Strictly-correlated-electron approach to excitation energies of dissociating molecules

Abstract

In this work we consider a numerically solvable model of a two-electron diatomic molecule to study a recently proposed approximation based on the density-functional theory of so-called strictly correlated electrons (SCE). We map out the full two-particle wave function for a wide range of bond distances and interaction strengths and obtain analytic results for the two-particle states and eigenenergies in various limits of strong and weak interactions, and in the limit of large bond distance. We then study the so-called Hartree-exchange-correlation (Hxc) kernel of time-dependent density functional theory which is a key ingredient in calculating excitation energies. We study an approximation based on adiabatic SCE (ASCE) theory which was shown to display a particular feature of the exact Hxc-kernel, namely a spatial divergence as function of the bond distance. This makes the ASCE kernel a candidate for correcting a notorious failure of the commonly used adiabatic local density approximation (ALDA) in the calculation of excitation energies of dissociating molecules. Unlike the ALDA, we obtain non-zero excitation energies from the ASCE kernel in the dissociation regime but they do not correspond to those of the true spectrum unless the interaction strength is taken to be very large such that the SCE theory has the right regime of validity, in which case the excitation energies become exact and represent the so-called zero point oscillations of the strictly correlated electrons. The commonly studied physical dissociation regime, namely large molecular separation at intermediate interaction strength, therefore remains a challenge for density functional approximations based on SCE theory. arXiv:1901.05266v1 [cond-mat.str-el]

Kinetic Correlation Functionals from the Entropic Regularization of the Strictly Correlated Electrons Problem

“…37 Moreover, this way to do the strongcoupling expansion is not the right one for problems such as bond breaking excitations, because in a molecular system the density close to the atoms remains high: only when we drive the whole system to low density the expansion is really able to capture the right physics. 38 The purpose of this work is to explore a different route, based on the entropic regularization of Optimal Transport, [39][40][41][42] which has been studied in mathematics and economics but also, more recently, has been applied in Data Sciences and Statistical Inference (see, for instance ref 42 and references therein).…”

“…The next leading term in the strong-coupling expansion, corresponding to zero-point oscillations in a metric dictated by the density, provides a “first-order” kinetic correlation energy correction, but it is difficult to evaluate in the general case, with its functional derivative displaying features that are too extreme . Moreover, this way to do the strong-coupling expansion is not the right one for problems such as bond-breaking excitations because in a molecular system, the density close to the atoms remains high: only when we drive the whole system to low density, the expansion is really able to capture the right physics . The purpose of this work is to explore a different route, based on the entropic regularization of optimal transport, − which has been studied in mathematics and economics, as well as, more recently, has been applied in data sciences and statistical inference (see, for instance, ref and references therein).…”