New Transition-State Optimization Methods By Carefully Selecting Appropriate Internal Coordinates

Abstract

Geometry optimization is a key step in the computational modeling of chemical reactions because one cannot model a chemical reaction without first accurately determining the molecular structure, and electronic energy, of the reactants and products, along with the transition state that connects them. These structures are stationary points— the reactant and product structures are local minima, and the transition state is a saddle point with one negative-curvature direction—on the molecular potential energy surface. Over the years, many methods for locating these stationary points have been developed. In general, the problem of finding reactant and product structures is relatively straightforward, and reliable methods exist. Converging to transition states is much more challenging. Because of the difficulty of transition-state optimization, researchers have designed optimization methods specifically for this problem. These methods try to make good choices for the initial geometry, the system of coordinates used to represent the molecule, the initial Hessian, the Hessian updating method, and the step-size. The transition-state optimization method developed in this thesis required considering all of these methods. Specifically, a new method for finding an initial guess geometry was developed in chapter 2; good choices for a coordinate system for representing the molecule were explored in chapters 2 and 6; different choices for the initial Hessian are considered in chapter 5; chapters 3 and 4 present, and test, a sophisticated new method for updating the Hessian and controlling the step-size during the optimization. iv The methods created in the process of this research led to the development of Saddle, a general-purpose geometry optimizer for transition states and stable structures, with and without constraints on the molecular coordinates. Saddle can be run in conjunction with the Gaussian program or almost any other quantum chemistry program, and it converges significantly more often than the other traditional methods we tested.