Improving the accuracy of ground-state correlation energies within a plane-wave basis set: The electron-hole exchange kernel

A new formalism was recently proposed to improve random phase approximation (RPA) correlation energies by including approximate exchange effects [1]. Within this framework, by keeping only the electron-hole contributions to the exchange kernel,two approximations can be obtained: An adiabatic connection analog of the second order screened exchange (AC-SOSEX) and an approximate electron-hole time-dependent Hartree-Fock (eh-TDHF). Here we show how this formalism is suitable for an efficient implementation within the plane-wave basis set. The response functions involved in the AC-SOSEX and eh-TDHF equations can indeed be compactly represented by an auxiliary basis set and the explicit calculation of unoccupied states can be avoided by using density functional perturbation theory techniques [2-3]. As shown by several applications to reaction energies and weakly bound dimers, the inclusion of the electron-hole kernel significantly improves the accuracy of ground-state correlation energies with respect to RPA and semi-local functionals.\\[4pt][1] B. Mussard, D. Rocca, G. Jansen, and J. Angyan, J. Chem. Theory Comput. 12, 2191 (2016) \\[0pt][2] Y. Ping, D. Rocca, and G. Galli, Chem. Soc. Rev. 42, 2437 (2013) \\[0pt][3] A. Dixit, J. Angyan, and D. Rocca, J. Chem. Phys. 145, 104105 (2016)