Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)

Department / School



Before quantum mechanics was developed, the theory of chemical bonding was generally discussed only qualitatively. Since then, however, several theories based on quantitative studies have been advanced. Even the use of quantum mechanics makes it possible to get exact results for only the simplest problems. Nevertheless quantitative results can be obtained for the n-boby problem by using approximation methods. The use of group theory in chemical bonding, first proposed by Bethe, simplified the problem a great deal. This allows one to take advantage of the symmetry properties of a molecule or ion in determining the bonding waves functions and energy levels in the cuboctahedral and icosahedral structures. The directed vvalence method was developed by Heitler, London, Pauling, and Slater has been employed to determine the cuboctahedral structure. This method is characterized by the “hybrid” orbitals of the central atom. The strength of these bonds are calculated and compared with those of the icosahedral structure. The bonds which could be formed in this structure are also discussed briefly. The molecular orbital method due to Lennard-Jones, Hund, and Mulliken is used to find the molecular orbitals and energy levels involved in bonding in both the cuboctahedral and icosahedral structures. In this method the bonding orbitals are considered to extend over the whole molecule, and they are formed from linear combinations of atomic orbitals of all the atoms involved. The difficulties encountered in applying the latter method to the icosahedral structure are discussed briefly, and other possible methods for obtaining a solution are suggested.

Library of Congress Subject Headings

Chemistry, Physical and theoretical
Quantum theory
Chemical bonds


Includes bibliographical references



Number of Pages



South Dakota State University