Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

Abstract

We derive an explicit expression for the functional derivative of the subleading term in the strong interaction limit expansion of the generalized Levy-Lieb functional for the special case of two electrons in one dimension. The expression is derived from the zero point energy (ZPE) functional, which is valid if the quantum state reduces to strongly correlated electrons in the strong coupling limit. The explicit expression is confirmed numerically and respects the relevant sum-rule. We also show that the ZPE potential is able to generate a bond mid-point peak for homo-nuclear dissociation and is properly of purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems, whereas the exact peaks should be finite.

Modified Interaction-Strength Interpolation Method as an Important Step toward Self-Consistent Calculations

“…We recall here that the exact SCE potential decays as −1/ r in the tail of the density. On the other hand, it was shown recently 117 that the functional derivative of an exact W ∞ ′ diverges in the tail for one-dimensional systems. This might indicate that the divergence is an exact feature of W ∞ ′ and W ∞ ′PC is a more accurate model.…”

Gradient expansions for the large-coupling strength limit of the Møller-Plesset adiabatic connection

“…. r min N } in eq (9), in turn, determine the next leading term, for which eq (7) provides a rigorous variational estimate for closed-shell systems. 20 This term is given by zero-point oscillations around the minimizing positions enhanced by the exchange operator K, which mixes in excited harmonic oscillator states.…”

“…20 These first three leading terms provide a rigorous framework to link MP perturbation theory with DFT, in terms of functionals of the HF density. In practice, we do not want to perform each time the classical minimization of eq (9), which is known to have many local minima and whose cost increases rapidly with N . We rather wish to find good semilocal approximations for the first two terms in the expansion (5).…”

“…The functional E el [ρ] of eq (9) is obtained by letting Ψ relax to its minimum in eq (17), which directly implies…”

“…2 In the opposite limit of large-coupling strengths (λ → ∞), the correlation energy is determined by the strictlycorrelated-electrons (SCE) physics, [3][4][5][6] which yields the leading term. The next order is given by zero-point (ZP) oscillations [7][8][9][10] around the SCE manifold. A possible strategy to build approximations for the correlation energy is to interpolate between these two opposite limits, generalizing to any non-uniform density 7,[11][12][13][14][15][16] the idea that Wigner 17 used for jellium.…”