Energy density functionals from the strong-coupling limit applied to the anions of the He isoelectronic series

Abstract

Anions and radicals are important for many applications including environmental chemistry, semiconductors, and charge transfer, but are poorly described by the available approximate energy density functionals. Here we test an approximate exchangecorrelation functional based on the exact strong-coupling limit of the HohenbergKohn functional on the prototypical case of the He isoelectronic series with varying nuclear charge Z < 2, which includes weakly bound negative ions and a quantum phase transition at a critical value of Z, representing a big challenge for density functional theory. We use accurate wavefunction calculations to validate our results, comparing energies and Kohn-Sham potentials, thus also providing useful reference data close to and at the quantum phase transition. We show that our functional is able to bind H − and to capture in general the physics of loosely bound anions, with a tendency to strongly overbind that can be proven mathematically. We also include corrections based on the uniform electron gas which improve the results.

Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

“…66,102 Here, local interpolation models are constructed from energy densities acquired by the Lieb maximization at the FCI level, as described in section 2.4, in the range 0 ≤ λ ≤ 1 and at λ = ∞ by evaluating the SCE functional on the λ = 1 density, also at the FCI level of theory.…”

Electron avoidance: A nonlocal radius for strong correlation

“…7 for a self-consistent treatment of the helium atom, both with the KS-NLR functional (52) and the KS-SCE functional. Both strong-correlation functionals gives a self-consistent energy which is low compared to the exact (−3.278 in KS-NLR and −3.357 in KS-SCE [43], whereas the true energy of helium is −2.904 [82]), and both also give a helium density much too contracted. This contraction gives KS-SCE and KS-NLR a larger kinetic energy and a more-negative potential energy than the exact helium atom.…”

“…8), resulting in severe overbinding [43]. The KS-SCE HOMO, however is often a good approximation to the affinity [34,43].…”

“…In the three dimensional (3D) case, algorithms to compute the SCE functional are currently applicable only to spherically symmetric systems, although progress is being made by several groups exploiting the formal similarity between the SCE problem and optimal transport (or mass transportation) theory [36][37][38][39][40][41], a field of mathematics and economics [42]. Another crucial point is that SCE requires suitable corrections [34,43] (e.g., local or semilocal) to make it useful for chemistry and solid-state physics, where both the strong and the weak correlation regimes need to be treated accurately by the same methodology. Despite these challenges, hybridizing with the SCE functional (or an approximation thereof) holds the promise of remedying strong correlation failures in present KS-DFT functionals.…”

The Importance of Being Inconsistent

“…For the most extreme example, see also Refs [MUMG14;GB15]. Using a reasonable basis set is often used to coax an electron affinity from a standard functional when evaluating on a data base involving anions [CPR10;HSXR13].…”