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 th e physical system. The correlation energy, the only unknown energy componen t in this process, is determined at fixed density, using a technique based on the Lieb Legendre transform definition of the universal density function al. Results are shown for this adiabatic coupling process for He, Ne8+, Be, Ne6+ as well as for the exponential densities n(N,zeta)(r) = N(zeta(3)/pi) e(-2 zeta r) (N = 2 or 4; zeta greater than or equal to 1; for N = 4 degene racy is present and D-1 and P-3 are analyzed). The data are fitted to a rat ional approximant and appear to be in good agreement with those given by th e less computationally demanding Harris-Jones adiabatic connection. (C) 199 9 American Institute of Physics. [S0021-9606(99)30806-0].