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    Exact differential and integral constraints for the Pauli potential in the pair density functional theory

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    In the ground state the pair density n can be determined by solving a single auxiliary equation of a two-particle problem. Exact differential and integral constraints for the Pauli potential of the effective potential of the two-particle equation are presented. The constraints are derived using the differential virial theorem and the Hiller-Sucher-Feinberg identity

    Effective potential in density matrix functional theory

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    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 function equation and the potential v(p) is established
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