Valence bond theory, symmetry

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. 

This chapter consists of the application of the symmetry concepts of Chapter 2 to the construction of molecular orbitals for a range of diatomic molecules. The principles of molecular orbital theory are developed in the discussion of the bonding of the simplest molecular species, the one-electron dihydrogen molecule-ion, H2+, and the simplest molecule, the two-electron dihydrogen molecule. Valence bond theory is introduced and compared with molecular orbital theory. The photo-electron spectrum of the dihydrogen molecule is described and interpreted. 

The exceptions to the octet rule described in the previous section, the xenon compounds and the tri-iodide ion, are dealt with by the VSEPR and valence bond theories by assuming that the lowest energy available d orbitals participate in the bonding. This occurs for all main group compounds in which the central atom forms more than four formal covalent bonds, and is collectively known as hypervalence, resulting from the expansion of the valence shell This is referred to in later sections of the book, and the molecular orbital approach is compared with the valence bond theory to show that d orbital participation is unnecessary in some cases. It is essential to note that d orbital participation in bonding of the central atom is dependent upon the symmetry properties of individual compounds and the d orbitals. 

Delocalization occurs in molecules wherever it is possible by symmetry considerations and wherever an energetic advantage can be gained from its operation. MO theory deals very satisfactorily with delocalization, but with valence bond theory the concept is somewhat clumsily incorporated as an addition to the conventional two-electron, two-centre bonding. In general, the stability conferred upon a molecule by delocalization is because the orbitals are more extensive, so that interelectronic repulsion is minimized. 

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. 

Throughout the book, theoretical concepts and experimental evidence are integrated An introductory chapter summarizes the principles on which the Periodic Table is established and describes the periodicity of various atomic properties which are relevant to chemical bonding. Symmetry and group theory are introduced to serve as the basis of all molecular orbital treatments of molecules. This basis is then applied to a variety of covalent molecules with discussions of bond lengths and angles and hence molecular shapes. Extensive comparisons of valence bond theory and VSEPR theory with molecular orbital theory are included Metallic bonding is related to electrical conduction and semi-conduction. 

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. 

FIGURE 17. Schematic representation of the symmetry-unique spin-coupling patterns in cyclopropane (above) and benzene (below). In the case of cyclopropane, carbon hybrid orbitals and, in the case of benzene, carbon p n orbitals are shown. For each structure, Gallup-Norbeck occupation numbers as determined by spin-coupled valence bond theory are given. All data from Reference 51... 

McWeeny has written a tribute to the valence-bond theory pioneers of 1927-1935.362 Shavitt has outlined the history and evolution of Gaussian basis sets as employed in ah initio molecular orbital calculations.363 Hargittai has interviewed Roald Hoffmann (b. 1937)364 of Cornell University and Kenichi Fukui (1918-1998)365 of Kyoto University, who were jointly awarded the Nobel Prize in Chemistry in 1981. Fukui developed the concept of frontier orbitals and recognized the importance of orbital symmetry in chemical reactions, but his work was highly mathematical and its importance was not appreciated until Robert Woodward (1917-1979) and Hoffmann produced their rules for the conservation of orbital symmetry from 1965 onwards.366... 

Use of Molecular Symmetry to Generate Covalent Excited States Based on Valence Bond Theory... 

Certainly one of the first conceptual problems which arises if one describes the ground state of a molecule in terms of Q-bonds is how to obtain a compatible description of the excited states and ion states which may have B, IT, or A symmetries. A discussion of how a compatible description is obtained has been given recently 11). However, since it is important for later discussions in this work, especially with respect to the connection between valence bond theory, localized molecular orbitals (LMOs) and canonical molecular orbitals (CMOs), a brief account is provided here. 

The introduction of Valence Bond theory has motivated the search for structural regularities that can be interpreted by models of local electronic features, such as the powerful model of Valence Shell Electron Pair Repulsion [93,94] theory. Alternative approaches, based on Molecular Orbital theory, have led to the discovery of important rules, such as the Woodward-Hoffmann orbital symmetry rules [95] and the frontier orbital approach of Fukui [96,97], As a result of these advances and the spectacular successes of ab initio computations on molecular... 

According to valence-bond theory, unpaired orbitals in the valence shells of two adjoining atoms can combine to form a chemical bond if they overlap significantly and are symmetry compatible. As emphasized by Linus Pauling, a measure of the bonding potential of two orbitals is the overlap integral... 

Molecules such as NHj and HjO etc. are described in terms of an inequivalent hybridization scheme based on sp in valence bond theory. The construction of hybridized orbitals in such molecules is different from that developed above. The tetrahedral molecule XAY3 (3) provides a useful starting point. Since the hyl is distinguished from hy2, hy3 and hy4, the symmetry-adapted linear combinations of these hybrids cannot be generated in terms of the spherical harmonic expansion in Eq. (1). But they can be derived as follows ... 

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