Orientation Adaptive Minimal Learning Machine: Application to Thiolate-Protected Gold Nanoclusters and Gold-Thiolate Rings

Abstract

Machine learning (ML) force fields are one of the most common applications of ML methods in the field of physical and chemical science. In the optimal case, they are able to reach accuracy close to the first principles methods with significantly lowered computational cost. However, often the training of the ML methods rely on full atomic structures alongside their potential energies, and applying the force information needs special modifications to standard algorithms. Here we apply distance-based ML methods to predict force norms and estimate the directions of the force vectors of the thiolate-protected gold nanoclusters. The method relies only on local structural information without energy evaluations. We apply the atomic ML forces on the structure optimization of the gold-thiolate rings, $\text{Au}_{25}(\text{SCH}_{3})_{18}$ nanocluster and two known structural isomers of the $\text{Au}_{38}(\text{SCH}_{3})_{24}$ nanocluster. The results demonstrate that the method is well-suited for the structural optimizations of the gold-thiolate systems, where the atomic bonding has a covalent nature in the ligand shell and at the metal-ligand interface. The methodology could be seen as an early attempt to introduce equivariant learning to distance-based ML methods.