Range separation combined with the Overhauser model: Application to the H₂ molecule along the dissociation curve

Abstract

ABSTRACT:The combination of density-functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution (range separation) is a successful strategy, which is raising more and more interest in recent years. We focus here on a range-separated method in which only the short-range correlation energy needs to be approximated, and we model it within the "extended Overhauser approach." We consider the paradigmatic case of the H 2 molecule along the dissociation curve, finding encouraging results. By means of very accurate variational wavefunctions, we also study how the effective electron-electron interaction appearing in the Overhauser model should be to yield the exact correlation energy for standard Kohn-Sham density functional theory.

Multi-configuration time-dependent density-functional theory based on range separation

“…The situation is of course less critical for larger µ values but, in this case, more electron correlation must be described by the MCSCF which is not appealing, in terms of computational cost, for larger scale calculations. Using a multi-configuration short-range exact exchange energy expression [58][59][60] while keeping µ = 0.4 a.u. is a possible alternative currently under investigation.…”

Excited states from range-separated density-functional perturbation theory

“…(17) properly reduces to the long-range Hamiltonian at l = 0,Ĥ µ,l=0 =Ĥ lr,µ , whereas, at l = 1, it correctly reduces to the physical Hamiltonian,Ĥ µ,l=1 =Ĥ. This is so because the short-range Hartree-exchange-correlation potential in the HamiltonianĤ lr,µ can be decomposed aŝ (22) corresponds to an alternative decomposition of the short-range Hartree-exchangecorrelation energy into "Hartree-exchange" and "correlation" contributions based on the multi-determinantal wave function Ψ µ 0 instead of the single-determinant KS wave function Φ KS 0 [60][61][62], which is more natural in range-separated DFT. This decomposition is especially relevant here since it separates the perturbation into a "Hartree-exchange" contribution that is linear in l and a "correlation" contribution containing all the higher-order terms in l.…”

On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation

“…Consequently, as already pointed out by Gori-Giorgi and Savin [32], even an infinitesimal µ value ensures that K µ is not strictly equal to zero, thus providing the correct multi-configurational description of the dissociated H 2 molecule in the ground state:…”