Abstract
Connections between the Görling–Levy (GL) perturbation theory and the parameters of double-hybrid (DH) density functional are established via adiabatic connection formalism. Moreover, we present a more general DH density functional theory, where the higher-order perturbation terms beyond the second-order GL2 one, such as GL3 and GL4, also contribute. It is shown that a class of DH functionals including previously proposed ones can be formed using the present construction. Based on the proposed formalism, we assess the performance of higher-order DH and long-range corrected DH formed on the Perdew–Burke–Ernzerhof (PBE) semilocal functional and second-order GL2 correlation energy. The underlying construction of DH functionals based on the generalized many-body perturbation approaches is physically appealing in terms of the development of the non-local forms using more accurate and sophisticated semilocal functionals.
Highlights
Nowadays, density functional theory (DFT)[1,2] becomes a standard framework of performing the electronic structure calculations of atoms, molecules, and solids, being an indispensable tool for quantum chemists and solid-state physicists
We investigate LRC-ωDFA-mthorder hybrids (mH) functionals defined via eq 17) where, as the SR part of density functional approximations (DFA), we have chosen the ωPBE92 functional and the functional family is denoted as LRC-ωPBE-DH (m, ω) as it is based on the m and empirically fitted ω
We have introduced a generalized theory of the DH density functional using the adiabatic connection (AC) formalism and higher-order many-body perturbation theory
Summary
Density functional theory (DFT)[1,2] becomes a standard framework of performing the electronic structure calculations of atoms, molecules, and solids, being an indispensable tool for quantum chemists and solid-state physicists. The first three rungs of the XC DFAs,[48] which are recognized as the local density approximation (LDA),[1] generalized gradient approximation (GGA),[49] and meta-generalized gradient approximation (meta-GGA),[50] are constructed using the local or semilocal quantities (i.e., density, the gradient of density, Laplacian of density, and Kohn−Sham (KS) kinetic energy density), being very accurate for the diverse nature of the molecular[51,52] and solid-state properties.[9,53−61] there are important limitations in semilocal functionals performance.[62] Several resolutions are adopted to improve the functional performance, such as the inclusion of Hartree− Fock (HF) exchange within the semilocal approximations Functionals constructed in this way are known as hybrid functionals, being extensively used for the chemical and solidstate properties.[51,63−82] Despite the attempt of constructing the best hybrid density functional, an important dynamic correlation, which is the key of the ab initio wave functional theory (WFT), are missing in density functional correlation energy functionals.
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