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The semiclassical (SC) initial value representation (IVR) for the time evolution operator e−iĤt/ℏ involves a phase space integral over the initial conditions of classical trajectories. It is shown in this paper how an IVR for the two time evolution operators in a typical quantum mechanical time correlation function, CAB(t)≡tr[ÂeiĤt/ℏBe−iĤt/ℏ], can be combined into one such phase space integral; i.e., time evolution from 0 to t and from t to 0 is combined into one overall SC-IVR propagation. This not only reduces the dimensionality of the phase space average, but the forward–backward (FB) nature of the net trajectory has a partial self-cancellation that reduces the oscillatory behavior of the integrand. Several applications of this FB-IVR to reactive flux correlation functions are presented to illustrate its possibilities.

A linearized approximation to the semiclassical initial value representation (SC-IVR), referred to herein as the LSC-IVR, was used by us in a recent paper [J. Chem. Phys. 108, 9726 (1998)] 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 Stuc...

An earlier paper of ours [J. Chem. Phys. 108, 9726 (1998)] used an approximate (linearized) version of the semiclassical initial value representation (SC-IVR) to calculate reactive flux correlation functions for a model of unimolecular isomerization, namely a 1-d double well potential coupled to an infinite set of harmonic oscillators, obtaining excellent agreement with accurate quantum results for this system. Here we analyze this linearized approximation (LA) further, however, and show that it is not capable of describing quantum interference/coherence effects in the longer time recrossing behavior of the isomerization dynamics. (The recrossing effects seen in our earlier work were due to classical mechanics.) To accentuate quantum effects in the recrossing dynamics, the present article considers the double well potential without the harmonic bath, using both the LA and the full SC-IVR. The results of the calculations show that the flux correlation functions given by the LA agrees well with the exact qu...

Two different semiclassical approaches are presented for extending flux correlation function methodology for computing thermal reaction rate constants, which has been extremely successful for the “direct” calculation of rate constants in small molecule (∼3–4 atoms) reactions, to complex molecular systems, i.e., those with many degrees of freedom. First is the popular mixed quantum-classical approach that has been widely used by many persons, and second is an approximate version of the semiclassical initial value representation that has recently undergone a rebirth of interest as a way for including quantum effects in molecular dynamics simulations. Both of these are applied to the widely studied system-bath model, a one-dimensional double well potential linearly coupled to an infinite bath of harmonic oscillators. The former approximation is found to be rather poor while the latter is quite good.

The semiclassical initial value representation (SC-IVR) is emerging as a practical way of generalizing classical trajectory simulation methods to include (approximately) the effects of quantum mechanics (i.e., interference and tunneling). This paper describes the application of the SC-IVR approach to determine the low lying vibrational states of the HCl dimer on a realistic potential energy surface. Overall agreement of the semiclassical energy levels with accurate quantum values is very good, including a good description of the tunneling splitting in the ground state. Issues regarding the applications of the SC-IVR methodology to the angular variables related to rotational degrees of freedom are explicitly discussed.

The semiclassical initial value representation (SC-IVR), which has recently seen a great deal of interest for treating nuclear dynamics on a single potential energy surface, is generalized to be able to describe electronically nonadiabatic (i.e., multisurface) processes. The essential idea is a quantization of the classical electron-nuclear Hamiltonian of Meyer and Miller [J. Chem. Phys. 70, 3214 (1979)] within the SC-IVR methodology. Application of the approach to a series of test problems suggested by Tully shows it to provide a good description of electronically nonadiabatic dynamics for a variety of situations.

Starting with the semiclassical initial value representation (IVR) for the description of a composite molecular system consisting of a “system’’ and a “bath,’’ we show a systematic procedure whereby one can retain the semiclassical IVR description of the “system’’—thus including quantum interference and tunneling effects for these degrees of freedom—while neglecting these effects in the “bath’’ degrees of freedom, thus reducing them to a classical description. The zeroth order version of this mixed semiclassical–classical model is seen to be the semiclassical equivalent of the Ehrenfest model (closely related to the TDSCF approximation), but higher order versions are also developed that go beyond this level of approximation. Two levels of this theory are explicitly worked out. Numerical tests on simple but illustrative problems are used to discuss the merit of these approaches.