Alternative separation of exchange and correlation energies in multi-configuration range-separated density-functional theory

Abstract

The alternative separation of exchange and correlation energies proposed by Toulouse et al. [Theor. Chem. Acc. 114, 305 (2005)] is explored in the context of multi-configuration range-separated density-functional theory. The new decomposition of the short-range exchange-correlation energy relies on the auxiliary long-range interacting wavefunction rather than the Kohn-Sham (KS) determinant. The advantage, relative to the traditional KS decomposition, is that the wavefunction part of the energy is now computed with the regular (fully interacting) Hamiltonian. One potential drawback is that, because of double counting, the wavefunction used to compute the energy cannot be obtained by minimizing the energy expression with respect to the wavefunction parameters. The problem is overcome by using short-range optimized effective potentials (OEPs). The resulting combination of OEP techniques with wavefunction theory has been investigated in this work, at the Hartree-Fock (HF) and multi-configuration self-consistent-field (MCSCF) levels. In the HF case, an analytical expression for the energy gradient has been derived and implemented. Calculations have been performed within the short-range local density approximation on H2, N2, Li2, and H2O. Significant improvements in binding energies are obtained with the new decomposition of the short-range energy. The importance of optimizing the short-range OEP at the MCSCF level when static correlation becomes significant has also been demonstrated for H2, using a finite-difference gradient. The implementation of the analytical gradient for MCSCF wavefunctions is currently in progress.

Excited states from range-separated density-functional perturbation theory

“…is a multi-determinantal (md) generalization of the usual short-range Hartree-exchange functional [60][61][62]. Using the variational property of the wave function Ψ µ,l [n], and for non-degenerate wave functions Ψ µ,l=0 [n], the expansion of E …”

“…(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

“…[20] and the references therein), but any separation like the simpler linear one [21] can be considered. Range separation, that is controlled by the µ parameter, is appealing as it enables to isolate the Coulomb hole and assign it to a density functional while long-range correlation can be described in WFT.…”

Polarizable Embedding Density Matrix Renormalization Group

“…As a consequence, dynamical electron correlation must be considered either a posteriori, for instance by perturbation the-ory [61,[65][66][67][68][69][70][71]] (diagonalize-and-then-perturb [72]), or a priori from the outset (in a perturb-and-then-diagonalize approach [72]). We recently investigated the latter option for DMRG [73] by employing a range-separated Hamiltonian [74] that recovers dynamical correlation through DFT by short-range (sr) density functionals (DMRGsrDFT) in close analogy to the MCSCF-srDFT ansatz [75][76][77]. The long-range part is then described by a DMRG wave function ansatz.…”