Effective potential in density matrix functional theory

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Abstract
In the previous paper it was shown that in the ground state the diagonal of the spin independent second-order density matrix n can be determined by solving a single auxiliary equation of a two-particle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a two-particle problem. The effective potential of the two-particle equation contains a term v p of completely kinetic origin. Virial theorem and hierarchy of equations are derived for v p and simple approximations are proposed. A relationship between the effective potential u p of the shape functionequation and the potential v p is established.