Abstract
The modified point charge plus continuum (mPC) model [ConstantinL. A.; Phys. Rev. B2019, 99, 085117] solves the important failures of the original counterpart, namely, the divergences when the reduced gradient of the density is large, such as in the tail of the density and in quasi-dimensional density regimes. The mPC allows us to define a modified interaction-strength interpolation (mISI) method inheriting these good features, which are important steps toward the full self-consistent treatment. Here, we provide an assessment of mISI for molecular systems (i.e., considering thermochemistry properties, correlation energies, vertical ionization potentials, and several noncovalent interactions), harmonium atoms, and functional derivatives in the strong-interaction limit. For all our tests, mISI provides a systematic improvement over the original ISI method. Semilocal approximations of the second-order Görling–Levy (GL2) perturbation theory are also considered in the mISI method, showing considerable worsening of the results. Possible further development of mISI is briefly discussed.
Highlights
The exact exchange−correlation (XC) functional can be formally defined using the adiabatic connection formalism as1−7 ∫1Exc[ρ] = Wλ[ρ]dλ (1)where ρ is the electron density, λ is the electron−electron interaction strength, andWλ[ρ] = ⟨Ψλ[ρ]|Vee|Ψλ[ρ]⟩ − U[ρ] (2)is the density-fixed linear adiabatic connection integrand, withΨ+ λλ[Vρe]e being while the antisymmetric wave function that minimizes Tyielding the density ρ (Tand Vee are the kinetic and electron−electron interaction operators, respectively), andU[ρ] being the Hartree energy.Many accurate hybrid XC functionals are based on, and explained by, this method,[4,6,8−10] which provides a rationale for mixing the Hartree−Fock (HF) exchange with semilocal XC functionals.[11]
The adiabatic connection formalism stays behind the more recent and sophisticated double hybrids[15] that are using either the second-order Møller−Plesset[16] (MP2) correlation mixed with fractions of HF exchange and semilocal XC functionals[17−23] into the generalized Kohn−Sham (KS) density functional theory (DFT) scheme[24,25] or GL2 correlation[13] combined with fractions of KS-DFT exact exchange and semilocal XC functionals[26] into the optimized effective potential (OEP) scheme of the true KS-DFT.[26−29] The adiabatic connection is of utmost importance for the ground-state calculations of linear-response time-dependent DFT, being part of the so-called adiabatic connection fluctuation-dissipation theorem that provides a framework for high-level, orbital-dependent methods based on XC kernel approximations.[30−45]
We have presented a small assessment and comparison of interaction-strength interpolation (ISI) and modified interaction-strength interpolation (mISI) methods showing that the utilization of the modified plus continuum (PC) model in ISI formula leads always to the improvement in the results
Summary
The exact exchange−correlation (XC) functional can be formally defined using the adiabatic connection formalism as[1−7]. Because GL2 depends on all occupied and unoccupied orbitals and orbital energies, its evaluation even with OEPx orbitals is still very expensive In this sense, semilocal approximations of EcGL2[ρ] are of interest for simplification of the ISI and mISI methods and for the development of correlation functionals compatible with exact exchange.[68,69] in our assessment, we consider the mISI@TPSS-GL2 method that replaces the true GL2 with the TPSS-GL2 metageneralized-gradient approximation (meta-GGA) correlation functional,[68] which is one of the most accurate GL2 approximations available nowadays (see Table S12 of ref 70 for a comparison of few GL2 models).
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