Basis convergence of range-separated density-functional theory

Abstract

Range-separated density-functional theory is an alternative approach to Kohn-Sham densityfunctional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the oneelectron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with the cardinal number X of the Dunning basis sets cc-p(C)VXZ, and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.

Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights

“…These observations were expected given the demonstrated exponential convergence of long-range correlation energies with respect to the cardinal number. 58 For reaction barrier heights, both the full-range and range-separated methods are relatively weakly dependent on the basis set. We now discuss results for the full-range and rangeseparated MP2, dRPA-I, and RPAx-SO2 methods on the larger AE49 and DBH24/08 datasets.…”

Excited states from range-separated density-functional perturbation theory

“…However, if the partial electron-electron interaction is only a relatively weak long-range interaction, we would expect a faster convergence of the eigenstates and eigenvalues with respect to the one-and many-electron CI expansion than for the full Coulomb interaction [50,52], so that a small CI or multi-configuration self-consistent field (MCSCF) calculation would be sufficiently accurate.…”

Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method

“…It would also be interesting to apply linear-response time-dependent DFT on our OEP-based self-consistent DH scheme to calculate excitation energies. Finally, the present procedure should be applied to the range-separated DH approach [94] which has the advantage of having a fast basis convergence [95].…”