Semiclassical theory of electronically nonadiabatic dynamics: Results of a linearized approximation to the initial value representation

Abstract

Articles you may be interested inA Cartesian classical second-quantized many-electron Hamiltonian, for use with the semiclassical initial value representation J. Chem. Phys. 137, 154107 (2012); 10.1063/1.4757935Semiclassical description of electronically nonadiabatic dynamics via the initial value representation Extremal path approach to rate constant calculations by the linearized semiclassical initial value representation A linearized approximation to the semiclassical initial value representation ͑SC-IVR͒, referred to herein as the LSC-IVR, was used by us in a recent paper ͓J. Chem. Phys. 108, 9726 ͑1998͔͒ to calculate reactive flux correlation functions for a model of a chemical reaction on a single potential energy surface. This paper shows how the LSC-IVR-which is much easier to apply than the full SC-IVR because it linearizes the phase difference between interfering classical trajectories-can be applied to electronically nonadiabatic processes, i.e., those involving transitions between different potential-energy surfaces. Applications to several model problems are presented to show its usefulness: These are the nonadiabatic scattering problems used by Tully to test surface-hopping models, and also the spin-boson model of coupled electronic states in a condensed phase environment. Though not as accurate as the full SC-IVR, the LSC-IVR does a reasonably good job for all these applications, even describing correctly Stuckelberg oscillations ͑interference between nonadiabatic transitions͒ and the transition between coherent and incoherent behavior in the spinboson example.

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation

“…(8) gives a time-stepping prescription for evolving the mean nuclear DOF with the force in Eq. (9). Finally quantum expectation values are computed using Eq.…”

“…Ehrenfest dynamics, or related mean-field approaches, such as the time dependent self consistent field (TDSCF), 4 or linearized semi-classical initial value representation (LSC-IVR) 9, 10 schemes, cannot in general, for example, provide an accurate description of bond breaking process where, once the wave packet emerges from the coupling region where the electronic states mix, the force that acts on the nuclear DOF should be that arising from a single surface potential, rather than the mean force averaged over multiple potentials. Surface hopping methods that branch trajectories between the different competing potential surfaces and integrate the electronic wave function coherently along the classical-like trajectories of the nuclear DOF, partially overcome this problem but require the use of ad hoc schemes to deal with the decoherence that arises as nuclear wave packets, born on the different surfaces move in different directions and their overlap modulates the off-diagonal coherence density matrix elements.…”

Mapping quantum-classical Liouville equation: Projectors and trajectories

“…The mapping basis has been used in a number of different quantum-classical formulations, often based on semi-classical path integral expressions for the dynamics [15][16][17][18][19][20][21][22][23][24][25][26][27][28] . The representation of the quantum-classical Liouville equation in the mapping basis leads to an equation of motion whose Liouvillian consists of a Poisson bracket term in the full quantum subsystem-classical bath phase space, and a more complex term involving second derivatives of quantum phase space variables and first derivatives with respect to bath momenta 12 .…”

Test of the consistency of various linearized semiclassical initial value time correlation functions in application to inelastic neutron scattering from liquid para-hydrogen

“…The simplest (and most approximate) version of the SC-IVR is its 'linearized' approximation (LSC-IVR) 9,26,[28][29][30][31][32][33][34][35] , which leads to the classical Wigner model [36][37][38][39] for time correlation functions; see Section IIB for a summary of the LSC-IVR. The classical Wigner model is an old idea, but it is important to realize that it is contained within the SC-IVR approach, as a well-defined approximation to it 28,29 .…”

“…There are other ways to derive the classical Wigner model (or one may simply postulate it) 9,35,40,41 , and we also note that the 'forward-backward semiclassical dynamics' (FBSD) approximation of Makri et al 32,[42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] is very similar to it. The LSC-IVR/classical Wigner model cannot describe true quantum coherence effects in time correlation functions-more accurate SC-IVR approaches, such as the Fourier transform forward-backward IVR (FB-IVR) approach 22,57 (or the still more accurate generalized FB-IVR 58 ) of Miller et al, are needed for this-but it does describe some aspects of the quantum dynamics very well 26,[30][31][32]34,[59][60][61][62] . E.g., the LSC-IVR has been shown to describe reactive flux auto-correlation functions (which determine chemical reaction rates) quite well, including strong tunneling regimes 31 , and velocity auto-correlation functions 26,32,60 and force auto-correlation functions 26,34,61,62 in systems with enough degrees of freedom for quantum re-phasing to be unimportant.…”