How to calculate linear absorption spectra with lifetime broadening using fewest switches surface hopping trajectories: A simple generalization of ground-state Kubo theory

Abstract

In this paper, we develop a surface hopping approach for calculating linear absorption spectra using ensembles of classical trajectories propagated on both the ground and excited potential energy surfaces. We demonstrate that our method allows the dipole-dipole correlation function to be determined exactly for the model problem of two shifted, uncoupled harmonic potentials with the same harmonic frequency. For systems where nonadiabatic dynamics and electronic relaxation are present, preliminary results show that our method produces spectra in better agreement with the results of exact quantum dynamics calculations than spectra obtained using the standard ground-state Kubo formalism. As such, our proposed surface hopping approach should find immediate use for modeling condensed phase spectra, especially for expensive calculations using ab initio potential energy surfaces.

Spectral lineshapes in nonlinear electronic spectroscopy

“…S (3) (t 1 ,t 2 ,t 3 ) depends parametrically on the delay times t 1 , t 2 and t 3 between the field-matter interactions. The time-dependent signal is Fourier-transformed along t 1 and t 3 (i.e.…”

“…the spectral diffusion), and the fluctuations of the respective oscillator strengths during the underlying ultrafast dynamics. [1][2][3][4] Another essential requirement for modeling nonlinear spectra of photoexcited molecules is the incorporation of higher lying ES. This is desirable for two reasons: first, absorptions to these states (excited state absorptions, ESA) dominate the spectra due to the high spectral density in the visible (Vis) and ultraviolet (UV) region; [5][6][7] second, ESA, together with the stimulated emission (SE) represent characteristic signatures of each photophysical or photochemical decay channel, and hence, their proper description will allow us to recognize electronic structural changes during the dynamics, as well as to disentangle dynamics occurring via competing channels.…”

“…Eqn (11) which we do not explicitely formulate here) takes into account the electronic fluctuations due to nuclear motion in the ES (i.e. spectral diffusion) and can be directly employed in the simulation of 2D electronic signals by a 2D Fourier-transformation of the third order response function R (3) (t 1 ,t 2 ,t 3 ) subject to field envelopes with respect to time delays t 1 and t 3 (eqn (1)), followed by averaging over an ensemble of trajectories. On the single trajectory level the Fourier-transformation can introduce dispersive contributions in the spectra if the electronic gap fluctuations induce a shift of the mean transition frequency within the dephasing timescale.…”

“…2), is not unique 2,20 as the bra and the ket side of the density matrix are subject to different electronic potentials. During coherence between the GS g and the singly excited manifold e, as well as between the singly ES manifold e and the higher ES manifold f we choose to propagate the nuclear degrees of freedom as if interacting with the singly excited electronic state e. Subotnik and co-workers proposed recently to use a swarm of trajectories propagated independently in the GS and in the ES, 3 thereby introducing two different reference Hamiltonians for either the bra or ket side and evaluating the coherence as the geometric average. The above approximation allows us to derive a simplified expression for each Feynman pathway (eqn (5) …”

Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics

“…26 Kocia and Heller have extended the method in order to compute the off-diagonal elements of the evolution operator, allowing its use as a general semiclassical propagator. 27 During a revision of our paper, Petit and Subotnik 28 have published a paper in which they compute linear absorption spectra of onedimensional model potentials using a geometric average of correlation functions computed with phase averaging using trajectories propagated on either the ground or excited electronic surface, sometimes obtaining results that are even more accurate than those based on trajectories propagated on the average surface.…”