Extension to Negative Values of the Coupling Constant of Adiabatic Connection for Interaction-Strength Interpolation

Abstract

A new exchange and correlation functional, called ISIN here, of the fifth rung of Jacob’s ladder is presented. It is based on the explicit approximation of Wλ, the integrand in the adiabatic connection (AC) with λ representing the coupling constant. Besides utilizing the two leading terms of each asymptotic expansion of Wλ at λ = 0 and ∞, the ISIN extends the coupling constant λ to negative values (i.e., to attractive electron−electron interactions). For the simple system of two electrons on the surface of a sphere (2ESS), the correlation energies yielded by the ISIN are in excellent agreement with the exact values. However, the ISIN seriously fails to approximate Wλ when W0′, the slope at λ = 0, goes to −∞, which leads to much more negative correlation energies for real systems.