Semiclassical nonadiabatic dynamics

One can also ask about the relationship of the FMS method, as opposed to AIMS, with other wavepacket and semiclassical nonadiabatic dynamics methods. We first compare FMS to previous methods in cases where there is no spawning, and then proceed to compare with previous methods for nonadiabatic dynamics. We stress that we have always allowed for spawning in our applications of the method, and indeed the whole point of the FMS method is to address problems where localized nuclear quantum mechanical effects are important. Nevertheless, it is useful to place the method in context by asking how it relates to previous methods in the absence of its adaptive basis set character. There have been many attempts to use Gaussian basis functions in wavepacket dynamics, and we cannot mention all of these. Instead, we limit ourselves to those methods that we feel are most closely related to FMS, with apologies to those that are not included. A nice review that covers some of the... 

Sun X, Wang H B and Miller W H 1998 Semiclassical theory of electronically nonadiabatic dynamics Results of a linearized approximation to the initial value representation J. Chem. Phys. 109 7064... 

Considering the semiclassical description of nonadiabatic dynamics, only the mapping approach [99, 100] and the equivalent formulation that is obtained by requantizing the classical electron analog model of Meyer and Miller [112] appear to be amenable to a numerical treatment via an initial-value representation [114, 116, 117, 121, 122]. Other semiclassical formulations such as Pechukas path-integral formulation [45] and the various connection... 

All approaches for the description of nonadiabatic dynamics discussed so far have used the simple quasi-classical approximation (16) to describe the dynamics of the nuclear degrees of freedom. As a consequence, these methods are in general not able to account for processes or observables for which quantum effects of the nuclear degrees of freedom are important. Such processes include nuclear tunneling, interference effects in wave-packet dynamics, and the conservation of zero-point energy. In contrast to quasi-classical approximations, semiclassical methods take into account the phase exp iSi/h) of a classical trajectory and are therefore capable—at least in principle—of describing quantum effects. 

Following a brief introduction of the basic concepts of semiclassical dynamics, in particular of the semiclassical propagator and its initial value representation, we discuss in this section the application of the semiclassical mapping approach to nonadiabatic dynamics. Based on numerical results for the... 

In contrast to the quasi-classical approaches discussed in the previous chapters of this review, Eq. (114) represents a description of nonadiabatic dynamics which is semiclassically exact in the sense that it requires only the basic semiclassical Van Vleck-Gutzwiller approximation [3] to the quantum propagator. Therefore, it allows the description of electronic and nuclear quantum effects. 

S. Bonella and D. F. Coker. Semiclassical implementation of the mapping Hamiltonian approach for nonadiabatic dynamics using focused initial distribution sampling. J. Chem. Phys., 118(10) 4370-4385, Mar 2003. 

C. C. Martens and J.-Y. Fang (1996) Semiclassical-limit molecular dynamics on multiple electronic surfaces. J. Chem. Phys. 106, pp. 4918-4930 A. Donoso, and C. C. Martens (1998) Simulation of Coherent Nonadiabatic Dynamics Using Classical Trajectories. J. Phys. Chem. A 102, pp. 4291-4300... 

As explained in the Introduction, one needs to distinguish the following kinds of surface hopping (SH) methods (i) Semiclassical theories based on a connection ansatz of the WKB wave function, " (ii) stochastic implementations of a given deterministic multistate differential equation, e.g. the quantum-classical Liouville equation, and (iii) quasiclassical models such as the well-known SH schemes of Tully and others. " In this chapter, we focus on the latter type of SH method, which has turned out to be the most popular approach to describe nonadiabatic dynamics at conical intersections. 

A semiclassical description is well established when both the Hamilton operator of the system and the quantity to be calculated have a well-defined classical analog. For example, there exist several semiclassical methods for calculating the vibrational autocorrelation function on a single excited electronic surface, the Fourier transform of which yields the Franck-Condon spectrum. ° In particular, semiclassical methods based on the initial-value representation of the semiclassical propagator,which circumvent the cumbersome root-search problem in boundary-value based semiclassical methods, have been successfully applied to a variety of systems (see, for example, the reviews Refs. 85, 86 and references therein). These methods cannot directly be applied to nonadiabatic dynamics, though, because the Hamilton operator for the vibronic coupling problem [Eq. (1)] involves discrete degrees of freedom (discrete electronic states) which do not possess an obvious classical counterpart. 

This section follows the above basic theory and method of path-branching representation of nonadiabatic dynamics with numerical examples. We also show the performance of the semiclassical Ehrenfest theory to compare with. What we present below is illustrative numerical realization rather than optimized practice for actual applications. 

Nonadiabatic So S2/Sj Absorption Spectrum of Pyrazine Mostofthe semiclassical theoretical models have been developed in the hmit of a dynamics taking place on a single electronic PES. In order to apply semiclassical methods to nonadiabatic dynamics, further generalization is needed and it is necessary to write down a Hamiltonian with a well-defined classical limit. In this context, the problem of the description of discrete quantum degrees of freedom (electronic states) can be tackled in two steps the first is a mapping onto continuous variables, and the second is a semiclassical treatment of the resulting problem [94,95]. These methods have been recently reviewed by Stock and Thoss [96]. 

Stock G and Thoss M 1997 Semiclassical description of nonadiabatic quantum dynamics Phys. Rev. Lett. 78 578... 

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