## Locally coupled open subsystems: A formalism for affordable electronic structure calculations featuring fractional charges and size consistency

## Abstract

This manuscript introduces a methodology (within the Born-Oppenheimer picture) to compute electronic ground-state properties of molecules and solids/surfaces with fractionally occupied components. Given a user-defined division of the molecule into subsystems, our theory uses an auxiliary global Hamiltonian that is defined as the sum of subsystem Hamiltonians, plus the spatial integral of a second-quantized local operator that allows the electrons to be transferred between subsystems. This electron transfer operator depends on a local potential that can be determined using density functional approximations and/or other techniques such as machine learning. The present framework employs superpositions of tensor-product wave functions, which can satisfy size consistency and avoid spurious fractional charges at large bond distances. The electronic population of each subsystem is in general a positive real number and is obtained from wave-function amplitudes, which are calculated by means of ground-state matrix diagonalization (or matrix propagation in the time-dependent case). Our method can provide pathways to explore charge-transfer effects in environments where dividing the molecule into subsystems is convenient and to develop computationally affordable electronic structure algorithms.

- Authors:

- Department of Chemistry and the Materials Research Center, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA

- Publication Date:

- Research Org.:
- Northwestern Univ., Evanston, IL (United States)

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

- OSTI Identifier:
- 1540228

- Alternate Identifier(s):
- OSTI ID: 1460915

- Grant/Contract Number:
- SC0004752

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 149; Journal Issue: 3; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Chemistry; Physics

### Citation Formats

```
Mosquera, Martín A., Ratner, Mark A., and Schatz, George C. Locally coupled open subsystems: A formalism for affordable electronic structure calculations featuring fractional charges and size consistency. United States: N. p., 2018.
Web. doi:10.1063/1.5038557.
```

```
Mosquera, Martín A., Ratner, Mark A., & Schatz, George C. Locally coupled open subsystems: A formalism for affordable electronic structure calculations featuring fractional charges and size consistency. United States. doi:10.1063/1.5038557.
```

```
Mosquera, Martín A., Ratner, Mark A., and Schatz, George C. Sat .
"Locally coupled open subsystems: A formalism for affordable electronic structure calculations featuring fractional charges and size consistency". United States. doi:10.1063/1.5038557. https://www.osti.gov/servlets/purl/1540228.
```

```
@article{osti_1540228,
```

title = {Locally coupled open subsystems: A formalism for affordable electronic structure calculations featuring fractional charges and size consistency},

author = {Mosquera, Martín A. and Ratner, Mark A. and Schatz, George C.},

abstractNote = {This manuscript introduces a methodology (within the Born-Oppenheimer picture) to compute electronic ground-state properties of molecules and solids/surfaces with fractionally occupied components. Given a user-defined division of the molecule into subsystems, our theory uses an auxiliary global Hamiltonian that is defined as the sum of subsystem Hamiltonians, plus the spatial integral of a second-quantized local operator that allows the electrons to be transferred between subsystems. This electron transfer operator depends on a local potential that can be determined using density functional approximations and/or other techniques such as machine learning. The present framework employs superpositions of tensor-product wave functions, which can satisfy size consistency and avoid spurious fractional charges at large bond distances. The electronic population of each subsystem is in general a positive real number and is obtained from wave-function amplitudes, which are calculated by means of ground-state matrix diagonalization (or matrix propagation in the time-dependent case). Our method can provide pathways to explore charge-transfer effects in environments where dividing the molecule into subsystems is convenient and to develop computationally affordable electronic structure algorithms.},

doi = {10.1063/1.5038557},

journal = {Journal of Chemical Physics},

number = 3,

volume = 149,

place = {United States},

year = {2018},

month = {7}

}

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Web of Science

Works referenced in this record:

##
NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations

journal, September 2010

- Valiev, M.; Bylaska, E. J.; Govind, N.
- Computer Physics Communications, Vol. 181, Issue 9, p. 1477-1489