Unified Valence Bond Theory of Electronic Structure

In complex scientific disciplines, such as chemistry, a command of the literature and an ability to recognize the common denominator of many apparently unrelated experimental observations often leads to the formulation of concepts and rules of broad applicability. One demonstration of how such a marriage of knowledge and intuition can bear offspring was given by Walsh, who, many years ago, recognized that many experimental facts, which were known at that time, could be explained in a self-consistent manner by assuming that the hybridization of a central atom (or core) depends on the electronic nature of the ligands attached to it and proposed the following rule: “If a Group X attached to Carbon is replaced by a more Electro-negative Group Y, then the Carbon Valency towards Y has more p Character than it had towards X”.¹ We shall refer to this as Walsh’s rehybridization rule. In recent times, this rule, in one form or another, has been applied to a variety of interesting chemical problems by many, most notably by Bent².

“Replacement of hydrogen atoms by lithium atoms may radically alter the stereochemistry of the parent hydrocarbon”. Thus can be summarized some of the most important findings of the imaginative computational work of Schleyer and his coworkers.¹ What fundamental property of lithium is primarily responsible for the unexpected geometrical preferences of perlithio hydrocarbons? Is there some way to predict the geometry of these molecules? These and related questions can be dealt with within the framework of MOVB theory in a way which illustrates the basic utility of the Induced Deexcitation (ID) model presented in the previous chapter as well as the way in which MOVB theory^2,3 can be used in order to produce novel insights regarding the mechanism of vacant orbital participation in chemical bonding. The former illustrative application of the theory is made possible by the fact that Li is a weak overlap binding (overbinding) ligand which can readily induce core deexcitation while the latter is made possible by the fact that Li has low lying vacant 2p orbitals which can combine with doubly occupied orbitals to define new bonds or they can function as hybridization “holes” to promote more efficient “covalent” carbon-lithium bonding. At the outset, we state that this work has been totally motivated by the calculational work of Schleyer and his collaborators⁴ which was published at the time when we were in sore need of well established facts to test the central ideas of MOVB theory, such as the ones described in this and other chapters.

The original monograph introducing qualitative Valence Bond (VB) and Molecular Orbital Valence Bond (MOVB) theory to the chemical community was entitled “Unified Valence Bond Theory of Electronic Structure”.^1,2 In this work, we begin to justify the use of the adjective “unified” by showing how the same MOVB concepts that are applicable to ground state chemistry can be applied to excited state chemistry. In particular, we shall use the MOVB theory and the accessory conceptual tools developed before in order to elucidate the energetic interrelationships of the low lying excited states of a given system and discover ways in which the energy ordering of these states can be altered. After reading the chapter describing the Induced Deexcitation model and this one, it is hoped that the reader will have no difficulty seeing that the energy ordering of different molecular states at fixed geometry and the energy ordering of different ground state geometrical structures are analogous problems which can be handled by the same MOVB concepts.

Hückel’s rule¹, the Woodward-Hoffmann rules², and, in a broader sense, Hückel Molecular Orbital (HMO) theory³ have had profound impact on chemistry in a way which is now well recognized and admired. Perhaps, the most important and time-lasting contribution of HMO theory has been the revelation of what in Valence Bond (VB) terms we call parity control of stereoselection⁴, or, in more familiar language, the revelation of the fact that a ground state molecule, a transition state, or, any molecular system, in general, can be thought of as the product of a “forbidden” or “allowed” union of two component fragments with the latter mode of union being energetically more favorable than the former one.

Nonbonded repulsion, commonly referred to as “steric effect”, is one of the priceless weapons of the conceptual arsenal of the chemist, especially the organic chemist. It is repeatedly invoked to rationalize why the most “crowded” arrangement of atomic nuclei is often the least stable one.¹ The simplicity of the concept, an intuitively obvious one, has much to do with the popularity it enjoys. While excellent for a posteriori rationalization, the concept of nonbonded repulsion has no predictive value. For example, ethane is staggered but water is non-linear. If we did not know the actual physical facts, we would predict ethane to be staggered and water linear on the basis of “steric effects”. Furthermore, the concept of nonbonded repulsion is really an empirical one for it was originally developed by experimentalists in order to codify a subset (not a complete set) of experimental observations which indicated that “crowding” of nonbonded atoms is energetically unfavorable. Thus, the concept of nonbonded repulsion is both nonpredictive and nontheoretical (heuristic).

According to Molecular Orbital-Valence Bond (MOVB) theory,¹ the vast majority of organic molecules in a reference geometry can be viewed as the result of a “forbidden” union of a core(C) and a ligand(L) fragment.^1–3 The transition from the reference geometry to the lowest energy geometry of the molecule is accompanied by an energy reduction which is a reflection of “forbiddeness” removal.⁴ The purpose of this paper is to focus on one and only one type of system, namely, A₂X₄ with fourteen valence electrons, in order to demonstrate how radically MOVB theory has changed our view of molecular stereochemistry.

