Open Access Dissertation
Date of Award
H B. Schlegel
The research presented in this dissertation is divided into 5 chapters. In Chapter 2, a method for reducing the number of coordinates required to accurately reproduce a known chemical reaction pathway by applying principal component analysis to a number of geometries along the pathway (expressed in either Cartesian coordinates or redundant internal coordinates) is described and applied to 9 example reactions. Chapter 3 introduces new methods for estimating the structure of and optimizing transition states by utilizing information about the atomic bonding in the reactants and products. These methods are then benchmarked against a standard transition state optimization approach utilizing a test set of 20 reactions, with energies computed at both semiempirical and density functional theory levels of theory. Chapter 4 is a collection of 3 new, alternative approaches (Flowchart Hessian updating, Scaled Rational Function Optimization, Quasi-Rotation coordinate propagation), to handling aspects of a typical Quasi-Newton minimization. These new approaches are then compared to their standard counterparts by optimizing a set of 20 molecules using either ab initio or density functional theory potential energy surfaces.
The final two chapters of this thesis focus on the development of a new path optimization framework, the Variational Reaction Coordinate (VRC) method. This framework seeks to improve upon the “chain of states” methods, which minimize the energy of a series of structures while using constraints, fictitious forces or reparameterization schemes to maintain the distribution of points along the path. In the VRC method, a functional representing the energy of the entire reaction is minimized by varying the expansion coefficients of a continuous function used to represent the reaction path. In Chapter 5, an algorithm is outlined along with the discussion and application of constraints and coupling terms that may be used to improve the efficiency and reliability of the method, with analytical test surfaces used to demonstrate the method’s performance. Chapter 6 focuses on the inclusion of redundant internal coordinates and methods for approximating the potential energy surface into the VRC framework, in order to reduce the per-iteration computational cost of the VRC method to something comparable to the “chain of states” approaches so that it may be practically applied to the study of reactions using high accuracy density functional theory and ab initio potential energy surfaces.
Birkholz, Adam Benjamin, "Development Of New Algorithms For Exploring The Potential Energy Landscape Of Chemical Reactions" (2015). Wayne State University Dissertations. 1367.