM modulates the relative phases of the different frequency comp onents by applying appropriate voltage to each element. The spectral phase modulation applied by pulse shaper is preserved during amplification. T he amplifier is pumped by the second harmonic of the Nd: YLF laser (Spectra - Physics, Evolution X, 1kHz) with a n output of 0.73 mJ/pulse centered at 800 nm with a 1 kHz repetition rate. The bandwidth of the amplified pulses is around 28nm FWHM, resulting in 35fs transform limited (TL) pulses. The amplifier works on the chirped pulse amplification technique that wa s developed by Mourou and co workers 6 in 1985 in order to mitigate the effects of nonlinear pulse distortion and damage of the gain me dium and other optical elements arising due to the high peak intensity of the optical puls es during the amplification process in the previous designs. 15 Figure 1. 3 Regenerative amplifier and CPA technique; (a) illustrates the temporal pulse shape evolution in CPA. (b), (c) and (d) illustrate the stretcher, regenerative amplifier and compressor , respectively. The combination of (a), (b) and (c) gives a full optical layout of a regenerative amplifier based on CPA. FI: Faraday isolator, Gl and G2: grating, CM: curved mirror, LM : long mirror, P: periscope, PC1 and PC2: Pockels cells, and /2 : half - wave plate. The idea of CPA is illustrated in Fig. 1.3 (a). The seed pulses from the oscillator are chirped, i.e. temporally stretched to a much longer (~ps) duration by highly dispersive optics, e.g., a stretcher comprising a pair of gratings ( Fig. 1 .3 ( b)), before they pass through the gain medium. The stretched pulses have significantly less peak intensity (3 - 5 orders of magnitude lower), and relieve the detrimental effects during amplification. The amplified pulses are then 16 temporally compressed to the temporal duration comparable to that of the seed pulses by removing the chirp with a grating - pair compressor (Fig. 1.3 (d)) and the very high peak intensity is restored. The optical layout of a regenerative amplifier with CPA is shown in Fig. 1.3 . The amplified systems used in this dissertation for all the experiments are based on the design introduced by Positive Light which first was marketed by Spectra Physics and then purchased by Coherent. The Spitfire and can generate - 35 fs pulses . 17 1.4 .2 Pulse Shaper and Pulse Compression Pulse shapers are devices that enable one to manipulate the phase and amplitude of individual frequency components of the laser pulses according to the specification and thus have become an important tool to cor rect for spectral phases and control laser - driven processes. S imple and routine pulse shaping tasks such as imposing a quadratic spectral phase (chirp) on a pulse can be carried out with passive optics such as prism - or grating - based compressors and are us ed in ultrafast amplifiers to compress the stretched amplified pulses after the regen cavity. M ore complex pulse shaping tasks such as imposing higher order (>2) polynomia l or sinusoidal spectral phases require the use of programmable pulse shapers. Applic ations of programmable pulse shapers include femtosecond laser pulse characterization and compression , control of non linear optical processes , 35 , 36 nonlinear microscopy , 37 , 38 and coherent control of ph ysicochemical processes . 39 Fourier - transform pulse shapers manipulate pulses in the frequency domain by spatial masking of the spatially dispersed frequ ency spectrum of the pulses . 40 In simple terms these devices advance or retard individual frequency components within the pulse. Figu re 1.4 shows the Fourier - transform pulse shaper apparatus, consisting of a pair of diffraction gratings and a pair of lenses arranged in a configuration known as "4 f configuration" or "zero dispersion pulse compressor", and a spatial light modulator (SLM) placed at the Fourier plane. The whole optical setup is called a 4 f setup since all optical elements are separated by the focal length f of the lenses . If the distance between the grating and lens ( L ) is less than the focal length ( f ), it behaves as a puls e stretcher, where red frequencies come ahead of blue frequencies while for the case of L > f , it becomes a pulse compressor. However, this layout will cause some spatial chirp in the 18 output pulses, which is unwanted and a signature of a poorly aligned shape r . So, in order to get the desired results the shaper should be ideally in a 4 - f layout. Figure 1 .4 Schematic of a 4f pulse shaper where a transform limited input pulse is transformed into an arbitrarily shaped pulse. The 4 - f scheme can be modified by folding the setup at the Fourier plane using a r eflection mirror placed behind the SLM as shown in Fig 1.5 . This approach reduces the number of optical elements and space and doubles the maximal phase retardance as compared to the transmission design since the light travels through the SLM twice . 19 Figure 1 .5 Schematic of a folded 4f pulse shaper . CM is a gold curved mirror and M3 is the back mirror . M1 and M2 are mirrors. The frequency components of the input beam are angularly dispersed by the first di ffraction grating (a prism can also be used) and then focused by the first lens (a focusing mirror can also be used). It is worth noting that the pair of the lenses forms a 1:1 telescope and both gratings are placed at the focal planes of the lenses. There fore, the different frequency components are spatially separated and focused by the first lens at the Fourier plane, i.e. at the plane in the center between the pair of lenses. This is equivalent to a Fourier transform of the pulse from the time domain to the frequency (or spectral) domain. The second half of the optical setup recombines all the frequency components, i.e. inverse Fourier transforms the pulses back into time domain. In the absence of the SLM the output should be identical to the input pulse (therefore the name "zero dispersion pulse compressor"). In a Fourier - transform pulse shaper a SLM is placed at the Fourier plane to manipulate the spatially dispersed frequency components of the beam. 20 The most popular kind of SLM is the liquid crystal (L C) - SLM, the device used for the research described in Chapters 2 , 5 and 6 in this dissertation. A LC - SLM is basically a thin layer of nematic liquid crystal sandwiched between two pieces of glass, with the inside surface of each piece coated with a thin and transparent electrically conducting material patterned into a number of separate electrodes, called pixels. When an electric field is applied to a pixel, the liquid crystal molecules tilt causing a change of the refractive index. The liquid crystal is bir efringent, therefore the applied voltage can introduce pure phase retardation or a combination of phase retardation plus polarization rotation depending on the polarization of the incoming light with respect to the liquid crystal axis. Both situations are useful for pulse shaping purposes. A pulse shaper (MIIPS - HD, Biophotonic Solutions Inc.) based on a newer kind of SLM known as Liquid Crystal on Silicon Spatial Light Modulator (LCOS - SLM , Hamamatsu Corp. ) was used for studies presented in Chapters 3 and 4 . This is a spatial light modulator having a structure in which a liquid crystal layer is arranged on a silicon substrate. The top layer consists of aluminum electrodes each of which controls its electrical potential independently. The electric field acros s the liquid crystal layer can be controlled pixel by pixel. The LCOS - SLM can be operated in both reflection mode and diffraction mode. In the diffraction mode the SLM acts as a grating and can achieve both phase and amplitude modulation by manipulating am ount of light in the different diffraction orders. Figure 1 .6 shows the construction of the LCOS - SLM and how the orientation of the liquid crystals shape the input light. 21 Figure 1.6 LCOS chip structure ( www.hamamatsu .com ) . Based on the manipulation of individual pixels and the resulting control of individual spectral components , the Dantus group developed and commercialized a pulse char ac terization and compression method known as Multiphoton Intrapulse Inter ference Phase Scan (MIIPS). 41 , 42 T he phase distortion in the original pulse can be determined b y adding a defined spectral phase to the laser spectrum and measuring the resulting change in the second harmonic ( SHG ) signal . The physical principle at the heart of this method is nonlinear interference of different frequency components within a pulse , which depends on the spectra l phase, and leads to changes in the SHG spectrum. The electric field of a pulse can be written as ( 0 . 7 ) where is the electric field of the pulse in the frequency domain and is the spectral phase of the pulse. This pulse when focused into a thin SHG crystal gives rise to the SHG signal which can be represented as, ( 0 . 8 ) 22 The phase modulation is typically a continuous function, therefore a Taylor series expansion around can be written . The Taylor series expansion of the sum of the phases at positive and negative detuning is represented as ( 0 . 9 ) where . To first approximation, neglecting higher order even terms, the SHG spectrum has a local maximum at when the second order phase distortio n, equals zero since the SHG spectrum is maximized when is zero according to eq 1.8. Therefore upon introduction of a reference phase , the SHG intensity at a certain frequency is maximized when where is the second derivative of the original phase of input pulses and is the second derivative of the reference phase. Usually a second o rder dispersion or a sinusoidal reference phase is applied in order to measure the original phase of the pulse. This is done by tracking the local maximum of the SHG signal corresponding to each scanning parameters. Assuming a transform limited pulse ( =0), f or a sinusoidal function the maxima are lines having a certain slope second order dispersion it is a straight line equal to zero. For different kinds of phase distortions deviation from this behavior is observed as shown in Fig 1. 7 . 23 Figure 1.7 Simulation of a MIIPS scan. Example of a sinusoida l phase scan for pulses having (a) flat phase, (b) 400 fs 2 second order dispersion and (c) 4000 fs 3 third order dispersion and chirp scan for pulses having (a) flat phase, (b) 400 fs 2 second order dispersion and (c) 4000 fs 3 third order dispersion. 24 1. 4 . 3 Time of Flight Mass Spectrometry The time of flight ( TOF ) mass spectrometer used for t he experiments presented in chapters 5 and 6 of this dis sertation is shown in Figure 1. 8 . The Wiley McLaren type mass spectrometer was rebuilt using components of a n existing molecular beam instrument. It has a linear geometry with a 0.5 meter field free drift region. The entire vacuum system has a base pressure of 10 9 Torr, which is maintained by a two stage differential pumping scheme with a turbomolecular vacuum pump backed by a mechanical roughing pump. The sample is allowed to effuse into the c hamber by an inlet valve up to typical pressure s of 10 6 Torr during the experiments . The pressure is an equilibrium reached by the vapor of the sample and the fast pumpin g speed of a 4 turbo molecular vacuum pump. This ensures very fast flow and prevents the accumulation of photoproducts in the chamber . When the sample valve is closed all ion signals disappear in less than one second and the pressure drops to 10 - 9 Torr. A glass tube connected to the chamber is kept liquid nitrogen in order to create a trap which helps in lowering the pressure of the chamber. The sample molecules are ionized by the laser beam, focused by a 300 mm lens at the entrance of the time of flight chamber and t he ions formed via strong field ionization are sent to the detector via a combined voltage of the repeller and extractor ion optics. For all the experiments the repeller plate was maintained at 2500 V and the extractor plate which is 1 cm away was maintained at 1600 V. Once the ions cross this stage, they enter a field free drift region where they get separated according to the m/z value. The extractor plate has a narrow slit (200 e focus. This is done in order to mitigate the effects of averaging due to the Gaussian distribution of the intensities at the laser focus. 25 The ions are detected using a dual micro channel plate (MCP) detector arranged in a Chevron configuration which is coupled to a 500 MHz digital oscilloscope (Infiniium 54820A, HP). Figure 1.8 Schematic of the time of flight (TOF) mass spectrometer . Repeller plate has a voltage of 2500 V, extractor plate has a voltage of 1600 V and the third plate is grounded. The fi eld free drift region is 0.5 m long. The sample is introduced into the chamber via a manual valve. A focused laser beam is shown in red. 26 A s imulation showing the dependence of power along the radius of a Gaussian beam (black) along with the radial probab ility of field ionization (red) and six - photon ionization of the molecules (blue) is shown on Fig . 1.9 to illustrate the likelihood of occurrence of the processes as a function of the radial distance. Figure 1. 9 Simulation showing the dependence of power along the radius of a Gaussian beam (black) along with the radial probability of field ionization (red) and six - photon ionization of the molecules (blue). R 0 represents the distance at which the probability of field ionization is zero. Radial probability i s the amount of molecules ionized within a cylinder of thickness dr at a distance r at the same intensity of I(r). In the above example, probability of ionization is 1 above threshold I th and zero below the threshold. Maximum intensity of the pulse is doub le that of the threshold value. The shaded gray area represents the very small contribution of the multiphoton ionization in absence of field ionization. The relative contribution can be estimated to be only about 1% of the total amount. 2 7 REFERENCES 28 R EFERENCES (1) Lewis, G. N. Journal of the American Chemical Society 1916 , 38 , 762. (2) Maiman, T. H. Nature 1960 , 187 , 493. (3) Herzberg, G. Molecular Spectra and Molecular Structure, Volume I, Spectra of Diat omic Molecules ; Krieger Publishing Company, 1989. (4) Herzberg, G. Molecular Spectra and Molecular Structure, Volume II, Infrared and Raman Spectra of Polyatomic Molecules ; Krieger Publishing Company, 1991. (5) Herzberg, G. Molecular Spectra and Molecular Structure, Volume III, Elec - tronic Spectra and Electronic Structure of Polyatomic Molecules , 1991. (6) Strickland, D.; Mourou, G. Opt Comm. 1985 , 55 , 447. (7) Bucksbaum, P. H. Science 2007 , 317 , 766. (8) Brumer, P.; Shapiro, M. Ann . Rev. Phys. Chem. 1992 , 43 , 257. 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Phys. 2008 , 25 , A140. 31 Chapter 2 Stokes Shift Dynamics using Chirped Femtosecond Pulses This chapter discusses the response of fluor escence and stimulated emission from solvated dye molecules when studied systematically as a function of chirp ed femtosecond pulses . The magnitude of the chirp effect on fluorescence and stimulated emission is found to depend quadratically on pulse energy, even where excitation probabilities range from 0.02 to 5%, in the so - chirp dependence on fluorescence and stimulated emission is found to be independent o f pulse energy. The chirp dependen ce reveals dynamics related to solvent rearrangement following excitation and also depends on electronic relaxation of the chromophore. The experimental results are successfully simulated using a four - level model in the presence of inhomogeneous broadening of the electronic transitions. This chapter has been adapted with permission from ( J. Phys. Chem. Lett . 2012, 3 ). Copyright (2012) American Chemical Society. 32 2.1 Introduction and Background New insights into the excited state dyna mics and energy transfer mechanisms of dye molecules, 1 macromolecules 2 and light harvesting photosynthetic aggregates 3 have been obtained owing to the development of multidimensional spectroscopic techniques aided by theoretical modeling. Evidence of long lived coherences in biological sy stems even at physiological temperatures 4 has provided an impetus to the already hot field of quantum coherence and its role in biological systems. Solvation of excited states, 5 , 6 relaxations and decoherence have emerged as key aspects that need to be measured and understood. Spectral p hase modulation has proven to be a n extremely powerful tool in the coherent control community for controlling condensed phase systems. Phase shapes ranging from sinusoidal 7 to chirp modulations 8 , 9 have been extensively investigated. Order of magnitude enhancement in the concerted elimination pathway leading to I 2 product formation in the photodissociation react ion of CH 2 I 2 by the use of positively chirped 312 nm femtosecond laser pulses has been demonstrated by Pastirk et al. 10 Quadratic phase on a pulse (chirp) has been also successful in selectively exciting coherent wave packet motion in the ground and excited state along with achieving complete population transfer betwee n electronic states. Shank and coworkers observed the effect of chirped pulses on the fluorescence intensity of LC690 and explained this effect using the wave - packet following hypothesis, 11 which was followed by several experimental and theoretical papers investigating th e chirp effect on resonant electronic transition in different systems while continuing to develop the wave - packet following model. 12 - 14 Cao et al also developed a s imple intra - pulse three level model to explain the chirp effect on fluorescence. 13 The role of stimulated transitions wi thout relaxation was discussed by Hashimoto et al 15 while the competition between stimul ated transition and relaxation have been discussed by 33 Bardeen et al. 16 Fainberg and co - workers on the other hand tried to include non - Markovian relaxation in the existing theory for ultrafast excitation and chirp effects. 17 - 19 The response to time inversion of shaped femtosecond pulses was i nvestigated for various non - linear processes and it was found that processes taking place on a very fast time scale (0 - 20fs) resulted in a symmetric response while asymmetry was found in processes taking place on a longer timescale. 20 Dynamic Stark shift and irreversible population loss upon chirped adiabatic passage in a two state quantum system has been theoretically analyzed as well to explain the asymmetry of t he chirp effect. 21 Solvation is responsible for the fast relaxation and rapid loss of coherence due to the interaction of the molecules with the surrounding solvent molecules. Coherent control of large molecules in solution within the linear laser intensity regime of excitation is also intrinsically related to the solvation induced decoherence and has been investigated in the isomerization of the retinal chromophore in bacteriorhodopsin 22 as well as for dye molecule, coumarin in non - polar solvents. 23 By varying the solvent viscosity, van der Walle et al 23 linked viscosity to the rapid loss of coherence which limits the action of th e pulse on the molecule . Katz et al 24 theoretically demonstrated the weak field control of a branching reaction by using chirp as the control knob and discussed the ro le of the dissipative environment in stabilizing the outcome in a short timescale in the linear regime of excitation. IR 144 is a tricarbocyanine dye and is perhaps the most important member of a set of tricarbocyanine dyes that have been used in the devel opment of nonlinear spectroscopic methods. It has been the subject of various studies because of its high absorption cross section at 800nm and its large solvent - dependent Stokes shift. Dynamic absorption methods were used to project the phase relationship s between the coherent wave - packet motions on the ground - state and excited - state potential - energy surfaces. 