EXPANSIONS OF THE PAIR DISTRIBUTION FUNCTION AND THE 2ND-ORDER DENSITY-MATRIX IN TERMS OF HOMOGENEOUS FUNCTIONALS

It has been shown previously that under certain circumstances the corr elation energy density functional E(c)[rho] and its kinetic T-c[rho] a nd potential V-c[rho] components can be expanded in terms of homogeneo us functionals A(n)[rho], with n = 1,2,3,..., and where A(n)[rho] is h omogeneous of degree (1-n) with respect to coordinate scaling. In this paper, we extend the analysis to expand similarly the pair distributi on function g(NC)([rho];r(1),r(2)) and the second-order density matrix rho(2)(r(1),r(2)). It is found that both of them can be expanded unde r certain circumstances in terms of functionals a(n)([rho];r(1),r(2)), with n = 1,2,3,..., that are homogeneous of degree - n incoordinate s caling. The A(n)[rho] are explicitly obtained in terms of the a(n)([rh o];r(1),r(2)).