Correlation energy generating potentials for molecular hydrogen

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Abstract
A variety of local correlation energy functionals are currently in use. All of them depend, to some extent, on modeling the correlation energy of a homogeneous electron fluid. Since atomic and molecular charge densities are neither uniform nor slowly varying, it is important to attempt to use known high accuracy wave functions to learn about correlation energy functionals appropriate to such systems. We have extended the definition of the correlation energy generating potentials Vc introduced by Ros. A charge density response to correlation has been allowed for by inclusion of an electron–nuclear component Venc in addition to the electron–electron component Veec. Two different definitions of Venc are given. We present the first calculations of Vc for a molecular system—H2. The results show that Venc, in either definition, is by no means negligible. Moreover, Veec and both forms of Venc show significant nonlocal dependence on the charge density. Calculations with ten different model correlation energy functionals show that none of them is particularly sensitive to the charge density. However, they are quite sensitive to the parametrization of the electron fluid correlation energy. The schemes which include self-interaction corrections (SIC) are found to be superior to those of Kohn–Sham type. The correlation energy generating potentials implied by the SIC type and empirical correlation energy functionals are found to correspond roughly to averages of one of the accurate potentials.