25 Pump - probe investigations performed by Yu et al 26 34 focused on t he solvatochromatic behavior of the cyanine dyes . Due to the prevalence of IR - 144 data in the literature, the fluorophore serves as an ideal model system for investigating the effects of chirped pulses . This chapter investigates the role of chirped femtos econd pulses on fluorescent dye mo lecules in solution, leading to the elucidation of some simple but very important pieces of the puzzle under the broad area encompassing weak field coherent control and Stokes shift in solvated dye molecules. 35 2.2 Chirped Femtosecond Pulses The spectral phase on a femtosecond pulse can be expanded as a Taylor series such that with and . The first term is known as the absolute phase, or the carrier envelope phase (CEP), which corresponds to the phase between the envelope of the electric field and the carrier. The second term simply corresponds to the pulse delay with respect to an arbitrary origin of time. The third term is the most w idely used factor of the Taylor expansion and is known as chirp. A quadratic phase around any frequency under the spectrum can be approximated as the tangent whose slope is the group delay that evolves linearly with the frequency. Simply put each frequency experiences a delay that linearly increases with time. The effect of positive or negative chirp (200 fs 2 ) on a 15 fs pulse is shown in Fig . 2.1. Linear chirp induces an increase in the pulse duration.and reduces the temporal intensity as shown in Fig . 2.1b and c. A positively chirped pulse has the low frequency components travelling faster than the high frequency ones and vice versa for the negatively chirped pulse as seen from the spectrogram. Fig . 2.1a shows the ideal condition when the pulse has a flat pha se and all the frequencies arrive at the same time on the sample. This kind of pulse is called a transform limited pulse and has the highest temporal intensity. The use of chirped pulses as a control parameter and as a probe of solvation have been elucidat ed in present and the following chapter. 36 Figure 2.1 Simulation of spectral intensity (black) and phase (blue) (first column), temporal intensity (black) (second column) and spectrogram (third column) corresponding to a 15 fs pulse having (a) zero phase, (b) positive chirp and (c) negative chirp. 37 2. 3 Experimental Methods The femtosecond laser system consists of a femtosecond amplified laser (Spitfire, Spectral physics). A pulse shaper (MIIPS BOX 640, Biophotonic Solutions Inc.) adaptively corrects hig h - order dispersion of the laser pulses and allows us to introduce exact chirp values at the sample (Fig. 2.2) . The system uses the MIIPS algorithm for measuring and compressing the pulses. 27 Experimental measurements included chirp scans performed by the pulse shaper, where the phase on the pulse introduced , where was varied from - 10,000 to 10,000 fs 2 . The fluorescence and forward emission signals were collected simultaneously using a spectrometer (USB 4000, Ocean Optics). A 10 - 6 M solution of IR144 in methanol was used as the sample at room temperature. The dye IR144 was purchased from Exciton and used without further purification. The beam spot size (when intensity drops to 1/e 2 ) is 3 mm and was measured using CCD based beam profiling system (Coherent). Figure 2.2 Experimental setup. The amplified output beam is attenuated and sent to a Spatial Light Modulator ( SLM ) based folded 4 - f shaper. 38 2.4 Results and Discussion 2.4.1 Experimental Results The experiments carried out involved a single shaped laser pulse and the collection of fluorescence (spontaneous emi ssion collected at right angles) and stimulated emission (coherent light detected along the laser propagation direction ) as a function of chirp in the excitation pulse. Note that the stimulated emission results from the single pulse used for excitation, th ere is no probe pulse causing the emission. Theoretical analysis using a four level system with homogeneous relaxation and inhomogeneous broadening further strengthens our hypothesis that the stimulated emission results from an ensemble of molecules with u n - relaxed electronic coherence between the ground and excited states similar to the free induction decay in nuclear magnetic resonance studies. In addition, this model successfully explains the shape of the chirp effect for both the population and coherenc e. The absorption spectrum (black) along with the emission signals, stimulated (blue) and fluorescence (green), and la ser spectrum (red) is shown in F igure 2.3. Figure 2.3 Absorption (black), spectra of the laser (red), fluorescence spectra (green), and coherence emission (blue). 39 A power dependence study while tracking the fluorescence and stimulated emission as a function of linear chirp was done in order to establish a definitive ruler as to what the scientific o explore where deviations from the linear regime are observed. Another important motivation behind carrying out the power dependence was to assess the magnitude of the effect at different probabilities of excitation upon chirp modulation. The present stud y was performed in the excitation range of 0.02% - 45% corresponding to maximum fluence of photons/cm 2 . The electric field in the frequency domain is represented as . can be expa nded as , is referred to as the chirp on the phase. The amplified pulse is compressed using the MIIPS algorithm (as discussed in the experimental section) and a corresponding i - XFROG plot of the Transform Limited (TL) pulse is sh own in Fig. 2.4 a. To demonstrate the accuracy with which the calibrated pulse shaper is able to deliver phase modulated pulses at the sample, we performed a chirp scan while monitoring the SHG at 400 nm. The experimental points (black dots) have been plott ed together with the theoretically predicted values of the integrated SHG intensity (red line) as s hown in Fig. 2.4 b. The shaper accuracy is seen from the close match between the experimental curve and the simulated values. The chirp dependence of the SHG intensity is symmetric and has no distortions that could affect the observed chirp - dependence curves. The chirp dependence of fluorescence and stimulated emission of IR 144 are shown respectively in Fig. 2.4 . Enhancement of the fluorescence relative to th e TL pulses is observed for positively chirped pulses as expected from the previous studies while the opposite behavior is observed for the stimulated emission as the negatively chirped pulses enhance this emission. The magnitude of enhancement of the stim ulated emission is ~40% as compared to ~15% 40 enhancement in fluorescence for the highest excitation power. This result is also in accordance to the recently observed out of phase behavior of fluorescence and stimulated emission when using pairs of noninterf ering pulse replicas. 28 An intensity dependent study reveals the gradual dependence of the sha pe of the curve from the excitation intensity as shown in Fig . 2.4 c and d. We define the chirp effect as the normalized difference between the observed signal with chirped and TL pulses for chirp values from - 10,000 fs 2 to 10,000 fs 2 . This is done in order to create a reference point to compare the curves corresponding to different excitation energies. This is plotted for the differe nt excitation powers in Fig. 2.4 e and f. 41 Figure 2.4 (a) Experimental interferometric frequency resolved optical grating ( xFROG ) trace for the transform limited 36 fs pulses. (b) Experimental data (black dots) for SHG Chirp scan along with the theoretically simulated curve (red line). Dependence of integrated intensity of fluorescence (c) and stimulated emission (d) as funct ion of chirp at different intensities of the laser pulse. Difference between fluorescence measured at different chirp values normalized to TL pulse excitation as a function of chirp for (e) fluorescence and (f) stimulated emission . 42 T he intensity dependence of fluorescence and stimulated emission for TL pulses are shown in Fig . 2.5a and b . 36 fs (FWHM) unfocussed TL pulses were used to acquire the data. The pulse duration corresponding to a 10,000 fs 2 chirped pulse is determined to be 770 fs. The sample irra diated area is ~26 mm 2 and the maximum and minimum pulse energies used during the study are 0.01 µ J and 50 µ J corresponding to peak powers of 10 6 and 10 10 W/cm 2 for transform limited pulses and 10 4 and 10 8 W/cm 2 for 10,000 fs 2 chirped pulses respectively. Deviation from linearity is observed at higher powers due to saturation of fluorescence. The overall behavior of the intensity dependence under TL excitation can be more clearly understood if we recalculate the y axis from normalized intensity to the total value of the effect calculated as the difference of the maximum and the minimum value (after normalizing the values corresponding to different pulse energies) of the observed signal intensity and is plotted as the function of probability of excitation, as shown in Fig . 2.5c and d . The probability of excitation P is calculated as where is the number of photon s /cm 2 and is the absorption cross section at 800 nm, calculated to be 2.6 10 - 16 cm 2 . 43 F igure 2 .5 Dependence of integrated intensity for (a) fluorescence and (b) stimulated emission as a function of average laser power flux for the TL excitation. The value of chirp effect as a function of calculated probability of one photon excitation with T L pulse are shown for (c) fluorescence and (d) stimulated emission. The y - axis is the difference between the maximum and minimum of the value measured at different pulse energies. The red curves represent quadratic fits to the experimental data. 44 The m agnitude of the chirp effect is quadratic for both the fluorescence and stimulated emission. This is a clear signature that the observed effect is nonlinear in nature. The quadratic dependence points to the fact that it is a two photon, pump - dump effect. I n order to provide concrete evidence regarding the nature of effect at extremely low probabilities of excitation ranging from 0.02 to 5%, the effect was normalized with respect to the intensity for TL pulses. In general if Effect varies as x 2 and Intensity varies as x , then Effect/Intensity = x . Thus the relative effect will be a linear function of excitation if the absolute effect is quadratic with respect to excitation. This is shown in Fig. 2.6. Figure 2.6 [Max (Intensity of fluorescence) Min (intens ity of fluorescence)] / (Intensity of fluorescence of TL pulse) plotted as a function of the probability of excitation for IR 144. Red line is the linear fit to the data. 45 Upon normalizing the curves in Fig. 2.4e and f , the shape and overall behavior of the dependence becomes very clear. The minimum value of the effect, min( I ) was subtracted from each curve and is normalized on the difference between maximum, max( I ) and minimum of the signals. This value [I - min( I )]/[max( I ) - min( I )] has an overall size of 1, as seen from Fig. 2.7 . The fluorescence and stimulated emission detected chirp effect for 3.5×10 - 4 J/cm 2 , 2.8×10 - 4 J/cm 2 , 2.1×10 - 4 J/cm 2 and 1.4×10 - 4 J/cm 2 are plotted in red and blue respectively. It is important to note that the magnitude of the tota l effect and shape of the chirp effect is practically independent from the energy of the pulse, which is a clear signature that the mechanism behind this effect does not depend on the laser power. Figure 2.7 Normalized fluorescence detected (red) and sti mulated emission detected (blue) chirp effect for different laser intensities. 46 2. 4 .2 Theoretical Simulations The simplest theoretical model capable of reproducing the observed data is a four level model having two ground and two excited states. A sch ematic represen ting the model is shown in Fig. 2.8. The irreversible relaxation from the second excited state to the first excited state is shown as a dashed arrow. Figure 2.8 Schematic of the four level model used to simulate the experimental results represent the transition frequency, is carrier frequency of the pulse, V is the dipole interaction of transitions with light, are the relaxation rates in ground and excited states, is the dephasing rates, are elements of density matrixes representing the population and the coherences . Liouville equation was used to model the system dynamics since the experiments clearly point towards the second order nonlinear nature of the observed chirp effect and also due to the possible role of relaxation/dephasing. These equations are shown as follows: 47 ( 0 . 10 ) ( 0 . 11 ) ( 0 . 12 ) where a or b re present the states of the system, are the diagonal elements of the density matrix representing population of the states and are the off - diagonal elements of the density matrix representing coherence betw een the states. The matrix element of dipole interaction with chirped pulse is represented as, ( 0 . 13 ) where is the corresponding matrix element of interaction, is duration of TL pulse and is value of scanned chirp. T he system of differential equ ations for the density matrix were numerically solve d without the condition of weak field interaction; pulse energies corresponding to the deviation from linearity and saturation of population transfer were used in the simulations. The diagonal elements of the density matrix (see Fig. 2.8 ) corresponding to the lower excited state at later times (when the pulse is over and relaxations are finished) is proportional to the observed fluorescence. The best fit between theory and experi ment (see Fig . 2.9 ) was found when the stimulated emission was considered to be the integrated absolute value square of the off diagonal elements of the density matrix (see Fig. 2.8 ) between the lowest exited state and highest gr ound state. 48 Figure 2.9 Normalized plots of (a) experimentally determined and (b) theoretically simulated chirp dependence of fluorescence (red) and stimulated emission (blue). Experimental curves are chirp effects averaged over inhomogeneous broadening of absorption and emission lines. T he stimulated emission was considered as the light emitted by the macroscopic polarization of the sample which is a coherent sum of the electromagnetic waves emitted by the microscopic coherences of dye molecules descr ibed by the off diagonal elements of density matrix. Position of the second ground state was kept close to the lowest level when the corresponding period of vibrations is . T g is longer than the pulse duration or relaxation/dephasin g times. The dephasing rate of off - diagonal matrix elements and are the sum of two contributions: half of the induced by solvent . In our case and . The ground state relaxation time, is long compared to the duration of the pulse or relaxation/dephasing times. It was determined that the best reproduc tion of the experimental results is obtained when the relaxation rate from upper excited state to lower one is comparable or even faster 49 than the TL pulse duration (when the value when intensity of puls e drops in e 2 times, in our case 21 fs). We also found that to reproduce the experimental chirp effect in the model we should put relaxation rate from second excited state to the lower excited state , faster than the collisional de phasing . Therefore to summarize the above mentioned findings we can state that the characteristic times in the model should satisfy the conditions , , or relaxation time from directly excited unrelaxed uppe r electronic state to the lower fluorescent state is comparable or shorter than the duration of the pulse and collisional dephasing time should be longer than the pulse duration. In the result presented in Fig. 5 = 20 fs , =100 fs are used although very close simulated curves are obtained for =20 fs, =200 fs , T g =1000 fs and =10,000 fs reflecting the fact that the most critical con dition is the fast relaxation between excited states and relatively slow relaxation or dephasing from lower excited state and even slower dynamics in the ground state. Physically it means that solvation dynamics is faster than dephasing of the polarization . In our model we put V 12 = V 21 and V 11 = V 22 =0 (see Fig. 2.8 ); these conditions reflect the idea that the lowest ground state is coupled with the upper state, but relaxed excited state is coupled with a different ground state. Our model is also able to corre ctly reproduce the independence of the shape of the chirp effect from the energy of the pulse (see Fig. 2.7 ) and therefore does not depend on the exact value of the amplitude of the electric field. It has also been found that the best reproduction of the e xperimental curves (fluorescence and stimulated emission) is obtained when inhomogeneous broadening is taken into account. This is included in the model of the upper and lower states in a very particular way. We use sets of homogeneous absorption lines to fill the actual absorption line, and for each absorption profile 50 (taken from experiment) we have corresponding line in fluorescence spectral profile, and it is very important for these lines to be symmetrical with the respect of the center point between th e two profiles; or physically speaking, the more energetically distorted line in inhomogeneous spectrum is more distorted in the solvated state. Experimental absorption, fluorescence, stimulated emission spectra and an example of the filling of inhomogeneo us profiles with homogeneous states are shown in the Fig 2.10 . Figure 2.10 Spectra of the states in the upper directly excited state (black) and second relaxed exited state (green) used in the model together with laser spectrum (red) . The symmetry of po sitions of corresponding states are marked with arrows. It is important to mention that results of simulation are sensitive to the line positions in the region where absorption and emission spectra overlap with the laser spectrum. Our four level model cl osely reproduces the experimental results and also has a physical sense of very fast motion from upper excited to lower one. The relaxation from excited state to the fluorescent state can be treated as the dynamical Stokes shift that occurs so fast that th ere is no time to reach equilibrium with the solvent. 51 2.5 Conclusion The chirp dependence of fluorescence and stimulated emission for different excitation pulse energies were measured and it was found that the value of chirp effect for both the emission s is quadratic with the res pect to probability of excitation . This is a clear signature that the phase - dependent emission results from a two - photon non - linear optical process, even for very low excitation probabilities (see Fig 2.6 showing this dependence from excitation probability ranging from 0.0002 to 0.06). This observation is significant, and should be considered when designing and discussing coherent It was also found that the shape of the chirp effec t curve is independent of the pulse energy. Theoretically , a model describing the experimental results was developed based on Liouville equations . In this model minimum number of parameters were used to match the experimental result. The time scale of Stok es shift from the excited state to the fluorescent state should be approximately equal to the TL pulse duration and faste r than dephasing by solvent. 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Lett . 2012 , 3, 1329. 55 Chapter 3 Solvent Environment Revealed by Positively Chirped Pulses The early response of the molecule and the solvent is difficult to study due to the ambiguity in assigning and differentiating inter - and intra - molecular contributions to the electronic and vibrational populations and coherence. This chapter focuses on the us e of chirped pulses as a tool for investigating the inter - and intra - molecular dynamics following excitation. Measurements compare the yield of fluorescence and stimulated emission for two laser dyes IR144 and IR125 as a function of chirp. While negatively chirped pulses are insensitive to solvent viscosity, positively chirped pulses are found to be uniquely sensitive probes of solvent viscosity. The fluorescence maxima for IR125 happens near transform limited pulses, however for IR144 it happens only after hundreds of femtoseconds. We conclude that chirped pulse spectroscopy is a simple one - beam method that is sensitive to early solvation dynamics. This chapter has been adapted with permission from ( J. Phys. Chem. Lett . 