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

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,Ne8+,Be,Ne6+ as well as for the exponential densities nN,ζ(r)=N(ζ3/π)e−2ζr (N=2 or 4; ζ⩾1; for N=4 degeneracy is present and 1D and 3P 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.