# Stochastic models for surface diffusion of molecules

## Abstract

We derive a stochastic model for the surface diffusion of molecules, starting from the classical equations of motion for an N-atom molecule on a surface. The equation of motion becomes a generalized Langevin equation for the center of mass of the molecule, with a non-Markovian friction kernel. In the Markov approximation, a standard Langevin equation is recovered, and the effect of the molecular vibrations on the diffusion is seen to lead to an increase in the friction for center of mass motion. This effective friction has a simple form that depends on the curvature of the lowest energy diffusion path in the 3N-dimensional coordinate space. We also find that so long as the intramolecular forces are sufficiently strong, memory effects are usually not significant and the Markov approximation can be employed, resulting in a simple one-dimensional model that can account for the effect of the dynamics of the molecular vibrations on the diffusive motion.

- Authors:

- Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada)

- Publication Date:

- OSTI Identifier:
- 22419926

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ATOMS; DIFFUSION; EQUATIONS OF MOTION; LANGEVIN EQUATION; MARKOV PROCESS; MASS; MOLECULES; SURFACES

### Citation Formats

```
Shea, Patrick, E-mail: patrick.shea@dal.ca, and Kreuzer, Hans Jürgen.
```*Stochastic models for surface diffusion of molecules*. United States: N. p., 2014.
Web. doi:10.1063/1.4890661.

```
Shea, Patrick, E-mail: patrick.shea@dal.ca, & Kreuzer, Hans Jürgen.
```*Stochastic models for surface diffusion of molecules*. United States. doi:10.1063/1.4890661.

```
Shea, Patrick, E-mail: patrick.shea@dal.ca, and Kreuzer, Hans Jürgen. Mon .
"Stochastic models for surface diffusion of molecules". United States.
doi:10.1063/1.4890661.
```

```
@article{osti_22419926,
```

title = {Stochastic models for surface diffusion of molecules},

author = {Shea, Patrick, E-mail: patrick.shea@dal.ca and Kreuzer, Hans Jürgen},

abstractNote = {We derive a stochastic model for the surface diffusion of molecules, starting from the classical equations of motion for an N-atom molecule on a surface. The equation of motion becomes a generalized Langevin equation for the center of mass of the molecule, with a non-Markovian friction kernel. In the Markov approximation, a standard Langevin equation is recovered, and the effect of the molecular vibrations on the diffusion is seen to lead to an increase in the friction for center of mass motion. This effective friction has a simple form that depends on the curvature of the lowest energy diffusion path in the 3N-dimensional coordinate space. We also find that so long as the intramolecular forces are sufficiently strong, memory effects are usually not significant and the Markov approximation can be employed, resulting in a simple one-dimensional model that can account for the effect of the dynamics of the molecular vibrations on the diffusive motion.},

doi = {10.1063/1.4890661},

journal = {Journal of Chemical Physics},

number = 4,

volume = 141,

place = {United States},

year = {Mon Jul 28 00:00:00 EDT 2014},

month = {Mon Jul 28 00:00:00 EDT 2014}

}