This study developed and implemented a semi-automatic material exploration scheme to modelize the solvent-solubility of tetraphenylporphyrin derivatives. In particular, the scheme involved the following steps: definition of a practical chemical search space, prioritization of molecules in the space using an extended algorithm for submodular function maximization without requiring biased variable selection or pre-existing data, synthesis & automatic measurement, and machine-learning model estimation. The optimal evaluation order selected using the algorithm covered several similar molecules (32% of all targeted molecules, whereas that obtained by random sampling and uncertainty sampling was ~7% and ~4%, respectively) with a small number of evaluations (10 molecules: 0.13% of all targeted molecules). The derived binary classification models predicted ‘good solvents’ with an accuracy > 0.8. Overall, we confirmed the effectivity of the proposed semi-automatic scheme in early-stage material search projects for accelerating a wider range of material research.

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.

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.