# Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

## Abstract

There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum golden-rule transition-state theory, which is equivalent tomore »

- Authors:

- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7/B2, 91058 Erlangen (Germany)

- Publication Date:

- OSTI Identifier:
- 22420119

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 7; 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; BORN-OPPENHEIMER APPROXIMATION; CORRELATION FUNCTIONS; COUPLING; POTENTIAL ENERGY; REACTION KINETICS; SIMULATION

### Citation Formats

```
Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de, and Thoss, Michael.
```*Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory*. United States: N. p., 2014.
Web. doi:10.1063/1.4892865.

```
Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de, & Thoss, Michael.
```*Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory*. United States. doi:10.1063/1.4892865.

```
Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de, and Thoss, Michael. Thu .
"Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory". United States.
doi:10.1063/1.4892865.
```

```
@article{osti_22420119,
```

title = {Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory},

author = {Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de and Thoss, Michael},

abstractNote = {There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum golden-rule transition-state theory, which is equivalent to Marcus theory in the classical harmonic limit. This new correlation function formalism thus provides a platform on which a wide variety of dynamical simulation methods can be built aiding the development of accurate nonadiabatic rate theories applicable to complex systems.},

doi = {10.1063/1.4892865},

journal = {Journal of Chemical Physics},

number = 7,

volume = 141,

place = {United States},

year = {Thu Aug 21 00:00:00 EDT 2014},

month = {Thu Aug 21 00:00:00 EDT 2014}

}