Resonance theory. V. Resonance energies of benzenoid and nonbenzenoid .pi. systems

Abstract

Structure-resonance theory for r-molecular systems based solely on covalent KekulC structures is justified phenomenologically and by reference to recent theoretical work. The idea of antiaromaticity is shown to be a logical extension of the theory, and a concept of a local ring aromaticity or antiaromaticity is quantitatively defined. Estimates of resonance stabilization energies are substantially lower than predictions based on Hiickel MO theory. The resonance theory results agree with those from SCF-LCAO-MO calculations. he recognition of extremely simple algorisms for T counting KekulC structures' and their permutations induced us to test a semiempirical quantum theory with a basis of KekulC structure functions. The mathematical equivalencies3-j between Hiickel molecular orbital (HMO) and valence bond (VB) theories for the benzenoid class of hydrocarbons led us to expect a correspondence of our results to previously known HMO quantities. The results2 were surprising in that it was found that calculated resonance energies, RE, for an extensive series did not correlate well with HMO delocalization energies (correlation coefficient, 0.493 for resonance energy per electron, REPE). Instead there was a congruity with resonance energy values obtained from SCF-LCAO-MO calculations6 (correlation coefficient, REPE, 0.991).The approach that we use is essentially a quantification of the structural resonance theory traditionally applied to structure-reactivity problems in organic chemistry.' In this paper we try to provide some justification for our procedures which will be described in more detail than in the previous communication.Calculations of resonance energies of several classes of aromatic compounds will then be presented, and comparisons with previous MO results and experimental properties will be delineated. We emphasize throughout that our computational procedure is so easily carried out and leads to such sensible results that it should be the method of choice for calculating resonance energies. Applications to the estimation of heats of formation8 and carcinogenic activitiesg of benzenoid hydrocarbons have already given good results, and a description of bond-order relationships will appear in a following article. Resonance TheoryThe formulism of the method is that of VB theory. l 1 For a n-electronic system each energy eigenfunction is written as given in eq 1. The $(u) are structure func-tions, the cf are coefficients, the index u indicates the type of electron distribution associated with the function, and the subscript i numbers the function. After selecting functions, the coefficients and eigenvalues can be evaluated by solving eq 2, where H is the Hamiltonianmatrix and S is the overlap matrix. A conventional approximation is to assume zero overlap of the wave functions so that off-diagonal elements in the matrix involve Hamiltonian integrals only. A significant simplification in obtaining a ground-state eigenvalue is also provided if one assumes a wave function consisting of equal contributions from the c...

Graph Theory of Aromatic Stabilization

“…611 Since 1970, several theories of aromaticity have been proposed in association with possible physical implications of DRE. 2,3 Homodesmotic reaction energy, 12,13 structureresonance-theory resonance energy, 14 and conjugated-circuit resonance energy 15 are among typical energetic quantities intended to reproduce DRE. Hess and Schaad elaborately defined DRE-type ASE, HessSchaad resonance energy (HSRE), within the framework of Hückel molecular orbital (HMO) theory.…”

Forcing, Freedom, & Uniqueness in Graph Theory & Chemistry

“…77,78; and with different physical consequences -as in Refs. [38][39][40]62,[79][80][81]38. On the other hand, from a molecular-orbital perspective, there are relevant spanning subgraphs (identified with Sachs subgraphs, 23 supplemented with single-site components to make the result spanning), for which forcing ideas might somehow also be relevant.…”

“…It is realized that e is chemically relevant in Pauling's work, 35,36 and C is relevant in "conjugated-circuits" theory. [37][38][39][40][41][42][43] Next, our initial view of "forcing" is indicated. 6 S of conjugated 6-cycles of G is 6-forcing if no other Kekule structure κ of G manifests the same subset of conjugated 6-cycles with the same conjugation pattern within each of these cycles.…”

“…Notably especially for large benzenoids the molecular boundaries might 50,51 severely constrain the Kekule structures, or even maximum matchings, whence the maximal ones can become not just contributory but crucial, and dominant. Indeed this recognition has enabled 38,39,52,53 general simple (chemical) results in understanding defects in graphenethat is, for the occurrence of unpaired electrons localized near boundaries, vacancy defects, and more.…”

The Scientific Legacy of Su-Moon Park: a Personal View

“…3 Park also met Professor William Herndon of the University of Texas at El Paso, who was a quantum chemist and an authority on conjugated π-bonded systems and graph theory. [4][5][6] From all three men, Park learned the art of identifying a fertile research area and then developing it intensively. From Song, he gained a deep appreciation of photochemistry.…”