# Surface hopping outperforms secular Redfield theory when reorganization energies range from small to moderate (and nuclei are classical)

## Abstract

We evaluate the accuracy of Tully’s surface hopping algorithm for the spin-boson model in the limit of small to moderate reorganization energy. We calculate transition rates between diabatic surfaces in the exciton basis and compare against exact results from the hierarchical equations of motion; we also compare against approximate rates from the secular Redfield equation and Ehrenfest dynamics. We show that decoherence-corrected surface hopping performs very well in this regime, agreeing with secular Redfield theory for very weak system-bath coupling and outperforming secular Redfield theory for moderate system-bath coupling. Surface hopping can also be extended beyond the Markovian limits of standard Redfield theory. Given previous work [B. R. Landry and J. E. Subotnik, J. Chem. Phys. 137, 22A513 (2012)] that establishes the accuracy of decoherence-corrected surface-hopping in the Marcus regime, this work suggests that surface hopping may well have a very wide range of applicability.

- Authors:

- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104 (United States)

- Publication Date:

- OSTI Identifier:
- 22415490

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; APPROXIMATIONS; BOSONS; COMPARATIVE EVALUATIONS; COUPLING; EQUATIONS OF MOTION; INTEGRO-DIFFERENTIAL EQUATIONS; MARKOV PROCESS; SPIN; SURFACES

### Citation Formats

```
Landry, Brian R., E-mail: landrybr@gmail.com, and Subotnik, Joseph E.
```*Surface hopping outperforms secular Redfield theory when reorganization energies range from small to moderate (and nuclei are classical)*. United States: N. p., 2015.
Web. doi:10.1063/1.4913494.

```
Landry, Brian R., E-mail: landrybr@gmail.com, & Subotnik, Joseph E.
```*Surface hopping outperforms secular Redfield theory when reorganization energies range from small to moderate (and nuclei are classical)*. United States. doi:10.1063/1.4913494.

```
Landry, Brian R., E-mail: landrybr@gmail.com, and Subotnik, Joseph E. Sat .
"Surface hopping outperforms secular Redfield theory when reorganization energies range from small to moderate (and nuclei are classical)". United States.
doi:10.1063/1.4913494.
```

```
@article{osti_22415490,
```

title = {Surface hopping outperforms secular Redfield theory when reorganization energies range from small to moderate (and nuclei are classical)},

author = {Landry, Brian R., E-mail: landrybr@gmail.com and Subotnik, Joseph E.},

abstractNote = {We evaluate the accuracy of Tully’s surface hopping algorithm for the spin-boson model in the limit of small to moderate reorganization energy. We calculate transition rates between diabatic surfaces in the exciton basis and compare against exact results from the hierarchical equations of motion; we also compare against approximate rates from the secular Redfield equation and Ehrenfest dynamics. We show that decoherence-corrected surface hopping performs very well in this regime, agreeing with secular Redfield theory for very weak system-bath coupling and outperforming secular Redfield theory for moderate system-bath coupling. Surface hopping can also be extended beyond the Markovian limits of standard Redfield theory. Given previous work [B. R. Landry and J. E. Subotnik, J. Chem. Phys. 137, 22A513 (2012)] that establishes the accuracy of decoherence-corrected surface-hopping in the Marcus regime, this work suggests that surface hopping may well have a very wide range of applicability.},

doi = {10.1063/1.4913494},

journal = {Journal of Chemical Physics},

number = 10,

volume = 142,

place = {United States},

year = {Sat Mar 14 00:00:00 EDT 2015},

month = {Sat Mar 14 00:00:00 EDT 2015}

}