| This thesis introduces a newly discovered relationship between calculated values of the delocalization index and Lewis bond orders, for polar bonds. Using the methods of the Theory of Atoms in Molecules, properties of individual atoms—defined as regions of real space—can be calculated from numerical molecular wavefunctions. In addition to determining the number of electrons in an atom, and thus the atomic charge, one can also calculate the extent to which the charge density on a given atom is delocalized to the each of the other atoms in the molecule. This property is known as the delocalization index.; For a non-polar bond (equal sharing of electrons), the delocalization index calculated from a Hartree-Fock wavefunction is found to correspond closely with the bond order predicted by the Lewis model of chemical bonding. The delocalization index decreases, however, as the bond polarity increases. The relationship between the decreasing delocalization index and the increasing atomic charges is quantified in this work. A simple quadratic relationship is observed between the delocalization index, δ(A,H) and the charge transfer, q(H), across the A-H bond in a series of hydrides, AHn. The same relationship, δ = 1 − q 2, is shown to be derived from the Hartree-Fock expressions for the delocalization index and the atomic charges and can be generalized to more than one pair of electrons. The same derivation applies to two other definitions of bond order proposed by other workers.; A method for employing these correlations, along with other calculated properties, to establish the Lewis bond order for a series of related molecules, with differently polarized bonds, is presented. The method is applied to seven series of phosphorus containing molecules and three series of nitrogen containing molecules. The octet rule is found to be more important for the nitrogen systems than for the phosphorus systems. |
