Semiclassical theory of electronically nonadiabatic chemical dynamics: Incorporation of the Zhu–Nakamura theory into the frozen Gaussian propagation method

Abstract

The title theory is developed by combining the Herman-Kluk semiclassical theory for adiabatic propagation on single potential-energy surface and the semiclassical Zhu-Nakamura theory for nonadiabatic transition. The formulation with use of natural mathematical principles leads to a quite simple expression for the propagator based on classical trajectories and simple formulas are derived for overall adiabatic and nonadiabatic processes. The theory is applied to electronically nonadiabatic photodissociation processes: a one-dimensional problem of H2+ in a cw (continuous wave) laser field and a two-dimensional model problem of H2O in a cw laser field. The theory is found to work well for the propagation duration of several molecular vibrational periods and wide energy range. Although the formulation is made for the case of laser induced nonadiabatic processes, it is straightforwardly applicable to ordinary electronically nonadiabatic chemical dynamics.

Nonadiabatic Chemical Dynamics: Comprehension and Control of Dynamics, and Manifestation of Molecular Functions

“…The outline of the formulation is described below so that the reader can grasp the essential ideas of the method. The details of the formulation can be found in the original papers [19,38]. The total wave function at time t in the HermanKluk approach is expressed as:…”

“…These methods have been developed for the adiabatic processes, namely, for the dynamics on a single adiabatic potential energy surface. Incorporation of the ZN theoy into them can extend their applicability to electronically nonadiabatic dynamics beyond the perturbative treatment [17,19]. A much simpler simulation method is the trajectory surface hopping (TSH) [20,21].…”

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

“…29 Finally, while it does capture some quantum effects on nuclear motion, the MSDR does not require the Hessian of the potential energy, which is typically the most expensive part of semiclassical calculations. [30][31][32][33][34][35][36] Nevertheless, the simplicity and efficiency come at the cost of accuracy. As demonstrated in fidelity calculations, in certain cases the MSDR breaks down, even though at least the initial decay of the correlation function is usually captured correctly.…”

Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation

“…8 Less accurate but also less expensive are various semiclassical approaches, which can also describe some quantum effects, especially on the nuclear motion. These include multiple-spawning methods, 9,10 methods based on the Herman-Kluk propagator, [11][12][13][14] or the surface hopping and jumping method of Heller et al 15 The most widely used are methods in which the nuclei are treated classically and the quantum effects enter only through interaction with electrons, which are described quantum mechanically. Among these belong methods based directly on the mixed quantum-classical Liouville equation, [16][17][18][19][20][21][22][23][24] the mean field Ehrenfest dynamics, various surface hopping methods, [25][26][27] or methods in which the classical limit is obtained by linearizing the path integral representation of the quantum propagator.…”