Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)




The object of this thesis is to examine a basic deficiency in the valence bond theory as developed by Heitler, London, Slater and Eyring and to offer an alternate general approach that leads to a greater reduction of the secular determinant for some molecular structures. It is observed that in the formation of independent valance bond eigenfunctions, there exists an implicit assumption that one is working with planar or near-planar molecules. But when a polyhedral structure is considered, it is found that the independent valence bond eigenfunctions are no longer suitable basis functions for the symmetry group of the structure. This is best seen in the fact that the function which correspond to the Kekule` and Dewar type structures are not independent in the polyhedral case. An alternate method is developed for obtaining eigenfunctions. Symmetry operators are used to form linear combinations of the spin state eigenfunctions having eigenvalue zero for Sz. These symmetry eigenfunctions are formed under different irreducible representations, thus reducing the secular determinant. Linear combinations of theses symmetry arguments so that each new linear combination is an eigenfunction of the total spin angular momentum operator, S2. Those final eigenfunctions having an eigenvalue of zero for S2 are solved to obtain the ground state energy. Square, hexagonal, tetrahedral, octahedral, and cubical configurations are considered by this method.

Library of Congress Subject Headings

Molecular orbitals
Chemistry, Physical and theoretical




South Dakota State University