Femtochemistry: Ultrafast Dynamics of the Chemical Bond

The following sections are included:

• General Introduction

• Contents

This paper, the first in a series of three papers, gives a detailed account of our studies on picosecond photofragment spectroscopy. The unimolecular reaction NCNO → CN+NO is examined in detail here. Microcanonical state-to-state rates are measured in molecular beams at different energies in the reagent NCNO using pump-probe techniques: one picosecond pulse initiates the reaction from an initial (ν,J) state and a second pulse, delayed in time, monitors the CN radical product in a specific rovibrational state, or the reagent NCNO (transient absorption). The threshold energy for reaction is determined to be 17 083 cm⁻¹ (bond energy = 48.8 kcal/mol). Measured rates are found to be sharply dependent on the total energy of the reagent, but independent of the rotational quantum state of product CN. Results of transient absorption measurements are used to argue that the ground state potential energy surface dominates the reaction in the range of excess energies studied. The energy dependence of the rates, k_MC (E), is compared with that predicted by statistical theories. Both standard RRKM (tight transition state) and phase space theory (loose transition state) fail to reproduce the data over the full range of energies studied, even though nascent product state distributions are known to be in accord with PST at these energies. Furthermore, k_MC (E) is not a strictly monotonically increasing function of energy but exhibits some structure which cannot be explained by simple statistical theories. We advance some explanations for this structure and deviations from statistical theories.

Using picosecond excitation in a supersonic jet, we present a full account of our earlier report on the dynamics of state-selective photoisomerization of t-stilbene. Collisionless isomerization in this case indicates the twisting of the molecule about the ethylene bond away from the trans configuration

Central to this reaction is the question of vibrational energy redistribution or IVR. From direct (single vibronic level) time -resolved measurements, relative fluorescence quantum yields from relaxed and unrelaxed states, and a thorough vibrational analysis from excitation and dispersed fluorescence spectra (previous paper), the following conclusions are reached: (i) The IVR yield is state selective being more extensive from combination modes than from fundamental modes of similar energy. The IVR yield becomes very significant above ≈900−1000 cm⁻¹. The rate is much faster than the reaction at all energies studies. (ii) The barrier to isomerization is observed at 3.3 ± 0.2 kcal/mol (1100−1200 cm−1). The radiative lifetimes, measured from the 0° level fluorescence decays, are 2. 7 ± 0.1 ns (h₁₂) and 2.5 ± 0.1 ns (d₁₂). (iii) The observed isomerization rates in the isolated molecule are approximately an order of magnitude less than the calculated RRKM rates and observed solution phase rates. (iv) The apparent non-RRKM behavior in the isolated behavior is explained by considering the nature of IVR and by adopting a diabatic representation of the reactive surface (i.e., an allowed surface) using a Landau-Zener-Stueckelberg model. (v) Finally, we compare t-stilbene with other related isolated molecules and to solution phase t-stilbene results in order to assess the role of mode mixing and the nature of the reactive surface.

In this paper we consider the dynamics of the photoisomerization of trans-stilbene and related molecules. New measurements of the deuterium isotope effect on reaction rates are presented, and details of RRKM behavior in isolated and solvated trans-stilbene are discussed. From measurements of fluorescence decay rates as a function of the excess vibrational energy in jet-cooled trans-stilbene-d₁₂, an energy threshold to the rates is found at ca. 1200-cm⁻¹ excess energy in the first excited singlet state. The threshold behavior is similar to that which occurs in the photoisomerization of trans-stilbene-h₁₂. The overall magnitudes of the perdeuterio rates are smaller, however, than the perprotio ones. As with trans-stilbene-h₁₂ the measured rates are found to be slower than those calculated by standard RRKM theory. Nevertheless, the observed slowing of the rates upon deuteration is predicted by the theory. The results and their interpretation are discussed in light of the results of other jet studies of trans-stilbene derivatives and of studies of the photoisomerization reaction in solution. The role of intramolecular vibrational energy redistribution and the nonadiabatic influences on the reaction are also discussed.

