# Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. III. Exact stochastic path integral evaluation

## Abstract

A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators, one can also immediately compute energy transfer rates using the multi-chromophoric Förster resonant energy transfer formalism. Benchmark calculations on the emission spectra of two level systems are presented demonstrating the efficacy of the stochastic approach. This is followed by calculations of the energy transfer rates between two weakly coupled dimer systems as a function of temperature and system-bath coupling strength. It is shown that the recently developed hybrid cumulant expansion (see Paper II) is the only perturbative method capable of generating uniformly reliable energy transfer rates and emission spectra across a broad range of system parameters.

- Authors:

- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (United States)

- Publication Date:

- OSTI Identifier:
- 22416205

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 9; 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; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ABSORPTION SPECTRA; BENCHMARKS; COUPLING; DIFFERENTIAL EQUATIONS; DIMERS; EMISSION; EMISSION SPECTRA; ENERGY TRANSFER; EVALUATION; EXPANSION; HYBRIDIZATION; MATHEMATICAL SOLUTIONS; PATH INTEGRALS; QUANTUM SYSTEMS; RESONANCE; SPECTRAL DENSITY; STOCHASTIC PROCESSES; TEMPERATURE DEPENDENCE

### Citation Formats

```
Moix, Jeremy M., Ma, Jian, and Cao, Jianshu, E-mail: jianshu@mit.edu.
```*Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. III. Exact stochastic path integral evaluation*. United States: N. p., 2015.
Web. doi:10.1063/1.4908601.

```
Moix, Jeremy M., Ma, Jian, & Cao, Jianshu, E-mail: jianshu@mit.edu.
```*Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. III. Exact stochastic path integral evaluation*. United States. doi:10.1063/1.4908601.

```
Moix, Jeremy M., Ma, Jian, and Cao, Jianshu, E-mail: jianshu@mit.edu. Sat .
"Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. III. Exact stochastic path integral evaluation". United States.
doi:10.1063/1.4908601.
```

```
@article{osti_22416205,
```

title = {Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. III. Exact stochastic path integral evaluation},

author = {Moix, Jeremy M. and Ma, Jian and Cao, Jianshu, E-mail: jianshu@mit.edu},

abstractNote = {A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators, one can also immediately compute energy transfer rates using the multi-chromophoric Förster resonant energy transfer formalism. Benchmark calculations on the emission spectra of two level systems are presented demonstrating the efficacy of the stochastic approach. This is followed by calculations of the energy transfer rates between two weakly coupled dimer systems as a function of temperature and system-bath coupling strength. It is shown that the recently developed hybrid cumulant expansion (see Paper II) is the only perturbative method capable of generating uniformly reliable energy transfer rates and emission spectra across a broad range of system parameters.},

doi = {10.1063/1.4908601},

journal = {Journal of Chemical Physics},

number = 9,

volume = 142,

place = {United States},

year = {Sat Mar 07 00:00:00 EST 2015},

month = {Sat Mar 07 00:00:00 EST 2015}

}