Semiclassical Initial Value Treatments of Atoms and Molecules

Abstract

This review describes some developments in the theory and application of the semiclassical initial representation for the treatment of the dynamical and static properties of atoms and molecules. The theoretical basis of initial value treatments for the propagator is discussed. A variety of useful alternative initial value expressions for the propagator and other quantities are presented as generalizations of the well-known Herman-Kluk approximation. Special emphasis is given to treatments that involve integration over only half the phase space variables. The recent development of semiclassical initial value expressions that are exact for specific, desired systems is reviewed and some of the implications are described.

Tunneling in two-dimensional systems using a higher-order Herman–Kluk approximation

“…3,4 However, while this approximation successfully describes quantum phenomena associated with interference and quantization, it does not treat all quantum effects in a consistently accurate way. In fact, one major limitation of the HK approximation is that it does not yield a reliable description of tunneling across barriers.…”

Including quantum effects in the dynamics of complex (i.e., large) molecular systems

“…The next section describes some current work in this regard. I, and others, have published more comprehensive reviews of the SC-IVR and its applications, [48][49][50] so the interested reader should consult these; the present paper is not such a review.…”

Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation

“…Since classical molecular dynamics (MD) simulation methods are the only generally applicable approach for describing the dynamics of large molecular systems, we have been pursuing the use of various initial value representations (IVRs) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] of semiclassical (SC) theory 18,19 to add quantum effects to classical MD simulations of time correlation functions. The SC-IVR provides a way for generating the quantum time evolution operator (propagator) by computing an ensemble of classical trajectories, much as is done in standard classical MD simulations.…”

“…The SC-IVR provides a way for generating the quantum time evolution operator (propagator) by computing an ensemble of classical trajectories, much as is done in standard classical MD simulations. As is well known from SC developments in the early 1970's 1,[18][19][20][21] , such approaches actually contain all quantum effects at least qualitatively, and in molecular systems the description is usually quite quantitative (see reviews [2][3][4][5]14,22,23 and some recent applications [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] ).…”