Robustness in the fitting of molecular mechanics parameters

Automated methods for force field parametrization have attracted renewed interest of the community, but the robustness issues associated with the often ill-conditioned nature of parameter optimization have been vastly underappreciated in the recent literature. For this reason, this article offers a detailed description of the origin and nature of these issues. This includes a discussion of the restrained electrostatic potential fit (RESP) charge model, which does contain explicit robustness-enhancing measures albeit not in the context of bonded parameters, and which forms an inspiration for the present work. It is also discussed how all the bonded parameters in a Class I force field can be simultaneously fit using the linear least squares (LLS) procedure, and a novel restraining strategy is presented that overcomes robustness issues in the LLS fitting of bonded parameters while minimally impacting the fitted values of well-behaved parameters. Two variants of this methodology are then validated through a number of case studies, including the fitting of bond-charge increments, which illustrates the method's potential for robustly solving general LLS problems beyond force field parametrization.