Abstract
A variational principle is formulated for Lowdin’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.
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