Application of cluster expansion techniques to open shells: Calculation of difference energies

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Abstract
In this paper, we have tested the efficacy of a recently developed nonperturbative open‐shell formalism in generating such difference energies as ionization potential (I. P.), electron affinity (E. A.) and excitation energy (E. E.). In the formalism, the difference energies come out directly as eigenvalues of a non‐Hermitian eigenproblem. Two different kinds of cluster expansion about multideterminant ‘‘model’’ wave functions have been considered: (a) an ordinary Ursell–Mayer type exponential form of cluster expansion; and (b) a normally ordered exponetial cluster ansatz. The key theoretical concept underlying our development is a generalization of the ‘‘core‐valence separability’’ concept of the open‐shell manybody perturbation theory which we have termed the ‘‘subsystem embedding condition’’ (SEC). SEC allows us to start with the zero valence problem and offers an unambiguous way of building up the successive one, two, ..., n‐valence problems hierarchically furnishing the difference energies. I. P., E. A., and E. E. of a selection of nitrogen heterocycles under the π‐electron approximation have been calculated and the performance of the methods has been assessed against the ‘‘model exact’’ full CI results. The trend of the results has been found to be encouraging.