thesis

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Linear-scaling methods in ab initio quantum-mechanical calculations
A dissertation submitted for the degree of
Doctor of Philosophy
at the University of Cambridge

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Peter David Haynes
Christ's College, Cambridge
July 1998

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Preface
Psalm 8
Acknowledgements
Contents
List of Figures
List of Tables
1. Introduction
2. Many-body Quantum Mechanics
3. Quantum Mechanics of the Electron Gas
4. Density-Matrix Formulation
5. Localised basis-set
6. Penalty Functionals
- 6.1 Kohn's method
  - 6.1.1 Variational principle
  - 6.1.2 Implementation problems
- 6.2 Corrected penalty functional method
7. Computational implementation
8. Relating linear-scaling and plane-wave methods
9. Results and discussion
- 9.1 Bulk crystalline silicon
- 9.2 Scaling
  - 9.2.1 System-size scaling
  - 9.2.2 Scaling with density-matrix cut-off
10. Conclusions
- 10.1 Summary
- 10.2 Further work
A. Bessel function identities
B. Conjugate gradients
Bibliography

Peter Haynes