Theoretical Chemistry Accounts

, 131:1084

Electron correlation methods based on the random phase approximation


  • Henk Eshuis
    • Department of ChemistryUniversity of California
  • Jefferson E. Bates
    • Department of ChemistryUniversity of California
    • Department of ChemistryUniversity of California
Regular Article

DOI: 10.1007/s00214-011-1084-8

Cite this article as:
Eshuis, H., Bates, J.E. & Furche, F. Theor Chem Acc (2012) 131: 1084. doi:10.1007/s00214-011-1084-8
Part of the following topical collections:
  1. 50th Anniversary Collection


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.


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

Supplementary material

214_2011_1084_MOESM1_ESM.pdf (75 kb)
Supplementary material (PDF 75.4 kb)

Copyright information

© Springer-Verlag 2012