My PhD thesis - Condensed Matter Theory - Imperial College London

More documents

Recommendations

Info

CHAPTER 8. APPLYING THE PLASMON NORMAL MODE THEORY TO SLAB SYSTEMS 0.06 LDA short-range Jastrow n(z) 0.04 0.02 0 0 s z Figure 8.18: The electron density profile for a Jastrow factor consisting of only the short-range two-body function u cusp and the corresponding one-body term χ cusp . than having the precise form of u. Up to this point, no optimisation has been carried out: all parameters have been calculated in advance, based only on theoretical considerations. To improve the plasmon Jastrow factor, a reasonable approach is to take the wave function of equation (8.121) as a starting point, and then to add a small one-body term with adjustable parameters, with the aim of restoring the initial density. 8.4.2 Bounded slab Although the plasmon Jastrow factor for the unbounded slab performed well, and should provide a good starting point for optimisation, the unoptimised form did not improve on the simple short-ranged Jastrow factor, which came closer to maintaining the LDA density and hence generated a lower energy. The bounded jellium slab is in some ways a more accurate representation of 160
CHAPTER 8. APPLYING THE PLASMON NORMAL MODE THEORY TO SLAB SYSTEMS 0.1 0.08 0.06 n(z) 0.04 0.02 LDA VMC 0 0 s z Figure 8.19: Electron density profile for the bounded slab, in LDA and VMC (with no Jastrow factor). the system for which the plasmon normal modes were derived; electrons are truly confined to the slab, as in the original model. In the bounded jellium slab, it is not necessary to smooth out the cusps at the slab edges, because the determinantal part of the wave function already goes to zero here. The smoothing is presumably one of the areas which contribute to the small but significant errors in the Jastrow factor for the unbounded slab; the fact that it is not required for the bounded slab suggests that the results for the plasmon Jastrow factor should be better here. Figures 8.19, 8.20, 8.21, 8.22, and 8.23 illustrate the electron density profiles for the various different versions of Jastrow factor; the corresponding energies are recorded in table 8.3. The effect of including only the short-range two-body term (figure 8.20) is to reduce the energy and move the electron density away from the centre of the slab; as in the unbounded slab, the change in the electron density is small. Even with the electrons confined to the slab, the plasmon two-body term com- 161
Page 1 and 2:
Improving the accuracy of surface s
Page 3 and 4:
Acknowledgements I am greatly indeb
Page 5 and 6:
CONTENTS 3.3.4 Importance-sampled d
Page 7 and 8:
CONTENTS 10 Conclusions 181 A The q
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 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
CHAPTER 3. QUANTUM MONTE CARLO METH
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
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: CHAPTER 7. THE ELECTRONIC GROUND-ST
Page 121 and 122: CHAPTER 8. APPLYING THE PLASMON NOR
Page 159: CHAPTER 8. APPLYING THE PLASMON NOR
Page 167 and 168: CHAPTER 9. ENERGY A NEW CALCULATION
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 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 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?