Analytical hessian fitting schemes for efficient determination of force-constant parameters in molecular mechanics

Building upon our recently developed partial Hessian fitting (PHF) method (Wang et al., J. Comput. Chem. 2016, 37, 2349), we formulated and implemented two other rapid force-field parameterization schemes called full Hessian fitting (FHF) and internal Hessian fitting (IHF), and comparisons were made among these three parameterization schemes to assess their performance. FHF minimizes deviation between the Hessian matrices in Cartesian coordinates computed by quantum mechanics (QM) and molecular mechanics (MM), to determine the best possible MM force-constant parameters. While PHF requires step-by-step fittings of 3 × 3 partial Hessian matrices, FHF compares the lower triangular part of the QM and MM Hessian matrices, which allows simultaneous determination of all force-constant parameters. In addition to this simple FHF scheme, IHF was developed such that it considers the Hessian matrices in redundant internal coordinates, where all possible internal coordinates that arise from the user-defined interatomic connectivity are utilized. The results show that IHF performs best overall, followed by PHF and then FHF. Python-based programing codes were developed to automate various tedious steps involved in the parameterization processes. © 2017 Wiley Periodicals, Inc.