Renormalization of the frozen Gaussian approximation to the quantum propagator

Journal Article · Thu Apr 07 04:00:00 EDT 2011 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3573566· OSTI ID:21560092

Tatchen, Joerg; Pollak, Eli ^[1]; Guohua, Tao; Miller, William H ^[2]

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1. Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovoth (Israel)
2. Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720 (United States)

The frozen Gaussian approximation to the quantum propagator may be a viable method for obtaining 'on the fly' quantum dynamical information on systems with many degrees of freedom. However, it has two severe limitations, it rapidly loses normalization and one needs to know the Gaussian averaged potential, hence it is not a purely local theory in the force field. These limitations are in principle remedied by using the Herman-Kluk (HK) form for the semiclassical propagator. The HK propagator approximately conserves unitarity for relatively long times and depends only locally on the bare potential and its second derivatives. However, the HK propagator involves a much more expensive computation due to the need for evaluating the monodromy matrix elements. In this paper, we (a) derive a new formula for the normalization integral based on a prefactor free HK propagator which is amenable to 'on the fly' computations; (b) show that a frozen Gaussian version of the normalization integral is not readily computable 'on the fly'; (c) provide a new insight into how the HK prefactor leads to approximate unitarity; and (d) how one may construct a prefactor free approximation which combines the advantages of the frozen Gaussian and the HK propagators. The theoretical developments are backed by numerical examples on a Morse oscillator and a quartic double well potential.

• OSTI ID: 21560092
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 13 Vol. 134; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
APPROXIMATIONS
CALCULATION METHODS
DEGREES OF FREEDOM
ELECTRONIC EQUIPMENT
ELEMENTS
EQUIPMENT
INTEGRALS
LEAD
MATRIX ELEMENTS
METALS
MORSE POTENTIAL
OSCILLATORS
POTENTIALS
PROPAGATOR
RENORMALIZATION
SEMICLASSICAL APPROXIMATION
UNITARITY