A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals

Abstract

Abstract:In molecular orbital theory, the bond integral parameter k is used to calculate the bond integral β for different molecular structures. The bond integral parameter k, which represents the ratio of bond integrals between two atoms of a diatomic molecule, is a function of the bond length. This parameter is usually obtained empirically; however, it will be shown that k can be determined analytically by utilizing the overlap integral S. k will be calculated for different atomic orbital combinations (ss,pp) of σ and π interactions as a function of bond length for a carbon-carbon diatomic molecule. The results, which are represented graphically, indicate that different atomic orbitals in different interactions can have the same, or very close to the same, k values. The graphs reveal some significant features for the different atomic orbital combinations with respect to magnitude and profile, as well as illustrate good agreement with experimental results, which validates the utilization of the overlap integral calculation method for the determination of the bond integral parameter k.