Femtosecond photoelectron spectroscopy of the I2− anion: A semiclassical molecular dynamics simulation method

Abstract

In this paper we describe a new semiclassical method for simulating femtosecond pump-probe photoelectron spectroscopy, and its implementation to study the excited state photodissociation dynamics of the I 2 Ϫ anion. Our algorithm involves a forward-backward ͑FB͒ semiclassical ͑SC͒ initial value representation ͑IVR͒ method for calculating the time dependent photodetachment spectrum P(⑀,⌬t) as a function of the kinetic energy ⑀ of the photodetached electron and the delay time ⌬t between the pump and probe pulses. We describe the radiation-chromophore interaction perturbatively to first order in both pulse fields, assuming the Condon approximation for the electronic transition dipole moments. Our computed spectra are in excellent agreement with full quantum mechanical simulations.

Quasiclassical dynamics methods from semiclassical approximations

“…Since many-body quantum calculations remain out of reach, quasiclassical methods offer the most practical choice for large-scale simulation. Quasiclassical expression with a simplified (usually Gaussian) approximation for the Wigner phase space density have been in use for a long time, and several more rigorous applications of forwardbackward semiclassical approximations have been reported in the last three years [35,45,47,48,51,[59][60][61]. Combined with an accurate description of the initial density through a Gaussian approximation or an imaginary time path integral representation, quasiclassical methods can provide semiquantitative results.…”

“…While none of the currently available methods satisfy both of these demands in diverse physical situations, much progress has been made through the development of initial value representations [3,6,[13][14][15][16][17][18][19], filtering techniques [20][21][22][23][24][25], semiclassical-classical [26] or linearized [27,28] approximations, and forwardbackward semiclassical methods [29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Indeed, a number of semiclassical calculations on small molecular systems have already been reported [22,23,[43][44][45][46][47][48][49][50][51], and there is growing interest for the extension of the emerging semiclassical methodology to condensed phase simulations.…”

Femtosecond Time‐Resolved Photoelectron Spectroscopy

“…The excited A′ state was empirically characterized to have a 17 ( 10 meV well at 6.2 ( 0.6 Å by fitting to a simulation performed with an efficient wave packet propagation scheme. 182 While TRPES experiments nominally provide information on the dynamics of the excited state accessed by the pump pulse, variations on this experiment can probe the ground state, generally by producing coherent vibrational wave packet motion on the ground state that can be followed by TRPES, as depicted schematically in Figure 15b. In the first example of this type, the pump pulse used to excite the A′ 2 Π g,1/2 r X 2 Σ u + transition in I 2 -was also shown to create a coherent superposition of the v ) 0 and v ) 1 vibrational levels on the ground X 2 Σ u + state, thereby creating a wave packet whose motion could be detected by oscillations in the TRPE spectrum at selected electron kinetic energies.…”

Iterative evaluation of the path integral for a system coupled to an anharmonic bath

“…The most rigorous of these approaches, semiclassical evolution with the Van Vleck propagator, 1,2 is often highly accurate, 3-8 yet extremely demanding numerically because it requires multidimensional integration of oscillatory functions as well as evaluation of a prefactor that scales nonlinearly with the number of particles. Current efforts to make it practical exploit filtering techniques, 9-11 the self-cancellation achieved via combined forward-backward propagation, [12][13][14][15][16] or formulations which avoid calculation of the prefactor. 11,[17][18][19] While these approaches appear promising, they are bound to fail at long propagation times or if tunneling effects are prominent.…”