TOWARDS A UNIFIED LOCALIZED DESCRIPTION OF THE ELECTRONIC-STRUCTURE OF SATURATED ORGANIC-MOLECULES

The common one-electron density matrix (DM) for saturated organic molecules in the basis of bond orbitals (BOs) and the relevant representation matrix of the localized MOs (LMOs) are expected to be interrelated analogously to those of alkanes (V. Gineityte, J. Mol. Struct. (Theochem), 288 (1993) 111). Accordingly, a single procedure yielding both matrices and implying the feasibility of a unified localized description of saturated molecules is being sought. To this end two relevant non-canonical problems, i.e. the commutation relation for the DM and the respective hamiltonian matrix and the Brillouin theorem for LMOs, are analyzed and compared. The 2n-dimensional space of BOs for a saturated system containing 2n electrons is divided into two n-dimensional subspaces of bonding and antibonding BOs, respectively. The off-diagonal intersubspace blocks of both the LMO representation matrix and the DM are shown to be determined by common equations, whereas the relevant diagonal blocks are expressed algebraically in terms of the off diagonal ones. Solving the above common equations is concluded to be sufficient to obtain the LMOs and DM of saturated organic molecules on a unified basis.