# An analysis of model proton-coupled electron transfer reactions via the mixed quantum-classical Liouville approach

## Abstract

The nonadiabatic dynamics of model proton-coupled electron transfer (PCET) reactions is investigated for the first time using a surface-hopping algorithm based on the solution of the mixed quantum-classical Liouville equation (QCLE). This method provides a rigorous treatment of quantum coherence/decoherence effects in the dynamics of mixed quantum-classical systems, which is lacking in the molecular dynamics with quantum transitions surface-hopping approach commonly used for simulating PCET reactions. Within this approach, the protonic and electronic coordinates are treated quantum mechanically and the solvent coordinate evolves classically on both single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Both concerted and sequential PCET reactions are studied in detail under various subsystem-bath coupling conditions and insights into the dynamical principles underlying PCET reactions are gained. Notably, an examination of the trajectories reveals that the system spends the majority of its time on the average of two coherently coupled adiabatic surfaces, during which a phase enters into the calculation of an observable. In general, the results of this paper demonstrate the applicability of QCLE-based surface-hopping dynamics to the study of PCET and emphasize the importance of mean surface evolution and decoherence effects in the calculation of PCET rate constants.

- Authors:

- Department of Chemistry, University of Alberta, Edmonton, Alberta AB T6G 2G2 (Canada)

- Publication Date:

- OSTI Identifier:
- 22419924

- 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; BOLTZMANN-VLASOV EQUATION; COUPLING; ELECTRON TRANSFER; MOLECULAR DYNAMICS METHOD; PROTONS; REACTION KINETICS; SOLUTIONS; SOLVENTS; SURFACES

### Citation Formats

```
Shakib, Farnaz A., and Hanna, Gabriel, E-mail: gabriel.hanna@ualberta.ca.
```*An analysis of model proton-coupled electron transfer reactions via the mixed quantum-classical Liouville approach*. United States: N. p., 2014.
Web. doi:10.1063/1.4890915.

```
Shakib, Farnaz A., & Hanna, Gabriel, E-mail: gabriel.hanna@ualberta.ca.
```*An analysis of model proton-coupled electron transfer reactions via the mixed quantum-classical Liouville approach*. United States. doi:10.1063/1.4890915.

```
Shakib, Farnaz A., and Hanna, Gabriel, E-mail: gabriel.hanna@ualberta.ca. Mon .
"An analysis of model proton-coupled electron transfer reactions via the mixed quantum-classical Liouville approach". United States.
doi:10.1063/1.4890915.
```

```
@article{osti_22419924,
```

title = {An analysis of model proton-coupled electron transfer reactions via the mixed quantum-classical Liouville approach},

author = {Shakib, Farnaz A. and Hanna, Gabriel, E-mail: gabriel.hanna@ualberta.ca},

abstractNote = {The nonadiabatic dynamics of model proton-coupled electron transfer (PCET) reactions is investigated for the first time using a surface-hopping algorithm based on the solution of the mixed quantum-classical Liouville equation (QCLE). This method provides a rigorous treatment of quantum coherence/decoherence effects in the dynamics of mixed quantum-classical systems, which is lacking in the molecular dynamics with quantum transitions surface-hopping approach commonly used for simulating PCET reactions. Within this approach, the protonic and electronic coordinates are treated quantum mechanically and the solvent coordinate evolves classically on both single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Both concerted and sequential PCET reactions are studied in detail under various subsystem-bath coupling conditions and insights into the dynamical principles underlying PCET reactions are gained. Notably, an examination of the trajectories reveals that the system spends the majority of its time on the average of two coherently coupled adiabatic surfaces, during which a phase enters into the calculation of an observable. In general, the results of this paper demonstrate the applicability of QCLE-based surface-hopping dynamics to the study of PCET and emphasize the importance of mean surface evolution and decoherence effects in the calculation of PCET rate constants.},

doi = {10.1063/1.4890915},

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}

}