Cluster expansion of the wavefunction. Structure of the closed-shell orbital theory

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Abstract
A new approach to the closed‐shell orbital theory is presented with the formalism of the cluster expansion of the wavefunction. The four independent excitation operators are used to represent the general determinantal wavefunction and also to discuss the stability of the Hartree–Fock solution. This leads to a new concept called the ’’stability dilemma,’’ which is the key not only in understanding the structure of the orbital theory but also for the extension of the orbital model. Only when the stability dilemma is removed, the correlation effect is taken into account within the framework of the orbital approximation. The closed‐shell orbital theory including the electron correlation is defined as ‖Φ〉=P exp[iF]‖0〉, where the F is the excitation operator to generate the variational space and the P is the projection operator to remove the stability dilemma. The various orbital theories (some are known but some are new) can be obtained by appropriate choices of the F and P. It is shown that the above cluster expression makes it possible to analyze and interconnect the various orbital theories in the form of the limited CI based on their own natural orbitals. The complex DODS theory is proposed. This new orbital theory is the most suitable one to include the correlation effect within the orbital model in the closed‐shell system.