End-to-End Differentiable Force Field Generator with Crystal Structure Differentiation and Matching

Differentiable programming has accelerated the development of force-field (FF) parameterization techniques. Specifically, automatic differentiation (AD) facilitates energy and force matching by differentiating them with respect to the FF parameters; hereinafter, referred to as force differentiation and matching (FDM). Conversely, crystal structure matching with AD has persisted as a challenge because the converged structures optimized by the iterative algorithm cannot be differentiated with respect to the FF parameters. Therefore, in this paper, we propose a structure differentiation and matching (SDM) method, wherein the converged structures are directly differentiated using the parameters with implicit function differentiation and matched with the experimental crystal structures. Subsequently, with a case study, we compared the reproducibility of the crystal structures, internal atomic coordinates, and lattice energies on eight exemplary molecules with the differentiable Ewald method for long-range interactions. The results indicated that SDM outperformed FDM on all three criteria. The FFs generated by SDM reproduced the lattice constants with a mean error of 0.56 %, the internal atomic coordinates with an error of 0.16 Angstrom, and the lattice energies with an error of 0.14 kcal/mol. The corresponding accuracies obtained with FDM were 1.2 %, 0.22 Angstrom, and 2.40 kcal/mol, respectively. Furthermore, we performed molecular dynamic simulations on a supercell, containing more than 3000 atoms, to confirm if the crystal structures were preserved under temperature fluctuations at 300 K.Overall, this method is not limited to Amber-type FFs and can be easily applied to the other types of FFs. Thus, we believe that SDM will emerge as one of the new standards for parameterizing FFs with crystal structures.