Localized molecular orbitals in the Hückel model of perturbed alternant hydrocarbons and their relation to the charge-bond order matrix

An interrelation is expected between the charge–bond order matrix and the relevant representation matrix of noncanonical (localized) molecular orbitals (NCMOs) of perturbed alternant hydrocarbons (PAHs), as was the case with parent AHs. Accordingly, a single procedure is developed to obtain these matrices directly on the basis of solution of respective noncanonical one‐electron problems in the framework of the simple Hückel model, i.e., of the commutation equation for the one‐electron density matrix and of the block‐diagonalization problem for the Hamiltonian matrix, the latter originating from the Brillouin theorem. The procedure consists of three principal steps: (i) an initial passing to the basis of NCMOs of parent AHs by means of the nonperturbative block diagonalization of the relevant common Hamiltonian matrix (H) represented in the basis of 2pz AOs of carbon atoms; followed by (ii) application of the noncommutative Rayleigh–Schrödinger perturbation theory to solve the above‐specified noncanonical problems; and (iii) subsequent retransformation of the power series obtained into the initial basis of 2pz AOs. Rederivation of the classical results concerning the charge and bond order redistributions in AHs due to perturbation (including the rule of the alternating polarity for one‐center perturbations) following from the above‐described procedure indicates that these results are actually part of the noncanonical theory of MOs for PAHs. The principal achievement of the study, however, consists of obtaining general algebraic expressions for the common NCMO representation matrix of PAHs in terms of submatrices (blocks) of the relevant charge–bond order matrix. These expressions permit not only investigation of the effect of perturbation on the shapes of localized MOs, but also demonstrate the relationship between the given reshaping of these MOs and the respective charge redistribution. For local perturbations of a specific Coulomb parameter, reshaping of a single NCMO is shown to reflect the rule of the alternating polarity, namely of NCMO whose principal AO coincides with the site of perturbation. Moreover, the overall reshaping pattern of NCMOs was found in line with predictions of the simple resonance theory about increased contributions of certain quinoidal structures to the electronic structures of PAHs due to perturbations. NCMOs of pyridine and biphenyl molecules are studied in detail as examples. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem,