# Using a Family of Dividing Surfaces Normal to the Minimum EnergyPath for Quantum Instanton Rate Constants

## Abstract

One of the outstanding issues in the quantum instanton (QI) theory (or any transition state-type theory) for thermal rate constants of chemical reactions is the choice of an appropriate ''dividing surface'' (DS) that separates reactants and products. (In the general version of the QI theory, there are actually two dividing surfaces involved.) This paper shows one simple and general way for choosing DS's for use in QI Theory, namely using the family of (hyper) planes normal to the minimum energy path (MEP) on the potential energy surface at various distances s along it. Here the reaction coordinate is not one of the dynamical coordinates of the system (which will in general be the Cartesian coordinates of the atoms), but rather simply a parameter which specifies the DS. It is also shown how this idea can be implemented for an N-atom system in 3d space in a way that preserves overall translational and rotational invariance. Numerical application to a simple system (the colliner H + H{sub 2} reaction) is presented to illustrate the procedure.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE Director. Office of Science. Office of Basic EnergySciences; US Office of Defense. Office of Naval Research Grant#N00014-01-1-0236

- OSTI Identifier:
- 891631

- Report Number(s):
- LBNL-59735

Journal ID: ISSN 0021-9606; JCPSA6; R&D Project: 401501; BnR: KC0301020; TRN: US0605454

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

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 125; Related Information: Journal Publication Date: 2006

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ATOMS; CARTESIAN COORDINATES; CHEMICAL REACTIONS; INSTANTONS; POTENTIAL ENERGY; ROTATIONAL INVARIANCE

### Citation Formats

```
Li, Yimin, and Miller, Wlliam H.
```*Using a Family of Dividing Surfaces Normal to the Minimum EnergyPath for Quantum Instanton Rate Constants*. United States: N. p., 2006.
Web.

```
Li, Yimin, & Miller, Wlliam H.
```*Using a Family of Dividing Surfaces Normal to the Minimum EnergyPath for Quantum Instanton Rate Constants*. United States.

```
Li, Yimin, and Miller, Wlliam H. Wed .
"Using a Family of Dividing Surfaces Normal to the Minimum EnergyPath for Quantum Instanton Rate Constants". United States.
doi:. https://www.osti.gov/servlets/purl/891631.
```

```
@article{osti_891631,
```

title = {Using a Family of Dividing Surfaces Normal to the Minimum EnergyPath for Quantum Instanton Rate Constants},

author = {Li, Yimin and Miller, Wlliam H.},

abstractNote = {One of the outstanding issues in the quantum instanton (QI) theory (or any transition state-type theory) for thermal rate constants of chemical reactions is the choice of an appropriate ''dividing surface'' (DS) that separates reactants and products. (In the general version of the QI theory, there are actually two dividing surfaces involved.) This paper shows one simple and general way for choosing DS's for use in QI Theory, namely using the family of (hyper) planes normal to the minimum energy path (MEP) on the potential energy surface at various distances s along it. Here the reaction coordinate is not one of the dynamical coordinates of the system (which will in general be the Cartesian coordinates of the atoms), but rather simply a parameter which specifies the DS. It is also shown how this idea can be implemented for an N-atom system in 3d space in a way that preserves overall translational and rotational invariance. Numerical application to a simple system (the colliner H + H{sub 2} reaction) is presented to illustrate the procedure.},

doi = {},

journal = {Journal of Chemical Physics},

number = ,

volume = 125,

place = {United States},

year = {Wed Feb 22 00:00:00 EST 2006},

month = {Wed Feb 22 00:00:00 EST 2006}

}