Link to HTML version of Power Point Slides for Lecture 14

The work of Car and Parrinello in 985 ushered in an entire new approach to calculation of the properties of materials. In one stroke they introduced new algorithms that are the core of modern iterative methods and the approach of dealing with structure and electronic properties in one method

• Brief outline of classical molecular dynamics
  • Verlet algorithm for numerical integration of coupled F=ma equations
  • Simulated annealing to lowest energy state
• Forces on atoms from the electrons - the force (Hellmann-Feynman) theorem
  • The electron density alone is sufficient to determine forces
• The Car-Parrinello Methods
  • References
    R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985)
    the original - very readable
    J. Garner, Computers in Physics 4, 395 (1990). Nice discussion; simple examples.
    M. Payne, et. al., Rev Mod. Phys. 64, 1045, (1992). Most complete recent large review
    
  • Solution of quantum equations by classical molecular dynamics
    • Solving quantum equations by using a "fictitious mass" and a fictitious set of Newtonian equations
    • Annealing by reducing the temperature leads system to ground state - the same solution as found by matrix diagonalization
    • Examples of simple quantum systems
      • A simple 2 x 2 Hamiltonian - solution by Car-Parrinello molecular dynamics and "simulated annealing"
      • Particle in a box
  • FFT's instead of dense matrix multiplication
  • Examples of use in large scale calculations
    • "Ab Initio" Molecular dynamics of solids and liquids
    • The real Newtonian equations for atoms with forces from electrons from the force theorem
    • Example: melting of Carbon