A Near Black Box Parameter Optimizer for NDDO-Descendant Semiempirical Methods: Demonstrations for MNDO and AM1

We provide a detailed description of an enhanced version of our previous geometry-corrected parameter optimization algorithm capable of accounting for reference geometries including all pertinent equations necessary for its implementation. The algorithm directly incorporates the derivatives of key lengths and angles, unlike PARAM, which relies on derived geometric functions. As a demonstration of the utility of our novel algorithm, reparameterizations for MNDO and AM1 using 1187 CHNO molecules in the PM7 training set are reported and compared to analogous results obtained with PARAM program used in the development of the PMx models; additional reparameterizations employing a partition of the full CHNO data set into training and validation subsets were also examined. Our AM1 reparameterizations achieve substantial improvements in the predicted geometrical properties (bond lengths, bond angles, and dihedral angles), demonstrating that the derived geometrical reference functions are ill-suited for parameter optimization and may also inadvertently incentivize smaller force constants for chemical bonds; however, this arises at the cost of decreased accuracies for reaction barrier heights, which is viewed to be a consequence of the absence of nonequilibrium geometries from the training set. Together, our results suggest that judicious parameter refinement could substantially enhance the performance of NDDO-descendant semiempirical models.