Interpretation of the Fermi hole curvature

Abstract

Two different interpretations are given for the Fermi hole curvature parameter used recently by Stoll et al., by Colle and Salvetti and by Becke to estimate the size of the correlation hole, by Becke et al. to clarify aspects of chemical shell structure and bonding, and by Luken and Culbertson to discuss mobility of the Fermi hole. The first, more straightforward interpretation involves the number of ‘‘other’’ electrons to be found in a small neighborhood near a given electron. The notion of other electrons leads naturally to correlation functionals which correctly vanish when only one electron is present. The second interpretation, made explicit by use of the Wigner pair distribution, involves the density of relative kinetic energy of pairs of spin-parallel electrons at point r. Since, in a classical interpretation at least, the correlation hole in a nonuniform Coulomb system depends both on density and relative kinetic energy of colliding pairs, one expects that both the Fermi hole curvature and the density should be significant in constructing theories of the correlation energy of such systems.