Ozone and Other 1,3-Dipoles: Toward a Quantitative Measure of Diradical Character

Abstract

Ozone and its sulfur-substituted isomers are studied by means of the Breathing Orbital Valence Bond ab initio method, with the objective of estimating their controversial diradical characters. The calculated weights of the various VB structures and their individual diabatic energies are found to be consistent with each other. All 1,3-dipoles can be described in terms of three major VB structures, one diradical and two zwitterionic ones, out of the six structures, forming a complete basis. Ozone has a rather large diradical character, estimated to 44%-49%. SOO and SOS are even more diradicalar, whereas SSO and especially OSO are better described as closed-shell zwitterions. Moreover, the description of 1,3-dipoles, in terms of the three major structures, yields VB weights in full agreement with simple chemical wisdom, i.e., a diradical weight of 33% when the three structures are quasi-degenerate, and a smaller (larger) value when the diradical structure is higher (lower) in energy than the zwitterionic ones. Therefore, the VB-calculated weight of the diradical structure of a molecule qualifies itself as a quantitative measure of diradical character, and not only as an indicator of tendencies. Other definitions of the diradical character, based on molecular orbital/configuration interaction methods, are discussed.

Bonding in Heavier Group 14 Zero‐Valent Complexes—A Combined Maximum Probability Domain and Valence Bond Theory Approach

“…Thanks to the use of non‐orthogonal strictly localized orbitals, classical VB wavefunctions are expanded into VB structures that directly map to corresponding chemical structures. Aside from the variational optimization of classical VB wavefunctions, quantitative VB weights could be assigned to the different possible chemical structures . Therefore, modern methods in classical VB theory are best suited to answer a questions such as: which chemical structure(s) best describe a given molecule?…”

“…Aside from the variational optimization of classical VB wavefunctions,q uantitative VB weights could be assigned to the different possible chemical structures. [29] Therefore, modernm ethods in classicalV Bt heory are best suited to answeraq uestionss uch as:w hichc hemical structure(s) best describe ag iven molecule?A nd, if several structures are in competition into ar esonance mixing, what are the weights of each of them?T he stabilizing ligands in the studied E 0 complexes, the "tetrylones", [24] that were selected in analogy and for the sake of comparison with previouss tudies, [1d, 24, 30] are phosphine (PMe 3 ), N-heterocyclic( NHC) and acyclic( C{NH 2 } 2 ) carbene ligands, cyclic tetrylene ligands (cycE) and carbon monoxide (CO) ( Figure 2).…”

Structural diradical character

“…We will show in the following that the structural diradical character correlates more with electronic diradical character than the MAE of absolute bond lengths does. To illustrate this (see Fig.…”

Decoding the Chemical Bond—On the Connection between Probability Density Analysis, QTAIM, and VB Theory

“…13 Six structures of the π system in general 1,3-dipoles. Labels are taken from Braïda et al 32 In VB theory, ozone is described best by six π resonance structures, see Figure 13. Harcourt was the first to stress the importance of the diradical 'long bond' structure D. 57 Goddard et al 58 and later Hiberty et al 59 verified Harcourts assumption with GVB calculations and CASSCF expansions respectively.…”

“…64,65 Even more recently, Braïda et al found a good correlation of some of these indices with VB weights (Chirgwin-Coulson and inverse definition) for 1,3-dipoles built from sulfur and oxygen. 32 For ozone, the structures D, Z 1 , and Z 2 are the three most important structures. Thus, the VB wave functions with only these three structures are compared with the full VBSCF wave functions (six structures) and, additionally, with the CAS and HF wave functions.…”