Extended constrained-search theory and its applications

Very recently, we have proposed an approximate scheme for calculating the PD on the basis of the extended constrained-search theory [10–14]. By introducing a noninteracting reference system [10,11], the resultant PD corresponds to the best solution within the set of PDs that are constructed from a single Slater determinant (SSD). This PD functional theory has two kinds of merit. The first is that the reproduced PD is necessarily N-representable. This is a strong merit because the necessary and sufficient conditions for the N-representable PD are not yet known exactly. The second merit is the tractable form of the kinetic energy functional. The kinetic energy functional cannot exactly be written by using the PD alone. Some approximation is required. In this theory, we have successfully given an approximate form of the kinetic energy functional with the aid of the coordinate scaling of electrons [10].