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Bond Valence Theory

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Bond Valences

Part of the book series: Structure and Bonding ((STRUCTURE,volume 158))

Abstract

This chapter shows that a unified concept of a chemical bond can be derived from a theoretical picture of the atom in which the Coulomb forces are described using the electric field rather than the electric potential. The localized chemical bond and its valence arises naturally from this picture, allowing the theorems of electrostatics to be used to describe the formation and properties of any chemical structure composed of localized bonds. There is no distinction made between ionic and covalent bonds. An empirical correlation links the theoretical bond valence to the experimental bond length. The resulting picture of chemical structure predicts where bonds will form, how long they will be, and in what direction they will point. It indicates the conditions for chemical stability, suggesting which reactions a compound might undergo either in solution or at a surface. Electronic anisotropies are handled in an ad hoc manner, in which the VSEPR theory of lone pairs is extended to cases where the lone pairs are inactive or only partially stereoactive. Steric constraints leading to compressed or stretched bonds are quantified by observing the difference between the real and theoretical structures. The potential of the bond valence theory is only beginning to be exploited.

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Notes

  1. 1.

    The terms used in this theory are shown in bold type and are defined in the Glossary (Appendix 1 in this volume).

  2. 2.

    Coordination numbers depend on the nature of both the bonded atoms and are sometimes different even between the same pair of atom types in different compounds. S O is taken arbitrarily to be an atomic property, but if the bonded atom is not oxygen, a different value of N might be more appropriate. For example, carbon has a coordination number of three with oxygen, but four with hydrogen. Reducing the coordination number increases the bonding strength and this is the usual mechanism by which the bond valences of two bonded atoms can be made exactly equal.

  3. 3.

    When the valence shells of two atoms overlap, they split into a low-energy bonding level localized in the overlap region between the atoms and a high-energy antibonding level localized behind the atoms. Because the overlap region is closer to the anion, the bonding level has more of the character of the valence shell of the anion and the antibonding level more the character of the cation. If more electrons are available for bonding than can fit into the anion-like bonding level, they must necessarily occupy the antibonding level, tending to destabilize the bond. The most stable bond is formed when the bonding level is full and the antibonding level is empty, a condition that is expressed by the octet rule. When both the bonding and antibonding levels are full, there is no bonding advantage in overlapping the valence shells, which explains the inertness of the noble gases. The repulsion that prevents the atoms from merging is provided by the electrostatic repulsion that occurs when their cores overlap (the overlap in this case providing no bonding advantage) as well as by the electrostatic repulsion between the two nuclei.

  4. 4.

    The core-and-valence-shell diagrams, used here to illustrate the formation of bonds, are purely schematic. The pairing of electron densities that forms the bond occurs at some place where the electron density of the two atoms overlaps, but its location depends on how the atoms are defined and in any case cannot be identified experimentally.

  5. 5.

    The coordination number of carbon with oxygen is three (cf., Table 1), which is also the coordination number found in elemental carbon (graphite). The coordination number of four is found only in compounds in which carbon is bonded to hydrogen or a halogen, or in compounds such as diamond that are formed under pressure. See Sect. 8.1.1 for a fuller discussion of the coordination number of hydrogen.

  6. 6.

    The changes in the distribution of the valence electron do not mean that the atom loses its spherical symmetry. Because the core and valence shell have similar energies, the distortion in the valence shell can be compensated by the distortion of the core.

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Authors and Affiliations

  1. Brockhouse Institute for Materials Research, McMaster University, Hamilton, ON, Canada, L8S 4M1

    I. David Brown

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  1. I. David Brown
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Correspondence to I. David Brown .

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Editors and Affiliations

  1. McMaster University Brockhouse Institute for Materials Resea, Hamilton, Ontario, Canada

    I. David Brown

  2. Department of Chemistry, Northwestern University, Evanston, Illinois, USA

    Kenneth R. Poeppelmeier

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Brown, I.D. (2013). Bond Valence Theory. In: Brown, I., Poeppelmeier, K. (eds) Bond Valences. Structure and Bonding, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/430_2012_89

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