201 4 , 5 , 924 928). Copyright (2014) American Chemical Society. 56 3.1 Introduction Understanding molecular dynamics soon after photon absorption, taking into account the solvent environment surrounding the molecule, is central to predicting the course of chemical reactio ns and biophysical processes. The relevant timescales regarding photo - excitation in solution are determined by the inter - and intra - molecular interactions and their corresponding energy fluctuations, which occur in the 10 - 100 fs regime. 1 - 8 The multiple inter - and intra - molecular processes occurring during this time, convoluted by inhomogeneous broadening as well as the spectral and temporal response function of the ex perimental setup complicate assignment of the observed decay processes. The previous chapter where I tried to determine and model the optical response of solvated dye molecules due to chirped femtosecond pulses laid the groundwork for the current chapter which focus es on the use of these particular kind of pulses as a tool to determine the solvation response as a function of viscosity and solvent type . For this purpose laser dyes IR144 and IR125 were used. IR125 undergoes non - polar solvation upon excitatio n , while IR144 undergoes polar solvation given the reduction in its dipole moment upon excitation. 5 , 9 The difference be tween the molecules is caused by the piperazine functional group in IR144 that hinders the isomerization . Pump - probe results have found no difference for IR144 when dissolved in methanol or in ethylene glycol, 5 even though ethylene glycol is approximately thirty times more viscous than methanol. Three - pulse photon - echo peak shift (3PEPS) measurements revealed a difference of 0.5 fs after the first 5 ps d elay of the population period for the same system. 10 This chapter deals with find ing spectroscopic probes of solvation environment that are sensitive and easier to implement for example in a microscope, in particular we evaluate here chirped femtosecond 57 pulses. These single - beam methods will be of p aramount importance when investigating microenvironment effects on single molecules, due to the relative ease of the experimental implementation. The main difference between stimulated emission and fluorescence is that stimulated emission is a coherent (3) process that gives rise to a third order polarization. The emission is greatest when the initial excitation has not undergone intramolecular vibrational randomization (IVR) and dephasing. This however is not necessarily true for pump - probe type of exp eriments, where the probe pulse interrogates a population excited by the pump pulse in a manner that is not phase sensitive. Fluorescence is a spontaneous emission process occurring after IVR that depends on the population that the chirped pulse achieves. The characteristic fluorescence depletion observed for negative chirped pulses is a result of enhanced stimulated emission as discussed in the previous chapter , and is favored for the blue - to - red frequency ordering of negatively chirped pulses. 58 3 .2 Experimental Methods The experimental apparatus used for these experiments is very similar to the setup described in the previous chapter. A chirped - pulse scan consisted of recording molecular emissions as a function of , the spectral chirp from negat ive to positive 20,000fs 2 , for . The chirp was scanned back and forth to eliminate any systematic errors. Given the initial pulse duration for TL pulses of 36fs, the pulses are stretched to have maximum pulse duration of 2.17ps FW HM , according to . In a sense, a chirp scan can be interpreted as two - color time - resolved measurements for which early changes such as those occurring at 100fs are observed near 1000fs 2 . For negative chirps, high frequencies arriv e before low frequencies, and for positive chirps the order is reversed. For all experiments unfocused la ser pulses, centered at 800 nm were used . The attenuated and shaped amplified pulses were energetic enough to achieve peak intensities (when TL) of 10 1 0 W/cm 2 . The relatively low repetition rate of the laser (1 kHz compared to oscillators with 100 MHz rates) permits sufficient time for relaxation between pulses and greatly reduces the need for flow in our measurements. The solutions with optical density of < 0.3 were placed in 2 mm cuvettes in order to minimize phase distortion and re - absorption effects. The cuvette was placed in a metal sample holder connected to an aluminum base. For the high temperature measurements, the base was heated and the temperat ure was let to equilibrate. For achieving the low temperatures, the whole assembly was immersed in an ice bath and a constant flow of dry N 2 was used to prevent condensation on the cuvette. 59 3.3 Experimental Results Measurements of the dependence of integ rated fluorescence intensity (detected at 90 degrees) and stimulated emission (detected in the forward direction along the excitation beam) were re corded as a function of chirp. Results for both dyes dissolved in ethylene glycol at different te mperatures a re shown in figure 3.1 . A secondary axis denoting the pulse duration of the chirped pulses has been provided in the figures to help elucidate the timing of inter - and intra - molecular processes taking place during the chirp scans. The data is normalized on t he asymptotic values of the chirp effect . For fluorescence (left column), the curves were normalized on the asymptotic values attained for negative chirp, while the stimulated emission curves (right column) were normalized on the positive chirp asymptotes. 60 Figure 3.1 Fluorescence and stimulated emission response to chirped pulses for IR125 (a) and (b) and for IR144 (c) and (d) respectively in ethylene glycol at three temperatures 278 K (blue) , 294 K (black), and 323K (red). The plots have been normalized o n the asymptotic value of the chirp effect . The changes in stimulated emission and fluorescence as a function of solvent and temperature are shown in Figs. 3.1a - d. Measurements for the two different dyes dissolved in ethylene glycol were performed at 278 K, 294 K, and 323 K and have been color coded as blue, black and red respectively. The viscosity of ethylene glycol at 5 o C , 2 0 o C and 50 o C are 45.4, 19.3 and 6.55 mPa s respectively. 11 Most importantly, the findings reveal that negative chirp, where historically most of the scientific research has focused, 12 - 30 is insensitive to solvent viscosity. 61 Negative chirp experiments can be thought of as being similar to pump - probe measurements, in which the bluer wavelength pump precedes the redder wavelength probe. This observation is consistent with pump - probe measurement s comparing IR144 in methanol and ethylene glycol, and finding no difference. 5 Negative chirp leads to enhanced stimulated emission and hence lower fluo rescence intensity. Positive chirp, because of the time ordering of the frequencies is not effective for stimulated emission. Interestingly, once the excited state is reached, the time ordering of the frequencies of positively chirped pulses is such that i t can stimulate a transition back to the ground state and again back to the excited state. Positive chirp, on the other hand, yields different dynamics as a function of temperature. When exploring IR125 fluorescence, it is observed that colder solvent lea ds to enhanced fluorescence near 800 fs 2 . This enhancement is not observed at higher temperatures. A similar fluorescence enhancement for colder solvent is observed for IR144, however, the maximum fluorescence is reached around 5000 fs 2 which corresponds t o 500 fs. The trends observed in fluorescence are reflected in stimulated emission. Stimulated emission intensity drops sharply for positively chirped pulses for IR125 while the rate is much slower for IR144. This decay rate decreases with increasing tempe ratures for both molecules. It is important to note that the chirp values found depend on the characteristics of the transform limited pulses, in particular the bandwidth. 62 3.4 Discussion The sensitivity to the solvent viscosity is clear from the exper imental results. The overall difference in the shape and decay rates between the two dyes can be attributed to molecular properties of the probe molecules. IR144 undergoes a change in dipole moment upon excitation and therefore undergoes polar solvation, w hich depends on solvent reorientation. This accounts for the slower dynamics of IR144 in ethylene glycol. IR125 on the other hand undergoes non - polar solvation due to the absence of any significant change in dipole moment upon excitation. The viscoelastic model for non - polar solvation predicts a rapid viscosity independent - induced response and slower viscosity dependent diffusive dynamics that relieve stress following excitation. 31 The diffusive dynamics have been shown to be sensitive to the vibrational dephasing in viscous media. 32 Building on the viscoelastic theory, photon echo studies have tried to distinguish between the fast modulation, spectral diffusion and quasi static dynamics based on the scaling of the echo decay time as a f unction of viscosity. 33 This distinction is difficult based on the relative insensitivity of the photon echo measurements. When 3PEPS measurements were fitted to five time constants, no change was observed in the first two fastest time constants (times less than 100fs) but a 0.5fs difference in the peak shift found for picosecond times were reflected in the third and fourth time constants where the decay rates measured for methanol were found to be three times faster than those involving ethylene glycol. 34 When ethylene glycol was heated to 397 K the results found from 3PEPS more closely matched methanol, this is something that is reproduced by our measurements (Fig 3.2). 63 Figure 3.2 Fluorescence (black) and stimulated emission (red) IR125 and IR144 dissolved in ethylene glycol at 323 K. Data were normalized to their minimum and maximum value s , to take into account differences in fluorescence quantum yield in the two solvents. Our positive chirp findin gs for IR125 are consistent with the rapid viscosity independent coherent phonon response (rise close to zero chirp) followed by the slower viscosity dependent diffusive dynamics observed as pulse duration increases. In contrast, the dipolar response of IR 144 depends on solvent reorientation, a process that is viscosity dependent, and thus delays the point where maximum fluorescence is observed. 64 3.5 Conclusion Chirp spectroscopy results presented in this chapter are found to be particularly sensitive to the solvent environment , especially during the first few hundred femtoseconds, where previous nonlinear spectroscopic approaches have been less sensitive. We are in the process of simulating these findings in order to place them in the context of moder n theoretical methods that take into account the evolution of the density matrix in the presence of a realistic solvation environment. The ability of phase shaped laser pulses to probe the solvent environment is particularly exciting given the relative eas e of these experiments compared to the much more complicated four wave mixing setup s . We plan to take advantage of chirped pulses to probe solvent environment effects of probe molecules in interesting environments such as protein pockets, membranes and und er single molecule conditions. 65 REFERENCES 66 R EFERENCES (1) Mukamel, S. Principles of nonlinear optical spectroscopy ; Oxford University Press: New York, 1995. (2) Joo, T.; Albrecht, A. C. Chem. Phys. 1 993 , 176 , 233. (3) Jimenez, R.; Fleming, G. R.; Kumar, P. V.; Maroncelli, M. Nature 1994 , 369 , 471. (4) Xu, Q. H.; Scholes, G. D.; Yang, M.; Fleming, G. R. J. Phys. Chem. A 1999 , 103 , 10348. (5) Yu, A. C.; Tolbert, C. A.; Farrow, D. A.; Jonas, D. M. J. Phy s. Chem. A 2002 , 106 , 9407. (6) Jonas, D. M. Ann. Rev. Phys. Chem. 2003 , 54 , 425. (7) Shim, S. - H.; Strasfeld, D. B.; Ling, Y. L.; Zanni, M. T. 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In this chapter it is show n that applying a sh arp spectral phase step on the excitation pulse causes absorption of the high frequency components and a sharp narrow - band enhanced emission of low frequency components . /2 step causes greater enhancement as compared to a step and the polarity of the / 2 step is felt by the system while the effect is exactly similar for positive and negative step. A theoretical model based on nonlinear response theory is provided that explains how the induced nonlinear optical polarization gives rise to the experimenta lly observed results . 70 4.1 Introduction Femtosecond pulses by virtue of their broad bandwidth and short duration are ideally suited for steering quantum system s towards a desired final state through light - matter interaction in a timescale shorte r than coherence dephasing . 1 The ultimate goal of quantum coherent control is to enhance a desired outcome while suppressing undesired ones by coherent manipulation of interferences among various multiphoton pathways. 2 - 7 D evelopment s in pulse shaping methods 8 ha ve immensely aided this field by offering ways to easily manipulate and control the spectral phase and amplitude to achi eve the desired temporal profile of the exciting pulse , and control coherently the nonlinear interactions between light and matter . 9 - 11 Control of two - photon excitati on in isolated atoms using a phase step was dem onstrated by Silberberg 12 , 13 and by Dantus et al. 14 , 15 in large molecules . Femtosecond resonance mediated (2+1) three photon ab sorption was effectively controlled via a phase step 16 , 17 and it was later used to enhance intermediate field two - photon absorption where the role of four photon transitions in addition to two photon transitions were discussed. 18 Control of Raman transitions via non - linear shaping was demonstrated by Weiner et al. 19 and Silberberg et. al. 20 , 21 while more recently Postma et. al. demonstrated the ap plication of phase steps in high resolution CARS spectroscopy. 22 Coherent control of two photon absorption and two photon fluorescence from a number of other systems via phase step modulation and the importance o f phase anti symmetry around one half of the transition frequency in enhancing these processes have also been discussed . 23 , 24 Recently , three - state selective population of dressed states via phase step modulation has also been demonstrated in the intense field regime. 25 Some of these fundamental findings have found their ways into applic ations such as ad aptive pulse compression 26 - 28 and standoff detec tion of ex plosives . 29 - 33 71 Interestingly, coherent stimulated emission from large polyatomic molecules 34 - 37 excited resonantly by femtosecond laser pulse has not received as much attention. Here we demonstrate the coherent control of stimulated emission from solvated laser dye molecules at room temperature using phase modulated laser pulses with intensities high enough to induce third order nonlinear optical effects and generate third order polarization of the media. We study the molecular response upon interaction with a sharp /2 spectral phase step of the excitation pulse, which is in resonance with the electronic absorption spectrum. Time - dependent perturbative theory carried out on the inhomogeneously broadened set of two - level systems reproduces the main features observed in the experiment. 72 4.2 Experimental Methods F or the study we use a Ti: Sapphire regenerative amplifier (~8 00 kHz) centered at 800 nm and a diffractive LCD based pulse shaper ( MIIPS - HD, Biophotonic Solutions Inc.). The shaper is used to measure and correct the high order distortions of the ampli fied laser output and produce transform limited pulses at the sample using the MIIPS 27 technology and to apply and scan the phase step required to carry out the requ ired experiments. A pulse with a phase step corresponds to a pulse that is transform limited having all frequency components with a phase equals to zero, being modified by adding a constant phase to a portion of its spectrum as shown in Fig. 4.1b. In our e xperiments the non - zero phase is scanned from the shorter to longer wavelength portion of the spectrum. The phase step in the spectral domain creates a temporal doubl e pulse structure as shown in Fig. 4.1c . - pulse s - pulse followed by a weaker one. The amplified spectrum is centered on the spatial light modulator (SLM) and roughly covers half of the 80 0 pixels. The phase steps are applied by cr eating a sharp phase discontinuity in the Fourier plane by the liquid crystal material in the SLM. Figure 4. 1 a shows the schematic of the setup . 73 Figure 4.1 (a) Experimental Setup. The pulse shaper placed after the amplifier is used to perform the phase s cans. The unfocuss ed beam is sent through the sample and stimulated emission is detected along the direction of propagation of laser via a compact spectrometer. (b) Spectrum The attenuated and unfocussed ~4 mm beam is used to excite the sample and the stimulated emission is detected in the direction of propagation using a fiber coupled compact spectrometer. The peak intensity at the sample when the pulses are transform - limited is ~ 5×10 9 W/cm 2 and the pulse energy is sufficient to excite approximately 3 0% of the molecules. A spectrum of the laser output and the second harmonic re sponse to the recorded prior to obtaining experimental data in order to ascertain the accuracy of the applied phases, and are shown along with simulations of the SHG signal in the supporting information (see Fig. 4.2). Experiments were performed on an OD ~0.3 solution of IR125 in methanol in a 1mm cuvette at room temperature. 74 Figure 4.2 onic spectrum as a function of s across the spectrum. 75 4.3 Res ults and Discussion 4.3.1 Experimental Results of IR125 is shown in Fig. 4.3. In comparison to excitation with TL pulses the phase step causes enhanced absorption of shorter wavelengths (high frequency components) and enhanced stimulated emission near the step position but on the longer wavelength side (low frequency side) . This narrow enhancement tracks along with the step position. Therefore, scanning the phase step position produces a characteristic diagonal line in a 2D plot , where the emission spectrum is plotted as a function of the step position on the excitation spe enhancement is very similar. A /2 phase step however, has a different effect on the stimulated emission. A positive phase step causes a sha rp enhanced emission in the stimulated emission spectrum.as shown in figure 4.3c. A negative step on the other hand causes a sharp dip in the stimulated emission spectrum (Fig. 4.3d) and like the effect due to the positive step, the depletion tracks along with the step as well. 76 Figure 4.3 Stimulated emission signal from a solu tion of IR125 in methanol when - phase step s are scanned over the excitation spectrum. - p. The slices obtained at 795.09 nm (black), 800.12 nm (red), 805.11 nm (blue), 810.07 nm (magenta), 815.18 nm (olive), 820.05 nm (navy) and 825.08 nm (violet) clearly illustrate the shift in the emission spectra as a function of the step position and the overall magnitude of the effect. 77 Figure 4.4 Experimental data obtained for IR125 solution in methanol. Sections at 795.09 nm (black), 800.12 nm (red), 805.11 nm (blue), 810.07 nm (magenta), 815.18 nm (olive), 820.05 nm (navy) and 825.08 nm (violet) show - 78 4.3.2 Theoretical Simulation s The experimental observations can be explained theoretically. S timulated emission is part of the optical response of molecules interacting with a laser field. The electronic coherence of the molecule is defined as the sum of non - diagonal elements of the density matrix between ground end excited states. The total sum of the microscopic electronic coherences for the molecules in so lution produces a macroscopic polarization of the sample interacting with laser field . The total field generated from the sample is the heterodyned sum of the laser field with the first and third order pol arization and the intensity is represented as . The resulting spectrum that is measured is the Fourier transform of the total field and is represented as . The electronic coherence as mentioned previously consists of a linear part (first order) which is mainly responsible for absorption and a nonlinear part (that appears as a third - order process) responsible for the coherent stimulated emission. Due to the broad absorption spectrum, the entire system is de fined as the sum of two level systems having a distribution of energy levels and cross section of excitation is reflected in the absorption spectrum. The third - order polarization of the sample is sensitive to phase changes in the excitation spectrum and it is responsible for the observed narrowband feature in the experiments. 