We report our study of the ultrafast dynamics of isomerization and IVR in a designed series of stilbenes. Striking structural effects on the dynamics are observed and related to the stabilization or destabilization of the planar and twisted states.

Vibrational predissociation of I₂ X_n (X = Ne, Ar) van der Waals clusters are studied in realtime using picosecond pump-probe (LIF) and molecular beam techniques. The state-to-state rates of vibrational predissociation are measured for specific vibrational levels by monitoring the rise of nascent I₂. Here, we report our study of

For I₂ Ne, the values of decrease nonlinearly from 216 ps for to 53 ps for . For , which undergo electronic and vibrational predissociation, the risetime of the nascent I₂ is found to be 70 ps when and 77 ps when . A number of theoretical models for vibrational predissociation (the energy-gap law, the momentum-gap law, quantum and classical calculations) are compared with our experimental results in an attempt to understand the key features of the dynamics and the potential energy surface.

The vibrational predissociation of several van der Waals complexes of t-stilbene has been studied by directly measuring, in real time, the fluorescence intensity from the initial reactant state and from the individual product states formed in the dissociation process after exciting single vibrational levels of the complex. With the aid of a kinetic model involving sequential processes, the individual rates for intramolecular vibrational redistribution and vibrational predissociation in the overall dissociation process are resolved and distinguished in several cases. In the stilbene-He complex, the dissociation is significantly faster from low energy outof-plane modes than it is from a higher energy in-plane mode.

In this communication we wish to report the measurement of photodissociation rates of jet-cooled solute-solvent complexes in various stages of solvation. The observation of fluorescence decays as a function of excess vibrational energy for isoquinoline (IQ), IQ–(methanol)n and IQ–(water)n complexes reveals threshold behavior for the decay rates of 1 : 1 solute-solvent complexes. The thresholds at ~ 3 kcal/mol provide new information on the breakage of excited state hydrogen bonds…

This paper, last in this series, reports on the picosecond dynamics of vibrational predissociation in beam-cooled van der Waals' clusters. Reaction rates have been measured for clusters (1:1) of phenol and cresol (p-methylphenol) with benzene by the picosecond pump-probe photoionization mass-spectrometry technique. Dissociation to form phenol (cresol) and benzene takes place from vibrational levels of the S₁ state of phenol (cresol) prepared by the pump laser. The predissociation rates were measured for a number of different excess energies upto ~2500 cm⁻¹, and the reaction threshold was found to be 1400 cm⁻¹ above the S₁ origin for phenol–benzene and ~1795 cm⁻¹ for cresol–benzene, respectively. For phenol–benzene, the predissociation rates, following excitation of ring-type modes, vs excess energy vary more or less smoothly. Cresol–benzene exhibits biexponential decay, with the fast component becoming more dominant at higher energies. A non-RRKM model involving division of the vibrational phase space is discussed to explain this observation.

The picosecond state-selective dynamics and photochemistry of the molecule A–(CH₂)₃– φ, where A and φ are aromatic chromophores, was studied under collision-free conditions in a supersonic beam. Time-resolved fluorescence measurements of the reactant and the charge transfer (exciplex) product were undertaken as a function of specific vibrational energy above the zero point level of S₁. From these studies along with an analysis of the excitation spectra, dispersed flourescence, and quantum yields, the following results and conclusions were reached: (i) IVR is much faster than reaction at all excess energies studied. (ii) The energy threshold for product formation is E₀≃900 cm⁻¹ (2.6 kcal/mol). The analysis of the rates using an effective temperature model gives a frequency factor of A₀ ≈ 1.2 × 10¹⁰ s⁻¹. Four torsions were identified as critical to the reaction dynamics which were modeled according to a multidimensional reaction coordinate using an RRKM scheme. (iii) The thermodynamics of the isolated charge transfer product indicates strong stabilization ΔH = − 9.2 kcal/mol and extensive charge transfer, the static dipole moment is 13 D, and the charge transfer contribution to the total electronic wave function |c₂|² is 0.86. (iv) A comparison of the present work to solution phase studies of A–(CH₂)₃– φ indicates similar static properties but different dynamics. The calculated thermal (room temperature) reaction time for exciplex formation in the vapor (540 ps) was compared to the shortest observed value in solution (1.4 ns) to assess the role of the solvent on the chain motions which lead to product formation.

