Simultaneous equations for calculating the pair density

We propose a practical scheme for calculating the pair density (PD) on the basis of the density functional theory. In order to avoid the N-representability problem of the PD, we implement the variational principle within the set of PDs that are constructed from the single Slater determinants (SSDs). For the kinetic energy functional, we utilize the approximate form that is developed by means of the electron-coordinate scaling laws. The variational principle results in the simultaneous equations for constituent orbitals of the SSD. It yields the best one within the SSD-representable PDs.