# Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations

## Abstract

A new self-consistent procedure for calculating the total energy with an orbital-dependent density functional approximation (DFA), the generalized optimized effective potential (GOEP), is developed in the present work. The GOEP is a nonlocal Hermitian potential that delivers the sets of occupied and virtual orbitals and minimizes the total energy. The GOEP optimization leads to the same minimum as does the orbital optimization. The GOEP method is promising as an effective optimization approach for orbital-dependent functionals, as demonstrated for the self-consistent calculations of the random phase approximation (RPA) to the correlation functionals in the particle–hole (ph) and particle–particle (pp) channels. The results show that the accuracy in describing the weakly interacting van der Waals systems is significantly improved in the self-consistent calculations. In particular, the important single excitations contribution in non-self-consistent RPA calculations can be captured self-consistently through the GOEP optimization, leading to orbital renormalization, without using the single excitations in the energy functional.

- Authors:

- Duke Univ., Durham, NC (United States). Dept. of Chemistry

- Publication Date:

- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Center for the Computational Design of Functional Layered Materials (CCDM)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1469927

- Grant/Contract Number:
- [SC0012575]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Physical Chemistry Letters

- Additional Journal Information:
- [ Journal Volume: 8; Journal Issue: 19; Related Information: CCDM partners with Temple University (lead); Brookhaven National Laboratory; Drexel University; Duke University; North Carolina State University; Northeastern University; Princeton University; Rice University; University of Pennsylvania]; Journal ID: ISSN 1948-7185

- Publisher:
- American Chemical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; catalysis (heterogeneous); solar (photovoltaic); energy storage (including batteries and capacitors); hydrogen and fuel cells; defects; mechanical behavior; materials and chemistry by design; synthesis (novel materials)

### Citation Formats

```
Jin, Ye, Zhang, Du, Chen, Zehua, Su, Neil Qiang, and Yang, Weitao. Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations. United States: N. p., 2017.
Web. doi:10.1021/acs.jpclett.7b02165.
```

```
Jin, Ye, Zhang, Du, Chen, Zehua, Su, Neil Qiang, & Yang, Weitao. Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations. United States. doi:10.1021/acs.jpclett.7b02165.
```

```
Jin, Ye, Zhang, Du, Chen, Zehua, Su, Neil Qiang, and Yang, Weitao. Tue .
"Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations". United States. doi:10.1021/acs.jpclett.7b02165. https://www.osti.gov/servlets/purl/1469927.
```

```
@article{osti_1469927,
```

title = {Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations},

author = {Jin, Ye and Zhang, Du and Chen, Zehua and Su, Neil Qiang and Yang, Weitao},

abstractNote = {A new self-consistent procedure for calculating the total energy with an orbital-dependent density functional approximation (DFA), the generalized optimized effective potential (GOEP), is developed in the present work. The GOEP is a nonlocal Hermitian potential that delivers the sets of occupied and virtual orbitals and minimizes the total energy. The GOEP optimization leads to the same minimum as does the orbital optimization. The GOEP method is promising as an effective optimization approach for orbital-dependent functionals, as demonstrated for the self-consistent calculations of the random phase approximation (RPA) to the correlation functionals in the particle–hole (ph) and particle–particle (pp) channels. The results show that the accuracy in describing the weakly interacting van der Waals systems is significantly improved in the self-consistent calculations. In particular, the important single excitations contribution in non-self-consistent RPA calculations can be captured self-consistently through the GOEP optimization, leading to orbital renormalization, without using the single excitations in the energy functional.},

doi = {10.1021/acs.jpclett.7b02165},

journal = {Journal of Physical Chemistry Letters},

number = [19],

volume = [8],

place = {United States},

year = {2017},

month = {9}

}

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