Intramolecular relaxation in isolated large molecules is of considerable current interest . The primary questions are: what is the nature of the states which are excited by the light source, and how does the deposited energy get transferred within the molecule? In this regard, the possibility of observing coherence effect the fluorescence decay of large molecules is very important. When large molecules are excited at finite temperatures the existence of many sequence transitions results in spectral broadening and in the masking of these possible coherence effects. Although recent supersonic molecular beam spectroscopy^1-3 has been successful in circumventing the congestion problem, the large density of excited statea may still prevent the observation of such effects…

With picosecond spectroscopy and molecular beams it is shown that nonchaotic multilevel vibrational energy flow is present in large polyatomic molecules. This Letter reports on this novel observation and its probing of the fundamental process of energy redistribution in molecules.

In this series of papers, theoretical and experimental results concerning the dynamical manifestations of intramolecular vibrational-energy redistribution (IVR) in temporally resolved fluorescence are presented. In this paper (I) we present a general treatment of IVR and coherence effects in multilevel vibrational systems. Specifically, the concern is with the derivation of the characteristics of the beatmodulated fluorescence decays which arise from vibrational coupling among N levels within a molecule. Relations connecting quantum beat frequencies, phases, and modulation depths to coupling parameters are presented. Likely sources of deviation of experimental results from theoretical predictions are considered. And, finally, the direct link between IVR and time-resolved fluorescence experiments is discussed with emphasis placed on the physical interpretation of vibrational quantum beats and the nature of IVR as a function of vibrational energy in a molecule.

In this paper, we discuss the dynamics of intramolecular vibrational-energy redistribution (IVR) in two limits: the coherent and incoherent limits. These descriptions are introduced to account for experiments done in time and frequency domains. We present a more general model for IVR, namely the model of overlapping resonances, which describes coherence (quantum beats), congestion and nonexponentional decays.

The development of the picosecond-jet technique is presented. The applications of the technique to the studies of coherence (quantum beats), photodissociation, isomerization and partial solvation of molecules in supersonic-jet beams are detailed with emphasis on the role of intramolecular energy redistribution. Experimental evidence for intramolecular threshold effect for rates as a function of excess molecular energy is given and explained using simple theory for the redistribution of energy among certain modes. Comparison with R.R.K.M. calculation is also made to assess the nature of the statistical behaviour of the energy redistribution.

Measurement of the rotational spectra and constants of molecules can be a powerful probe of excited state geometries and intramolecular dynamics. The conventional approach for obtaining rotationally resolved spectra is to use high-resolution (frequency domain, time-integrated) laser excitation. For medium-sized molecules, recent advances in these high-resolution techniques have made it possible to obtain Doppler-free spectra of benzene¹ (using two-photon excitation), and jet-cooled spectra of tetrazine,² pyrazine³ and others.⁴ These results on medium-sized molecules have provided valuable information on geometries,^1,2 and on the dynamics of intramolecular singlet-triplet coupling^3,5 and the "channel 3" decay in benzene.¹ For large molecules, to obtain rotationally resolved spectra one needs stable, ultranarrow bandwidth lasers together with a scheme to reduce Doppler broadening to less than several megahertz…

A method is presented here for one-photon sub-Doppler measurement of excited-state rotational constants and coherence of large polyatomic molecules. The method, which relies on the concept of purely rotational coherence in molecules, utilizes (polarized) picosecond pump-probe multiphoton ionization (MPI) mass spectrometry. It offers improved temporal resolution (pulse width limited) and is applicable to weakly or nonfluorescing molecules. The present implementation in a molecular beam provides measurements of the rotational constants in the excited (S₁) state of trans-stilbene and gives information on the direction of the relevant transition moments involved. From the coherence decay of the initially prepared state we obtain the dephasing time, which we discuss in relation to experiments involving vibrational / rotational energy redistribution.

