# Linear-scaling evaluation of the local energy in quantum MonteCarlo

## Abstract

For atomic and molecular quantum Monte Carlo calculations, most of the computational effort is spent in the evaluation of the local energy. We describe a scheme for reducing the computational cost of the evaluation of the Slater determinants and correlation function for the correlated molecular orbital (CMO) ansatz. A sparse representation of the Slater determinants makes possible efficient evaluation of molecular orbitals. A modification to the scaled distance function facilitates a linear scaling implementation of the Schmidt-Moskowitz-Boys-Handy (SMBH) correlation function that preserves the efficient matrix multiplication structure of the SMBH function. For the evaluation of the local energy, these two methods lead to asymptotic linear scaling with respect to the molecule size.

- Authors:

- Publication Date:

- Research Org.:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)

- Sponsoring Org.:
- USDOE Director. Office of Science. Basic EnergySciences

- OSTI Identifier:
- 919376

- Report Number(s):
- LBNL-61257

R&D Project: 401101; BnR: KC0301020; TRN: US0806363

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Conference

- Resource Relation:
- Conference: Pacifichem 2005 International Chemical Congressof Pacific Basin Societies, Honolulu, Hawaii, December 15-20,2005

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; CORRELATION FUNCTIONS; EVALUATION; IMPLEMENTATION; MODIFICATIONS; SLATER METHOD

### Citation Formats

```
Austin, Brian, Aspuru-Guzik, Alan, Salomon-Ferrer, Romelia, and Lester, Jr, William A.
```*Linear-scaling evaluation of the local energy in quantum MonteCarlo*. United States: N. p., 2006.
Web.

```
Austin, Brian, Aspuru-Guzik, Alan, Salomon-Ferrer, Romelia, & Lester, Jr, William A.
```*Linear-scaling evaluation of the local energy in quantum MonteCarlo*. United States.

```
Austin, Brian, Aspuru-Guzik, Alan, Salomon-Ferrer, Romelia, and Lester, Jr, William A. Sat .
"Linear-scaling evaluation of the local energy in quantum MonteCarlo". United States. https://www.osti.gov/servlets/purl/919376.
```

```
@article{osti_919376,
```

title = {Linear-scaling evaluation of the local energy in quantum MonteCarlo},

author = {Austin, Brian and Aspuru-Guzik, Alan and Salomon-Ferrer, Romelia and Lester, Jr, William A},

abstractNote = {For atomic and molecular quantum Monte Carlo calculations, most of the computational effort is spent in the evaluation of the local energy. We describe a scheme for reducing the computational cost of the evaluation of the Slater determinants and correlation function for the correlated molecular orbital (CMO) ansatz. A sparse representation of the Slater determinants makes possible efficient evaluation of molecular orbitals. A modification to the scaled distance function facilitates a linear scaling implementation of the Schmidt-Moskowitz-Boys-Handy (SMBH) correlation function that preserves the efficient matrix multiplication structure of the SMBH function. For the evaluation of the local energy, these two methods lead to asymptotic linear scaling with respect to the molecule size.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2006},

month = {2}

}