Perturbational non-canonical theory of molecular orbitals and its applications

TL;DR

This paper presents a generalized perturbational non-canonical molecular orbital (PNCMO) theory that extends traditional methods by using block-diagonalization and non-commutative perturbation theory to analyze molecular structures and properties.

Contribution

The paper introduces a novel PNCMO theory that generalizes existing approaches through non-canonical problems and non-commutative perturbation theory, providing new algebraic expressions for quantum-chemical characteristics.

Findings

Derived algebraic expressions for molecular properties.

Applied theory to saturated and conjugated hydrocarbons.

Proposed a new framework for qualitative chemical analysis.

Abstract

The article contains a summary of fundamentals of the perturbational non- canonical molecular orbital (PNCMO) theory formerly developed by the author. In some respects, the PNCMO theory is a generalization of the well-known simple PMO theory: First, the usual diagonalization problem (and/or the eigenvalue equation) for a certain model Hamiltonian matrix ($\mathbf{H}$) is now replaced by two interrelated non-canonical one-electron problems, namely by the block-diagonalization problem for the matrix $\mathbf{H}$\ following from the Brillouin theorem and determining non-canonical (localized) MOs (NCMOs) and by the commutation equation for the respective one-electron density matrix (charge-bond order (CBO)) matrix. Second, perturbative solutions of the above-specified alternative problems are sought in terms of entire submatrices (blocks) of the matrix $\mathbf{H}$\ instead of usual matrix elements (e.g. of Coulomb and resonance parameters). Third, a generalized version of the perturbation theory (PT) is used in place of the standard Rayleigh-Schr\"{o}dinger PT (RSPT), wherein non-commutative quantities stand for the usual (commutative) ones (cf. the so-called non-commutative RSPT (NCRSPT)). As a result, algebraic expressions are derived for the principal quantum-chemical characteristics (including the CBO matrix, the NCMO representation matrix and the total energy) that embrace definite classes of Hamiltonian matrices and thereby of molecules. To illustrate the point, saturated and conjugated hydrocarbons are taken as examples. Arguments are given that the PNCMO theory possibly forms the basis of a novel way of qualitative chemical thinking.