Structure and Symmetry Properties of Correlation Functions in the Sinanoğlu Nonclosed-Shell Many-Electron Theory

The general nonclosed-shell many-electron theory of Sinanoğlu is analyzed to show the structure of the correlation functions which arise. A particular representation of these functions as projections from the exact many electron wavefunction is developed. The origin of the three distinct types of correlation effects—internal, semi-internal, and all external—present in open shell states is discussed. The representation of the correlation functions as projections is employed to examine their transformation properties under the operations of the symmetry group of the Hamiltonian.