Contents

• List of Tables
• List of Figures
• Quantum Monte Carlo and the JAGP wave-function
  • Variational Monte Carlo
    • Forces with finite variance
  • Functional form of the wave function
    • Pairing determinant
    • One body term
    • Two body Jastrow term
    • Three Body Jastrow term
  
  
• Optimization Methods
  • Stochastic Reconfiguration
    • Setting the SR parameters
    • Stabilization of the SR technique
  • Structural optimization
  • Hessian Optimization
  
  
• Results on Molecules
  • Application of the JAGP to molecules
  • Small diatomic molecules, methane, and water
  • Benzene and its radical cation
  
  
• Quantum Monte Carlo on extended systems
  • Periodic Wave-Function
    • Periodic orbitals
    • The wave-function for high pressure hydrogen
  • Coulomb Interactions in periodic systems
    • Ewald Sums
    • Forces with finite variance in periodic systems
  • How to evaluate pressure
  • Empirical laws of melting
  
  
• A new technique for the simulation of electronic systems at finite temperature by means of noisy QMC forces
  • The Born-Oppenheimer approximation
  • Dealing with Quantum Monte Carlo noise
  • Canonical ensemble by Generalized Langevin Dynamics
    • Numerical integration of the Generalized Langevin Equation
  • Practical implementation of the finite temperature dynamics
    • Setting the parameters in the Langevin dynamics
    • Following the ionic dynamics
    • Reducing the number of parameters
  
  
• Preliminary results on high pressure hydrogen
  • Comparison with previous calculations
  • Pair Correlation Functions
  • Another possible phase in liquid hydrogen
  
  
• Conclusions
  • Future developments
  
  
• Re-sampling methods
  • Jackknife
  
  
• Local Energy and its derivatives
  • Kinetic Energy
    • Derivatives of the Kinetic Energy
  • Pairing determinant
  • Three-body
  
  
• Cusp conditions
• Determinant derivatives
• Error Analysis due to finite time step in the GLE integration in a simple case
• Bibliography