Prediction of Molecular Properties Including Symmetry from Quantum-Based Molecular Structural Formulas, VIF Joseph D. Alia,* Bess Vlaisavljevich, Matthew Abbot, Hallie Warneke, and Tyson Mastin UniVersity of Minnesota, Morris, DiVision of Science and Math, 600 East Fourth Street, Morris, Minnesota 56267 ReceiVed: December 21, 2007; ReVised Manuscript ReceiVed: May 22, 2008 Structurally covariant valency interaction formulas, VIF, gain chemical significance by comparison with resonance structures and natural bond orbital, NBO, bonding schemes and at the same time allow for additional prediction such as symmetry of ring systems and destabilization of electron pairs with respect to reference energy of -1/2 E h . Comparisons are based on three chemical interpretations of Sinanog ˘ lu’s theory of structural covariance: (1) sets of structurally covariant quantum structural formulas, VIF, are interpreted as the same quantum operator represented in linearly related basis frames; (2) structurally covariant VIF pictures are interpreted as sets of molecular species with similar energy; and (3) the same VIF picture can be interpreted as different quantum operators, one-electron density or Hamiltonian; for example. According to these three interpretations, bond pair, lone pair, and free radical electrons understood in terms of a localized orbital representation are recognized as having energies above, below, or equal to a predetermined reference, frequently -1/2 E h . The probable position of electron pairs and radical electrons is predicted. The selectivity of concerted ring closures in allyl anion and cation is described. Symmetries of conjugated ring systems are predicted according to their numbers of π-electrons and spin-multiplicity. The π-distortivity of benzene is predicted. The 3c/2e - H-bridging bonds in diborane are derived in a natural way according to the notion that the bridging bonds will have delocalizing interactions between them consistent with results of the NBO method. Key chemical bonding motifs are described using VIF. These include 2c/1e - , 2c/2e - , 2c/3e - , 3c/2e - , 3c/3e - , 3c/4e - ,4n antiaromatic, and 4n+2 aromatic bonding systems. Some common organic functional groups are represented as VIF pictures and because these pictures can be interpreted simultaneously as one-electron density and Hamiltonian operators, the valence shell electron pair repulsion method is applied toward understanding the energies of valence NBOs with respect to the reference energy of -1/2E h . I. Introduction The application of quantum mechanical reasoning to molec- ular structural formulas began soon after the inception of quantum mechanics in the mid 1920s. 1 The idea of mesomer- ism, 2 later to be known as resonance, is a staple of qualitative reasoning in chemistry. Notions of hybridization and resonance rationalize bond lengths and angles in a wide variety of organic molecules. In addition, the notion of resonance stabilization has been helpful for summarizing a great deal of chemical reactivity. Other properties like the high symmetry of aromatic rings and the simultaneous distortion of antiaromatic rings are more easily understood through the use of qualitative molecular orbital ideas. One can just as easily draw resonance structures for the benzene molecule as for cyclobutadiene but for benzene the carbon - carbon bond lengths are the same and in singlet cyclobutadiene there are distinct single and double bonds. This difference can be understood as a Jahn-Teller distortion 3 and typical of aromatic and antiaromatic classifications distinguished by their number of π-electrons, 4n+2 or 4n respectively. 4,5 According to Shaik and Hiberty, computational valence bond theory does give correct predictions for cyclobutadiene once ionic resonance structures are included in the calculation. 6 Early researchers such as Pauling used valence bond theory or molecular orbital theory based on what was most practical for the particular application. 7 The valency interaction formula method, VIF, 8-10 makes salient features of both qualitative VB and qualitative MO theories available in a unified approach. In this paper, key chemical bonding motifs are examined using quantum mechanically derived molecular structural formulas. Resonance structures are compared to VIF pictures related by the two pictorial VIF rules. Unlike the resonance structures, VIF pictures as one-electron density operators can be used to predict the symmetries of aromatic and anti-aromatic rings according to the number of paired and unpaired electrons in the π-system. Due to the fact that VIF is a one-electron theory and the pictorial VIF rules are linear transformations, the VIF pictures have a closer relationship with natural bond orbitals, 11 NBOs, and natural resonance structures, NRS, than they do with the many-electron wave functions of valence bond theory. The correspondence between VIF pictures as one-electron density operators and as one-electron Hamiltonian operators allows the calculated energies of NBOs with respect to the VIF reference energy of -1/2E h to be interpreted in terms of valence shell electron pair repulsion (VSEPR) 12 theory. II. Theory of Structural Covariance The mathematical foundations for the VIF method were formulated by Sinanog ˘ lu and presented in a series of five papers in 1984. 13 In the fourth of the five papers, “Structural Covariance of Graphs”, Sinanog ˘lu shows how an algebraic structure such as a linear operator can be represented with a graph, G, and states that all {G, G′, G′′,...} obtained by transforming the initial * Author for correspondence. E-mail: aliaj@morris.umn.edu. J. Phys. Chem. A 2008, 112, 9784–9795 9784 10.1021/jp7120214 CCC: $40.75  2008 American Chemical Society Published on Web 09/18/2008