Investigating Molecular Dynamics with Sparse Grid Surrogate Models

Molecules in nature conform to a geometry that minimizes their potential energy, and some molecules have multiple potential energy minima. One can study how a molecule transitions from one stable geometry to another by studying dynamics on its potential energy surface. The potential energy of a molecule with N atoms is a function of 3N - 6 molecular coordinates and is computed via an expensive optimization process, thus modeling reaction pathways in all 3N - 6 coordinates can be cumbersome for large molecules. In this thesis we describe a cheaper surrogate model for the potential energy surfaces constructed using a sparse grid interpolation algorithm initially developed by Smolyak [198]. Evaluation of the surrogate is much less expensive than the evaluation of the actual energy function, so our technique offers a more computationally efficient way to study dynamics than traditional methods. Furthermore, molecular vibrations and thermal fluctuations can cause randomness in dynamics, so it is of interest to follow many reaction paths at once, necessitating a fast and efficient implementation of Smolyak's interpolation algorithm. We describe a new implementation that computes analytical gradients of Smolyak's interpolating polynomial and is designed to evaluate a large number of points simultaneously. We compare performance times of our implementation to MATLAB's Sparse Grid Interpolation Toolbox [121] and present dynamical simulations for various test molecules.;We also describe how one could extend our new reaction path following method to nonadiabatic dynamics, or dynamics where the Born-Oppenheimer approximation breaks down. In particular, we are interested in studying intersystem crossing dynamics of iron-based molecular complexes for an application to solar cells. We present three-dimensional potential energy surfaces for the [Fe(terpy) 2]2+ complex, the first time these surfaces have been studied in more than two dimensions.;Finally, we employ sparse grids for Bayesian inference for a groundwater model. Interpolation and integration on sparse grids offer an alternative to other expensive methods such as Markov Chain Monte Carlo (MCMC) algorithms to estimate summary statistics for quantities of interest. Here we interpolate the likelihood function and compute marginal densities using sparse grids for four parameters to verify results from MCMC.