# A general method for constructing multidimensional molecular potential energy surfaces from {ital ab} {ital initio} calculations

## Abstract

A general interpolation method for constructing smooth molecular potential energy surfaces (PES{close_quote}s) from {ital ab} {ital initio} data are proposed within the framework of the reproducing kernel Hilbert space and the inverse problem theory. The general expression for an {ital a} {ital posteriori} error bound of the constructed PES is derived. It is shown that the method yields globally smooth potential energy surfaces that are continuous and possess derivatives up to second order or higher. Moreover, the method is amenable to correct symmetry properties and asymptotic behavior of the molecular system. Finally, the method is generic and can be easily extended from low dimensional problems involving two and three atoms to high dimensional problems involving four or more atoms. Basic properties of the method are illustrated by the construction of a one-dimensional potential energy curve of the He{endash}He van der Waals dimer using the exact quantum Monte Carlo calculations of Anderson {ital et} {ital al}. [J. Chem. Phys. {bold 99}, 345 (1993)], a two-dimensional potential energy surface of the HeCO van der Waals molecule using recent {ital ab} {ital initio} calculations by Tao {ital et} {ital al}. [J. Chem. Phys. {bold 101}, 8680 (1994)], and a three-dimensional potential energy surfacemore »

- Authors:

- Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009 (United States)

- Publication Date:

- OSTI Identifier:
- 278465

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 104; Journal Issue: 7; Other Information: PBD: Feb 1996

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 40 CHEMISTRY; MOLECULES; CHEMICAL REACTION KINETICS; CALCULATION METHODS; HILBERT SPACE; INTERPOLATION; MOLECULAR IONS; AB INITIO CALCULATIONS; POTENTIAL ENERGY SURFACES; VAN DER WAALS BINDING

### Citation Formats

```
Ho, T., and Rabitz, H.
```*A general method for constructing multidimensional molecular potential energy surfaces from {ital ab} {ital initio} calculations*. United States: N. p., 1996.
Web. doi:10.1063/1.470984.

```
Ho, T., & Rabitz, H.
```*A general method for constructing multidimensional molecular potential energy surfaces from {ital ab} {ital initio} calculations*. United States. doi:10.1063/1.470984.

```
Ho, T., and Rabitz, H. Thu .
"A general method for constructing multidimensional molecular potential energy surfaces from {ital ab} {ital initio} calculations". United States. doi:10.1063/1.470984.
```

```
@article{osti_278465,
```

title = {A general method for constructing multidimensional molecular potential energy surfaces from {ital ab} {ital initio} calculations},

author = {Ho, T. and Rabitz, H.},

abstractNote = {A general interpolation method for constructing smooth molecular potential energy surfaces (PES{close_quote}s) from {ital ab} {ital initio} data are proposed within the framework of the reproducing kernel Hilbert space and the inverse problem theory. The general expression for an {ital a} {ital posteriori} error bound of the constructed PES is derived. It is shown that the method yields globally smooth potential energy surfaces that are continuous and possess derivatives up to second order or higher. Moreover, the method is amenable to correct symmetry properties and asymptotic behavior of the molecular system. Finally, the method is generic and can be easily extended from low dimensional problems involving two and three atoms to high dimensional problems involving four or more atoms. Basic properties of the method are illustrated by the construction of a one-dimensional potential energy curve of the He{endash}He van der Waals dimer using the exact quantum Monte Carlo calculations of Anderson {ital et} {ital al}. [J. Chem. Phys. {bold 99}, 345 (1993)], a two-dimensional potential energy surface of the HeCO van der Waals molecule using recent {ital ab} {ital initio} calculations by Tao {ital et} {ital al}. [J. Chem. Phys. {bold 101}, 8680 (1994)], and a three-dimensional potential energy surface of the H{sup +}{sub 3} molecular ion using highly accurate {ital ab} {ital initio} calculations of R{umlt o}hse {ital et} {ital al}. [J. Chem. Phys. {bold 101}, 2231 (1994)]. In the first two cases the constructed potentials clearly exhibit the correct asymptotic forms, while in the last case the constructed potential energy surface is in excellent agreement with that constructed by R{umlt o}hse {ital et} {ital al}. using a low order polynomial fitting procedure. {copyright} {ital 1996 American Institute of Physics.}},

doi = {10.1063/1.470984},

journal = {Journal of Chemical Physics},

number = 7,

volume = 104,

place = {United States},

year = {Thu Feb 01 00:00:00 EST 1996},

month = {Thu Feb 01 00:00:00 EST 1996}

}