79 Figure 4.5 Energy level diagram consisting of single ground electronic and a number of vibrational excited states used for simulating the nonlinear stimulated emission. and signify the first and third order density matrix elements and is the dephasing rate. The excitation spectrum (red) is shown along with the absorption spectrum for IR125. The observed en hancement being restricted to a spectrally narrow emission indicates that a certain small number of excited states selectively emit based on the position of the phase step. The phase difference (and not the temporal signature of the sub - pulses) between par ticular sets of frequencies within the excitation spectrum play an important role in enhancing absorption and subsequently enhanc ing stimulated emission from a small number of excited states . The overall process can be thought of as a pump - dump process fro m a distribution of excited states. The pump - dump scheme can be thought of as a folded two - photon excitation process with an intermediate level, which for this case is the excited state. It has been shown previously 38 that two - photon excitation with an intermediate state can be enhanced when a sharp phase step is imprinted on the excitation spectrum. The enhancement arises from the constructive interference of the photon pairs. Similarly the stimulated emi ssion from a narrow band of excited states (depending on the step position) is enhanced due to the constructive interference between the 80 nonlinear polarization and the excitation field. The effect of /2 and - /2 step on stimulated emission was simulated using the method discussed above and is shown in Figure 4.6. The simulations are a close match when compared to the experimental results (see Fig. 4.3c and d). Figure 4.6 Simulations. Stimulated emis sion signal from a solut ion of IR125 in methanol when /2 or (b) /2 phase step s are scanned over the excitation spectrum. A section from the simulated plots when the /2 and - /2 step is at 805.6 nm is plotted along with the experimental results i n figure 4.7. 81 Figure 4.7 Comparison of the experimental s timulated emission signal (black) with the simulated signal (red) for /2 or (b) /2 phase step s applied at 805.6 nm on the excitation spectrum. It was found that to reproduce the observed results we have to consider an inhomogeneous set of excited states and a dephasing rate of electronic coherence between ground and excited states of 100 fs. These parameters define the inhomogeneous and homogeneous spectral widths. 82 4.4 Conclusion A phase step on the excitation spectrum was used to study the stimulated emission response from solvated dye molecules. Information regarding the inhomogeneous and homogeneous spectral widths can be obtained by modeling the results. Obtaining these paramete rs typically requires a coherent spectroscopic method such as three - pulse photon echo peak shift. Here, a sharp phase step creates two separated pulses with a fixed time and phase relation between them. They generate a third - order polarization from the sam ple that is heterodyned by the remaining laser field. In essence, the necessary conditions (delay time, phase and non - linearity) to measure dephasing rates of systems in a single beam experiment are present in the experiment. This method is very simple to implement experimentally and with few fitting parameters one is able to simulate the data and obtain dephasing rates. This single - pul se method may be used as a comple mentary method to multi - pulse nonlinear optical methods to study processes of energy trans fer in complex systems in solution. 83 REFERENCES 84 R EFERENCES (1) Zewail, A. H. Phys. Today 1980 , 33 , 27. (2) Tannor, D. J.; Rice, S. A. J. Chem. Phys. 1985 , 83 , 5013. (3) Tannor, D. 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D.; Lozovoy, V. V.; Dantus, M. J. Phys. Chem. Lett. 2012 , 1329. (36) Konar, A.; Lozovoy, V. V.; Dantus, M. J. Phys. Chem. Lett. 2012 , 3 , 2458. (37) van der Walle, P.; Milder, M. T. W.; Kuipers, L.; Herek, J. L. Proc. Natl. Acad. Sci. 2009 , 106 , 7714. (38) Dudovich, N.; Dayan, B.; Gallagher Faeder, S. M.; Silberberg, Y. Phys. Rev. Lett. 2001 , 86 , 47. 86 Chapter 5 Polyatomic Molecules under Intense Femtosecond Laser Irradiation Interaction of intense laser pulse s with atoms and molecules is at the forefront of atomic, molecular, and optical physics. It is the gateway to powerful new tools that include above threshold ionization, high harmonic generation, electron diffraction, molecular tomography, and attosecond pulse generation. Intense laser pulses are ideal for probing and manipulating chemical bonding. Though the behavior of atoms in strong fields has been well studied, molecules under intense fields are not as well understood and current models have failed in certain important aspects. Molecules, as opposed to atoms, present confounding possibilities of nuclear and electronic motion upon excitation. The dynamics and fragmentation patterns in response to the laser field are structure sensitive; therefore, a mol theoretical calculations exploring the behavior of a large collection of aryl alkyl ketones when irradiated with intense femtosecond pulses. Specifically, it is considered to what extent molecules retain their molecular identity and properties under strong laser fields. This chapter has been adapted with permission from ( J. Phys. Chem. A . 2014, 118 , 87 5.1 Introduction Before attempting to understand the behavior of polyatomic molecules under strong fields, a brief survey of the behavior of atoms and small molecules along with the prevalent theo ries in a more or less chronological order has been discussed in the following paragraphs. The behavior of noble gas atoms in strong laser fields has been studied for decades and has been modeled successfully using the quasi - static field and assuming a sin gle active electron (SAE). 1 - 6 These approximations, also known as the ADK (Ammosov - Delone - Krainov) model successfully explain the strong - field tunneling ionization process and rates. 6 Studies on diatomics, where the strong - field ionization (SFI) rate was compared directly to that of a noble gas atom with similar ionization energy, found similar behavior in many cases, such as N 2 and Ar. However, significant differences were found for some comparisons; for O 2 vs Xe, the O 2 molecule showed an order - of - magnitude suppressed ionization, explained as arising from its open - shell g round state electronic structure. 7 , 8 Overall, however, diatomics were interpreted as structureless atom - like particle clusters. 8 SAE was found to fail when predicting the ionizati on rate of large polyatomic molecules, and this led to the development of the molecular length corrected quasi - static model known as the molecular single active electron (MSAE) approximation, which corrects the Keldysh parameter to account for molecular le ngth. 9 MSAE had some limited success in explaining the behavior of polyaromatic molecules. Such systems ionize more easily in the presence of the el ectric field with increasing numbers of aromatic rings because their spatial extent leads to lowering of the barrier height as compared to an atom with similar ionization potential. A survey of a wider variety of molecules found that polyatomic molecules r eached saturated ionization at higher intensities, known as I sat , than would be expected for atoms of the same ionization 88 potential. 10 In that study, experimental I sat values were compared with values predicted by ADK s ionization potential. On average I sat was a factor of two greater than I ADK . This same study found that in the 10 13 to 10 14 W/cm 2 intensity regime, 100% ionization could take place without multiple ionization and Coulomb explosion. A second study looking into the ionization and fragmentation of polycyclic aromatic hydrocarbons found much less fragmentation than previously reported, 11 clearly in dicating the difficulty in reproducing early strong - field studies in polyatomics. 12 Efforts to address the failures of MSAE, and to explain results on rare gas clusters for 13 , 14 led to the development of non - adiabatic multi electron theory (NME). 15 , 16 The transi tion from the adiabatic response to the field observed for atoms to the non - adiabatic response proposed for molecules, arises from the time it 15 The principle of NME is that multiple electrons in a polyatomic molecule respond to the strong field such that during a typical laser pulse consisting of 10 - 20 optical cycles in dur ation (30 - 60 fs FWHM), a number of internal electrons oscillate with the field forming a plasma - like quasi - continuum state and as a result deposit a significant amount of energy. The many - electron participation leads to dynamic shielding of the field which results in a higher ionization threshold compared to a molecule with fewer electrons but the same ionization potential. Ionization of one or more electrons results in a cation with significant intramolecular energy, and this intramolecular energy, togethe r with multiple charges, leads to multiple bond dissociation events via Coulomb explosion. It is argued that ionization occurs when the lowest unoccupied molecular orbital (LUMO) is Stark - shifted just above the Coulomb barrier; however, the LUMO 89 which acts as a doorway state must be populated through the nonadiabatic interaction with the field. 17 Early experimental evidence for NME compared results from hexatrien e, decatetraene and - carotene, three molecules with increasing numbers of atoms and more importantly increasing numbers of conjugated double bonds. 16 According to NME, the longer the molecule, the longer the path through which the electrons traverse and therefore the greater the amount of in ternal energy deposited by the strong field. 16 Upon irradiation with 800 nm pulses, it was found that the intensity of the intact molecular ion diminishes from hexatriene to decatetraene and is - carotene. Irradiation with 1455 nm, with the same pulse dur ation and peak power density results in much less fragmentation. The explanation provided is that a longer wavelength implies fewer optical cycles and hence less internal energy acquired by the molecule. The general observation that it is rare to see the i ntact molecular ion for large molecules under intense radiation seems to lend support to the NME theory. One of the conclusions from NME is that under strong fields, the Stark shifts of delocalized molecular orbitals approach the ionization potential and t he discrete electronic structure becomes irrelevant. 17 A modified ADK theory, (MO - ADK) was introduced and refined to explain suppressed ionization in diatomics. 18 The key concept behind the modification was that tunneling ionization occurs through the suppressed potential barrier of the combined molecular and external electric field, and therefore, the wave function of the outermost electron(s) in the asymptotic region needs to be calcul ated. 18 MO - ADK works well for diatomics and some triatomics, but requires extensive molecular electronic structure calculations which are just becoming practical for large polyatomic molecules. 90 A modification of the NME theory known as sequential nonadiabatic excitation introduced the concept of a doorway state having charge transfer character, which helps in excitation to the quasicontinuum state. 17 This process is exponentially enhanced by the dynamic polarization of multiple electrons and finally the fragmentation results from the sequential energy deposition in the neutral and the resulting molecular ion. However, given that post - ionization excitation of the ionic ground state can lea d to observation of ionic fragmentation, the observation of fragment ions does not constitute proof that SFI directly accessed excited ionic electron makes a laser - induced transition on a sub - cycle time scale as the continuum electron 19 The non - adiabatic interchannel coupling is required in order to reach the excited ionic state, which is forbidden in a sub - optical cycle SFI process. The obs ervation of molecular angle dependence on the ionization and fragmentation of molecules 20 - 23 inspired the development of channel resolved above threshold ionization ( CRATI). 19 In that study the strong field ionization of 1,3 - butadiene and n - butane were investigated. In particular, butadiene was found to have two distinct channels: production of the parent ion, (90%) through excitation to the ionic ground state, and fragmentation (10%) to form C 3 H 3 + and C 4 H 5 + . The results of angle - resolved CRATI measurements, were modeled better by a time dependent mixed orbital - grid method using multielectron orbital - based bound states of the neutral and cationic molecule (time dependent resolution in ionic states; TD - RIS) than to the semi - classical single - electron MO - ADK theory. 24 Clearly the level of theory and description of the electronic structure used for the TD - RIS as compared to the limited MO - ADK resulted in more realistic ionization probabilities. However, evidence for non - adiabatic multielectron processe s during SFI is not clear. We find ample experimental evidence in the literature 91 demonstrating molecules have more than one SFI pathway, and this may lead to different fragmentation channels, such as those found for 1,3 butadiene, N 2 and CO 2 . 20 - 23 Along the same lines, different SFI pathways were observed when N 2 O 4 was ionized at the inner or outer turning point of the NO 2 - NO 2 stretch. 25 In general, different molecular orientation with respect to the electric field vector and different intramolec ular structure (such as inner or outer turning points of a stretch or twisting angles of a double bond) expose different SFI pathways. The existence of multiple SFI pathways, however, does not imply NME when NME is narrowly defined as the process in which two or more electrons are promoted to a different state within a single optical cycle. As the field strength increases above 10 14 W/cm 2 , the possibility of electron recollision with the molecule increases. Electron recollision has been explained as a thre e step model involving (i) tunnel ionization of the highest energy electron, (ii) acceleration of the free electron in the laser field, and (iii) recombination of the electron to the state from which it originated. 5 This process opens new fragmentation pathways tha t are dependent on the time, phase and energy of the recolliding electron, as evidenced in carrier envelope phase control of molecular fragmentation. 26 Similarly, experiments involving measurement of HHG emission and finding evidence for the participation of multiple SFI pathways involving (HOMO - n , for n depend on electron recollision. The transition from atoms to diatomic, triatomic and even larger polyatomic molecules increases the number of degrees of freedom linearly. The additional degrees of freedom participate according to a hierarchy of timescales. Given that SFI takes place within an optical cycle, all nuclear degrees of freedom can be considered frozen. It should be noted tha t here SFI is referred to as an ionization process that includes tunneling and or multiphoton ionization. At 92 lower peak intensities (~10 13 W/cm 2 ), when only a fraction of the molecules ionize within an optical cycle, ionization may occur every half - optical cycle provided the intensity is above some threshold. For sub - 40fs, the ionization process occurs on a sub - 10fs timescale and the approximation of a frozen molecular structure is still valid. The observation of ultrafast proton transfer 27 - 29 is an understandable exception due to the low mass of the proton. The extra degrees of freedom in molecules, however, play two important roles. First, larger molecules, especiall y those with multiple double bonds and with linear geometries, are expected to have a greater number of electronic states and the spacing between the electronic states of both the neutral and the cation is expected to be much smaller. Based on a simple par ticle in a box approximation the number of states grows with the number of conjugated electrons and the spacing between electronic states shrinks with the length of the molecule squared. Here we note as the only caveat that symmetry can greatly reduce the number of non - degenerate electronic states. Cyclooctatetraene, the cyclic analogue of decatetraene was found to be more stable showing higher molecular ion yields and almost no fragmentation as compared to decatetraene. This can be explained due to the red uction of density of excited states due to the higher symmetry, or simply based on the fact that unlike a linear chain, to fragment a ring at least two bonds need to be broken. Also, the greater number of vibrational degrees of freedom provides a dense bat h for intramolecular vibrational relaxation and dephasing. Based on the density and distribution of electronic energy levels of polyatomic molecules, an alternative hypothesis to NME is entertained here: while multiple electrons are polarized by the strong field, the most polarizable electron, which is likely in the highest occupied molecular orbital (HOMO), responds more strongly to the field than the remaining electrons, and upon its ultimate ejection, it leaves behind a much less polarizable cation. This 93 hypothesis is similar to the basis for SAE; however, it is clear that a polyatomic cation is much more complex than an atomic ion. Single electron ionization does not explain the extensive fragmentation that often accompanies strong - field irradiation of p olyatomics. It has been proposed that dissociation results from non - adiabatic multielectron excitation. 15 , 16 However , a simpler explanation is that the nascent cations absorb additional photons. This proposal is based on the model introduced by Schlag and Lin when studying the ionization and fragmentation of benzene under intense laser irradiation with nanosecond lasers . 30 They proposed that unimolecular dissociation competes with further photon absorption, leading to a cut - off in the excitation ladder and a switch to a new ladder of product ions which absorb additional photons. The ladder switching mechanism was supported by work on a broad range of polyatomic molecules using nanosecond and picosecond pulses. 31 Clearly, in the picosecond and nanosecond timescales there is plenty of time for dissociation to take place while the field is still present. In the femtosec ond regime, ladder climbing and switching can only take place when the pulses are longer than ~50 fs, allowing dissociation to compete with further ionization. Fragmentation and ionization of a broad range of polyatomic molecules with shaped pulses was exp lored systematically and the conclusion was that longer near - IR femtosecond laser pulses lead to more dissociation, a process closely linked to the likelihood of the ionized molecules to absorb additional photons. 32 The likeliho od that further single or multi - photon absorption by the cation explains fragment ion formation has been proposed and experimentally tested by a number of research groups on different types of molecular systems. 33 - 41 The drastically different mass spectra obtained for hexatriene and 1,3 - cyclohexadiene, two compounds with the same ionization energy, can be explained by differences in the absorption spectrum of the respect ive cations. 