# Extrapolation and perturbation schemes for accelerating the convergence of quantum mechanical free energy calculations via the Fourier path-integral Monte Carlo method

## Abstract

We present two simple but effective techniques designed to improve the rate of convergence of the Fourier path-integral Monte Carlo method for quantum partition functions with respect to the Fourier space expansion length, K, especially at low temperatures. The first method treats the high Fourier components as a perturbation, and the second method involves an extrapolation of the partition function (or perturbative correction to the partition function) with respect to the parameter K. We perform a sequence of calculations at several values of K such that the statistical errors for the set of results are correlated, and this permits extremely accurate extrapolations. We demonstrate the high accuracy and efficiency of these new approaches by computing partition functions for H{sub 2}O from 296 to 4000 K and comparing to the accurate results of Partridge and Schwenke. (c) 2000 American Institute of Physics.

- Authors:

- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352 (United States)
- Department of Chemistry, Chemical Physics Program and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)

- Publication Date:

- OSTI Identifier:
- 20216375

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 112; Journal Issue: 20; Other Information: PBD: 22 May 2000; Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM MECHANICS; MONTE CARLO METHOD; PARTITION FUNCTIONS; FREE ENERGY; ALGORITHMS; THEORETICAL DATA

### Citation Formats

```
Mielke, Steven L., Srinivasan, Jay, and Truhlar, Donald G.
```*Extrapolation and perturbation schemes for accelerating the convergence of quantum mechanical free energy calculations via the Fourier path-integral Monte Carlo method*. United States: N. p., 2000.
Web. doi:10.1063/1.481491.

```
Mielke, Steven L., Srinivasan, Jay, & Truhlar, Donald G.
```*Extrapolation and perturbation schemes for accelerating the convergence of quantum mechanical free energy calculations via the Fourier path-integral Monte Carlo method*. United States. doi:10.1063/1.481491.

```
Mielke, Steven L., Srinivasan, Jay, and Truhlar, Donald G. Mon .
"Extrapolation and perturbation schemes for accelerating the convergence of quantum mechanical free energy calculations via the Fourier path-integral Monte Carlo method". United States. doi:10.1063/1.481491.
```

```
@article{osti_20216375,
```

title = {Extrapolation and perturbation schemes for accelerating the convergence of quantum mechanical free energy calculations via the Fourier path-integral Monte Carlo method},

author = {Mielke, Steven L. and Srinivasan, Jay and Truhlar, Donald G.},

abstractNote = {We present two simple but effective techniques designed to improve the rate of convergence of the Fourier path-integral Monte Carlo method for quantum partition functions with respect to the Fourier space expansion length, K, especially at low temperatures. The first method treats the high Fourier components as a perturbation, and the second method involves an extrapolation of the partition function (or perturbative correction to the partition function) with respect to the parameter K. We perform a sequence of calculations at several values of K such that the statistical errors for the set of results are correlated, and this permits extremely accurate extrapolations. We demonstrate the high accuracy and efficiency of these new approaches by computing partition functions for H{sub 2}O from 296 to 4000 K and comparing to the accurate results of Partridge and Schwenke. (c) 2000 American Institute of Physics.},

doi = {10.1063/1.481491},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 20,

volume = 112,

place = {United States},

year = {2000},

month = {5}

}