Describing Chemical Bonds Valence Bond Theory

5 Describing Chemical Bonds Valence Bond Theory 

How does electron sharing lead to bonding between atoms Two models have been developed to describe covalent bonding valence bond dieory and molecular orbital theory. Each model has its strengths and weaknesses, and chemists tend to use them interchangeably depending on the circumstances. Valence bond theory is the more easily visualized of the two, so most of the descriptions we ll use in this book derive from that approach. 

Released when bond forms Absorbed when bond breaks 

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Another approach is spin-coupled valence bond theory, which divides the electrons into two sets core electrons, which are described by doubly occupied orthogonal orbitals, and active electrons, which occupy singly occupied non-orthogonal orbitals. Both types of orbital are expressed in the usual way as a linear combination of basis functions. The overall wavefunction is completed by two spin fimctions one that describes the coupling of the spins of the core electrons and one that deals with the active electrons. The choice of spin function for these active electrons is a key component of the theory [Gerratt ef al. 1997]. One of the distinctive features of this theory is that a considerable amount of chemically significant electronic correlation is incorporated into the wavefunction, giving an accuracy comparable to CASSCF. An additional benefit is that the orbitals tend to be... 

According to Pauling [6-9], valence bond theory can also be used to describe metallic systems. At a first glance, this seems to be contradictory, since VB deals with localized chemical bonds and a metallic bond is thought of as completely delocalized. Pauling s argument is that the metal atoms in the crystal have an available orbital to receive an extra electron and thus form an extra covalent bond, through a mechanism he called unsynchronized resonance. 

All this history is somewhat more fully discussed (from several points of view) in a couple review articles [2] as well as the first two chapters of [9] Valence-Bond Theory and Chemical Structure. These reviews describe through the period of this eclipse VB-theoretic work which was continued by a (prestigious or perhaps stubborn) minority of researchers (including Daudel, Hartmann, Simpson, Kotani, McWeeny, Lowdin,... 

There are many texts that make the point very clearly that the bonding in a molecule such as SFfi has very little to do with the availability of d atomic orbitals, but this is normally done in the context of MO theory, whereas the general ideas of utilizing d orbitals are much more closely allied with the ideas of classical valence bond theory. This, perhaps, is one of the reasons for the continued survival of such models. The purpose of this Chapter is to describe various calculations which have been performed using modern valence bond theory, in its spin-coupled form, resulting in a useful aide memoire which we term the democracy principle. We argue that there are no significant qualitative differences between the hypercoordinate nature of first-row, second-row and noble gas atoms in appropriate chemical environments. 

For a chemical interpretation of this picture, note that the r-electron density is concentrated between carbon atoms 1 and 2, also between carbon atoms 3 and 4. Thus, the predominant structure of butadiene has double bonds between these two pairs of atoms. Each double bond consists of a r-bond, in addition to the underlying a-bond. However, this is not the complete story, because we must also take into account the residual r-electron density between carbons 2 and 3 and beyond the terminal carbons. In the terminology of valence-bond theory, butadiene would be described as a resonance hybrid with the predominant structure CH2—CH-CH=CH2, but with a secondary contribution from CH2—CH= CH— CH2 . The reality of the latter structure is suggested by the ability of butadiene to undergo 1,4-addition reactions. 

Soon after the development of the quantum mechanical model of the atom, physicists such as John H. van Vleck (1928) began to investigate a wave-mechanical concept of the chemical bond. The electronic theories of valency, polarity, quantum numbers, and electron distributions in atoms were described, and the valence bond approximation, which depicts covalent bonding in molecules, was built upon these principles. In 1939, Linus Pauling s Nature of the Chemical Bond offered valence bond theory (VBT) as a plausible explanation for bonding in transition metal complexes. His application of VBT to transition metal complexes was supported by Bjerrum s work on stability that suggested electrostatics alone could not account for all bonding characteristics. 

In valence bond theory, a chemical bond is described in terms of overlap between atomic orbitals on the bonded atoms. 

The valence bond theory is a quantum mechanical model of the chemical bond that was proposed by Heitler and London in 1927. It uses Lewis s concept of a covalent bond as a shared pair of electrons and the idea that a molecule is described by a series of resonance structures. 

To clarify the discussion further concerning conducting polyaromatics, it is worthwhile to elaborate on some principles described by the valence-bond (VB) theory. The ideas of the (VB) (resonance) theory are found to be of aid to organic chemists for rationalizing in a simple manner the facts of organic structure and reactions. However, quantitative application is much harder for the VB method than for the molecular orbital (MO) method. Indeed, for quantitative calculations, the MO method has overshadowed the VB method. The main advantage of the VB method is that it is based on the familiar chemical ideas of bonding and structure [1050]. 

Write a short paragraph describing chemical bonding according to the Lewis model, valence bond theory, and molecular orbital theory. Indicate how the theories differ in their description of a chemical bond and indicate the strengths and weaknesses of each theory. Which theory is correct ... 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

The classic HLSP-PP-VB (Heitler-London-Slater-Pauling perfect-pairing valence-bond) formalism and its chemical applications are described by L. Pauling, The Nature of the Chemical Bond. 3rd edn. (Ithaca, NY, Cornell University Press, 1960 G. W. Wheland, The Theory of Resonance (New York, John Wiley, 1944) and H. Eyring, J. Walter, and G. E. Kimball, Quantum Chemistry (New York, John Wiley, 1944). 

In this contribution, we describe and illustrate the latest generalizations and developments[1]-[3] of a theory of recent formulation[4]-[6] for the study of chemical reactions in solution. This theory combines the powerful interpretive framework of Valence Bond (VB) theory [7] — so well known to chemists — with a dielectric continuum description of the solvent. The latter includes the quantization of the solvent electronic polarization[5, 6] and also accounts for nonequilibrium solvation effects. Compared to earlier, related efforts[4]-[6], [8]-[10], the theory [l]-[3] includes the boundary conditions on the solute cavity in a fashion related to that of Tomasi[ll] for equilibrium problems, and can be applied to reaction systems which require more than two VB states for their description, namely bimolecular Sjy2 reactions ],[8](b),[12],[13] X + RY XR + Y, acid ionizations[8](a),[14] HA +B —> A + HB+, and Menschutkin reactions[7](b), among other reactions. Compared to the various reaction field theories in use[ll],[15]-[21] (some of which are discussed in the present volume), the theory is distinguished by its quantization of the solvent electronic polarization (which in general leads to deviations from a Self-consistent limiting behavior), the inclusion of nonequilibrium solvation — so important for chemical reactions, and the VB perspective. Further historical perspective and discussion of connections to other work may be found in Ref.[l],... 

Quantum mechanics provide many approaches to the description of molecular structure, namely valence bond (VB) theory (8-10), molecular orbital (MO) theory (11,12), and density functional theory (DFT) (13). The former two theories were developed at about the same time, but diverged as competing methods for describing the electronic structure of chemical systems (14). The MO-based methods of calculation have enjoyed great popularity, mainly due to the availability of efficient computer codes. Together with geometry optimization routines for minima and transition states, the MO methods (DFT included) have become prevalent in applications to molecular structure and reactivity. 

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