A general range-separated double-hybrid density-functional theory

Abstract

A range-separated double-hybrid (RSDH) scheme which generalizes the usual range-separated hybrids and double hybrids is developed. This scheme consistently uses a two-parameter Coulomb-attenuating-method (CAM)-like decomposition of the electron-electron interaction for both exchange and correlation in order to combine Hartree-Fock exchange and second-order Møller-Plesset (MP2) correlation with a density functional. The RSDH scheme relies on an exact theory which is presented in some detail. Several semi-local approximations are developed for the short-range exchange-correlation density functional involved in this scheme. After finding optimal values for the two parameters of the CAM-like decomposition, the RSDH scheme is shown to have a relatively small basis dependence and to provide atomization energies, reaction barrier heights, and weak intermolecular interactions globally more accurate or comparable to range-separated MP2 or standard MP2. The RSDH scheme represents a new family of double hybrids with minimal empiricism which could be useful for general chemical applications.

Range-separated double-hybrid density-functional theory with coupled-cluster and random-phase approximations

“…In the RSDH approach, the exact ground-state electronic energy of a N-electron system is expressed as [12] E = min Ψ Ψ|T +V ne +Ŵ lr,µ ee + λŴ sr,µ ee |Ψ…”

“…Recently, a range-separated double-hybrid (RSDH) approximation [12] has been constructed based on the following decomposition of the Coulomb electronelectron interaction w ee (r 12 ) = 1/r 12 w ee (r 12 ) = w lr,µ ee (r 12 ) + λw sr,µ ee (r 12 ) +(1 − λ)w sr,µ ee (r 12 ),…”

Global Hybrid Multiconfiguration Pair-Density Functional Theory

“…). [20] The exchange part of the complement functional is easily defined, as it simply scales linearly with the mixing parameter λ [19,20,25]…”

“…The correlation contribution to the complement OTPD functional can be obtained through uniform coordinate scaling of the density as [19,20,25]…”

Computation of covalent and noncovalent structural parameters at low computational cost: Efficiency of the DH‐SVPD method

“…[11][12][13] Others are based on the range-separation exchange (RSX) scheme [14] to (partially) cure the self-interaction and delocalization errors [15] (SIE and DE, respectively). [16][17][18][19] However, all of them conserve similar features, that is, a fraction of EXX generally larger than 50% and a fraction of PT2 correlation ranging between 10% and 40%, which allow them to reach the chemical accuracy when modeling a large panel of properties ranging from ground-state energies [20] to structures [21,22] and extending to singlet-singlet vertical excitation energies. [23,24] Despite their undeniable robustness, DHs remain more computationally demanding than standard density functionals.…”