Quantum Molecular Dynamics

• Introduction

  • Scope of Physical/Chemical Problems
  • Scaling of Many-Body Methods with Basis Set Size
  • Nucleonic Motion

• Born-Oppenheimer Approximation

  • Basics
  • Derivation of Born-Oppenheimer Approximation
  • Discussion of Nucleonic Motion
  • Validity of Born-Oppenheimer Approximation

• Density Functional Theory

• Quantum Molecular Dynamics

  • Classical Limit of Born-Oppenheimer Approximation
  • Classical Limit of Time-Dependent Density Functional Theory
  • Car-Parrinello Dynamics: I) Formalism and Interpretation
  • Car-Parrinello Dynamics: II) Practical Realization
  • Advanced Optimization Techniques

• Normconserving Pseudopotentials

  • Basic Idea
  • Concepts for Construction of Pseudopotentials
  • Transferability
  • Explicit Construction of Troullier-Martins Pseudopotentials
  • Unscreening
  • Convergence Issues
  • Illustrative Results

• Periodic Systems

  • Bravais Lattices
  • Reciprocal Lattice
  • Electrons in Periodic Potentials: Bloch States
  • Electrons in Periodic Potentials: Integration
  • Orthonormality and Completeness
  • Energy Bands, Fermi Surface
  • Explicit Example: Periodic Square Well Potential
  • Lattice Potential: Consequences of Periodicity
  • Lattice Potential: Long-range singularity and Kleinman-Bylander Transformation
  • Kohn-Sham Equations
  • Total Energy: Ewald Decomposition
  • Gradient of Total Energy
  • Supercell Concept

• Appendix 1: Basic Commutators

• Appendix 2: Derivation of Preconditioned Conjugate Gradient Updating Formula

• Appendix 3: Basic Properties of the Maxwell-Boltzmann Distribution

• Appendix 4: Number of Nodes of Lowest Eigenstate

• Appendix 5: Relativistic Troullier-Martins Pseudopotentials

• Appendix 6: Higher Brillouin Zones

• Appendix 7: Error Function and Basic Ewald Integral

• Appendix 8: Multipole Expansion of Electrostatic Interaction

• Bibliography