Development and Evaluation of Geometry Optimization Algorithms in Conjunction with ANI Potentials

An efficient yet accurate method for producing a large amount of energy data for molecular mechanical force field (MMFF) parameterization is on demand, especially for torsional angle parameters which are typically derived to reproduce ab initio rotational profiles or torsional potential energy surfaces (PESs). Recently, an active learning potential (ANI-1x) for organic molecules which can produce smooth and physically meaningful PESs has been developed. The high efficiency and accuracy make ANI-1x especially attractive for geometry optimization at low cost. To apply the ANI-1x potential in MMFF parameterization, one needs to perform constrained geometry optimization. In this work, we first developed a computational protocol to constrain rotatable torsional angles and other geometric parameters for a molecule whose geometry is described by Cartesian coordinates. The constraint is successfully achieved by force projection for the two conjugated gradient (CG) algorithms. We then conducted large-scale assessments on ANI-1x along with four different optimization algorithms in reproducing DFT energies and geometries for two CG algorithms, CG backtracking line search (CG-BS) and CG Wolfe line search (CG-WS), and two quasi-Newton algorithms, Broyden-Fletcher-Goldfarb-Shanno (BFGS) and low-memory BFGS (L-BFGS). Note that CG-BS is a new algorithm we developed in this work. All four algorithms take the ANI energies and forces to optimize a molecule geometry. Last, we conducted a large-scale assessment of applying ANI-1x in MMFF development in three aspects. First, we performed full optimizations for 100 drug molecules, each consisting of five distinct conformations. The average root-mean-square error (RMSE) between ANI-1x and DFT is about 1.3 kcal/mol, and the root-mean-square displacement (RMSD) of heavy atoms is about 0.35 Å. Second, we generated torsional PESs for 160 organic molecules, and constrained optimizations were performed for up to 18 conformations for each PES. We found that the RMSE of all the conformers is 1.23 kcal/mol. Last, we carried out constrained optimizations for alanine dipeptide with both ϕ and φ angles being frozen. The Ramachandran plots indicate that the two CG algorithms in conjunction with the ANI-1x potential could well reproduce the DFT-optimized geometries and torsional PESs. We concluded that CG-BS and CG-WS are good choices for generating PESs, while CG-WS or BFGS is ideal for performing full geometry optimization. With the continuously increased quality of ANI, it is expected that the computational algorithms and protocols presented in this work will have great applications in improving the quality of an existing small-molecule MMFF.