A Comparison of the Molecular Orbital (MO) and Orbital Exchange Methods for Calculating the Chemical Bond

This paper discusses the major differences between the linear combination of atomic orbitals MO and orbital exchange methods for calculating chemical bonds. The MO method employs explicit functions whereas the orbital exchange method performs calculations numerically. The MO method assumes that the overlapping orbitals of the bonding atoms are distinguishable. The combined orbital method postulates that overlapping atomic orbitals are indistinguishable to the extent of overlap/(1.0+overlap). The distinction between orthogonality and distinguishability is discussed. The combined-orbital orbitals are little changed from the atomic orbitals of the bonding atoms. The MO orbitals are significantly changed from the atomic orbitals. The orbital exchange method calculates the bond energy directly; the MO method calculates the total energy of the molecule. The orbital exchange method utilizes no or few variable parameters, to produce more accurate results than the MO method. The MO method optimizes the bond energy in terms of a large number of variable parameters, sometimes a very large number.