33 As noted above, however, fragmentation of a ring requires two bonds to be broken. 94 Similarly, differences in the fragment ion formation between 1, 3 - and 1,4 - cyclohexadiene were ascribed to the large difference of the absorption spectra of the molecular cations. 34 The fragmentation and ionization of three metal carbonyls (Ni, Fe, and Cr) excited at two different wavelengths (0.8 and 1.35 µm), 36 show that fragmentation is dominated by resonances in the ionic state and relaxation of the nascent parent ion, which is possible with longer excitation pulses. Static as well as dynamic r esonances in the nascent ion have been identified and used in pump - probe measurements to observe wave packet dynamics. 37 - 40 The cationic absorption premise has been challenged by a study where the ionization and fragmentation patterns for a number of polycyclic aromatic hydrocarbons were analyzed. 11 The fi ndings indicate that despite having strong absorption resonances, some molecules remain bound showing strong parent ion peaks in the mass spectrum, and form doubly and triply ionized entities. In the discussion section we address this study and offer as a possible explanation the fact that fragment formation for the polycyclic molecules studied requires at least two chemical bonds to be broken. More recently, the role of intermediate Freeman resonances in strong field ionization of polyatomic (halogenated m ethane) molecules has been studied, finding clear signals in the photoelectron spectrum for the presence of resonance - enhanced ionization vs non - resonant ionization. 42 - 45 Electron - ion correlation studies aided by velocity map imaging have helped to determine direct as well as indirect reaction paths and pulse shaping has helped to find Freeman resonances. 42 - 45 The nascent molecular cation has a distribution of electronic quantum states that can be sparse or dense depending on the size and symmetry of the molecule. These cases are illustrated in figure 1 where the ground and c ationic excited states for hexatriene, decatetraene, - carotene have been estimated using a low level quantum chemical method. The neutral states have been curtailed at the experimental IP and the blue lines represent 95 the cationic gro und and excited states. Optical transitions induced by the 800nm (1.55 eV) photons to the first excited state typically take 4 photons (200 nm, 6.2 eV), and ionization typically takes 6 photons (9.3 eV). Upon ionization, the nascent electron takes away add itional energy, as evidenced by above threshold ionization (ATI), 6 which has also been observed in molecules 46 - 48 and by high harmonic generation (HHG) from molecules. 22 , 49 Following SFI the remaining cation may absorb additio nal photons, which provide sufficient energy for breaking chemical bonds. Given that ionic excited states are also accessible within the few eV range, photodissociation of the ions is in many cases resonantly enhanced. As we show schematically in Fig. 5.1, the sparse electronic states of hexatriene lead to limited ionization and fragmentation, 15 while dense electronic s tates lead to resonantly enhanced ionization and fragmentation. The state density argument combined with resonantly enhanced cation excitation and fragmentation seems to provide an alternate explanation to NME, at least as it was originally stated. 96 Figur e 5.1 Four cases illustrate schematically the behavior of polyatomic molecules under strong field excitation. Case (a) in the case of sparse electronic states such as in hexatriene, the threshold for ionization is typically a three or four photon excitatio n to the first excited state, followed by resonant multiphoton ionization. Excitation is typically limited to the ground state of the cation, and double ionization is observed for very intense fields. Case (b) the intermediate case involves additional reso nances that result in the opening of additional ionization and photodissociation channels, resulting in a wider variety of fragment ions such as in the case of decatetraene. Case (c) reduction in the density of non - degenerate states is observed due to the introduction of symmetry in the molecule. Case (d) offers a denser electronic state distribution and leads to a very wide range of photoionization and photodissociation pathways, making it unlikely to find the intact molecular ion present in the mass spect - carotene. The energy levels have been roughly approximated using Kohn - Sham (KS) orbital energies obtained at the B3LYP/6 - 31++G** level of theory. Neutral excitation energies were approximated as orbital energy differences, with the lowest excitation energy shifted to match the experimental first excitation energy. Occupied orbital energies have been shifted to the experimental IP to 97 approximate the energies of the cationic states. Neutral energy levels (black) have been cut - off at the experimental IP and the blue lines represent the cationic ground and excited states. The red arrow represents energy of 1.5 eV. The proposed single - active electron SFI followed by resonantly enhanced cation excitation and fragmentation (SA E - RECEF) hypothesis implies the loss of an electron within an optical cycle, presumably before the peak intensity of the laser pulse is reached. The electron carries away most of the excess energy leaving the lowest ionic state accessible behind. The predi ctions of this model are as follows: First, one is likely to see the intact molecular ion of molecules whose cation has a low probability of absorbing one or two additional photons, Fig. 5.1 Case (a). This observation depends as well on the stability of th e resulting molecular ion. Second, when the molecular cation has one - or two - photon resonant transitions then the intensity of the molecular ion peak decreases, see Fig.5.1 Cases (c, and d), this is especially the case as the intensity of the laser is incr eased. A systematic study on a large number of polyatomic molecules supports this general trend. 32 Benzene and toluene were found to undergo very limited fragmentation under near - IR femtosecond laser excitation using 36 fs pulse s, presumably due to the scarcity of electronic states leading to the poor absorption cross section of the nascent cations. Nitro - toluenes on the other hand undergo significant fragmentation because of the greater electronic state density introduced by the non - bonding electrons in the nitro functional group, increasing the long wavelength absorption of the cations. Third, the sudden ionization leaves little or no internal energy, and therefore should lead to non - ergodic (non - thermal or non - statistical) acti vation. This implies that while some strong bonds may break, other more labile bonds in the molecule may not. This idea is consistent with work on peptide activation using strong - field femtosecond laser induced dissociation (fs - LID). 50 An example is studies on 98 phosphorylated peptides, where activation of the peptide ions by an intense femtosecond laser is shown to break peptide bonds (3.1 eV, ~300 kJ/mol) while leavin g the phosphorylation (1.3 - 1.9 eV, ~125 - 180 kJ/mol) intact. 50 - 55 Fourth, the behavior of molecules under intense near IR fields is determined by ground state molecul ar structure more than by ionization energy; functional groups and positional isomerism largely dictate the ionization and fragmentation processes. Fifth, the hypothesis being proposed implies that the ionization behavior of polyatomic molecules, and the c oherent dynamics observed soon after their strong - field excitation would be consistent with ab initio calculations and molecular dynamics based on the departing electron taking away most of the excess energy. Thus ionization leaves little or no intramolecu lar excitation, and further fragmentation is dictated by the presence of one or two photon resonant excited states. The work presented here provides experimental and theoretical evidence that supports these ideas. Additional evidence found in the literatur e is provided in the discussion section. In this chapter the focus is narrowed to an investigation of the dynamical behavior of the excited states of aromatic ketones. The rationale for the molecules chosen in this study is to transition from the broad sur vey presented earlier by our research group, where more than 25 molecules were studied, to a group of molecules with similar chemical motifs where we could compare experiments and theory. 32 In addition most aromatic ketones pres ent low frequency coherent torsional motion following excitation that provides an internal molecular thermometer. Strong field excitation of acetophenone has been the subject of closed loop optimal control studies. 56 - 58 SFI followed by cation absorption was proposed to explain the fragmentation pattern of acetophenone along with many other polyatomic molecules. 32 Acetophenone and its methy l derivatives have been studied using time - resolved pump - probe experiments. 59 More 99 recently, frequency resolved strong field NIR excitation was used to locate a one - photon resonance to the D 2 electronic state of the cation. 60 This wavelength scanning method was later extended to propiophenone 61 and hydroxyacetophenone isomers 62 where it was proposed that following tunnel ionization, population transfer to the D 2 state occurs if the acetyl group twists and if the pulse contains resonant photons. The molecules studied here have been divided (see schemes in Figure 5.2) into four general groups. The first group corresponds to benzaldehyde, acetophenone, propiophenone and benzophenone. The second grou p corresponds to aromatic ketones with locked geometry such that the carbonyl group is constrained in plane with the aromatic ring. The third group corresponds to singly substituted acetophenone derivatives. Here we explore positional isomerism for substit uents with different degrees of electronegativity and steric demand. The fourth group corresponds to doubly substituted methyl acetophenone derivatives. 100 Figure 5.2 The chemical structures of the molecu les being studied are shown and have been divided into four groups according to various trends. The first group corresponds to alkyl phenyl ketones having different alkyl substituents. The second group corresponds to similar compounds where the alkyl group is chemically bonded to the phenyl ring such that the keto group is in 101 plane. The third group represents alkyl phenyl ketones with different substituents at different positions on the phenyl ring. The fourth group consists of di - subs tituted methyl acetophenones. The experiments are carried out by using an intense - pump pulse followed by a weak - probe pulse that interrogates the nascent molecular ion and determines the extent of internal excitation following ionization. In parallel, ab initio calculations on most of the molecules in Figure 5.2 were performed and this was aimed at determining the electronic states of the nascent cation and the lower lying excited cationic states. In addition, calculations were carried out to determine th e potential energy surface beyond the Franck - Condon region and molecular dynamics simulations were run in order to predict the ensuing dynamics following sudden vertical ionization. The discussion section focuses initially on the body of experimental and t heoretical work presented here and then broadens to encompass results in the literature on a variety of molecules that have been studied under intense fields. Finally, conclusions are drawn as to the merits of the proposed mechanism for polyatomic molecule s under intense laser radiation and point to observations that remain unexplained. 102 5.2 Experimental Methods The femtosecond laser system comprises a regeneratively amplified Ti:Sapphire laser (Spectra Physics, Spitfire) capable of producing 0.8 mJ 35 fs pulses at 1kHz. The output pulses from the oscillator (KM Labs) are sent to a phase only pulse shaper (placed between the oscillator and amplifier) consisting of a 640 pixel spatial light modulator (MIIPS Box, Biophotonic Solutions Inc) at the Fouri er plane before amplification. Phase distortions introduced by the laser system and the optical setup are compensated via MIIPS 63 while monitoring the second harmoni KDP crystal placed at the sample plane. The output pulses are split and spatially recombined with an adjustable delay via a beam splitter to create a pump - probe delay line. The experiments are carried out on a Wiley McLaren time of flight (TOF) mass spectrometer having a 0.5 m long field free drift region. The mass spectrometer consists of an ultra - high - vacuum chamber maintained at a base pressure of 8×10 - 9 Torr. The turbo vacuum pump is backed by a two stage rotary vane pump. A schematic diagram of the setup is shown in Figure 5.3. Figure 5.3 Schematic of the experimental setup. The amplified beam is split into two parts and recombined using beam splitters (BS) before sending it through an o ptical delay line consisting of a corner cube (CC). The collinear pump and probe beams are focused into the time of flight (TOF) mass spectrometer. 103 All the samples were purchased from Sigma Aldrich and used without further purification. The sample is int roduced into the chamber via a leak valve and fast - flow conditions are maintained while keeping the pressure constant around 4×10 - 6 Torr. The pressure is an equilibrium reached by the vapor of the sample and the fast pumping speed of a 4 inch turbomolecula r vacuum pump ensuring very fast flow and preventing the accumulation of photoproducts in the chamber, which is confirmed by observing the fast decay of the signal when closing the valve (See Figure 5.4). When the sample valve is closed all ion signals dis appear in less than one second and the pressure drops to 10 - 9 Torr. Figure 5.4 The intensity of acetophenone molecular ion, the most abundant photoproduct from acetophenone, drops to zero within a half second after closing the valve, which confirms the fast flow of our system. 104 The pump and probe beams are collinearly focused onto the effusive beam of gaseous sample with a 300 mm plano convex lens. Pump pulse energies of 100 µJ ( ) were chosen such that only a small percenta ge of molecular SFI occurs via a mixture of tunneling and multiphoton processes, given the molecules and laser parameters we calculate a Keldysh parameter of ~1.3. The probe pulse energies were maintained at 50 µJ ( ), an intensity that causes minimal amount of new ions but is sufficient for causing fragmentation through multiphoton absorption of the cations. Both pump and probe pulses are horizontally polarized as they enter the mass spectrometer and the ions are extracted at right angles to the laser polarization. A 200 µm wide slit perpendicular to the laser excitation is used as the extraction optics such that only the ions produced at the center of the focused beam are extracted. This is done in order to mitigate the axial Gauss ian intensity distribution inherent with laser excitation. 64 , 65 The ions are detected using a dual micro - channel pla te in Chevron configuration coupled to a 500 MHz digital oscilloscope. The TOF spectra are collected for each delay and integrated ion yields are plotted as function of time delay between pump and probe beam for each fragment ions. Time delay is varied in steps of 50fs, from - 500 fs to +5 ps. At each time delay point mass spectra were averaged over 30 laser shots and this reduced the shot - to - shot fluctuations. To improve the signal to noise ratio and to minimize the effect of longer - term variations, our fi nal transient was an average of 50 scans. The integrated area under the peak of the molecular and fragment ions following background subtraction of the mass spectrum is plotted as a function of delay of the probe pulse. 105 5.3 Quantum Chemical Calculation s Quantum chemical calculations were applied to address three questions: (a) which acetophenone derivatives twist about the phenyl - acetyl bond upon ionization, (b) how does substitution control s the propensity for this twisting and (c) which cation states r esonantly enhance fragmentation by the laser field. Torsional potential energy surfaces (PESs) for the various acetophenone derivative cations were computed to determine their propensity to twist upon ionization. The derivatives were optimized in their neu tral ground states (S 0 ) at the Moller - Plesset second order perturbation (MP2) level of theory using the 6 - 311++G** basis set. This same method was previously found to provide a structure in reasonable agreement with gas - phase electron diffraction results f or the ortho - methyl derivative. 66 From these optimized neutral structures, the acetyl groups were twisted relative to the phenyl ring with all other internal coordinates re - optimized on the neutral MP2 ground state PES, and the energies at these structures were computed at the two - hole - one - particle (2 h /1 p ) ionization potential equation - of - motion coupled cluster (IP - EO M - CC) level of theory 67 - 70 using the 6 - 31+G* basis set. PESs predicted at this level of theory are in excellent agreement with gas phase electron diffraction results . 71 The existence of resonances in the cation manifold was investigated by computing higher energy cationic states at the IP - EOM - CC level of theory. To investigate the electronic structure of the various cations, singly occupied molecular orbitals (SOMOs) were calculated. Natural molecular orbitals were calculated at the multireference configurat ion interaction with singles and doubles (MRCI) theoretical level using an active space of five electrons in eight orbitals and the 6 - 31+G* basis set. In all cases the MRCI states have roughly the same chemical character as the corresponding IP - EOM - CC stat es, as determined by comparison of the MRCI SOMOs to the IP - EOM - CC amplitudes and 106 associated Hartree - Fock orbitals. The SOMOs were computed at a planar constrained S 0 minimum structure and a 35º - twisted structure; the planar structure was chosen to facilit ate interpretation. All IP - EOM - CC calculations were performed using the Q - Chem and GAMESS electronic structure software packages, 72 - 76 while density functional, MP2, and MRCI calculations were performed using the MolPro package. 77 107 5.4 Results 5.4.1 Mass Spectra Experimental mass spectra obtained when probe pulses precede pump pulses (negative time delay) for the majority of the compounds studied are shown in figure 5.5. Notably the ion yield for a prob e pulse alone is negligible compared with the ion yield for the pump. All the spectra have been obtained at identical laser intensities ( ) and sample pressure. The intensity was chosen to minimize multi - electron ionization while p roviding reasonable ion yield and hence signal - to - noise ratio. Mass spectra corresponding to all the compounds except 3,5 - dimethylacetophenone obtained using 70eV commercial mass spectrometer have been plotted in Figs 5.6 and 5.7 in order to compare and co ntrast the peak intensities and type of ions formed and ratios of the molecular ion to the other major fragments. One of the main observations when comparing the ionization due to femtosecond pulses is that it leads to enhanced fragmentation and creates sm aller species such as C + and H + ions. When comparing different isomers for example for methyl acetophenones there is almost no difference in the intensity of the molecular ion peak when ionized using 70eV electrons. However noticeable differences in the ma ss spectra is observed for all three isomers when ionized using femtosecond pulses. The origin of this difference lies in the ionization mechanism and subsequent stabilization of the ions and will be discussed later during the development of the model. 