In this and the accompanying paper we present a theoretical treatment and experimental study, respectively, of the phenomenon termed purely rotational coherence. This phenomenon has been demonstrated to be useful as a time domain means by which to obtain high resolution spectroscopic information on excited state rotational levels of large molecules [Felker et al., J. Phys. Chem. 90, 724 (1986); Baskin et al., J. Chem. Phys. 84, 4708 (1986)]. Here, the manifestations in temporally resolved, polarization-analyzed fluorescence of coherently prepared rotational levels in samples of isolated symmetric and asymmetric top molecules are considered. These manifestations, for reasonably large molecules at rotational temperatures characteristic of jet-cooled samples, take the form of polarization-dependent transients and recurrences with temporal widths of the order of tens of picoseconds or less. The transients, which arise from the thermal averaging of many single molecule coherences, are examined with respect to their dependences on molecular parameters (rotational constants, transition dipole directions) and experimental parameters (polarization directions and temperature). A physical picture of rotational coherence as a reflection of the time-dependent orientation of molecules in the sample is developed. And, the influence of rotational coherence in experiments designed to probe intramolecular energy flow is discussed. In the accompanying paper, we present experimental results for jet-cooled t-stilbene and anthracene. For t-stilbene we determine rotational constants for vibrational levels in the S₁ electronic state (from the recurrences) and we monitor the trends in rotational coherence vs vibrational coherence as the total energy in the molecule increases.

Picosecond time-resolved fluorescence measurement of purely rotational coherence is developed as a Doppler-free technique for the determination of rotational constants of large molecules in their excited states. We present detailed analyses of purely rotational coherence measurements, supplying new information about the rotational constants and structures of the first excited electronic states of t-stilbene, four t-stilbene van der Waals complexes, and anthracene, including values for all three anthracene S₁ rotational constants. Evidence is considered in the case of stilbene for a transition dipole with a significant component perpendicular to the a inertial axis, and the consequences of such a dipole are explored by way of numerical simulations. Excited-state structures are proposed for stilbene and stilbene–rare-gas complexes and comparisons made with model calculations of the van der Waals potential. Application of the new spectroscopic technique to molecules of large asymmetry is demonstrated by the analysis of fluorene and fluorine–argon measurements, and the results are compared with data from previously published high-resolution frequency domain studies.

Coherent laser spectroscopy of large molecules is a new and challenging area of study. The strength of this type of optical spectroscopy is that it can probe important dynamical molecular processes that are not amenable to conventional methods such as absorption and emission spectroscopy. One such dynamical process is optical dephasing…

A quantum-mechanical theory of vibronic dephasing of impurity molecules in condensed media is presented. An expression for the dephasing time is derived that exhibits explicit dependences upon microscopic properties of both impurity and medium. The expression, which contains the temperature dependence and the cross section for dephasing, is used to predict qualitatively and semiquantitatively some features of vibronic spectral lines in solids. Of particular interest are systems in which the influence of intramolecular properties (of the impurity) upon dephasing is separable from that of intermolecular properties (of the medium). The distinction between vibrational and purely electronic effects on vibronic dephasing is also emphasized.

This paper examines two problems that are central to the question raised in the title. First, we describe formally the origin of homogeneous broadening of ODMR and optical transitions in the presence and absence of spin-orbital couplings between the lowest triplet and other triplet or singlet states. Second, we deduce expressions that relate the spin-to-orbital widths to the rates of orbital and spin scatterings in the singlet and triplet states. In the absence spin-orbital coupling, it is found that the optical width caused by pure dephasing has a much different origin than the ODMR width. In the presence of spin-orbital coupling, on the other hand, the two widths are related and depend on the phonon-induced scattering cross section of the ground electronic state and the other spin sublevel that is involved in the ODMR transition and is not perturbed by spin-orbital interactions. Throughout the paper the coupling of only one triplet sublevel to the singlet was chosen to sufficiently represent the effect of spin-orbital coupling on ODMR and optical widths. Finally, using these theoretical findings we compare the results with some available data on aromatics (ππ*states) and azines and carbonyls (nπ*states) and also conjecture on possible future experiments.

