Evaluation of the importance of spin-orbit couplings in the nonadiabatic quantum dynamics with quantum fidelity and with its efficient “on-the-fly” ab initio semiclassical approximation

Abstract

We propose to measure the importance of spin-orbit couplings (SOCs) in the nonadiabatic molecular quantum dynamics rigorously with quantum fidelity. To make the criterion practical, quantum fidelity is estimated efficiently with the multiple-surface dephasing representation (MSDR). The MSDR is a semiclassical method that includes nuclear quantum effects through interference of mixed quantumclassical trajectories without the need for the Hessian of potential energy surfaces. Two variants of the MSDR are studied, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics. The fidelity criterion and MSDR are first tested on one-dimensional model systems amenable to numerically exact quantum dynamics. Then, the MSDR is combined with "on-the-fly" computed electronic structure to measure the importance of SOCs and nonadiabatic couplings in the photoisomerization dynamics of CH 2 NH + 2 considering 20 electronic states and in the collision of F + H 2 considering six electronic states.

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

“…[More generally, the NOP approximation only implies that all interactions with E pr follow all interactions with E pu ; altogether there are four such terms since the last of the four interactions-the one in Eq. (A21)-is always with E pr ; however, only the above-mentioned term ( E pu ) 2 ( E pr ) 2 survives since the terms E pu ( E pr ) 3 and ( E pu ) 3 E pr with odd interactions with the pump do not propagate in the direction of the probe beam, 6 and ( E pr ) 4 vanishes in the differential spectrum since two identical terms of this type cancel each other in the differential polarization δ P (3) = P pu+pr,(3)…”

“…Using dipole moment projections (14) and (15), denoting similarly δP (3) (t) := δ P (3) (t) · pr , within the NOP approximation Eqs. (A21)-(A23) for H (3) simplify to…”

“…Assuming the widths of the pump and probe pulses to be much smaller than the delay τ , one may make the NOP approximation, which mathematically amounts to computing the differential density δρ (3) I (t) from Eq. (A23) forρ j, (3) I (t) by replacing E j with E pu at times t 1 and t 2 and with E pr at time t 3 , as well as by replacing the upper limit t 3 with ∞ in the integral over t 2 .…”

“…Using the TDPT, the leading term of the differential polarization δ P is δ P (3) since the first-order terms P pu+pr,(1)…”

“…In this paper, we develop such a method based on the multiplesurface dephasing representation (MSDR). [2][3][4] Originally used to estimate nonadiabaticity of quantum molecular dynamics, the MSDR is here generalized into a method capable of computing various linear and pump-probe electronic spectra, including those involving nonadiabatic effects. As we shall show, the proposed semiclassical method retains the efficiency and scaling properties of classical dynamics and, at the same time, captures some quantum effects on nuclear motion via the interference of (almost) classical trajectories.…”