Quantum Monte-Carlo Programming : For Atoms, Molecules, Clusters, and Solids.

Quantum Monte- Carlo Programming -- Contents -- Preface -- 1 A First Monte Carlo Example -- 1.1 Energy of Interacting Classical Gas -- 1.1.1 Classical Many-Particle Statistics and Some Thermodynamics -- 1.1.2 How to Sample the Particle Density? -- 2 Variational Quantum Monte Carlo for a One-Electron System -- 3 Two Electrons with Two Adiabatically Decoupled Nuclei: Hydrogen Molecule -- 3.1 Theoretical Description of the System -- 3.2 Numerical Results of Moderate Accuracy -- 3.3 Controlling the Accuracy -- 3.4 Details of Numerical Program -- 4 Three Electrons: Lithium Atom -- 4.1 More Electrons, More Problems: Particle and Spin Symmetry -- 4.1.1 Antisymmetry and Decomposition of the Many-Body Wave Function -- 4.1.2 Three-Electron Wave Function -- 4.1.3 General Wave Function -- 4.1.4 Relaxing Symmetry of Total Spin -- 4.2 Electron Orbitals for the Slater Determinant -- 4.3 Slater Determinants: Evaluation and Update -- 4.4 Some Important Observables in Atoms? -- 4.4.1 The Module "observables" -- 4.5 Statistical Accuracy -- 4.6 Ground State Results -- 4.6.1 Results for Lithium Atom -- 4.6.2 Code of Main Program, Modules of Variables, of Statistic, of Jastrow Factor, and of Output -- 4.7 Optimization? -- 5 Many-Electron Confined Systems -- 5.1 Model Systems with Few Electrons -- 5.2 Orthorhombic Quantum Dot -- 5.2.1 Confined Single-Particle Wave Functions -- 5.2.2 Details of Program -- 5.2.3 Energy and Radial Density -- 5.2.4 Pair-Correlation Function -- 5.2.5 Program of the Pair-Correlation Function -- 5.3 Spherical Quantum Dot -- 5.3.1 Fundamentals of DFT -- 5.3.2 DFT Calculation of the Jellium Cluster: Methodology -- 5.3.3 QMC Calculation of the Jellium Cluster: Methodology -- 5.3.4 QMC Code for the Calculation of Jellium Clusters -- 5.3.5 Comparison between DFT and QMC Calculations of Jellium Clusters.

6 Many-Electron Atomic Aggregates: Lithium Cluster -- 6.1 Clusters and Nanophysics -- 6.2 Cubic BCC Arrangement of Lithium Atoms -- 6.2.1 Structure of the Main Program -- 6.2.2 Single-Electron Wave Functions and Structure of the Determinant -- 6.2.3 Geometric Setting of the Cluster -- 6.2.4 Changes in the Program -- 6.3 The Cluster: Intermediate between Atom and Solid -- 6.3.1 111 Cluster: Li2 -- 6.3.2 222 Cluster -- 6.3.3 333 Cluster -- 6.3.4 444 Cluster -- 6.3.5 Cluster Size -- 7 Infinite Number of Electrons: Lithium Solid -- 7.1 Infinite Lattice -- 7.1.1 The Lattices -- 7.1.2 Structure of the Electrostatic Potential -- 7.1.3 Ewald Summation and Tabulation -- 7.1.4 Finite-Size Effects -- 7.2 Wave Function -- 7.2.1 Linear Combination of Atomic Orbitals -- 7.2.2 Plane Waves -- 7.3 Jastrow Factor -- 7.3.1 Standard Choice -- 7.3.2 Principal Ideas and Extensions -- 7.4 Results for the 333 and 444 Superlattice Solid -- 8 Diffusion Quantum Monte Carlo (DQMC) -- 8.1 Towards a First DQMC Program -- 8.1.1 Relating Schrödinger Equation to Diffusion -- 8.1.2 Generate Gaussian Random Numbers -- 8.1.3 Application -- 8.2 Conclusion -- 9 Epilogue -- Appendix -- A.1 The Interacting Classical Gas: High Temperature Asymptotics -- A.2 Pseudorandom Number Generators -- A.3 Some Generalization of the Jastrow Factor -- A.4 Series Expansion -- A.5 Wave Function Symmetry and Spin -- A.5.1 Four Electrons -- A.6 Infinite Lattice: Ewald Summation -- A.7 Lattice Sums: Calculation -- References -- Index.

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