One purpose of this paper is to present new studies on the effect of bandwidth and the coherence properties of the excitation source on the decay and the dephasing of isolated large molecules. A detailed study of the system pentacene in a p-terphenyl matrix is presented utilizing three different excitation sources, a single mode dye laser (60 KHz-6 MHz bandwidth depending on the time scale of the experiment) a multimode dye laser (240 GHz bandwidth), and an incoherent N₂ flash lamp. Optical T₁ (the longitudinal relaxation time) and T₂ (the transverse relaxation time) are measured from the coherent and incoherent transients observed either in the forward direction of the laser or at right angles to the exciting beam. At 1.8 K, the optical transition (¹A_1g → ¹B_2u) of pentacene in p-terphenyl exhibits four sites, the lowest of which at 16887 cm⁻¹ has the following parameters: T₂ = 44±2 ns; T₁ = 24.9±2 nsec, and μ = 0. 7±0.1 D. The transition moment μ, is obtained directly from the optical nutation, which exhibits a Rabi nutation time (ħ/μ∈) of 27.3 ns, and is corrected for the effect of the Lorentz local field inside the terphenyl crystal. The experiments presented here are categorized into two time regimes for theoretical analysis; a transient coherence regime where the observed decay is comparable with (ħ/μ∈) and T₂, and a steady-state coherence regime where transient dephasing is complete and the offdiagonal elements of the density matrix have decayed to their steady-state values in the presence of the field of amplitude ∈. Using the Wilcox-Lamb method, rate equations (with T₂ expressions) describing the population flow in the “complete” level structure of pentacene (ground|0〉, singlet |p〉, and triplet (|1)) are derived from the density matrix equations of motion. When these equations are averaged over the inhomogeneous width of the optical transition and the measured Gaussian transverse profile of our laser we obtain T_1P0 = 24.9±2 ns and T_1pl = 15.7 μs, the time constants by which pentacene spontaneously decays to |0〉 or crosses over into l, as well as the averaged population at time t. In an effort to be complete, attention is placed upon the relationship between theory and the experimental findings. First, expressions for the OFID and nutation in the solid are presented for the pentacene case in order to relate T₁, T₂, and p. to the level structure. Second, at low temperatures (1.8 K), the origin of dephasing is identified as spontaneous emission from p→0 since experimentally T₂≃2T₁, in agreement with other work. At higher temperature, however, a strongly temperature dependent dephasing process with an onset at 3.7 K takes place. Armed with these observations we present a theoretical treatment of these distinct dephasing channels and their temperature dependences. A discussion regarding the influence of “accepting” phonon modes (either optical or acoustic) on optical dephasing is also given. The results indicate that the treatment of Jones et al., can (1) explain the observed temperature dependence of T₂ in pentacene; (2) distinguish dephasing as a result of scattering by acoustic phonons from that due to resonance or quasilocalized phonons with clear connections to gas and liquid state theories, but without invoking more than two optical levels; (3) explain both the level shift and line width changes as a result of “conventional” dephasing or dephasing by exchange mechanisms; and (4) relate the pure dephasing term to an anisotropy in the scattering amplitudes (between the ground and excited states in the system) which contribute largely to the homogeneous width of the transition. Optical site selection of these transitions is also reported and discussed in relation to vibrational relaxation and to both homogeneous and inhomogeneous broadenings. The studies of the homogeneous broadening of the vibronic origin (267 cm⁻¹) indicate that vibrational relaxation is fast (ps) in the excited singlet manifold of pentacene. Finally from more than ten independent experiments including single and multimode excitation, on- and offresonance scattering, Zeeman effect and the transient decay as a function of excess energy in the molecule, a more complete picture of the pentacene level structure {| l 〉} is given. With this in mind, the influence of the laser bandwidth and coherence properties on state preparation and subsequent dephasing and decay is concluded. It is proposed that the slow decay, (~15 μs) observed during narrow-band excitation represents intersystem crossing to nearby triplet manifolds after the transient coherence of the 0↔p subsystem is decayed. In addition, the decay of the primary state prepared in these experiments is not sensitive to the bandwidth or the correlation time of our excitation sources.

The following sections are included:

• Publication of the Author and His group

• General Index

• About the Author