And MO theory

These examples show quite dearly the dose relationship between this new stmc-ture representation embedded in RAMSES and MO Theory. 

The examples that have been presented in this section illustrate the approach that is used to describe structure and reactivity effects within the framework of MO description of structure. In the chapters that follow, both valence bond theory and MO theory will be used in the discussion of structure and reactivity. Qualitative valence bond terminology is normally most straightforward for saturated systems. MO theory provides useful insights into conjugated systems and into effects that depend upon the symmetry of the molecules under discussion. 

The VB and MO theories are both procedures for constructing approximations to the wavefunctions of electrons, but they construct these approximations in different ways. The language of valence-bond theory, in which the focus is on bonds between pairs of atoms, pervades the whole of organic chemistry, where chemists speak of o- and TT-bonds between particular pairs of atoms, hybridization, and resonance. However, molecular orbital theory, in which the focus is on electrons that spread throughout the nuclear framework and bind the entire collection of atoms together, has been developed far more extensively than valence-bond... 

The ab initio calculations of various three-electron hemibonded systems [122, 123] indicated that the inclusion of electron correlation corrections is extremely important for the calculation of three-electron bond energies. The Hartree-Fock (HF) error is found to be nonsystematic and always large, sometimes of the same order of magnitude as the bond energy. According to valence bond (VB) and MO theories, the three-electron bond is attributed to a resonance between the two Lewis structures... 

Hyp. III.3 is in reality a mathematical formulation of the original electron-pair idea (3) without any explicit reference or connection to quantum chemistry. However, the electron-pair concept is built into both VB and MO theory through postulates of the types Hyps. III. 1, III.2, and... 

VB and MO theories can be applied to simple molecular systems as follows. According to VB theory, if (p.A and

wave functions of independent systems a and b then the total wave function iff and total energy E are written as follows ... 

Here Slater functions (a3 2/7r 1/2) exp( —a r — ra ) with the atom being centered at position vectors ra. The overlap between these functions is given by S. After an FT and integrating over momentum coordinates of one particle, the EMD of H2 molecule within VB and MO theory are derived as... 

One very important difference between VSEPR theory and MO theory should be noted. The MOs of the water molecule which participate in the bonding are three-centre orbitals. They are associated with all three atoms of the molecule. There are no localized electron pair bonds between pairs of atoms as used in the application of VSEPR theory. The existence of three-centre orbitals (and multi-centre orbitals in more complicated molecules) is not only more consistent with symmetry theory, it... 

Two major theories of the covalent bond are described in this book the main features of valence bond theory are treated in terms of the VSEPR theory of molecular shapes, and MO theory which is based on the symmetry properties of the contributing atomic orbitals. The latter theory is applied qualitatively with MO diagrams being constructed and used to interpret bond orders and bond angles. The problems associated with bond angles are best treated by using the highest symmetry possible for a molecule of a particular stoichiometry. 

VSEPR/valence bond theory and MO theory were applied to molecules with more than three atoms. 

Apply VSEPR and MO theory to the carbonate ion, CO,2, and also sketch the canonical forms of the ion which would allow valence bond theory to represent the bonding as accurately as possible. The single bond covalent radii of C and O are 77 and 74 pm, respectively. The C- O bond distance in the carbonate ion is 129 pm. 

As noted in Section 9.1, there are three closely related theories of the electronic structures of transition metal complexes, all making quite explicit use of the symmetry aspects of the problem but employing different physical models of the interaction of the ion with its surroundings as a basis for computations. These three theories, it will be recalled, are the crystal field, ligand field, and MO theories. There is also the valence bond theory, which makes less explicit use of symmetry but is nevertheless in accord with the essential symmetry requirements of the problem. We shall now briefly outline the crystal field and ligand field treatments and comment on their relationship to the MO theory. 

Valence bond theory thus gives a good description of the 0-0 cr bonds but a poor description of the tt bonding among p atomic orbitals, whose four electrons are spread out, or delocalized, over the molecule. Yet this is exactly what MO theory does best—describe bonds in which electrons are delocalized over a molecule. Thus, a combination of valence bond theory and MO theory is used. The cr bonds are best described in valence bond terminology as being localized between pairs of atoms, and the tt electrons are best described by MO theory as being delocalized over the entire molecule. 

A recent summary of the history and dynamics of the theoretical models of benzene39 cites a view that even though the current molecular orbital (MO) view of benzene seems complete and ultimate while the valence bond (VB) view seems obsolete, the recent findings about zr-distortivity in benzene indicate that the benzene story is likely to take additional twists and turns that will revive the VB viewpoint (see footnote 96 in ref 39). What the present review will show is that the notion of delocalized zr-systems in Scheme 1 is an outcome of both VB and MO theories, and the chemical manifestations are reproduced at all levels. The use of VB theory leads, however, to a more natural appreciation of the zr-distortivity, while the manifestations of this ground state s zr-distortivity in the excited state of delocalized species provides for the first time a physical probe of a Kekule structure .3... 

UPS and MO theory are inextricably linked. It is impossible to interpret UPS measurements without at least a qualitative MO treatment, and it is now commonplace to perform quantitative calculations for comparison with the UPS data. The development of UPS techniques since about 1960 helped to popularise MO theory, and semi-empirical MO methods are often calibrated by appeal to UPS data. Thus an approximation which greatly simplifies an MO calculation is held to be justifiable if, over a fair range of molecules, the calculated orbital energies are in good agreement with UPS binding energies. 

This equivalence clearly projects that the MO—VB rivalry, discussed in Chapter 1, is unfortunate and senseless. Both VB and MO theories are not so diametrically different that they exclude each other, but rather two representations of reality, which are mathematically equivalent. The best approach is to use these two representations jointly and benefit from their complementary insight. In fact, from the above discussion of how to write a VB wave function, it is apparent that there is a spectrum of orbital representations that stretches between the fully local VB representations through semilocalized CF orbitals, to the use of delocalized fragment orbitals VB (FO—VB), and all... 

The Sn2 reactions are good examples to highlight the different merits of VB and MO theories in quantum chemistry [65]. In the VB method, the atomic features are preserved and the focus is the two-electron-two-center bonds, and each molecule is formed with bonds (plus the lone and core pairs). Whereas one resonance structure is not enough to describe a molecule, multi-resonance structures are adopted. In fact, the resonance theory can also be applied to illustrate the reactions in an intuitive way. For example, for the chloride-exchange reaction... 

Stereochemistry is not discussed in great detail, except in the context of the Woodward-Hoffmann rules. Molecular orbital theory is also given generally short shrift, again except in the context of the Woodward-Hoffmann rules. I have found that students must master the basic principles of drawing mechanisms before additional considerations such as stereochemistry and MO theory are loaded onto the edifice. Individual instructors might wish to put more emphasis on stere-oelectronic effects and the like as their tastes and their students abilities dictate. 

Combining VB and MO theories -> VB and MO theory are sometimes jointly invoked to describe... 

The crystal field model requires that q = + 2 and MO theory confined to a-bonding indicates that q lies in the range + /2 to + The available MOs of [CoCl ] " and [CoBr4] incorporating jr-bonding in additiongive q a positive value. 

The best way to combine DFT and MO theory is to incorporate x and rj into the commonly used orbital energy diagrams. Figure 2.2(a) shows such a diagram. A typical case of a molecule where I — lOeV and A = —2qV is taken. Within the validity of Koopmans theorem, the frontier orbital energies are given by... 

F. Cortes-Guzman, R. F. W. Bader. Complementarity of QTAIM and MO theory in the study of bonding in donor-acceptor complexes. Coord. Chem. Rev. 249, 633-662 (2005). 

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