108 Figure 5.5 Mass spectra of (a) benzaldehyde, acetophenone and propiophenone, (b) o - methylacetophenone, m - methylacetophenone and p - methylacetophenone, (c) o - fluoroacetophenone, m - fluoroacetophenone and p - fluoroacetophenone and (d) 2,4 - dimethylacetopheno ne, 3,4 - dimethylacetophenone and 3,5 - dimethylacetophenone corresponding to negative time delay s when the probe pulse precedes the pump. 109 Figure 5.6 Mass spectra of (a) benzaldehyde, (b) acetophenone (c) propiophenone, (d) o - methylacetophenone, (e) m - methy lacetophenone and (f) p - methylacetophenone, obtained using 70 eV electron ionization. (Source: webbook.nist.gov) 110 Figure 5.7 Mass spectra of (a) 2 - fluoroacetophenone, (b) 3 - fluoroacetophenone (c) 4 - fluoroacetophenone, (d) 2,5 - dimethylacetophenone and (e) 3,4 - dimethylacetophenone obtained using 70 eV electron ionization. (Source: webbook.nist.gov) 111 At lower intensities ~10 13 W/cm 2 the nascent molecular (parent) ion is nearly as intense as the benzoyl ion and both of these peaks are much more intense than other fragment ions, see Figure 5.8. Figure 5.8 Mass spectrum of acetophenone corresponding to W/cm 2 35 fs pulses showing limited fragmentation and the formation of lower mass fragments. Note that molecular and benzoyl io ns have similar yield. The thermodynamic values associated with fragmentation of the acetophenone ion are given in Table 1, and provide a clear explanation for the relative abundance of the benzoyl and phenyl ions. Production of benzoyl requires a single additional photon of energy from the field, while production of phenyl requires two photons. 112 Table 5.1 Energy required to dissociate the acetophenone radical cation via various fragmentation channels. These values were calculated from the heats of formation of different species obtained from NIST. The values given for correspond to the number of photons that would be required given photon energy of 1.55eV. Fragmentation Channel kcal/mol eV 19.9 0.86 0.55 46.3 2.0 1.3 77.3 3.3 2.1 88.6 3.8 2.4 98.8 4.3 2.7 123.7 5.3 3.4 Of particu lar interest when comparing the different mass spectra is the ratio between the molecular ion, benzoyl ion and phenyl ion; the three heaviest masses observed, corresponding to bond cleavage near the carbonyl group. Table 5.2 summarizes the ratio between th ese peaks (normalized to benzoyl ion yield) for most of the compounds studied. In the first group, benzaldehyde is the only compound that undergoes limited molecular ion dissociation. While the ratio for ortho and para isomers is similar, we find the meta isomer fragments less. This kind of positional isomer dependent fragmentation is not observed in case of electron impact mass spectrometry. Among the methylated compounds, ortho, or para - substitution stabilizes the benzoyl ion more than meta - substitution. Note that the molecular ion is much more abundant than the benzoyl ion for the di - meta isomer. Meta substitution also results in lower overall ion yield. The differences in the parent ion yield can be explained using the concept of positive charge stabiliz ation on an aromatic ring, illustrated in figure 5.9. Loss of a methyl radical 113 resonance structures; structures 3 and 4 having the positive charge on the ortho and para position respectively are stabilized by a sigma or pi donor functional groups. This in turn favors the fragmentation of the parent ion. Therefore compounds having these groups at the ortho and para positions show lower molecular ion to benzoyl ion ratios, as compared to compounds with substitution at the meta position. The classical concepts of organic chemistry occurring in the ground state and in condensed phase are valid and help explain the behavior of isolated polyatomic molecules subjected to intense femtosecond laser fields. Figure 5.9 R esonance structures of the b enzoyl cation. Cyanoacetophenones have slightly different mass spectra (shown in figure 5.10) when compared to the other compounds. The overall ion yield for these compounds is lower, esp ecially for the meta isomer. These compounds exhibit extensive fragmentation, the large proton yield indicative of higher energy ionization and fragmentation processes. Cyanobenzoyl ions are the dominant ions. The higher overall fragmentation but lower ove rall yield point to the fact that it is hard to ionize these molecules. Their higher single - ionization potential leads the observation of double ionization causing the appearance of Coulomb explosion fragments such as H + , and C + (vide infra). 114 Figure 5.10 Mass spectra of (a) m - cyanoacetophenone and (b) p - cyanoacetophenone. 115 Table 5.2 Fragment ion yield ratios with respect to benzoyl ion yield for most of the compounds. Unusual ratios have been highlighted in bold. Phenyl Ion Parent Ion Benzald ehyde 0.85 3 Acetophenone 0.18 0.06 Propiophenone 0.57 0.14 o - Methylacetophenone 0.21 0.54 m - Methylacetophenone 0.22 0.81 p - Methylacetophenone 0.45 0.7 o - Fluoroacetophenone 0.1 0.24 m - Fluoroacetophenone 0.28 0.88 p - Fluoroacetophenone 0.2 0.2 m - Cya noacetophenone 0.15 0.15 p - Cyanoacetophenone 0.29 0.09 2,4 - Dimethylacetophenone 0.29 0.29 3,4 - Dimethylacetophenone 0.18 0.9 3,5 - Dimethylacetophenone 0.2 1.8 116 5.4.2 Preliminaries The goal of the study undertaken in this chapter is to provide an in tuitive understanding of the behavior of polyatomic molecules under intense laser fields. This requires us to probe the dynamics soon after the molecules interact with a strong laser field. For this purpose we use a pump - probe arrangement in which the stro ng field interacts with the molecule and a weaker field interrogates the resulting molecules and cations in the wake of the intense pump pulse. Given the intensity of the pump pulse, the majority of the molecules ionize; therefore the pump pulse creates an ensemble of molecular ions along with some fragments and the probe laser interrogates their dynamic behavior. The probe pulse depletes the molecular ion yield as it induces further fragmentation. The fragmentation pattern following the pump - probe sequence is shown in figure 5.11. The fragment ions and radicals can undergo further fragmentation following absorption of multiple photons. 117 Figure 5.11 Schematic illustrating the strong - field ionization pump followed by the weaker probe laser pulse and fragment ation pathways for acetophenone. Strong - field ionization to the ground ionic state leads to twisting to a lower energy configuration. Subsequent excitation by the probe to higher excited ion states depletes the ion and leads to formation of products. The t wist angle refers to the torsional motion of the acetyl group relative to the benzene ring. The preliminary results from this kind of experiment are summarized in Figure 5.12. It was determined that the oscillations are caused by the change in the polariz ability of the molecular ion due to the torsional motion of the acetyl group which controls the efficiency and selectivity of probe induced excitation and fragmentation. 59 118 Pump - probe transients corresponding to the molecular ion (black squares), benzoyl ion (blue triangle s) and phenyl ion (red circles) from acetophenone as a function of time delay of the probe pulse illustrate the fragmentation mechanism. The ion yields corresponding to the molecular ion (intensity×10) and benzoyl ion (loss of methyl group) are modulated a lmost in phase, with only a ~60fs lag, while the phenyl ion yield is out of phase. This observation indicates that the probe photons cause loss of methyl or acetyl groups depending on the dynamic behavior of the molecular ion, or more specifically as we sh all see later, with the torsional angle of the carbonyl group. The dip in the molecular ion yield is caused when the acetyl group twists out of plane leading to enhanced fragmentation and will be elaborated later on the basis of Norrish type reactions. Figure 5.12 Normalized transients corresponding to the acetophenone molecular ion (black squares) along with the products, benzoyl (blue triangles) and phenyl (red circles) ions. The transients have been color coded according to the fragments and normalize d to unity at negative time delays. 119 5.4.3 Carbonyl Group Substituents and Locked Compounds The results pertaining to the first group of molecules is presented where the alkyl group has been varied to study the effect of the mass of the rotor on the ensu ing torsional dynamics in the cationic ground and excited states. Figure 5.13 shows the molecular ion yield corresponding to benzaldehyde, acetophenone, propiophenone and benzophenone, together with the corresponding fit to the oscillations observed. Fi gure 5.13 Normalized molecular ion yields (black dots) as a function of delay of the probe pulse for the molecular ions from (a) Benzaldehyde, (b) Acetophenone, (c) Propiophenone and (d) Benzophenone along with the fit to the damped oscillations (red line) . The plots have been normalized to unity at negative time delays. 120 yield, vide infra. Acetophenone has oscillation frequencies with periods of 647±15 fs. The period fo und for propiophenone is 690±18 fs, while the period for benzophenone is 1.611±0.050 ps. The period between the first oscillation and time zero is different than that between first and second oscillations for benzophenone. This may be due to an initial rel axation of the structure following ionization which is followed by the slow torsional motion of the phenyl group. The closeness in the periods of acetophenone and propiophenone point to the fact that a simple reduced mass (moment of inertia) argument of th e rotor is insufficient to explain the observed periods. In order to assess the dynamical behavior of the molecules upon ionization, the relaxed PESs of the cationic ground state (D 0 ) of this group of molecules was calculated along the acetyl twisting coo rdinate, relaxing all other nuclear degrees of freedom on the neutral surface at each point (Fig. 5.14). It is found that twisting is energetically favorable for acetophenone, but is unfavorable for benzaldehyde. It should however be noted that a two photo n excitation state (3 eV) above D 0 is present for both the molecules (Fig. 5.15). The absence of a driving force to twist can be directly linked to the lack of oscillations observed for benzaldehyde. An orbital picture based argument will be used following the discussion of the results to further enhance the understanding. 121 Figure 5.14 The D 0 energy of benzaldehyde (red circles) and acetophenone (black squares) as a function of the twist angle is shown. Figure 5.15 The D 0 , D 1 , D 2 , D 3 , D 4 , D 5 and D 6 s tate energies of acetophenone and benzaldehyde as a function of the twist angle of the acetyl group are shown in (a) and (b) respectively. Arrows indicate the positions of the S 0 minimum structures. The cationic ground state dynamics of aromatic ketones w here the carbonyl group is chemically locked in plane was also investigated. As shown in figure 5.16, oscillations in the molecular ion yield were not observed for indanone and fluorenone. This is consistent with our 122 association of the modulations in the i on yield to the torsional wave packet motion on the cationic ground state. Changes in the oscillation period as a function of the moment of inertia of the rotor further confirm the assignment. Figure 5.16 Normalized ion yields (black dots) as a function of delay of the probe pulse for the molecular ions (a) Indanone and (b) Fluorenone. The plots have been normalized to unity at negative time delays. 123 5. 4 .4 Functional Groups and Positional Isomerism Next the effects of functional groups and their positions on the phenyl ring on the ensuing dynamics were studied. To that end we studied the dynamics of methyl, fluoro and cyano acetophenone isomers. Figure 5.17 shows the normalized molecular ion yields of the methyl and dimethyl acetophenone isomers. It can be clearly seen that the functional group and its position on the phenyl ring have dramatic effects on the observed torsional dynamics of the acetyl group. o - methylacetophenone has prolonged oscillations having longer period (1.083±0.03 ps) as compa red to the para isomer (730±10 fs). The longer period can be attributed to the steric hindrance presented by the methyl group at the ortho position as opposed to the other isomers. No fast oscillations are observed in the yield of the meta isomer. A very l ong single hump is however observed, which may be due to some other mode of the molecule. It is observed that the parent ion yield of the isomer having methyl groups at both the ortho and para(2, 4) positions oscillates with a period of 980±12 fs. These os cillations die down around 5 ps, as shown in figure 5.17d. The oscillation period is shorter than that of o - methylacetophenone but longer than that of the para isomer. The introduction of a methyl group at the meta position of p - methylacetophenone leads to rapid damping of the first oscillation and the dimeta isomer behaves like m - methylacetophenone, having a single 1 ps long hump. (see Fig . 5.17e and f). 124 Figure 5.17 Normalized ion yields (black dots) as a function of delay of the probe pulse for the mole cular ions of (a) o - methylacetophenone, (b) m - methylacetophenone, (c) p - methylacetophenone, (d) 2,4 - dimethylacetophenone, (e) 3,4 - dimethylacetophenone and (f) 3,5 - dimethylacetophenone along with the fit to the damped oscillations (red line). The plots have been normalized to the corresponding yield at negative time delays. In order to assess the dynamical behavior of the para - , meta - , and ortho - methylacetophenone molecules upon ionization, the PESs of the cationic ground state (D 0 ) of these derivatives we re calculated along the relaxed acetyl twisting coordinate (Figure 5.18a). It is found that twisting of meta - methylacetophenone is energetically unfavorable. Twisting is favorable for the para derivative, as well as for the ortho derivative, which is alrea dy twisted by 26.4º in its neutral structure. Calculations help to explain the large differences in the behavior of these structural isomers. Initial optimization of the three neutral ground - state ring - methyl isomers results in structures where the acetyl group is twisted relative to the phenyl units to 125 varying degrees. The para and meta isomers are only slightly twisted, with O - C1 - C2 - C3 dihedral angles of 7.0º and 6.3º, respectively (See the inset of Figure 5.18a for the definition of the O - C1 - C2 - C3 dihedr al angle.). The ortho isomer is however strongly twisted, with an O - C1 - C2 - C3 angle of 26.4º, as previously demonstrated by gas - phase electron diffraction and related computation. 66 Presence of two photon resonance between cationic ground and excited state was also determined through calculations (see Fig. 5.19). Figure 5 .18 (a) The D 0 energies of ortho - , meta - , and para - methylacetophenone as a function of the twist angle of the acetyl group are shown in black, red, and blue, respectively. Arrows indicate the positions on each curve corresponding to the S 0 minimum structu res. Yellow lines superimposed on the geometric insets mark the four atoms which define the O - C1 - C2 - C3 dihedral angle. (b) Singly occupied molecular orbitals of the D 0 state of para - , meta - , and ortho - methylacetophenone cations at the neutral minimum ener gy geometries. 126 Figure 5.19 The D 0 , D 1 , D 2 , D 3 state energies of ortho - , meta - and para - methylacetophenone as a function of the twist angle of the acetyl group are shown in (a), (b) and (c), respectively. In order to understand how methyl substitution can have such a dramatic effect on the PES, one must understand how the driving force for twisting arises. To develop this understanding, the three singly occupied molecular orbitals (SOMOs) corresponding to the three lowest cation states at idealized plan ar and 35º - twisted structures were investigated. The relative ordering of these three states differs in the various substituted acetophenones studied, but like the p - methylacetophenone case shown in Figure 5.20, their energies all fall within 0.5 eV of one another at the S 0 minimum structure. In particular, we will concentrate on the SOMOs for this isomer (Figure 5.21). 127 Figure 5.20 The D 0 , D 1 and D 2 energies of para - methylacetophenone cation as a function of the twist angle of the acetyl group. It is i mportant to recognize that these SOMOs represent the hole left behind after ionization. Upon ionization there is a tendency for the nuclei to relax in such a way as to raise the energy of this hole, thus lowering the energy of the remaining electrons. In t he planar structure, the acetophenone derivative cations have three low - lying states: two in which the SOMO is nonbonding lone pair (n) orbital (Figure 5.21, left). The relative ordering of these three states differs in the various substituted acetophenones , but their energies are within 0.5 eV of one another at the S 0 minimum structure for all derivatives studied. In the case of the para - methyl derivative the D 1 SOMO is of n character while the D 0 and D 2 oupled by symmetry in this planar structure but upon twisting they mix and split (Figure 5.21, right), leading to a decrease in energy of D 0 via the pseudo - Jahn - Teller effect. In chemical terms, upon twisting, the SOMO of D 0 (Figure 5.21 top right) becomes orbitals, which correspond to the SOMOs of D 0 and D 1 in the planar structure. Twisting 128 densities into close proximity, thereby resulting in an increase in the energy of the SOMO and a corresponding decrease in the energy of the D 0 state. The SOMO in D 1 and D 2 correspond to nonbonding and bonding combinations of these orbitals (Figure 5.21, bottom and middl e right, respectively), and thus twisting does not result in a decrease in the energies of these states. The role that methylation plays in determining the energetics of twisting is illustrated in Figure 5.18b, which shows the SOMOs of D 0 for para - , meta - , and ortho - methylacetophenone in 0 is determined by the position of the methyl group, with the largest density on the methylated carbon. For para - and ortho - methylacetophenone, the with the oxygen lone pair, and thus there is a large driving force for twisting. In contrast, in meta - thu s only a very weak effect is expected. Investigation of the SOMOs also suggests how twisting can modulate the probability of different fragmentation pathways. The D 0 SOMO of the twisted structure (Figure 5.21, top right) has significant density in the in - p lane lone pair orbital of the ketone oxygen atom. This unpaired electron density is well positioned to interact with and destabilize the C - C bonds between the ketone carbon and the alpha carbons on either side of the ketone group. Such an interaction is re miniscent of the Norrish type I reaction, 78 in which the excitation of an electron out of the oxygen lone pair orbital of a ketone leads to cleavage of one of the alpha carbons. The D 0 SOMO of the nearly planar S 0 minimum structure (Figure 5.21, top left), on the other hand, exhibits no population in the in - plane lone pair, and thus one would expect the propensity for such a Norrish - like cleavage to be strongly modulated by twisting of the acetyl group. 129 Figure 5.21 SOMOs of the three lowest - energy cation states (D 0 , D 1 , and D 2 ) of para - methylacetophenone in the planar - constrained S 0 minimum energy structure (left) and 35º twisted structure (right). Top and side views of each orbital are provided. 130 Unlike in methylacetophenones, oscillations in the ion signal were observed in ortho - , meta - , and para - fluoroacetophenone as shown in figure 5.22. Oscillatory behavior is obse rved in the yield of all the ring - substituted isomers of fluoro - acetophenone. The ortho, meta and para isomers have periods of 698±26 fs, 668±12 fs and 675±5 fs respectively. It is interesting to note that the para isomers for both the methyl and fluoroace tophenones show deeper oscillations than their isomers. This is most probably due to the higher polarizability of the para isomers due to their greater length which in turn enhances their induced dipole moment. When compared to ortho isomers, para substitu tion causes no steric hindrance and provides charge stabilization. Figure 5.22 Normalized ion yields (black dots) as a function of delay of the probe pulse for the molecular ions of (a) o - fluoroacetophenone, (b) m - fluoroacetophenone and (c) p - fluoroaceto phenone. The plots have been normalized to unity at negative time delays. 