Asymptotic Convergence Rates of Fourier Path Integral Methods

Authors

Maria Eleftheriou
J. D. Doll
E. Curotto, University of Rhode Island
David L. Freeman, University of Rhode IslandFollow

Document Type

Article

Date of Original Version

4-8-1999

Department

Chemistry

Abstract

The asymptotic rates of convergence of thermodynamic properties with respect to the number of Fourier coefficients, k_max, included in Fourier path integral calculations are derived. The convergence rates are developed both with and without partial averaging for operators diagonal in coordinate representation and for the energy. Properties in the primitive Fourier method are shown to converge asymptotically as 1/k_max whereas the asymptotic convergence rate is shown to be 1/k_max 2 when partial averaging is included. Properties are shown to converge at the same rate whether full partial averaging or gradient partial averaging is used. The importance of using the proper operator to optimize convergence rates in partial averaging calculations is emphasized.

Citation/Publisher Attribution

Eleftheriou, M., Doll, J. D., Curotto, E., & David L. Freeman, D. L. (1999). Asymptotic Convergence Rates of Fourier Path Integral Methods. Journal of Chemical Physics, 110(4), 6657-6672. doi: 10.1063/1.478573

Available at: http://dx.doi.org/10.1063/1.478573

Publisher Statement

© 1999 American Institute of Physics.