A consistent semiempirical theory for the calculation of ground and excited state properties

It is shown that all valence semiempirical theories are incapable of treating screening effects in a consistent fashion. This is due to their development in terms of the zero differential overlap assumption which leads to an imbalance of interactions in off-diagonal matrix elements. A new formulation of semiempirical theories is presented which is based on an expansion of the Fock operator in terms of averaged potentials centered either on atoms or in bonds. STO-3G calculations are carreid out to demonstrate that our averaging procedure is a reasonable one. The form of current semiempirical theories is easily recovered although many of the integrals are ascribed a somewhat different meaning. Screening now arises naturally as does a valence index and obvious corrections that should be made upon changes in hybridization. The resonance integral is given a somewhat modified interpretation and on this basis, a unified treatment of both ground and excited state properties is developed. A new method of calculation is proposed which makes use of CNDO/S matrix elements and wave functions and hence, yields reliable ionization potentials and transition energies. Ground state properties are calculated with a modified, theoretically consistent expression for the total energy and new parameters are introduced for this purpose.