Development of machine learning framework to fit quantum-mechanical ab-initio potential energy surface to a cite-cite molecular potential

An inter-molecular potential is key information required to perform molecular dynamics simulations. Computationally, it can be developed by obtaining an approximate numerical solution of the Schrodinger wave equation for the system and then performing a regression analysis to fit the obtained energy values to a site-site potential. However, such a regression analysis is an NP-hard problem, and therefore, is a challenging task. In this work, we attempt to develop a framework for fitting potential energies obtained through quantum-mechanical ab-initio calculations to a site-site potential. We use the potential energy data given by Robert Hellmann for the N2-H2O system (J. Chem. Eng. Data 64.12: 5959-5973, 2019) to demonstrate our approach. The function governing the value of interaction potential between any two sites depends upon inter-site distance and six constants, i.e., charge on both the sites and four parameters specific to the site pair. These constants along with the local coordinates of the sites inside the molecule are the parameters being optimized in the regression process. Several algorithms including gradient-descent, trust-region, Levenberg-Marquardt algorithm, genetic algorithm, RMSprop, and ADAM has been tested and their results have been reported.