DIRECT DETERMINATION OF PURE-STATE DENSITY MATRICES .V. CONSTRAINED EIGENVALUE PROBLEMS

A density-matrix approach to constrained eigenvalue problems is presented. It is shown that all of the linearly independent eigenvectors of an Hermitian matrix can be generated with the idempotency equations (P equations) developed in previous papers of this series. In particular, the method is applied to variational calculations in H2+ and He. Since the local-energy method assumes eigenvalue form, it also can be formulated in terms of the P equations. Various local energies for H2+ and He are calculated. Direct methods of incorporating local energies as constraints are suggested. An orthogonal operator formalism for the P equations is given. Such operators ok, Ol have the property that TrOkOl=0 for kL. The iterative P equations, then, assume the simple form Pn+1=Pn+k[(Ok-TrPOk)TrOk2]Ok, where P3P2-2P2 and the constraints, TrPOk=Ok, are now identically satisfied. © 1969 The American Physical Society.