1. Title
1.1. Abstract
1.2. Dedication
2. Contents
2.1. List of Figures
2.2. List of Tables
2.3. Acknowledgements
3. 1 - Introduction
4. Part I - Quantum Monte Carlo Theory
4.1. 2 - Intro to Monte Carlo Techniques
4.2. Fig 2.1 estimate pi with hit-or-miss
4.2.1. 2.2 - Time Propagator & the Density Matrix
4.3. 3 - Imaginary Time Schrodinger Equation
4.3.1. 3.2 - Quantum Monte Carlo Method
4.4. 4 - Importance Sampling
4.4.1. 4.1 - Ab Initio Wavefunctions
4.4.2. 4.2 - Correlation Functions
4.4.2.1. 4.2.1 - Electron-Nuclear Cusp Condition
4.4.2.2. 4.2.2 - Types of Correlation Functions
4.4.2.3. 4.2.3 - Density Dependent Correlation
4.4.3. Fig 4.2 e-e Pade-Jastrow
4.4.4. Fig 4.3 e-e double exponential
4.5. 5 - Variational QMC
4.5.1. 5.1 - Metropolis Algorithm
4.5.2. 5.2 - Variational QMC Algorithm
4.5.3. Fig 5.2 Hydrogen Atom V-QMC Results
4.6. 6 - Diffusion QMC
4.6.0.1. 6.1.1 - Fixed-Node Boundary Conditions
4.6.0.2. 6.1.2 - Released-Node Boundary Conditions
4.6.1. 6.2 - Diffusion QMC Algorithm
4.6.2. 6.3 - Time-Step Bias
4.6.2.1. 6.3.1 - Finite Time-Step Perturbation Potential
4.6.2.2. 6.3.2 - Evaluation Time-Step Errors
4.6.2.3. 6.3.3 - Time-Step Bias of the Hydrogen Atom
4.6.2.4. 6.3.4 - Short-Time Approximation and Nodal Boundary Condtions
4.6.3. Fig 6.2 Hydrogen Atom D-QMC Results
4.6.4. Fig 6.3 Hydrogen Atom D-QMC with Metropolis Results
4.6.5. Fig 6.4 Random Walker Crossing Nodal Boundaries
5. Part II - Alkali Metal Clusters
5.1. 7 - Cluster ``Magic'' Numbers
5.1.1. 7.2 - Shell Model
5.1.2. Table 7.1 Anisotropic Harmonic Oscillator
5.1.3. Fig 7.1 Close icosahedral packing of spheres
5.1.4. Fig 7.2 Initial Li8 geometry
5.1.5. Fig 7.3 Final Li8 geometry
5.2. 8 - D-QMC Lithium Cluster Results
5.2.1. 8.1 - Geometry Optimization
5.2.2. 8.2 - QMC Results
5.2.3. Fig 8.1 CASSCF Li Cluster Geometries
5.2.4. Table 8.2 Li Cluster Energies
5.2.4.1. 8.2.2 Ionization Potential
5.2.4.2. 8.2.3 Binding Energy
5.2.5. Fig 8.2 Li Cluster Ionization Potentials
5.2.6. Fig 8.3 Odd-Even Effect
5.2.7. Fig 8.4 Li Cluster Binding Energies
5.2.8. 8.3 - Lithium One-Electron Densities
5.2.8.1. 8.3.2 - One-Electron Density and Nonnuclear Attractors
5.2.9. Fig 8.5 Li Dimer
5.2.10. Fig 8.6 `Obtuse' Li Trimer
5.2.11. Fig 8.7 `Acute' Li Trimer
5.2.12. Fig 8.8 Planar Li Quadramer
5.2.13. Fig 8.9 Planar Li Quadramer Scatter Plot
5.2.14. Fig 8.10 Planar Li Quadramer - Verticle Cut
5.2.15. Fig 8.11 Triplet Li Quadramer
5.2.16. Fig 8.12 Planar Li Pentamer
5.2.17. Fig 8.13 Planar Li Pentamer Scatter Plot
5.2.18. 8.4 - QMC Computational Scaling
5.2.19. 8.5 Li Cluster Time-Step Bias
5.2.20. Fig 8.14 Li Cluster CPU Time Scaling
5.2.21. 8.6 - Conclusion and Future Work
6. Bibliography
7. App.A - Diffusion/Drift/Branching
7.1. A.2 - Green's Function Stochastic Simulation
7.2. A.3 Renormalization
8. App.B - Expectation Values
8.1. B.2 - Approximate Expectation Values
8.1.1. B.2.2 - Exact Expectation Values by Future Walking
9. App.C - Program Documentation

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