The thermal conversion of 1,3-butadiene to cyclobutene may occur in a conrotatory or a disrotatory fashion. In the former case, an axis of symmetry is maintained along the reaction coordinate while in the latter case a plane of symmetry is preserved during the conversion or reactants to products. This difference with respect to the existing symmetry elements becomes responsible for a difference in the symmetry labels of reactant and product orbitals. In turn, this becomes responsible for the existence of a barrier in the case of disrotation and the absence of a barrier in the case of conrotation at the level of Hückel MO theory. This is clearly revealed by the Longuet-Higgins-Abrahamson-Woodward-Hoffmann MO correlation diagrams¹ for con- and dis-rotatory ring closure of 1,3-butadiene. The conrotatory ring closure of 1,3-butadiene is termed a symmetry “allowed” and the disrotatory ring closure of the same molecule is termed a “forbidden” reaction.

One of the most fascinating trends of molecular stereochemistry is the tendency of ligands to segregate into sets when attached on carbon cores. A typical example is provided by the comparison of 1,1 and cis 1,2-difluoroethylene, henceforth referred to as G and C 1,2 difluoroethylene, respectively.

In a previous work, we have outlined the Molecular Orbital-Valence Bond (MOVB) theory of chemical bonding, based on the core(C)-ligand(L) dissection.¹ In previous chapters, we have applied this brand of theory to a variety of structural problems with the aim to demonstrate its conceptual and formal advantages over previous and current qualitative theoretical approaches to bonding. We now observe that the Core-Ligand (C-L) dissection allows a classification of molecules which contain an even number of valence electrons into four major types depending upon the presence or absence of electron pairs or holes in the core and/or ligand fragments in the perfect pairing (R) Configuration Wavefunction (CW) representing the entire system.

The purpose of this paper is to rephrase the fundamental concepts of inorganic chemistry in the language of MOVB theory¹ as a prelude to a reexamination of the electronic structure of inorganic molecules. For illustrative purposes we reformulate the concepts of the coordinate bond,² the Dewar-Chatt-Duncanson (DCD) model,³ and the concept of high and low spin complexes⁴ and we apply MOVB theory to the problem of the ground stereochemistry of prototypical inorganic complexes, the thermodynamics of olefin coordination in complexes, and the problem of the “trans effect” in the equilibrium geometries of inorganic complexes.⁵

A₂X₄ molecules with ten valence electrons, assuming that the X ligands are monovalent groups, have a choice of adopting one of the following two “extreme” geometries: A planar, D_2h, or, a perpendicular, D_2d, conformation.

Hückel MQ (HMO) theory,^1,2 predicts that pi benzene is more stable than three pi ethylenes. This conclusion seems to be compatible with the fact that the heat of hydrogenation of benzene is much less than the heat of hydrogenation of three cyclohexenes³ and the known unwillingness of benzene to undergo addition reactions, opting for “aromatic” substitution instead. These data have prompted an on-going preoccupation with “resonance energies”, “aromaticity”, and the like. In this chapter, we suggest that, while the experimental facts are indisputable, the concepts which chemists have devised over more than a century are most likely erroneous and that benzene is pi destabilized but operationally “aromatic”.

In a recent communication¹, Wiberg and Walker reported the synthesis of the presumably “superstrained” (1.1.1.) propellane which, according to previous SCP-MO computations by Newton and Schulman², has no bond linking the bridgehead carbons, but, nonetheless, it is comparatively very stable¹. I now show that MOVB theory^3,4 easily accounts for these “strange” observations by comparing the electronic structures of the following three molecules.

The literature on the electronic structure of carbon cyclic compounds such as cyclopropane, cyclohexane, benzene, etc., is so enormous that citation of some works but not others is mandatory and, thus, unfair.¹ The essential point is that many aspects of the bonding of these molecules have been successfully dealt with but a fundamental understanding of the electronic structure of these molecules still eludes us. Why do I say so?

The purpose of this chapter is threefold:

Organic “diradicals” are important for the synthetic chemist who wants to exploit them as precursors of target molecules, for the mechanistic chemist who seeks to unravel reaction pathways, for the quantitative theoretician who is anxious to test different computational schemes on such molecules because of the formalistic intricacies involved, and for the qualitative theoretician who seeks to understand how these species are bound. Specialists of the latter two types most often adhere to MO theory and they discuss the electronic properties of “diradicals” in the following way: They depart from Hückel MO theory and point out why neglect of interelectronic repulsion renders it inapplicable to problems involving “diradicals”. Then, the discussion shifts to the SCF-MO level and various formal drawbacks and resulting pitfalls are recognized. Finally, one is forced to examine the problem at the SCF-MO-CI level, something which guarantees that the potential audience of the paper is exponentially reduced and that the ensuing discussion is rendered cumbersome and lengthy. In a recent work,¹ we advanced the argument that qualitative Valence Bond theory has the formal correctness and conceptual clarity which can allow one to dispense with problems which are hard to deal with within the MO theoretical framework in the space of a paragraph or two. In particular, in treating homonuclear systems involving relatively weak pi bonds, one can use the Approximate Heitler-London (AHL) theory outlined in the original monograph.

