# Interpolating moving least-squares methods for fitting potential energy surfaces : computing high-density potential energy surface data from low-density ab initio data points.

## Abstract

A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating-moving-least-squares (IMLS)-based method is developed using low-density ab initio Hessian values to compute high-density PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modified-Shepard-based methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in high-order IMLS-based methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which high-order IMLS is used with low-density ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even high-order IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modified-Shepard interpolation,more »

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 915032

- Report Number(s):
- ANL/CHM/JA-59873

Journal ID: ISSN 0021-9606; JCPSA6; TRN: US200817%%70

- DOE Contract Number:
- DE-AC02-06CH11357

- Resource Type:
- Journal Article

- Journal Name:
- J. Chem. Phys.

- Additional Journal Information:
- Journal Volume: 126; Journal Issue: May 11, 2007; Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- ENGLISH

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 97; INTERPOLATION; NEURAL NETWORKS; POTENTIAL ENERGY; SURFACES; LEAST SQUARE FIT; HYDROCYANIC ACID; HYDROGEN PEROXIDE

### Citation Formats

```
Dawes, R., Thompson, D. L., Guo, Y., Wagner, A. F., Minkoff, M., Chemistry, Univ. of Missouri-Columbia, and Oklahoma State Univ.
```*Interpolating moving least-squares methods for fitting potential energy surfaces : computing high-density potential energy surface data from low-density ab initio data points.*. United States: N. p., 2007.
Web. doi:10.1063/1.2730798.

```
Dawes, R., Thompson, D. L., Guo, Y., Wagner, A. F., Minkoff, M., Chemistry, Univ. of Missouri-Columbia, & Oklahoma State Univ.
```*Interpolating moving least-squares methods for fitting potential energy surfaces : computing high-density potential energy surface data from low-density ab initio data points.*. United States. doi:10.1063/1.2730798.

```
Dawes, R., Thompson, D. L., Guo, Y., Wagner, A. F., Minkoff, M., Chemistry, Univ. of Missouri-Columbia, and Oklahoma State Univ. Fri .
"Interpolating moving least-squares methods for fitting potential energy surfaces : computing high-density potential energy surface data from low-density ab initio data points.". United States. doi:10.1063/1.2730798.
```

```
@article{osti_915032,
```

title = {Interpolating moving least-squares methods for fitting potential energy surfaces : computing high-density potential energy surface data from low-density ab initio data points.},

author = {Dawes, R. and Thompson, D. L. and Guo, Y. and Wagner, A. F. and Minkoff, M. and Chemistry and Univ. of Missouri-Columbia and Oklahoma State Univ.},

abstractNote = {A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating-moving-least-squares (IMLS)-based method is developed using low-density ab initio Hessian values to compute high-density PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modified-Shepard-based methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in high-order IMLS-based methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which high-order IMLS is used with low-density ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even high-order IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modified-Shepard interpolation, or approximate IMLS. Results that are indicative of the accuracy, efficiency, and scalability are presented for one-dimensional model potentials as well as for three-dimensional (HCN) and six-dimensional (HOOH) molecular PESs},

doi = {10.1063/1.2730798},

journal = {J. Chem. Phys.},

issn = {0021-9606},

number = May 11, 2007,

volume = 126,

place = {United States},

year = {2007},

month = {5}

}