Löwdin’s bracketing function revisited

A variational principle is formulated for Löwdin’s bracketing function. Setting the bracketing function stationary leads to the eigenvalue equation of the resolvent operator. An Eckart-type inequality is derived for the wavefunction optimized this way. A linearized approximation of the resolvent eigenvalue equation—reminiscent of the simplest coupled electron pair (CEPA0) treatment—is examined. We prove that the asymmetric energy formula of the resulting approximate function is a strict lower bound.