Approximate calculation of femtosecond pump–probe spectra monitoring nonadiabatic excited-state dynamics

Abstract

The nonradiative decay of the allyl radical excited B 2 A 1 state studied by picosecond time-resolved photoelectron spectroscopy An approximate theory of femtosecond spectroscopy of nonadiabatically coupled electronic states is developed. Neglecting the commutators of vibrational Hamiltonians pertaining to different diabatic electronic states, the formulation represents a generalization of the semiclassical Franck-Condon approximation to the case of nonadiabatic dynamics. Explicit expressions for various time-and frequency-resolved spectra are derived which allow for a simple interpretation of femtosecond spectroscopy of vibronically coupled molecular systems. Employing multidimensional model problems describing ͑i͒ the nonadiabatic cis-trans isomerization of an electronic two-state system, and ͑ii͒ the S 2 →S 1 internal conversion of pyrazine, exact reference data are compared to approximate calculations of transient absorbance and emission as well as time-resolved photoelectron spectra. In all cases considered, the approximation is shown to be appropriate for probe-pulse durations that are shorter than the period of the fastest relevant vibrational mode of the molecular system. Reducing the numerical costs of pump-probe simulations to the costs of a standard time-dependent wave-packet propagation, the approximate theory leads to substantial computational savings.where the time-dependent excited-state wave function ͉⌿ 0 (t d )͘ depends on its preparation by the pump pulse and the stimulated-emission projection operator P incorporates the action of the probe pulse.Assuming short probe pulses, we may evaluate the pump-probe signal within the semiclassical Franck-Condon a͒ Electronic

Calculating time-resolved differential absorbance spectra for ultrafast pump-probe experiments with surface hopping trajectories

“…With the advent of femtosecond laser pulses, nonlinear spectroscopy has become a powerful experimental tool for probing chemical reactions, photochemistry, energy transfer, and nonadiabatic dynamics in real time. [1][2][3][4][5][6][7][8][9][10][11][12][13] The interpretation and theoretical modeling of these experiments often begins with the application of perturbation theory to the fieldmatter interactions, leading to an expansion of the optical response of the molecular system in orders of the applied field, 7,8,[14][15][16][17][18][19][20][21][22][23][24][25] although nonperturbative approaches have been reported. 16,26,27 In particular, outside of anisotropic systems, nonlinear spectroscopy is dominated by third-order processes in which the system experiences three interactions with the applied electromagnetic fields.…”

“…We are not the first to develop semiclassical descriptions of pump-probe spectroscopy that include the effects of nonadiabatic wave packet dynamics. 19,27,[29][30][31][32]62 Indeed, surface hopping approaches have previously been used to model the inhomogeneous component of pumpprobe signals associated with time-resolved photoelectron spectroscopy and time-resolved absorption. 29,31,32,63 FSSH has also recently been used to introduce electronic relaxation during the evolution of electronic populations as part of a larger calculation of two-dimensional electronic spectra.…”

Ultrafast photodynamics of furan

“…[1][2][3][4][5] TRPES is a pump-probe technique where an ultrashort pump pulse creates a wavepacket in an electronically excited state of the neutral system whose time evolution is probed by a time delayed pulse causing photoionization. Parallel to the development of experimental techniques, theoretical approaches for the simulation of TRPES using the full quantum mechanical description of nuclear motion [17][18][19][20][21][22][23][24][25][26][27] as well as the semiclassical description based on the Wigner distribution approach 8,15,28,29 have been devised. The theoretical interpretation of TRPES spectra and exploration of underlying a) Present address: Institute for Molecular Science, Okazaki 444-8585, Japan.…”

Collision-induced bound state motion in I2. A classical molecular dynamics study

“…The latter is obtained as the Fourier transform of the pump-pulse temporal shape function with respect to the difference U B (R)ϪU X (R) between the potentials of the two electronic states which are involved in the transition. [26][27][28][29][30] We assumed a Gaussian pulse-shape function exp(Ϫt 2 /2 2 ), where the parameter was chosen such that the width ͑full width at half maximum͒ of the electric field intensity is 70 fs. The fluorescence signal from the E state is assumed to be proportional to the population of this state created in the probe transition.…”