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The article contains a summary of fundamentals of the perturbational non-canonical molecular orbital (PNCMO) theory formerly developed by the author. Insome respects, the PNCMO theory is a generalization of the well-known simplePMO theory: First, the usual diagonalization problem (and/or the eigenvalueequation) for a certain model Hamiltonian matrix ($\mathbf{H}$) is now replacedby two interrelated non-canonical one-electron problems, namely by theblock-diagonalization problem for the matrix $\mathbf{H}$\ following from theBrillouin theorem and determining non-canonical (localized) MOs (NCMOs) and bythe commutation equation for the respective one-electron density matrix(charge-bond order (CBO)) matrix. Second, perturbative solutions of theabove-specified alternative problems are sought in terms of entire submatrices(blocks) of the matrix $\mathbf{H}$\ instead of usual matrix elements (e.g. ofCoulomb and resonance parameters). Third, a generalized version of theperturbation theory (PT) is used in place of the standardRayleigh-Schr\"{o}dinger PT (RSPT), wherein non-commutative quantities standfor the usual (commutative) ones (cf. the so-called non-commutative RSPT(NCRSPT)). As a result, algebraic expressions are derived for the principalquantum-chemical characteristics (including the CBO matrix, the NCMOrepresentation matrix and the total energy) that embrace definite classes ofHamiltonian matrices and thereby of molecules. To illustrate the point,saturated and conjugated hydrocarbons are taken as examples. Arguments aregiven that the PNCMO theory possibly forms the basis of a novel way ofqualitative chemical thinking.

Perturbational non-canonical theory of molecular orbitals and its applications