THE COMMON QUANTUM-MECHANICAL PROBLEM FOR THE WHOLE CLASS OF ALKANES AS A MATRIX GENERALIZATION OF THE DEFINITE 2-LEVEL PROBLEM

The common hamiltonian matrix for the whole class of alkanes (H) has been considered as a generalization of the definite two-dimensional matrix (h), where the usual Coulomb and resonance parameters are replaced by the N x N-dimensional matrices (N stands for the number of chemical bonds in an alkane). A similar relation between the two analytical expressions for the one-electron density matrices of alkanes and of the relevant two-level two-electron system described by the hamiltonian matrix h has been established. The block-diagonalization procedure for the matrix H following from the Brillouin theorem and resulting in the localized MOs (LMOs) of alkanes has been shown to be an analogous matrix generalization of the usual eigenvalue problem for the two-dimensional matrix h. These results imply a kind of similarity between the class of alkanes and the unique two-level system and form the basis for describing the former as a single quantum-mechanical object. The relation between the actual occupation numbers of the bond orbitals and the extent of delocalization of the respective LMOs and the proportionality of the stabilization energy to the total delocalization of the occupied LMOs have been shown to result from the established similarity between alkanes and the two-level system.