Restoring Size Consistency of Approximate Functionals Constructed from the Adiabatic Connection

Abstract

Approximate exchange–correlation functionals built by modeling in a nonlinear way the adiabatic connection (AC) integrand of density functional theory have many attractive features, being virtually parameter-free and satisfying different exact properties, but they also have a fundamental flaw: they violate the size-consistency condition, crucial to evaluate interaction energies of molecular systems. We show that size consistency in the AC-based functionals can be restored in a very simple way at no extra computational cost. Results on a large set of benchmark molecular interaction energies show that functionals based on the interaction strength interpolation approximations are significantly more accurate than second-order perturbation theory.

Investigation of the Exchange-Correlation Potentials of Functionals Based on the Adiabatic Connection Interpolation

“…However, it has been recently shown that this size consistency error can be easily corrected at no additional computational cost. 33 All these tests have concerned only the quality of the computed energies, whereas no information has been gathered on the XC potentials delivered by the functionals.…”

Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

“…Via (42), δF ZPE /δρ(x) indeed introduces a correction in the mid-bond region. In fact, since we have [42] f [ρ D ](x → 0 + ) ∼ log(x) − R + log 2 1 + e −R , (51) from our treatment in section III D, the divergence in the mid-bond region can be readily evaluated inserting (51) (52) For any fixed x = 0, we find δF ZPE /δρ D (R; x) → 0 as R → ∞ while similarly, due to the fact that ω(x) = ω f (x) , a divergence of the XC potential appears also at large x. Thus, the kinetic correlation energy introduced by the ZPE creates a divergence instead of a finite peak in the bond mid-point, and this divergence occurs on a region that shrinks when R → ∞.…”

Communication: Strong-interaction limit of an adiabatic connection in Hartree-Fock theory

“…24,25 Mixing KS DFT with Hartree-Fock (HF) ingredients is an approximation strategy that has a long history in chemistry, already starting with hybrids 1-3,26-29 and double hybrids, 4-7 but also by simply inserting the HF density into a given approximate XC density functional. [30][31][32][33][34][35] Very recently, it has also been observed that rather accurate interaction energies, 36,37 particularly for noncovalent complexes, 38 can be obtained from models for W DFT λ [ρ] that interpolate between the two limits of Eq. (4) -retaining only the first term, GL2, in the GL series -and of Eq.…”

“…To be more precise, −v H (r, [ρ]) is more attractive than the one-body potential v ∞ (r, [ρ]). In fact, the potential v ∞ (r, [ρ]), which has been studied in several works 21,[44][45][46] is generated by a charge that integrates to N − 1, 21,45…”

“…For finite systems, the state Ψ HF ∞ [ρ] is thus more compact than the state Ψ DFT ∞ [ρ]: this is due to the density constraint in the DFT adiabatic connection, which forces Ψ DFT ∞ [ρ] to have the given quantum mechanical density ρ(r). 21,46 We note in passing that, for given occupied HF orbitals, we have the chain of inequalities…”