First-Principle Oligopeptide Structural Optimization with Physical Prior Mean-Driven Gaussian Processes: A Test of Synergistic Impacts of the Kernel Functional and Coordinate System

First-principle molecular structural determination is critical in many aspects of computational modeling, and yet, the precise determination of a local minimum for a large-sized organic molecule is time-consuming. The recently developed nonparametric model, the physical Gaussian Processes (GPs) with physics-informed prior mean function, has demonstrated its efficiency in exploring the potential-energy surfaces and molecular geometry optimizations. Two essential ingredients in physical GPs, the kernel functional and the coordinate systems, could impact the optimization efficiency, and yet the choice of which on the model performance has not yet been studied. In this work, we constructed a testing dataset consisting of 20 oligopeptides and performed a systematic investigation using various combinations of coordinates (structural descriptors) and kernel functionals to optimize these biologically interesting molecules to local minima at the density-functional tight-binding (DFTB) quantum mechanical level. We conclude that the combination of the kernel functional form and coordinate systems matter significantly in model performance as well as its robustness in locating local minima. For our testing set, the synergy between the periodic kernel and the non-redundant delocalized internal coordinates yields the best overall performance for physical GPs, significantly superior to other choices.