Evaluating and Improving Approximate LCAO-MO Theory with Restored Overlap and Bond Order Bond Energy Corrections

<p>Modified Neglect of Differential Overlap semi-empirical models PM6 and PM7 were tested against a wide array of systems. Noble gas dimers, noble gases with small polar molecules, hydrocarbon dimers, hydrogen bonded dimers, Army Research Labs and University of Delaware high energy compounds and metal dimers were used to examine non-covalent interactions which have been explicitly included in PM7. The W1BD test set composed of enthalpies of formation, ionization potentials, electron affinities and proton affinities was used to understand the behavior of the models on properties for which they are principally parameterized.</p> <p>Before testing could be completed it was found that the correction in PM7 had numerical instabilities. A new correction was designed to mimic PM7 as closely as possible without the numerical instabilities. This new model was called PM7R8 and displayed nearly identical functionality to PM7 with improved potential curves and continuous analytic first and second derivatives.</p> <p>With the instabilities removed the models PM6, PM7 and PM7R8 were tested. Non-covalent bound systems showed promising results in PM7/PM7R8 for systems which had the correct underlying behavior. Other systems were disastrously wrong and exposed some fundamental problems in the underlying model. The results on the the W1BD test set were mixed. Error cancellation within the model was not effective and it was shown that a few reactions would get worse despite the individual components being better described. Problems also arose in the energies of atomic orbitals which may be the cause of some of the failures in the model.</p> <p>Work continued by development of new semi-empirical models. First the overlap was restored to the MNDO Hamiltonian to explore the effects of having the correct physics in the model. Ultimately this research led all the way back to understanding the approximations in the two electron integrals. The second path followed was a fully empirical density based correction. Parameters were fit to reproduce APF/STO-3g values.</p>