Correlation energies for some two- and four-electron systems along the adiabatic connection in density functional theory

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Abstract
Switching on the electron–electron interaction connects the Kohn–Sham to the physical system. The correlation energy, the only unknown energy component in this process, is determined at fixed density, using a technique based on the Lieb Legendre transform definition of the universal density functional. Results are shown for this adiabatic coupling process for He,Ne 8+ ,Be,Ne 6+ as well as for the exponential densities n N,ζ (r)=N(ζ 3 /π)e −2ζr (N=2 or 4; ζ⩾1; for N=4 degeneracy is present and 1 D and 3 P are analyzed). The data are fitted to a rational approximant and appear to be in good agreement with those given by the less computationally demanding Harris–Jones adiabatic connection.