# Simulation methodology for the kinetics of solid state atomic systems

## Abstract

A major challenge in computational chemistry and solid-state atomic systems is overcoming the limitations of molecular dynamics (MD) simulations by utilizing alternative methods to efficiently calculate the rate of chemical reactions and diffusion events. The focus of my dissertation is the following: 1) development of new methods to overcome the time scale limitations of MD; 2) greater understanding of the failures of current methods; and 3) application of the current methods to solid-state atomic systems.

Harmonic transition state theory (HTST) is a powerful approximation within the transition state theory (TST) framework that reduces the problem of capturing reaction rates to indentifying the lowest energy first order saddle points. In this work, the biased gradient squared descent (BGSD) saddle point finding method is introduced. BGSD first converts all critical points into global minima by transforming the PES into the gradient squared landscape. A biasing term is added to stabilize critical points at a specified energy levels and destabilize other critical points. BGSD is shown to be competitive with the dimer method in terms of force evaluations required to find a set of low-energy saddle points around a reactant minimum.

We use adaptive kinetic Monte Carlo simulations to investigate the transformation of a topologically closed packed (TCP) structure to a cubic phase in molybdenum. Molybdenum is one refractory element added to nickel-based superalloys to improve properties of the material for high-temperature applications. However, when the concentrations of refractory elements are too high TCP phases can form and degrade properties of the material. This study is a first step towards an atomistic description of the transformation of TCP phases to cubic phases.

A successful method for accelerating MD simulations is Voter's hyperdynamics approach, which adds a non-negative bias potential to the system's potential energy surface (PES). A novel bias potential is introduced which utilizes a machine learning technique and constructs the bias potential based off of the distance to the ridge. The bias potential is shown to produce boost factors, or computational acceleration, that scale well with dimensionality.

HTST does a remarkably good job of capturing reaction rates at low temperatures. However, as the temperature increases results generated by HTST can di ffer from direct MD rates by an order of magnitude. The successes and failures of HTST to capture reactions rates are investigated with the goal of inspiring increased accuracy at less cost than other existing methods.