# Stochastic algorithm for size-extensive vibrational self-consistent field methods on fully anharmonic potential energy surfaces

## Abstract

A stochastic algorithm based on Metropolis Monte Carlo (MC) is presented for the size-extensive vibrational self-consistent field methods (XVSCF(n) and XVSCF[n]) for anharmonic molecular vibrations. The new MC-XVSCF methods substitute stochastic evaluations of a small number of high-dimensional integrals of functions of the potential energy surface (PES), which is sampled on demand, for diagrammatic equations involving high-order anharmonic force constants. This algorithm obviates the need to evaluate and store any high-dimensional partial derivatives of the potential and can be applied to the fully anharmonic PES without any Taylor-series approximation in an intrinsically parallelizable algorithm. The MC-XVSCF methods reproduce deterministic XVSCF calculations on the same Taylor-series PES in all energies, frequencies, and geometries. Calculations using the fully anharmonic PES evaluated on the fly with electronic structure methods report anharmonic effects on frequencies and geometries of much greater magnitude than deterministic XVSCF calculations, reflecting an underestimation of anharmonic effects in a Taylor-series approximation to the PES.

- Authors:

- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States)
- (Japan)

- Publication Date:

- OSTI Identifier:
- 22415408

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 24; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; APPROXIMATIONS; ELECTRONIC STRUCTURE; EVALUATION; INTEGRALS; MONTE CARLO METHOD; POTENTIAL ENERGY; POTENTIALS; SELF-CONSISTENT FIELD; STOCHASTIC PROCESSES; SURFACES

### Citation Formats

```
Hermes, Matthew R., Hirata, So, E-mail: sohirata@illinois.edu, and CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012.
```*Stochastic algorithm for size-extensive vibrational self-consistent field methods on fully anharmonic potential energy surfaces*. United States: N. p., 2014.
Web. doi:10.1063/1.4904220.

```
Hermes, Matthew R., Hirata, So, E-mail: sohirata@illinois.edu, & CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012.
```*Stochastic algorithm for size-extensive vibrational self-consistent field methods on fully anharmonic potential energy surfaces*. United States. doi:10.1063/1.4904220.

```
Hermes, Matthew R., Hirata, So, E-mail: sohirata@illinois.edu, and CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012. Sun .
"Stochastic algorithm for size-extensive vibrational self-consistent field methods on fully anharmonic potential energy surfaces". United States.
doi:10.1063/1.4904220.
```

```
@article{osti_22415408,
```

title = {Stochastic algorithm for size-extensive vibrational self-consistent field methods on fully anharmonic potential energy surfaces},

author = {Hermes, Matthew R. and Hirata, So, E-mail: sohirata@illinois.edu and CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012},

abstractNote = {A stochastic algorithm based on Metropolis Monte Carlo (MC) is presented for the size-extensive vibrational self-consistent field methods (XVSCF(n) and XVSCF[n]) for anharmonic molecular vibrations. The new MC-XVSCF methods substitute stochastic evaluations of a small number of high-dimensional integrals of functions of the potential energy surface (PES), which is sampled on demand, for diagrammatic equations involving high-order anharmonic force constants. This algorithm obviates the need to evaluate and store any high-dimensional partial derivatives of the potential and can be applied to the fully anharmonic PES without any Taylor-series approximation in an intrinsically parallelizable algorithm. The MC-XVSCF methods reproduce deterministic XVSCF calculations on the same Taylor-series PES in all energies, frequencies, and geometries. Calculations using the fully anharmonic PES evaluated on the fly with electronic structure methods report anharmonic effects on frequencies and geometries of much greater magnitude than deterministic XVSCF calculations, reflecting an underestimation of anharmonic effects in a Taylor-series approximation to the PES.},

doi = {10.1063/1.4904220},

journal = {Journal of Chemical Physics},

number = 24,

volume = 141,

place = {United States},

year = {Sun Dec 28 00:00:00 EST 2014},

month = {Sun Dec 28 00:00:00 EST 2014}

}