My PhD thesis - Condensed Matter Theory - Imperial College London

More documents

Recommendations

Info

CONTENTS 7 The electronic ground-state wave function from classical plasmon normal modes 106 7.1 Derivation of the classical plasmon Hamiltonian and Lagrangian . . . 107 7.2 Quantisation and diagonalisation of the Hamiltonian . . . . . . . . . 111 7.3 The ground-state wave function . . . . . . . . . . . . . . . . . . . . . 114 7.4 Normal modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 8 Applying the plasmon normal mode theory to slab systems 120 8.1 Classical plasmons in slabs . . . . . . . . . . . . . . . . . . . . . . . . 120 8.1.1 The metal conductivity . . . . . . . . . . . . . . . . . . . . . . 121 8.1.2 Solving Maxwell’s equations . . . . . . . . . . . . . . . . . . . 122 8.1.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 124 8.1.4 Surface plasmons . . . . . . . . . . . . . . . . . . . . . . . . . 125 8.1.5 Bulk plasmons . . . . . . . . . . . . . . . . . . . . . . . . . . 130 8.1.6 Surface plasmons in electrostatic theory . . . . . . . . . . . . 134 8.2 The plasmon wave function for slab systems . . . . . . . . . . . . . . 137 8.2.1 Approximate analytic solution for an infinite slab . . . . . . . 141 8.3 Creating a realistic Jastrow factor . . . . . . . . . . . . . . . . . . . . 143 8.3.1 Removing undesirable cusps . . . . . . . . . . . . . . . . . . . 147 8.3.2 Applying the electron-electron cusps . . . . . . . . . . . . . . 148 8.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 8.4.1 Unbounded slab . . . . . . . . . . . . . . . . . . . . . . . . . . 155 8.4.2 Bounded slab . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 9 A new calculation of the jellium surface energy 166 9.1 Improved orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 9.2 Alternative k-point sampling . . . . . . . . . . . . . . . . . . . . . . . 169 9.3 Surface energy calculations . . . . . . . . . . . . . . . . . . . . . . . . 174 9.3.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 9.3.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 6
CONTENTS 10 Conclusions 181 A The quasi-2D Ewald sum 184 A.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 A.2 Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 B The cusp conditions 192 C Integrating the cusp function 196 D Reconstructing a probability density function 200 D.1 Use of a weighting function . . . . . . . . . . . . . . . . . . . . . . . 200 D.2 Projection onto basis functions . . . . . . . . . . . . . . . . . . . . . 204 Bibliography 207 7
Page 1 and 2: Improving the accuracy of surface s
Page 3 and 4: Acknowledgements I am greatly indeb
Page 5: CONTENTS 3.3.4 Importance-sampled d
Page 9 and 10: LIST OF FIGURES 5.3 The LDA energy
Page 11 and 12: LIST OF FIGURES 8.4 The x- and z-co
Page 13 and 14: LIST OF FIGURES 8.20 Electron densi
Page 15 and 16: List of Tables 8.1 The function F k
Page 17 and 18: Chapter 1 Introduction In recent de
Page 19 and 20: CHAPTER 1. INTRODUCTION A successfu
Page 21 and 22: CHAPTER 2. MECHANICS THE SIMPLIFICA
Page 31 and 32: CHAPTER 3. QUANTUM MONTE CARLO METH
Page 57 and 58:
Chapter 4 Errors in QMC simulations
Page 59 and 60:
CHAPTER 4. ERRORS IN QMC SIMULATION
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
CHAPTER 5. THE JELLIUM SLAB The jel
Page 73 and 74:
CHAPTER 5. THE JELLIUM SLAB 0.08 0.
Page 75 and 76:
CHAPTER 5. THE JELLIUM SLAB The DMC
Page 77 and 78:
CHAPTER 5. THE JELLIUM SLAB -9.125
Page 79 and 80:
CHAPTER 5. THE JELLIUM SLAB -0.3 Su
Page 81 and 82:
CHAPTER 5. THE JELLIUM SLAB 0.14 be
Page 83 and 84:
CHAPTER 5. THE JELLIUM SLAB At the
Page 85 and 86:
CHAPTER 6. THE MODIFIED PERIODIC CO
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
CHAPTER 7. THE ELECTRONIC GROUND-ST
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
CHAPTER 8. APPLYING THE PLASMON NOR
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
CHAPTER 9. ENERGY A NEW CALCULATION
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Chapter 10 Conclusions The original
Page 183 and 184:
CHAPTER 10. CONCLUSIONS pling and o
Page 185 and 186:
APPENDIX A. THE QUASI-2D EWALD SUM
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
APPENDIX B. THE CUSP CONDITIONS may
Page 195 and 196:
APPENDIX B. THE CUSP CONDITIONS wit
Page 197 and 198:
APPENDIX C. INTEGRATING THE CUSP FU
Page 199 and 200:
APPENDIX C. INTEGRATING THE CUSP FU
Page 201 and 202:
APPENDIX D. RECONSTRUCTING A PROBAB
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Bibliography [1] P. H. Acioli and D
Page 209 and 210:
BIBLIOGRAPHY [19] A. G. Eguiluz and
Page 211 and 212:
BIBLIOGRAPHY [39] P. R. C. Kent, R.
Page 213 and 214:
BIBLIOGRAPHY [59] H. J. Monkhorst a
Page 215:
BIBLIOGRAPHY [80] C. J. Umrigar, K.
show all

My PhD thesis - Condensed Matter Theory - Imperial College London

Create successful ePaper yourself

Delete template?

Save as template?