Relationship between the effective potentials determining the density and the pair density

A link between density and pair density functional theories is presented. The method of Levy, Perdew and Sahni is used to derive a relationship between the effective potentials of the Euler equation of the density functional theory and the Pauli potential of the pair density functional theory and between the effective potential for the spherically and system-averaged pair density and the Pauli potential of the pair density functional theory. These expressions can be considered constraints that the Pauli potential and the effective potentials should fulfil. They might be very useful in constructing approximations.