DIRECT DETERMINATION OF PURE-STATE DENSITY MATRICES .2. CONSTRUCTION OF CONSTRAINED IDEMPOTENT ONE-BODY DENSITIES

A formalism is developed for the determination of a constrained idempotent one-body density matrix P. The method ensures pure-state representability in the Hartree-Fock sense. This is accomplished by minimizing the quantity Tr(P2-P)2 subject to either empirical or theoretical constraints. The method leads to an iterative matrix equation of the form Pn+1=3Pn2-2Pn3+kλk(n)Ok, where -λk is the kth Lagrangian multiplier pertaining to the constraint TrPOk=Ok, and Ok is the expectation value of the observable Ok. Applications to several diatomic molecules are reported using the electrostatic and virial theorems as empirical constraints. Several calculations are carried out in order to corroborate the following result: If the above iterative equations are constrained with a sufficient number of bona fide Hartree-Fock conditions, the solution is the Hartree-Fock P matrix. © 1969 The American Physical Society.