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 b een considered as a generalization of the definite two-dimensional mat rix (h), where the usual Coulomb and resonance parameters are replaced by the N x N-dimensional matrices (N stands for the number of chemica l bonds in an alkane). A similar relation between the two analytical e xpressions for the one-electron density matrices of alkanes and of the relevant two-level two-electron system described by the hamiltonian m atrix 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 mat rix generalization of the usual eigenvalue problem for the two-dimensi onal matrix h. These results imply a kind of similarity between the cl ass of alkanes and the unique two-level system and form the basis for describing the former as a single quantum-mechanical object. The relat ion between the actual occupation numbers of the bond orbitals and the extent of delocalization of the respective LMOs and the proportionali ty of the stabilization energy to the total delocalization of the occu pied LMOs have been shown to result from the established similarity be tween alkanes and the two-level system.