## Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

## Abstract

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. As a result, we present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

- Authors:

- California Inst. of Technology (CalTech), Pasadena, CA (United States). Division of Chemistry and Chemical Engineering

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1498059

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 148; Journal Issue: 10; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Tao, Xuecheng, Shushkov, Philip, and Miller, III, Thomas F. Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics. United States: N. p., 2017.
Web. doi:10.1063/1.5005544.
```

```
Tao, Xuecheng, Shushkov, Philip, & Miller, III, Thomas F. Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics. United States. doi:10.1063/1.5005544.
```

```
Tao, Xuecheng, Shushkov, Philip, and Miller, III, Thomas F. Tue .
"Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics". United States. doi:10.1063/1.5005544. https://www.osti.gov/servlets/purl/1498059.
```

```
@article{osti_1498059,
```

title = {Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics},

author = {Tao, Xuecheng and Shushkov, Philip and Miller, III, Thomas F.},

abstractNote = {We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. As a result, we present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.},

doi = {10.1063/1.5005544},

journal = {Journal of Chemical Physics},

number = 10,

volume = 148,

place = {United States},

year = {2017},

month = {12}

}