Block-diagonalization problem for the common Hückel-type Hamiltonian matrix of alternant hydrocarbons and its nonperturbative solution

The block‐diagonalization problem originating from the Brillouin theorem and determining the noncanonical molecular orbitals (NCMOs) has been formulated and solved for the common Hamiltonian matrix H of alternant hydrocarbons in the framework of the simple Hückel model. The well‐known way of partitioning of the total basis set of 2pz AOs of carbon atoms of these molecules into two subsets allowed the problem to be solved nonperturbatively in terms of entire subsets of atomic orbitals (AOs), and thereby of respective submatrices (blocks) of the matrix H, without specifying either the internal structures or dimensions of the latter. As a result, the NCMOs of alternant hydrocarbons proved to be characterized by common peculiarities, including uniform total extents of delocalization. A close relationship has been established between the block‐diagonalization problem under study and the commutation equation determining the respective one‐electron density matrix (DM) directly without invoking the canonical molecular orbitals (CMOs). In particular, the off‐diagonal blocks both of the NCMO representation matrix C and of the DM P were shown to follow from the same matrix condition originally suggested by G. G. Hall on the basis of structures of CMOs of alternant hydrocarbons. The relationship between the two fundamental noncanonical problems gave an additional insight into the origin of the observed similarity between constitutions of matrices C and P. It has been concluded on this basis that the common DM of alternant hydrocarbons (the charge‐bond order matrix) is among noncanonical (localized) ways of describing electronic structures whatever the actual method of its derivation. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005