Gradient Expansions for the Large-Coupling Strength Limit of the Møller-Plesset Adiabatic Connection.

The adiabatic connection that has, as weak-interaction expansion, the Møller-Plesset perturbation series has been recently shown to have a large coupling-strength expansion, in terms of functionals of the Hartree-Fock density with a clear physical meaning. In this work, we accurately evaluate these density functionals and we extract second-order gradient coefficients from the data for neutral atoms, following ideas similar to the ones used in the literature for exchange, with some modifications. These new gradient expansions will be the key ingredient for performing interpolations that have already been shown to reduce dramatically MP2 errors for large noncovalent complexes. As a byproduct, our investigation of neutral atoms with large number of electrons N indicates that the second-order gradient expansion for exchange grows as N log(N) rather than as N, as often reported in the literature.

Variations of the Hartree-Fock fractional-spin error for one electron.

Fractional-spin errors are inherent in all current approximate density functionals, including Hartree-Fock theory, and their origin has been related to strong static correlation effects. The conventional way to encode fractional-spin calculations is to construct an ensemble density that scales between the high-spin and low-spin densities. In this article, we explore the variation of the Hartree-Fock fractional-spin (or ghost-interaction) error in one-electron systems using restricted and unrestricted ensemble densities and the exact generalized Hartree-Fock representation. By considering the hydrogen atom and H+ 2 cation, we analyze how the unrestricted and generalized Hartree-Fock schemes minimize this error by localizing the electrons or rotating the spin coordinates. We also reveal a clear similarity between the Coulomb hole of He-like ions and the density depletion near the nucleus induced by the fractional-spin error in the unpolarized hydrogen atom. Finally, we analyze the effect of the fractional-spin error on the Møller-Plesset adiabatic connection, excited states, and functional- and density-driven errors.

Noncovalent Interactions from Models for the Møller-Plesset Adiabatic Connection.

Given the omnipresence of noncovalent interactions (NCIs), their accurate simulations are of crucial importance across various scientific disciplines. Here we construct accurate models for the description of NCIs by an interpolation along the Møller-Plesset adiabatic connection (MP AC). Our interpolation approximates the correlation energy, by recovering MP2 at small coupling strengths and the correct large-coupling strength expansion of the MP AC, recently shown to be a functional of the Hartree-Fock density. Our models are size consistent for fragments with nondegenerate ground states, have the same cost as double hybrids, and require no dispersion corrections to capture NCIs accurately. These interpolations greatly reduce large MP2 errors for typical π-stacking complexes (e.g., benzene-pyridine dimers) and for the L7 data set. They are also competitive with state-of-the-art dispersion enhanced functionals and can even significantly outperform them for a variety of data sets, such as CT7 and L7.

Large coupling-strength expansion of the Møller-Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms.

We study in detail the first three leading terms of the large coupling-strength limit of the adiabatic connection that has as weak-interaction expansion the Møller-Plesset perturbation theory. We first focus on the H atom, both in the spin-polarized and the spin-unpolarized cases, reporting numerical and analytical results. In particular, we derive an asymptotic equation that turns out to have simple analytical solutions for certain channels. The asymptotic H atom solution for the spin-unpolarized case is then shown to be variationally optimal for the many-electron spin-restricted closed-shell case, providing expressions for the large coupling-strength density functionals up to the third leading order. We also analyze the H2 molecule and the uniform electron gas.

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

We have studied the correlation potentials produced by various adiabatic connection models (ACMs) for several atoms and molecules. The results have been compared to accurate reference potentials (coupled cluster and quantum Monte Carlo results) as well as to state-of-the-art ab initio DFT approaches. We have found that all the ACMs yield correlation potentials that exhibit a correct behavior, quite resembling scaled second-order Görling-Levy (GL2) potentials and including most of the physically meaningful features of the accurate reference data. The behavior and contribution of the strong-interaction limit potentials have also been investigated and discussed.