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
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.
PACS: 31.15.Kb – Path-integral methods / 02.70.Lq – Monte Carlo and statistical methods
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
