### Abstract

In the past decade, the random phase approximation (RPA) has emerged as a promising post-Kohn-Sham method to treat electron correlation in molecules, surfaces, and solids. In this review, we explain how RPA arises naturally as a zero-order approximation from the adiabatic connection and the fluctuation-dissipation theorem in a density functional context. This is contrasted to RPA with exchange (RPAX) in a post-Hartree-Fock context. In both methods, RPA and RPAX, the correlation energy may be expressed as a sum over zero-point energies of harmonic oscillators representing collective electronic excitations, consistent with the physical picture originally proposed by Bohm and Pines. The extra factor 1/2 in the RPAX case is rigorously derived. Approaches beyond RPA are briefly summarized. We also review computational strategies implementing RPA. The combination of auxiliary expansions and imaginary frequency integration methods has lead to recent progress in this field, making RPA calculations affordable for systems with over 100 atoms. Finally, we summarize benchmark applications of RPA to various molecular and solid-state properties, including relative energies of conformers, reaction energies involving weak and covalent interactions, diatomic potential energy curves, ionization potentials and electron affinities, surface adsorption energies, bulk cohesive energies and lattice constants. RPA barrier heights for an extended benchmark set are presented. RPA is an order of magnitude more accurate than semi-local functionals such as B3LYP for non-covalent interactions rivaling the best empirically parametrized methods. Larger but systematic errors are observed for processes that do not conserve the number of electron pairs, such as atomization and ionization.

Original language | English |
---|---|

Article number | 1084 |

Journal | Theoretical Chemistry Accounts |

Volume | 131 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2012 |

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### Keywords

- Density functional theory
- Electronic structure theory
- Random phase approximation
- Resolution-of-the-identity (RI) approximation
- Thermochemistry
- Van-der-Waals forces

### Cite this

*Theoretical Chemistry Accounts*,

*131*(1), [1084]. https://doi.org/10.1007/s00214-011-1084-8

}

*Theoretical Chemistry Accounts*, vol. 131, no. 1, 1084. https://doi.org/10.1007/s00214-011-1084-8

**Electron correlation methods based on the random phase approximation.** / Eshuis, Hendrik; Bates, Jefferson E.; Furche, Filipp.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Electron correlation methods based on the random phase approximation

AU - Eshuis, Hendrik

AU - Bates, Jefferson E.

AU - Furche, Filipp

PY - 2012/1/1

Y1 - 2012/1/1

N2 - In the past decade, the random phase approximation (RPA) has emerged as a promising post-Kohn-Sham method to treat electron correlation in molecules, surfaces, and solids. In this review, we explain how RPA arises naturally as a zero-order approximation from the adiabatic connection and the fluctuation-dissipation theorem in a density functional context. This is contrasted to RPA with exchange (RPAX) in a post-Hartree-Fock context. In both methods, RPA and RPAX, the correlation energy may be expressed as a sum over zero-point energies of harmonic oscillators representing collective electronic excitations, consistent with the physical picture originally proposed by Bohm and Pines. The extra factor 1/2 in the RPAX case is rigorously derived. Approaches beyond RPA are briefly summarized. We also review computational strategies implementing RPA. The combination of auxiliary expansions and imaginary frequency integration methods has lead to recent progress in this field, making RPA calculations affordable for systems with over 100 atoms. Finally, we summarize benchmark applications of RPA to various molecular and solid-state properties, including relative energies of conformers, reaction energies involving weak and covalent interactions, diatomic potential energy curves, ionization potentials and electron affinities, surface adsorption energies, bulk cohesive energies and lattice constants. RPA barrier heights for an extended benchmark set are presented. RPA is an order of magnitude more accurate than semi-local functionals such as B3LYP for non-covalent interactions rivaling the best empirically parametrized methods. Larger but systematic errors are observed for processes that do not conserve the number of electron pairs, such as atomization and ionization.

AB - In the past decade, the random phase approximation (RPA) has emerged as a promising post-Kohn-Sham method to treat electron correlation in molecules, surfaces, and solids. In this review, we explain how RPA arises naturally as a zero-order approximation from the adiabatic connection and the fluctuation-dissipation theorem in a density functional context. This is contrasted to RPA with exchange (RPAX) in a post-Hartree-Fock context. In both methods, RPA and RPAX, the correlation energy may be expressed as a sum over zero-point energies of harmonic oscillators representing collective electronic excitations, consistent with the physical picture originally proposed by Bohm and Pines. The extra factor 1/2 in the RPAX case is rigorously derived. Approaches beyond RPA are briefly summarized. We also review computational strategies implementing RPA. The combination of auxiliary expansions and imaginary frequency integration methods has lead to recent progress in this field, making RPA calculations affordable for systems with over 100 atoms. Finally, we summarize benchmark applications of RPA to various molecular and solid-state properties, including relative energies of conformers, reaction energies involving weak and covalent interactions, diatomic potential energy curves, ionization potentials and electron affinities, surface adsorption energies, bulk cohesive energies and lattice constants. RPA barrier heights for an extended benchmark set are presented. RPA is an order of magnitude more accurate than semi-local functionals such as B3LYP for non-covalent interactions rivaling the best empirically parametrized methods. Larger but systematic errors are observed for processes that do not conserve the number of electron pairs, such as atomization and ionization.

KW - Density functional theory

KW - Electronic structure theory

KW - Random phase approximation

KW - Resolution-of-the-identity (RI) approximation

KW - Thermochemistry

KW - Van-der-Waals forces

UR - http://www.scopus.com/inward/record.url?scp=84855574249&partnerID=8YFLogxK

U2 - 10.1007/s00214-011-1084-8

DO - 10.1007/s00214-011-1084-8

M3 - Article

AN - SCOPUS:84855574249

VL - 131

JO - Theoretical Chemistry Accounts

JF - Theoretical Chemistry Accounts

SN - 1432-881X

IS - 1

M1 - 1084

ER -