TY - JOUR

T1 - Correct short time propagator for Feynman path integration by power series expansion in Δt

AU - Makri, Nancy

AU - Miller, William H.

N1 - Funding Information:
This work has been supportedb y the Director, Office of Energy Research,O ffice of Basic Energy Sciences, Chemical SciencesD ivision of the US Departmento f Energy under Contract No. DE-AC03-76SF00098. Support of the Berkeley Theoretical Chemistry Computational Facility by National Science Foundation Grant CHE8C16345 is gratefully acknowledged.

PY - 1988/10/7

Y1 - 1988/10/7

N2 - The most commonly used short time propagator in a discretized Feynman path integral (and also several more sophisticated "improved" ones) is not correct through first order in the time increment Δt. The correct result for the phase (i.e. the action) of the short time propagator is developed in this paper as a power series in Δt, explicit expressions being given for the terms of order Δt-1, Δt, and Δt3. Test applications to the standard harmonic oscillator and also to a double well potential (typical for intramolecular H-atom transfer) show the first-order propagator (i.e. the correct result through order Δt) to be a significant improvement over previous ones; inclusion of the third-order term gives considerable additional improvement (i.e. faster convergence).

AB - The most commonly used short time propagator in a discretized Feynman path integral (and also several more sophisticated "improved" ones) is not correct through first order in the time increment Δt. The correct result for the phase (i.e. the action) of the short time propagator is developed in this paper as a power series in Δt, explicit expressions being given for the terms of order Δt-1, Δt, and Δt3. Test applications to the standard harmonic oscillator and also to a double well potential (typical for intramolecular H-atom transfer) show the first-order propagator (i.e. the correct result through order Δt) to be a significant improvement over previous ones; inclusion of the third-order term gives considerable additional improvement (i.e. faster convergence).

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U2 - 10.1016/0009-2614(88)80058-7

DO - 10.1016/0009-2614(88)80058-7

M3 - Article

AN - SCOPUS:0002328137

SN - 0009-2614

VL - 151

SP - 1

EP - 8

JO - Chemical Physics Letters

JF - Chemical Physics Letters

IS - 1-2

ER -