The spin selection problem revolves about the determination of the sign and magnitude of the energy difference between two different spin states \( {\Lambda _1}\;and\,{\Lambda _2} \) for a given geometry, g, and a given number of electron pairs, n. For our purposes, g can be either a Hückel AO (HAO) or Möbius AO (MAO) geometry.

In a previous note¹, I gave an example of why an effective bond can exist when a real bond is absent within Single Determinant SCF-MO (SD-SCF-MO) theory. I now consider a much more complex problem, which is soluble only at the level of SCF-MO-CI theory, in order to further illustrate the conceptual and formal advantages of VB-type theories.

In every scientific discipline, the accumulated knowledge regarding the structure of fundamental entities raises the question of their interaction. Thus, in zoology, we inquire as to how bone and tissue are connected (i.e., interact) so that their combined actions can produce motion. In molecular biology, we inquire as to how an enzyme and an effector molecule combine (i.e., interact) in order to produce a complex which is catalytically active, or, inactive. Finally, reaching further down to the foundation of physical reality, one can inquire as to how bonds interact within molecules in order to produce the lowest possible energetic state. Now, one of the difficulties which thwart studies of the latter type is the mere fact that, in order to investigate interaction, one must be able to define the interacting elements. This is not a problem in, e.g., zoology, where we can unequivocally define bone, tissue, etc., but, it does constitute a problem in quantum chemistry because clear definitions of “non-interacting bonds” and “after-interaction-bonds” are possible within the framework of one but not of another theoretical approach. That is to say, one must appropriately choose among different theoretical vehicles before undertaking a study of interaction at the electronic level since the construct of “bond” is only a model-dependent construct. The purpose of this paper is to exploit the formal and conceptual advantages of Valence Bond (VB) theory¹ in order to provide a blueprint for the study of interaction at the electronic level through formulation and illustrative application of concepts that may ultimately lead to a good understanding of electronic control mechanisms within atoms and molecules.

In the original monograph,¹ we distinguished five different types of MOVB interaction matrix elements shown in Figure 1. In previous chapters, we have focused primary attention on the chemical implications of CT interaction and we have also seen what role bielectronic polarization plays in problems of molecular electronic structure, with the confines of VB and MOVB theory. Our intention now is to rationally design systems in which monoelectronic polarization and bielectronic correlation becomes as important as CT interaction and probe the stereochemical consequences of CW interaction brought about by the p_ij and W_ij interaction matrix elements. For reasons that will become apparent, we shall refer to bonding effected by the p_ij and W_ij. matrix elements as coulomb polarization refering to the specific mechanisms as either p or W polarization. For pedagogical reasons, we develop the theory of p and W polarization using elementary systems from which we ultimately generalize to the polyelectronic species. As we shall see, coulomb polarization becomes important when the constituent atoms of a system are weak overlap binders. Thus, this is yet another dimension of the general problem of weak binding first discussed in chapters 1 and 2.

One of the great advantages of MOVB theory is that it forms the basis for a logical and coherent interpretation of chemical phenomena. The situation is quite different in the case of MO theory: Within this framework, one typically solves the problem at the SCF-MO level and then corrects the solution by re-solving it at the SCF-MO-CI level. In the process, one generates two apparently distinct conceptual frameworks with the result that the appearance is created that there are “MO effects” and “CI effects”. This is quite inappropriate since the “CI effects” are nothing else but consequences of the solution of the SCF-MO equations, unless by “CI effects” one implies the chemical consequences of nonvalence orbitals which are not included in the monodeterminantal calculation. Perusal of the vast theoretical literature reveals that this point has not been properly appreciated. We believe that this is due to the fact that there has been no conceptual tool capable of revealing the nature of error involved at the Single Determinant (SD) MO level and how it is linked to fundamental electronic mechanisms which are grossly reproduced by SD MO theory. With MOVB theory as our weapon, we now attempt to answer the following question: What is the meaning of the term, “valence correlation effect”, or, more briefly, “correlation effect”?

As the amount of experimental research reported in the literature continually increases, as the number os scientific journals grows unabated, and as theory becomes more and more sophisticated because of continual forward strides in computer technology, experimentalists can no longer afford to use primitive concepts in their daily planning of syntheses and their quests of new mechanisms as well as in communications with collegues and educating students. For the same reasons, theoreticians can no longer pretend to interpret the results of highly complex computations through usage of elementary qualitative MO concepts. This two part work attempts to establish a common language for experimentalists and theoreticians alike for discussing, analyzing, and resolving chemical problems and for rationally designing “new chemistry”. This new language makes principal use of the MOVB bond diagrammatic representation of the electronic structure of molecules. Our goal has been to teach this new formalism so that the reader can come to the point that, by a few strokes of the pen, i.e., by the construction of one or more bond diagrams, he can resolve controversial issues, rectify mistaken impressions, and predict new phenomena, without the need of explicit computations and without the necessity of lengthy discussions and clarifications.