131 The computed D 0 energies of these three derivatives as a function of the twist angle of the acetyl group are shown in Figure 5.23. Consistent with the suggestion that the experimen tally observed oscillations arise from twisting of the acetyl group on the D 0 state, twisting is favorable in all three of these derivatives. Presence of two photon resonance between cationic ground and excited state was also determined through calculation s. Figure 5.23 The D 0 energies of ortho - , meta - , and para - fluoroacetophenone as a function of the twist angle of the acetyl group are shown in black, red, and blue, respectively. Arrows indicate the locations of the S 0 minimum structures on each curve. Pump probe photofragmentation studies were also performed on para - and meta - cyanoacetophenone in order to explore the effects of pi acceptor groups on the electronic structure. Oscillatory signatures were not as clearly observed for these compounds, as sh own in figure 5.24. Based on calculations, however, twisting is favorable in the D 0 state of both the meta and para isomer, as shown in Figure 5.25, and therefore we would expected to observe oscillations. From the mass spectra (shown in figure 5.10) we fo und cyano compounds have a significantly lower overall ion yield. This observation is consistent with their 0.5 eV higher ionization potential compared to acetophenone. This implies ionization requires the equivalent of 7 photons (instead of 6), with exces s energy after ionization of at least 1 eV. The mass spectra 132 for the cyano compounds show extensive fragmentation and a significant yield of protons, and even C 2+ . These observations are consistent with higher energy fragmentation pathways that may include electron recollision and multiple ionization. This is also evident in the observation of protons in the mass spectra, a signature of, Coulomb explosion signatures. The low molecular ion yield in these compounds led to a much lower signal - to - noise ratio in the transients. When the transients are fit, we find both cyanoacetophenones show oscillations, although these seem to be buried in the noise. Figure 5.24 Normalized ion yields (black dots) as a function of delay of the probe pulse for the molecular ion s of (a) m - cyanoacetophenone and (b) p - cyanoacetophenone. The plots have been normalized to unity at negative time delays. 133 Figure 5.25 The D 0 energies of meta - , and para - cyanoacetophenone as a function of the twist angle of the acetyl group are shown in red and blue respectively. 134 5.5 Discussion Understanding the behavior of polyatomic molecules under intense fields requires drawing links between strong - field physics, ab initio calculations, organic chemistry, spectroscopy and the chemistry of radical cations. We have presented experimental evidence that is consistent with strong - field ionization of acetophenone and several other derivatives followed by absorption of additional photons from the probe laser. The dynamics observed as a functio n of time - delay between pump and probe pulses are consistent with the creation of a relatively cold ground state cation, followed by torsional motion of the carbonyl moiety, confirmed by the observation of a lack of torsional dynamics in fluorenone and ind anone, for which such motion is prevented by the locked - in - place structure, and changes in the oscillation period in response to the moment of inertia of the rotor. Ab initio calculations on most of the molecules are found to support the experimental obser vations, and are consistent with ionization to the ground electronic state of the cation D 0 . Benzaldehyde and m - methylacetophenone were found to be vertically ionized such that they are already near the energy minimum, and therefore torsion to larger angle s is not energetically favorable. As the ionic molecular structure resulting from strong field ionization seeks to relax to a more energy favorable configuration, a large number of degrees of freedoms are explored. The observed coherence, in the case of s ome acetophenones, involves nuclear rearrangements. Along the way, conical intersections are traversed, and these determine the final structures as well as the photofragmentation products. Following ionization, cation chemistry is related to ion stability as shown in the mass spectra of the compounds (Fig. 5.4). The stability can be determined through ab initio calculations and is consistent with simple o, m, p - aromatic ring substitution. With respect to the carbonyl functional group in ketones, Norrish typ e I reactions are expected 135 upon excitation. This type of reaction follows through the cleavage of either of the bonds next to the carbonyl group, producing two radicals. In the experiments methyl loss is found to be out of phase with acetyl loss (see Fig. 5.11), likely due to the varying coupling between non - bonding electrons on the oxygen and the benzene group as a function of twisting angle. The findings are consistent with a number of studies in the literature. We start from the examples given to suppor t the NME theory. 15 , 16 It was argued that the increased molecular length and number of electrons is what causes gre ater intramolecular energy which is acquired through multiple electrons oscillating in the field and results in fragmentation after SFI. Here, it is showed in Fig. 5.1 that there is a simpler explanation to the observed fragmentation of those molecular sys tems, which is related to the HOMO - LUMO gap and the density of states which facilitates SFI. Molecular fragmentation results from the absorption of additional photons by the nascent cation, which is again facilitated by the density of states. Fragmentation of the nascent cation and the cation after post - ionization excitation depends on radical ion stability and may take place in a broad range of timescales stretching from femtoseconds to microseconds. At intensities greater than 10 14 W/cm 2 , not discussed he re, fragmentation results from interaction between the leaving photoelectron and the molecular system through recollision. This process is usually accompanied by multiply charged fragments and Coulomb explosion. More recent studies exploring possible NME p rocesses have included oriented molecules. Experiments on HCl identified differences that were attributed to sequential double ionization. 79 High harmonic interferometry has also identified multi - electron dynamics, however, here again recollision is involved. 22 A recent study tracking channel and angle resolved above threshold ionization, explored NME. 19 , 24 Results showed that indeed each ionization channel displays a unique angular dependence; however, it is not clear that non - adiabatic multielectron effects were 136 identified. The influence of molecular symmetry on strong - field i onization of oriented polyatomic molecules has been probed and the results were confirmed by MO - ADK. 80 , 81 It was found that the ionization yields were primarily determined by the nodal surface structure of the molecular orbitals, without the need to invoke NME. Relating molecular fragmentation to the probability that the cation absorbs further photons can be easily tested by comparing experiments with different pulse durations. F or example, experiments on C 60 carried out with 100fs pulses 82 led to the observation of sign ificant fragmentation while those carried out with sub - 50fs found very little fragmentation. 83 Fragmentation of C 60 was found only after the appearance of C 60 ++ , presumably through electron recollision. More recent experiments similarly find little or no fragmentation at lower intensities. 84 Experiments on p - nitroaniline found substantially more fragmentation as chirp increased. 85 The amount of chirp was also found to increase the fragmentation of S 8 . 86 The fragmentation of ethanol was also found to increase with chirp. 87 , 88 More recent experiments using coincidence photoelectron and photoion detection of ethanol found the averaged internal energy o f C 2 H 5 OH + just before the dissociation is found to increase when the laser field intensity increases from 9 to W/cm 2 and when the laser pulse duration increases from 35 to 800 fs. 89 Intense fields capable of double ionization, a regime not studied here, create high - energy photoelectrons that interact with the molecule causing significant fragmentation and the generation of smaller ionic species incl uding C + and H + . Work from our group on ortho - nitrotoluene showed a smooth progression from transform limited pulses to highly stretched pulses using binary phase shaping, indicating that longer pulses caused additional fragmentation. 90 A broader study presented results on 16 different molecules subjected to intense shaped 800nm puls es. 32 We found that the extent of fragmentation was 13 7 primarily dictated by pulse duration. For acetophenone, short pulses with peak intensity ~10 13 W/cm 2 , lead to limited fragmentation and a strong molecular ion (see figure 5.7), while 1ps pulses at all energies lead to complete fragmentation of the molecular ion (see figure 5 .26 ). A few notable exceptions to this general pulse duration trend were found . Acetone, acetyl chloride, benzene, and toluene were found to be less sensitive to pulse duration. 32 The reason behind the insensitivity to pulse duration in these cases is the low probability for single or multiphoton excitation of the nascent cations. Figure 5 .26 Time of flight mass spectra of acetophe none corresponding to different peak intensities corresponding to a 1 ps pulse. Absence of any molecular ion peak points towards the fact that fragmentation is pulse duration dependent. 138 During strong - field ionization of polyatomic molecules there is a goo d possibility of encountering multiphoton resonances and near resonances. The presence of such resonances may cause a delay in the ionization process, making it slower than a sub - optical cycle. The term adiabatic often implies there is no electronic resona nce in the ionization process. 15 , 16 In the NME theory, it is argued that non - adiabatic ionization leads to a large absorption of energy by the molecule. 15 , 16 The data presented in this study is consistent with the creation of internally cold cations, and thus supports a vertical ionization process. Our model argu es strong - field ionization by short sub - 50fs pulses in molecules is consistent with the creation of relatively cold molecular ions, without invoking multi - electron processes that deposit the energy required for fragmentation of the resulting molecular ion or cause simultaneous multielectron transitions. This conclusion is supported by the experimental and theoretical results presented here. What is most remarkable is that this conclusion is supported by experiments on molecules with molecular weights in the thousands of Dalton. Experiments carried out on peptide ions, whereby the mass - selected ions are subjected to SFI, are consistent with prompt ionization followed by radical cation bond cleavage. 51 , 91 If molecular size determined the amount of intramolecular energy gained by the cation during SFI, experiments on peptides should result in extensive ergodic fragmentation that reflects the distribution of energy throughout the molecule. Our findings, however, are that fragmentation follows well - known radical - cation fragmentation pathways, and most importantly the fragmentation is non - ergodic. 51 In fact, the significance of femtosecond laser - induced fragmentation of peptides is the ability to cleave strong bonds while leaving weak bonds intact. 51 The value of this ability for biological mass spectrometry is the ability to preserve weakly bound peptide modifications such as phosphorylation while being able to cleave peptide back - bone amide bonds in order to obtain sequencing information. 92 139 Our experiments highlight coherent vibrational (torsion) motions i n the product ions. This to few tens of percent. The timing of the coherence can be used to identify o, m, p substitution when strong - field excitation is used for analytical chemistry purposes. 93 - 95 In fact, electron impact mass spectrometry is very similar to strong - field mass spectrometry provided that the laser pul ses used are short. 32 This is consistent with the fact that electron impact occurs with an associated short timescale determined by the transient time of the electron past the molecule and the ensuing ionization. In electron imp act there are no laser photons for the cation to absorb and yield further dissociation, therefore the fragmentation is determined purely by ion stability. Here we have considered a molecular - structure dependent SFI process that is closely followed by photo dissociation of the resulting cations. We note that this model depends on the molecular density of electronic states, n - photon resonances (with n=1,2,3), ion stability, and pulse duration in terms of optical cycles. The observation of resonances in this wo rk is consistent with the observation of different degrees of fragmentation observed when using different wavelengths. 15 , 16 The wavelength dependence, however, is related more to resonances than to the participation of multiple electrons. 96 It is noteworthy that all of the above arguments, which explain the origin of the oscillatory signal in para - and ortho - methylacetophenone and the surprising absence in the meta derivative, are based on the assumption that upo n interaction with the strong laser field a single electron is ejected from the molecule without significant excitation of the remaining electrons. This is confirmed by the success of ab initio calculations starting from the ground state geometry predictin g the observed behavior without the need for additional intramolecular energy. 140 5. 6 Conclusion This work has explored the strong - field photofragmentation of a large family of substituted aromatic ketone mole cules. It was found that : (i) when peak intensity is low and pulse duration is short, the fragmentation following SFI is limited (see figure 5 .8 ). (ii) Longer pulses lead to increased fragmentation (see figure 5.25). (iii) Vibrational coherence in the yield of the molecular ion implies that it is formed in the ground state with relatively low internal energy. (iv) The extent of subsequent fragmentation depends on electronic resonance with the excitation field. (v) Even in strong field excitation, chemical principles such as functional groups and positiona l isomerism are good predictors of the ensuing chemistry. (vi) Advanced ab initio electronic structure calculations support our inference that the cations are formed via a process akin to vertical ionization(Franck - Condon), taking them to the electronic gr ound state of the ion whereupon nuclear relaxation may occur. The success of these calculations indicates that it is safe to assume that SFI with short pulses leaves the nascent cation with little internal energy. This study serves to provide a model for the behavior of polyatomic molecules under strong fields that is consistent with a photoelectron that promptly leaves the molecule, takes most of the absorbed energy with it. This process conjures the mental picture of the trick in which the table cloth is quickly pulled off the table, leaving the plates and glasses intact. This rather simple analogy is consistent with the observation of non - ergodic photofragmentation of polyatomic molecules by ultrafast laser pulses predicted by Zewail in 1980, 97 and with subsequent observations made in femtosecond lase r induced dissociation mass spectrometry of phosphorylated proteins, where strong bonds are cleaved while weak bonds are left intact. 50 The proposed behavior of poly atomic molecules under intense fields is prompt ionization leaving a relatively cold ion followed by ion - fragmentation enhanced through single and multiphoton 141 resonance. The extent of fragmentation is proportional to the duration of the laser pulse. Predic tive analysis of the behavior of polyatomic molecules in strong fields requires knowledge of molecular structure (ground and ion electronic states) and molecular alignment with respect to the field. 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Molecular Physics 2013 , 112 , 1102. 149 Chapter 6 Reverse Diels Alder Reaction following Strong Field Ionization Understanding the behavior of large polyatomic molecules under strong non - resonant IR laser fields is an interesting endeavor that combines Physics and Chemistry to discern the mechanisms and dynamics as the molecular ion breaks into fragment ions. This chapter deals with the coherent dynami cs of dicyclopentadiene and its reverse Diels Alder fragment cyclopentadiene following strong field ionization. Signatures of coherent bond dissociation for both the species were observed where the oscillation frequency is found to gradually increase with time. High - level ab - initio calculations are used to identify the vibrational modes most closely associated with the observed dynamics. 150 6.1 Introduction Femtosecond laser pump - probe spectroscopy as a tool for understanding the dynamical process in atoms and molecules has enabled us in understanding many elementary processes in chemistry, physics, and biology and has paved way for the development of improved and robust quantum chemical theories regarding the behavior of molecules in a diverse ran ge of environments. 1 - 4 It was known since the early days that femtosecond laser even when not resonant with an electronic transition was capable of excitati on, ionization and fragmentation. When the laser fields are sufficiently short and intense, strong field ionization precedes bond breaking processes. 5 - 7 Chemistry und er strong field excitation leads to the formation of a number of fragment ions. Fragment ion yields are sensitive to the laser pulse properties, and this sensitivity has been used to control strong - field chemistry. 8 - 11 Strong - field pump - probe spectroscopy can be used as an important tool to learn about the ground and excited cationic states, direct and indirect bond breakage, curve crossing dynamics and their overall mol ecular dynamics following ionization. A recent investigation regarding the dynamics of a family of alkyl - phenyl ketones 12 , 13 following strong field ionization found that the position and chemical nature of functional groups on the benzene ring can influence the wave packet motion on the cationic ground state leading to different time - resolved transients. In this chapter we investigate the femtosecond coherent dynamics of the molecular and fragment ions upon strong field ionization of dicyclopentadiene (DCPD). Dicyclopentadiene can undergo a reverse Diels - Alder reaction to produce two cyclopentadiene molecules when it has en ough energy to overcome the reaction barrier. Cyclopentadiene molecules undergo a Diels - Alder reaction at room temperature to form dicyclopentadiene when in liquid state as shown in Figure 6.1. Femtosecond real - time studies of reverse Diels Alder processes were first studied by 151 Zewail et. al 14 - 17 where they resonantly excited the molecules using a UV pump and detected the products via ionization. This was done in order to determine the mechanism of the reaction pathway and they concluded that the reaction can follow pure stepwise and concerted trajectories along with trajectories that involve many other transient configurations depending on the asymmetry of the molecular structure, location of the transition state(s) and the barrier height. In this chapter studies pertaining to the bond dissociation dynamics of dicyclopentadiene following ionization by non - resonant 800 nm femtosecond pulses have been presented. Figure 6.1 Photofragmentation scheme of dicyclopentadiene into two cyclopentadiene moieties under laser irradiation. The bonds marked in yellow break and rearrange to form the cyclopentadiene molecules. 152 6.2 Experimental Methods The experimental setup ha s been described in details in the previous section. DCPD was purchased from Sigma and used without any modifications. 