Lower-Bound Procedure for Energy Eigenvalues by the Partitioning Technique

Abstract

A lower‐bound procedure for obtaining energy eigenvalues by use of the partitioning technique and bracketing theorem, which have been developed by Löwdin, is extended to the case of a multidimensional reference manifold and is applied to the ground state of the two‐electron isoelectronic series. Except for H⁻, the agreement between upper and lower bounds is quite satisfactory. The process of obtaining lower bounds for excited states is considered.