Reduced Density Matrices of Atoms and Molecules. I. The 2 Matrix of Double-Occupancy, Configuration-Interaction Wavefunctions for Singlet States

Certain general features of the second-order reduced density matrix, or 2 matrix, for configuration-interaction (CI) wavefunctions are reviewed, with special reference to the simplifying features of spin singlet states. A restricted form of CI in which all spatial orbitals are doubly occupied (DOCI) is proposed for singlet states. The 2 matrix of the DOCI function is derived and shown to have an extremely simple (largely diagonal) structure in a spin symmetry basis of Heitler—London-like geminals constructed from the natural orbitals of the system. Of the three types, λi, Λij, λij, of nonvanishing 2-matrix elements, the λi are shown to be the occupation numbers of the 1 matrix, the Λij are occupation numbers of the 2 matrix, while the off-diagonal λij mix together the uncorrelated basis geminals to produce correlated natural geminals of singlet ``homogeminal'' type. The structural features of the DOCI 2 matrix are interpreted in terms of electronic correlation, and the physical applicability of the DOCI model is discussed.