Local approximation of the correlation energy functional in the density matrix functional theory

A local approximation formula of the correlation energy functional E, in terms of the first-order reduced density matrix (1-RDM) is :presented. With the contracted Schrodinger equation the principal dependence of E-c on the natural occupation numbers n(i) is identified. Using the effective mass theory, E-c is expressed as a functional of the local density and the local variable, J = Sigma(i)rootn(i)(1 - n;)\phi(i)\(2) where So; are the natural spin orbitals. This local approximation satisfies the homogeneous coordinate scaling relation, gives the exact result for a one-electron system, and is almost free from the exchange energy error. It reproduced about 90% off the correlation energies of atoms and molecules.