My PhD thesis - Condensed Matter Theory - Imperial College London

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CHAPTER 9. ENERGY A NEW CALCULATION OF THE JELLIUM SURFACE 0.4 0.3 Lowest sub-band wave function 0.2 0.1 0 infinite cell 600 electrons, anti-periodic 600 electrons, periodic 1600 electrons, anti-periodic 1600 electrons, periodic 0 s z Figure 9.4: The lowest sub-band for different boundary conditions and cell sizes. The infinite-cell form is included for reference. Number of electrons Phase Occupation of sub-band 1 2 3 4 5 6 600 0 178 138 134 90 50 10 600 π 168 152 120 104 48 8 1140 0 322 290 242 178 90 18 1140 π 312 296 240 176 104 12 1600 0 442 394 354 242 138 30 1600 π 432 416 328 240 152 32 Table 9.2: The occupation numbers of each sub-band for two cell sizes and periodic or anti-periodic boundary conditions. 172
CHAPTER 9. ENERGY A NEW CALCULATION OF THE JELLIUM SURFACE Number of electrons Phase Fractional occupation of sub-band 1 2 3 4 5 6 600 0 0.297 0.23 0.223 0.15 0.083 0.017 600 π 0.28 0.253 0.2 0.173 0.08 0.013 1140 0 0.282 0.254 0.212 0.156 0.079 0.016 1140 π 0.274 0.260 0.211 0.154 0.091 0.011 1600 0 0.276 0.246 0.221 0.151 0.086 0.019 1600 π 0.27 0.26 0.205 0.15 0.095 0.02 ∞ - 0.279 0.252 0.210 0.154 0.087 0.018 Table 9.3: The fractional occupation of each sub-band. This is simply the occupation number divided by the total number of electrons, and allows the results of finite-cell calculations to be compared with those obtained in the infinite-cell limit. Number of electrons Phase VMC energy DFT correction Corrected energy 600 0 32.56 ± 0.11 -0.268 32.29 600 π 32.32 ± 0.11 -0.128 32.19 1140 0 32.75 ± 0.13 -0.117 32.63 1140 π 32.41 ± 0.14 0.210 32.62 1600 0 32.92 ± 0.14 -0.072 32.85 1600 π 32.73 ± 0.18 0.070 32.80 Table 9.4: Comparison of energies calculated with different versions of the exchange-correlation potential. All energies are in mHa. The trial wave function for the VMC calculations contained no Jastrow factor. usual independent-particle finite-size error correction has been applied, the results are identical to within the statistical error: this is reassuring, but shows that using alternative boundary conditions cannot reduce the remaining finite-size error. The results are in agreement with the hole-squashing model proposed in chapter 6 to explain this error. 173
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Improving the accuracy of surface s
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Acknowledgements I am greatly indeb
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CONTENTS 3.3.4 Importance-sampled d
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CONTENTS 10 Conclusions 181 A The q
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LIST OF FIGURES 5.3 The LDA energy
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LIST OF FIGURES 8.4 The x- and z-co
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LIST OF FIGURES 8.20 Electron densi
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List of Tables 8.1 The function F k
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Chapter 1 Introduction In recent de
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CHAPTER 1. INTRODUCTION A successfu
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CHAPTER 2. MECHANICS THE SIMPLIFICA
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CHAPTER 3. QUANTUM MONTE CARLO METH
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Chapter 4 Errors in QMC simulations
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CHAPTER 4. ERRORS IN QMC SIMULATION
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CHAPTER 5. THE JELLIUM SLAB The jel
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CHAPTER 5. THE JELLIUM SLAB 0.08 0.
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CHAPTER 5. THE JELLIUM SLAB The DMC
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CHAPTER 5. THE JELLIUM SLAB -9.125
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CHAPTER 5. THE JELLIUM SLAB -0.3 Su
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CHAPTER 5. THE JELLIUM SLAB 0.14 be
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CHAPTER 5. THE JELLIUM SLAB At the
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CHAPTER 6. THE MODIFIED PERIODIC CO
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CHAPTER 7. THE ELECTRONIC GROUND-ST
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Page 207 and 208: Bibliography [1] P. H. Acioli and D
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Page 215: BIBLIOGRAPHY [80] C. J. Umrigar, K.
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My PhD thesis - Condensed Matter Theory - Imperial College London

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