title: The RPA Atomization Energy Puzzle.
abstract: There is current interest in the random phase approximation (RPA), a "fifth-rung" density functional for the exchange-correlation energy. RPA has full exact exchange and constructs the correlation with the help of the unoccupied Kohn-Sham orbitals. In many cases (uniform electron gas, jellium surface, and free atom), the correction to RPA is a short-ranged effect that is captured by a local spin density approximation (LSDA) or a generalized gradient approximation (GGA). Nonempirical density functionals for the correction to RPA were constructed earlier at the LSDA and GGA levels (RPA+), but they are constructed here at the fully nonlocal level (RPA++), using the van der Waals density functional (vdW-DF) of Langreth, Lundqvist, and collaborators. While they make important and helpful corrections to RPA total and ionization energies of free atoms, they correct the RPA atomization energies of molecules by only about 1 kcal/mol. Thus, it is puzzling that RPA atomization energies are, on average, about 10 kcal/mol lower than those of accurate values from experiment. We find here that a hybrid of 50% Perdew-Burke-Ernzerhof GGA with 50% RPA+ yields atomization energies much more accurate than either one does alone. This suggests a solution to the puzzle: While the proper correction to RPA is short-ranged in some systems, its contribution to the correlation hole can spread out in a molecule with multiple atomic centers, canceling part of the spread of the exact exchange hole (more so than in RPA or RPA+), making the true exchange-correlation hole more localized than in RPA or RPA+. This effect is not captured even by the vdW-DF nonlocality, but it requires the different kind of full nonlocality present in a hybrid functional.
authors.affiliation: Department of Physics and Quantum Theory Group, 2001 Percival Stern Hall, Tulane University, New Orleans, Louisiana 70118 and Department of Inorganic and Analytical Chemistry, Budapest University of Technology and Economics, Szt. Gellért tér 4, Budapest, H-1111, Hungary.
authors.forename: Adrienn
authors.initials: A
authors.lastname: Ruzsinszky
authors.affiliation: Department of Physics and Quantum Theory Group, 2001 Percival Stern Hall, Tulane University, New Orleans, Louisiana 70118 and Department of Inorganic and Analytical Chemistry, Budapest University of Technology and Economics, Szt. Gellért tér 4, Budapest, H-1111, Hungary.
authors.forename: John P
authors.initials: JP
authors.lastname: Perdew
authors.affiliation: Department of Physics and Quantum Theory Group, 2001 Percival Stern Hall, Tulane University, New Orleans, Louisiana 70118 and Department of Inorganic and Analytical Chemistry, Budapest University of Technology and Economics, Szt. Gellért tér 4, Budapest, H-1111, Hungary.
authors.forename: Gábor I
authors.initials: GI
authors.lastname: Csonka