Second-order effects in the Hückel model of perturbed alternant hydrocarbons and their coincidence for specific one- and two-center perturbations

Explicit algebraic expressions are derived and analyzed for the second‐order corrections to the charge‐bond order (CBO) matrix of perturbed alternant hydrocarbons (PAHs) in terms of entire blocks of the common Hamiltonian matrix of parent AHs in the framework of the simple Hückel model. The derivation is based on the direct means of solution of the commutation equation for the one‐electron density matrix by means of passing to the basis of noncanonical molecular orbitals of parent AHs followed by application of the noncommutative Rayleigh–Schrödinger perturbation theory and retransformation of the results into the initial basis of 2pz AOs of carbon atoms. The second‐order corrections obtained are shown to determine alterations in bond orders between chemically bound pairs of atoms under influence of the most popular types of perturbation, viz. changes in the Coulomb parameter(s) and emergence of new intermolecular resonance parameter(s). The same corrections are also demonstrated to play an important role in the formation of stabilization energies of PAHs vs. those of parent AHs. On this basis, an additional insight is given into the content of the classical formulae for total energies of PAHs in terms of self‐polarizabilities of atoms and bonds, viz. an energy correction is shown to be made up of a difference between the primary stabilizing contribution of perturbation (which is twice as large as the final stabilization energy) and the destabilizing increment related to weakening of remaining chemical bonds. A detailed comparison of CBO matrices and stabilization energies is made for compounds originating from the same parent hydrocarbon (R) after perturbation of the Coulomb parameter of a certain AO χr and after building up a composite AH RR′ by formation of a new bond between AOs χr and χ r′ of two identical AHs R and R′ (e.g., pyridine and biphenyl). The first‐order corrections to CBO matrices of these systems are shown to be expressible in terms of the same submatrices, whereas the respective second‐order corrections contain coinciding submatrices referring to parent fragments R and R′. As a result, coincidences are established (i) between the self‐polarizability of the rth atom of the parent AH R and that of the bond between atoms r and r′ of the composite AH RR′, (ii) between alterations in orders of chemical bonds due to both types of perturbation, and (iii) between stabilization energies referring to a single fragment R or R′ under an assumption