153 6.3 Results 6.3.1 Intensity Dependence of Mass Spectrum DCPD has an extremely low ionization threshold as compared to other polyatomic molecules. Cyclopentadiene ion is almost always formed even at extremely low intensities. DCPD + ion is produced at extremely low laser intensities and the CPD + ion yield is comparable to that of DCPD + at these intensities (Fig. 6.2). F igure 6.2 Mass spectrum of Dicyclopentadiene obtained with pulses having an average power of 7µJ/pulse. At these low excitation powers CPD + yield is comparable to that of the DCPD + ion yield. 154 However as the laser intensity increases, there is an expo nential rise in the yield of CPD + ions and for certain intensities 40 times more CPD + as compared to DCPD + is formed (Fig 6.3). Figure 6.3 (a) Normalized ion yield of DCPD + (black squares) and CPD + (red circles) as a function of laser power. (b) Ratio o f CPD + and DCPD + ion yields (black circles) along with the linear fit. DCPD + has a second order dependence to ionize while CPD + has a third order dependence at the low intensity limit determined by plotting the logarithm of the ion yield to the logarithm of the pulse intensity (Fig. 6.4). This double logarithmic representation is useful in studies of strong field ionization since the ion yields rise as where n is the number of photons involved, appear as straight line with slope n . These properties make this molecule a unique system that needs further investigation under strong fields. Therefore the time resolved dynamics of the laser induced reverse Diels - Alder reaction using non - resonant 800 nm photons is presented in this chapte r. 155 Figure 6.4 Double logarithmic plot of ion yield as a function of peak intensity for (a) DCPD + and (b) CPD + along with the linear fits (red line). The slope of the fit provides information about the number of photons involved to reach an intermediate neutral excited state during the ionization process. Slopes of 2 and 3 for DCPD and CPD respectively point to a two and three photon process. 156 6.3.2 Pump - probe T ransients The time delay transients for molecular and the fragment ions as a fun ction of the probe delay are shown in Figure 2(a) - (e). The time delay plots have been normalized to ion yields at zero delay, the ion yield increases for the par ent ion as well as for all the fragment ions when the pump and probe pulse overlap in space and time. Figure 6.5 Normalized molecular ion yields (black dots) as a function of delay of the probe pulse for (a) C 10 H 12 + , (b) C 5 H 6 + , (c) C 4 H 4 + and (d) C 3 H 3 + an d (e) C 2 H 2 + ions. Plots (e) - (j) show the fast oscillations along with the fits (red) for the parent and fragment ions. The left plots have been normalized to unity at negative time delays and the right plots were constructed by subtracting the slow decayin g envelope from the raw data in order to extract the fast oscillations. 157 For positive time delays when the probe arrives after the pump pulse, it can cause further fragmentation by depositing additional energy and thus depletes the ion yield as observed for the dicyclopentadiene and cyclopentadiene ions, whereas the yield of the C 4 H 4 + , C 3 H 3 + and C 2 H 2 + ions increase at positive time delays as more of these species are formed from the dissociation of the parent and CPD + ions. Therefore we are monitoring the dissociation dynamics for DCPD + and CPD + ions and the formation dynamics for the smaller fragments. Coherent oscillations are observed in the pump - probe transients for the parent ion as well as the fragment ions. The fast oscillations are isolated by subt racting the slow decay from the raw data and were fit using a damped cosine function para meters for the different fragment ions are listed in Table 1. The ion yield for the fragment ions C 4 H 4 + , C 3 H 3 + and C 2 H 2 + have only been fit up till 600 fs since the yield decays sharply after that. Table 6.1 Fitting parameters for the ion yield modulation s of the parent and fragment ions using the formula . Ion A (fs - 1 ) (fs) (fs 2 ) (rad) (fs) C 10 H 12 + 0.013 0.038 162±4 - 1.5×10 - 5 - 0.22 719±5 C 5 H 6 + 0.028 0.027 226±5 - 1.3×10 - 5 - 0.16 563±6 C 4 H 4 + 0.04 0.021 286±4 - 1.9× 10 - 6 - 0.58 251±4 C 3 H 3 + 0.04 0.022 285±10 - 3.3×10 - 6 3 500±8 C 2 H 2 + 0.08 0.022 285±5 - 6.8×10 - 6 - 1.1 280±5 158 The parent ion (DCPD + ) transient has faster oscillations and slower decay rate unlike the fragment ions. The extracted oscillation period for the par ent ion is ~162±4 fs and is significantly faster than the fragment ions that have periods ranging from 230 - 280 fs. One of the interesting and important observation from these results is that the fragment ions have different coherent vibrational motions com pared to the molecular ion. CPD + ion yield depletion oscillates with a period of 226±5 fs and has a decay time of 536±6 fs. The ion yield for the fragment ions C 4 H 4 + , C 3 H 3 + and C 2 H 2 + are out of phase with respect to the CPD + ion yield. C 4 H 4 + , C 3 H 3 + and C 2 H 2 + have very similar oscillation frequency however the decay rate of C 3 H 3 + is almost twice that of the other two fragments. The second important observation is that for all the ions the oscillation frequency change is an order of magnit ude greater for the parent ion and the CPD + ion as compared to the other fragment ions, as shown in Table 1. In order to understand the experimental observables, the physicochemical processes occurring upon multiphoton excitation of DCPD should be first un derstood and analyzed. A schematic illustration of the same is shown in Figure 6.6. 159 Figure 6.6 Schematic illustration of the mechanism behind quantum coherent control of dicyclopentadiene fragmentation. Each red arrow corresponds to one 1.55 eV photon from the near - IR laser. 160 For this schematic the UV - Vis spectra measured by our group and the photoelectron spectroscopy of DCPD 18 were combined with spectroscopic information for this and related systems. 19 The initial excitation using 1.55 eV photons occurs through a 3 - 4 photon resonance to the first absorption band near 280 nm, assigned as the superposition of two singlet - triplet transitions 19 and a much more intense band at 200 nm. Calculations at the EOM - CCSD/6 - 31+G** level of theory 20 identified five low - lying electronic states of neutral DCPD in the regions between 6.4 and 7.0 eV in ver tical excitation energy (as determined at the B3LYP/6 - 31G** ground state minimum energy geometry, see Fig. 6.7). These states likely correspond to the bright absorption band at 6 eV. States of both character are observed in this low energy region and are known to originate from ethylene. 21 Excited cationic states resonant(single or multiphoton) with the excitation photons play a major role in t he further fragmentation of the molecular ion. 13 Calculations at the IP - EOM - CCSD/6 - 31G** level of theory 22 were performed to identify the lowest lying cationic states of DCPD at the neutral minimum energy structure. The three lowest excited cationic states were identified at 0.55, 1.99, and 2.27 eV above the cation ground state. This spacing is in reasonable agreement with features observed in the experimental photoelectron spectrum 18 and can facilitate the absorption of further photons leading to dissociation of the mole cular ion on various surfaces through conical intersections as shown in Fig. 6.6. 161 6.4 Discussion The two and three photon laser intensity dependence of the DCPD + and CPD + ions respectively (Fig. 6.4) point s to the presence of an intermediate state tha t facilitates the ionization character as described earlier. This observation has important implications for studies using non - resonant pulses since a very weak pulse or the pedestal on a pulse will be enough to cause ionization. Previous studies on DCPD by Goswami et. al 23 . investigating the effect of chirp on the relative yield of CPD + ion found a four photon dependence towards ionization for both DCPD + and CPD + ions and were able to detect ions only when using energies of 180 and conclusion regarding control with negatively chirped pulses . Instead of foll owing the reverse Diels Alder process for the neutrals through multiphoton ionization, we investigated the bond dissociation dynamics following ionization and follow the evolution of the molecular and fragment ions depleted/formed as a function of a probe. The oscillations in the transients are due to coherent vibrational motions on the cationic ground state. Differences among the dissociation pathways will lead to different pump probe transient modulations depending on the motion of the wavepacket on the c ationic ground state surface. The depleted signal will be modulated depending on the polarizability of the cation controlled by the vibrational motion of dissociating bonds. The observation that the period of the ion yield oscillation increases with time h as been observed for the first time and points to a slow process that modulates the bond dissociation process. Our results show that the parent ion has significantly different oscillation frequency than the rest of the fragment ions. The out of phase relat ionship of the smaller fragment ions (C 4 H 4 + , C 3 H 3 + and C 2 H 2 + ) with respect to the CPD + 162 indicates that these products are most likely formed due to the dissociation of CPD + ion. The oscillation frequency of DCPD + of 162 fs corresponds to a frequency of 205 cm - 1 . Calculations at the neutral ground state geometry using B3LYP/6 - 311G level of theory predicts a Raman mode of DCPD that involves the stretching of the C - C bonds connecting the two cyclopentadiene rings having a similar frequency of 200 cm - 1 . We beli eve that the dissociation of these bonds is a stepwise process. One of the C - C bonds dissociates in the cationic state upon ionization giving rise to a conformationally relaxed DCPD + ion which can subsequently absorbs photons to access excited cationic sta te that evolves to produce the CPD + ions as shown in Figure 3. The C 3 H 3 + and C 2 H 2 + ions are formed as a result of the dissociation of the CPD + ion via absorption of further photons. The oscillations rapidly disappear for both of these ions, however one wou ld expect 3 H 3 + fit. This might be due to the cationic wavepacket encountering a conical intersection that leads to the rapid dissociation into other smaller fragments. 163 6. 5 Conclusion We have demo nstrated here how femtosecond photoionization followed by fragmentation by a probe can be used to probe the ultrafast dynamics of photoionization - induced bond vibrations in dicyclopentadiene cation. A coherent vibrational motion where the oscillation frequ ency gradually increases with time having a period of about 162 fs has been observed. Theoretical calculations suggested that the oscillation arises from vibrational motion corresponding to a Raman breathing mode of neutral DCPD. The oscillation for the sm aller fragments is damped rapidly, indicating the presence of conical intersections in the higher cationic excited states of DCPD. Because there is no other decay channel present for the cation ground state with the limited amount of deposited energy, it p rovides us with a unique opportunity to observe, in real time, the photoionization - induced bond dissociation of one of the C - C bonds connecting the cyclopentadiene rings and the further dissociation of the cyclopentadiene molecule into smaller fragments. T his method enables us to explore chemistry under strong field excitations and study the similarities and differences in the mechanism compared to neutral molecules. 164 REFERENCES 165 R E F E R E N C E S (1) Dantus M.; Rosk er, M. J. Z., A.H J. Phys. Chem. 1988 , 89 , 6128. (2) R.M. Bowman, M. D., A.H. Zewail Chem. Phys. Lett. 1990 , 174 , 546. (3) Zewail, A. H. The J. Phys. Chem. A 2000 , 104 , 5660. (4) Dantus, M.; Zewail, A. Chem. Rev. 2004 , 104 , 1717. (5) Corkum, P. B. Phys. Re v. Lett. 1993 , 71 , 1994. (6) Hankin, S. M.; Villeneuve, D. M.; Corkum, P. B.; Rayner, D. M. Phys Rev. 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A summary of the most important findings along with the possible future direction is pre sented. 168 7.1 Single Beam Phase Shaped Pulses for Probing Solvated Molecules Chirped femtosecond pulses were rigorously tested and later developed into an important tool for probing solvated dye molecules. F luorescence and stimulated emissio n for different excitation pulse energies were measured as a function of chirp and it was found that the value of chirp effect for both the emissions is quadratic with the respect to probability of excitation. This points to the fact that the phase - depende nt emission results from a two - photon non - linear optical the sha pe of the chirp effect curve is independent of the pulse energy. A model describing the experimental results was developed theoretically based on solution of Liouville equations. It was found that the time scale of Stokes shift from the excited state to th e fluorescent state should be approximately equal to the TL pulse duration and faster than dephasing by solvent. It was also found that inhomogeneous broadening plays an important role and it helps in the improved agreement of the simulations with the expe rimental data. After determining the physical processes responsible for the observation of the chirp effect, it was used as a tool to probe changes in the solvent environment of solvated dyes. It was found that the chirped pulses are particularly sensitive in the first few femtoseconds where other non - linear studies have been less sensitive. In particular the positively chirped pulses are sensitive to the intermolecular changes while the negatively chirped pulses, which are similar to two color pump probe a re sensitive to the intramolecular changes. The theoretical model developed earlier is being refined in order to reproduce the effects of the experiment. Furthermore, the effect of different phase steps on the stimulated emission spectrum was investigated and it was found that a phase step on the excitation spectrum creates a narrow 169 enhancement on the lower wavelengths and this feature tracks the step position. It was found that step causes greater results were also modeled using the Liouville equations under the perturbation approxima tion and it was found that to reproduce the observed results we have to consider an inhomogeneous set of excited states and use a dephasing rate of 100 fs for electronic coherence between ground and excited states. These parameters define the inhomogeneous and homogeneous spectral widths. Preliminary experim ents on dyes dissolved in a viscous medium at different temperatures, not reported here, have found differences in the magnitude and width of the main feature. The theoretical simulations are currently being improved in order to explain the recent findings . Future studies can be performed using very short (<4 fs) laser pulses by taking advantage of these shaped pulses generated using a pulse shaper to probe solvent environment effects of probe molecules in interesting environments such as protein pockets, m embranes and ultimately under single molecule conditions where the implementation of the multidimensional nonlinear methods such as 3PEPS will be a challenging task. Single molecule experiments will help identify the difference between microscopic (associa states) decoherence and macroscopic (associated with interference between emissions from different molecules) decoherence. These methods could be also used to study and control the excitation of IR144 and IR125 di mers and focus on controlling the final emissive state taking advantage of the electronic coupling between the two chromophores. Measurements on single heterodimer s will be able to determine the electronic coherence time in the absence of heteroge 170 focusing on the light harvesting complex LH2 could also be carried out given that the i nterest in photochemical reactions has greatly increased in recent years due to the realization that capturing solar energy is one of the most promising avenues for attaining a sustainable source of energy. 171 7.2 Behavior and Dynamics of Polyatomic Molecules under Strong Field The strong - field photofragmentation of a large family of substituted aromatic ketone mole cules was investigated and a model for strong field ionization and fragmentation was proposed based on the results and supporting calculations. It was found that for low peak intensites and short pulse duration , the fragmen tation followi ng SFI is limited . On the other extreme, l onger pulses were found to enhance fragmentation . Vibrational coherence in the yield of the molecular ion implies that it is formed in the ground state with relatively low internal energy. The extent of subsequent fragmentation depends on the presence of electronic resonance in the cationic excited manifold with the excitation field. C hemical principles such as functional groups and positional isomerism were found to be excellent predictors of the ensu ing chemistry even under strong fields of several V/Å . The hypothesis that the cations are formed via a process akin to vertical ionization(Franck - Condon), taking them to the electronic ground state of the ion whereupon nuclear relaxation may occur is well supported by the ab initio quantum chemical calculations . The success of these calculations indicates that it is safe to assume that SFI with short pulses leaves the nascent cation with little internal energy. This study serves to provide a model for the behavior of polyatomic molecules under strong fields that is consistent with a photoelectron that promptly leaves the molecule, takes most of the absorbed energy with it. The proposed behavior of polyatomic molecules under intense fields is prompt ionizat ion leaving a relatively cold ion followed by ion - fragmentation enhanced through single and multiphoton resonance. Predictive analysis of the behavior of polyatomic molecules in strong fields requires knowledge of molecular structure (ground and ion electr onic states) and molecular alignment with respect to the field. 172 Future studies will be focused on several important aspects pertaining to strong field processes. In particular orientation dependent ionization of polyatomic molecules is one such field that needs attention since it can shed light on the kind of orbital participating in the ionization process. Unlike the previous experiments, for these experiments, field - free alignment following an alignment pulse will be performed that is intense but not eno ugh to ionize. Once the temporal locations for molecular alignment are determined, conventional pump probe and chirped pulse type of experiments for can be performed exclusively on the cations, for which alignment along a single axis can be easily achieved and perpendicular excitation is expected to reach a different ion state than the one reached for parallel excitation. The key to these experiments will be to identify molecules that undergo structural changes upon ionization and as a result have slightly different rotational recurrence time. I have also d esign ed and construct ed a Photo Electron Photo Ion Coincidence Imaging setup and collect ed preliminary data for demonstration of feasibility. All the experiments performed in our group till now consider th e energetics and time resolved behavior of the fragment ions resulting from the strong field interaction. To get a complete picture of the energetics of the different pathways involved in the dissociation mechanism and to determine the outcome of different molecular orientation on SFI, it is very important to study the behavior of the electrons. Photo Electron Photo Ion Coincidence Imaging spectrometer will enable us to acquire time resolved images of both the ions and the electrons in coincidence. These im ages will be instrumental in determining the photo - fragment angular distribution which will be helpful in determining the symmetry of electronic states and the rotational dynamics of the molecular species.