Eur. Phys. J. D 10, 353-362 (2000)
https://doi.org/10.1007/s100530050559

Molecular structure calculations via path integral simulations: Estimating finite-discretization errors

¹ Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69029 Heidelberg, Germany
² Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany

Received: 13 September 1999
Revised: 18 November 1999
Published online: 15 June 2000

Abstract

Path integral simulations are now recognized as a useful tool to determine theoretically the structure of complex molecules at finite temperatures including quantum effects. In addition to statistical errors due to incomplete sampling, also systematic errors are inherent in this procedure because of the finite discretization of the path integral. Here, useful "back of the envelope"estimates to assess the systematic errors of bond-length distribution functions are introduced. These analytical estimates are tested for two small molecules, HD⁺ and H, where quasi-exact benchmark data are available. The accuracy of the formulae is shown to be sufficient in order to allow for a reliable assessment of the quality of the discretization in a given simulation. The estimates will also be applicable in condensed phase path integral simulations, and the basic idea can be generalized to other observables than those presented.