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

In this paper, we present a new force field (FF) parameterization method with direct matching of crystal structures and atomic charges optimization in end-to-end differentiable manner. The advancement of force field (FF) parameterization methods has been accelerated by differentiable programming. Automatic differentiation (AD) has facilitated energy and force matching by differentiating these quantities with respect to the FF parameters, which we mention as force differentiation and matching (FDM). Nevertheless, crystal structure matching with AD remains difficult due to the converged structures optimized by the iterative algorithm being non-differentiable with respect to the FF parameters. To overcome this limitation, we introduce structure differentiation and matching (SDM) technique for generating FFs of small organic molecules using reference data, including stable monomer structures, crystal structures, lattice energies, and potential energy surfaces (PESs) of dihedral angles. SDM employs implicit function differentiation (IFD) and differentiable Ewald techniques to optimize FF parameters and atomic charges correspondingly. Our case study of eight exemplified molecules demonstrates that SDM substantially outperforms the conventional FDM, with error factors reduced to less than one-quarter with the charge optimization method called SDM(q-opt). This strategy achieves remarkable precision in reproducing lattice constants, atomic configurations, lattice energies, and PESs. Furthermore, molecular dynamics simulations confirm the stability of the generated crystal structures. This method can be adapted to other FF categories, such as polarized FFs and those with explicit hydrogen bonding interactions. We foresee that SDM(q-opt) will emerge as a standard method for parameterizing FFs using crystal structures.