# The adiabatic limit of the exact factorization of the electron-nuclear wave function

## Abstract

We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model of proton-coupled electron transfer in different non-adiabatic regimes.

- Authors:

- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg (Germany)
- Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle (Germany)

- Publication Date:

- OSTI Identifier:
- 22679021

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 145; Journal Issue: 5; Other Information: (c) 2016 Author(s); 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; ELECTRON TRANSFER; FACTORIZATION; WAVE FUNCTIONS

### Citation Formats

```
Eich, F. G., and Agostini, Federica, E-mail: agostini@mpi-halle.mpg.de.
```*The adiabatic limit of the exact factorization of the electron-nuclear wave function*. United States: N. p., 2016.
Web. doi:10.1063/1.4959962.

```
Eich, F. G., & Agostini, Federica, E-mail: agostini@mpi-halle.mpg.de.
```*The adiabatic limit of the exact factorization of the electron-nuclear wave function*. United States. doi:10.1063/1.4959962.

```
Eich, F. G., and Agostini, Federica, E-mail: agostini@mpi-halle.mpg.de. Sun .
"The adiabatic limit of the exact factorization of the electron-nuclear wave function". United States.
doi:10.1063/1.4959962.
```

```
@article{osti_22679021,
```

title = {The adiabatic limit of the exact factorization of the electron-nuclear wave function},

author = {Eich, F. G. and Agostini, Federica, E-mail: agostini@mpi-halle.mpg.de},

abstractNote = {We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model of proton-coupled electron transfer in different non-adiabatic regimes.},

doi = {10.1063/1.4959962},

journal = {Journal of Chemical Physics},

number = 5,

volume = 145,

place = {United States},

year = {Sun Aug 07 00:00:00 EDT 2016},

month = {Sun Aug 07 00:00:00 EDT 2016}

}

DOI: 10.1063/1.4959962

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.