University of Cambridge
Department of Chemistry
Pathways and Energy Landscapes

A thesis submitted to the University of Cambridge in partial fulfilment of the requirements for the degree of Doctor of Philosophy.

Semen A. Trygubenko
Darwin College
January 2006

List of Abbreviations
Glossary of Symbols
1 Introduction
 1.1 The Force Field
 1.2 Creating a Coarse-grained Model
 1.3 Working with a Coarse-grained Model
 1.4 Thesis Overview
2 Finding Rearrangement Pathways
 2.1 Introduction
 2.2 A Double-ended Method: Nudged Elastic Band
 2.3 Optimisation of the Nudged Elastic Band
 2.4 A Single-ended Method: Eigenvector-following
 2.5 Results
 2.6 Summary
3 Properties of Rearrangement Pathways
 3.1 Introduction
 3.2 Localisation
 3.3 Cooperativity
 3.4 Applications to LJ13 and LJ75 Clusters and BLJ256 Liquid
 3.5 Summary
4 Ensembles of Rearrangement Pathways
 4.1 Introduction
 4.2 Chain Graphs
 4.3 Complete Graphs
 4.4 Graph Transformation Method
 4.5 Applications to Sparse Random Graphs
 4.6 Overlapping Sets of Sources and Sinks
 4.7 Applications to Lennard-Jones Clusters
 4.8 Summary
5 Conclusions
 5.1 Summary of Contributions
 5.2 Future Research
 5.3 Outlook
A Rotamers in the CHARMM19 Force Field
B Algorithms
C Pathway Sums for Chain Graphs, 𝒮α,βCN
D Total Escape Probability for Chain Graphs, ΣβCN
E Finding the Shortest and the Fastest Paths