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 W_λ, the integrand in the adiabatic connection (AC) with λ representing the coupling constant. Besides utilizing the two leading terms of each asymptotic expansion of W_λ at λ = 0 and ∞, the ISIN extends the coupling constant X 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 W_λ when W0, the slope at λ = 0, goes to -∞, which leads to much more negative correlation energies for real systems.
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