random_notes.txt

Ab initio -> Schrodinger eq for electrons and classical for ions (I can
 simulate not too many atoms and I may lose some symmetry of the system, not
  always best choice)

Classical -> no electrons, only classical for ions using a suitable
 potential (must be choosen in an appropriate way otherwise bad results,
  main problem in classical molecular dynamics is to choose, sometimes you
   can't find a good potential at all)
   

Silver is good with two atoms potential, while Silicon no because the
 molecule has angles. Two atoms potential is good with closely packed
  lattice (ex fcc). Lennard Jones, not terrible job using it for Silver.
   Important 1/r^6 because it's Van der Walls.
   

We expect zero force to act on the internal atoms of the bulk, and non zero
 in the external. In a infinite lattice all atoms have zero force, because
  there are always two symmetric atoms that balance.
  

In a molecular dynamics code the time step is of the order of femtoseconds,
 so the total time of the simulation is going to be of order of nanoseconds,
  maybe microseconds, but cannot reach for example one hour (would require
   too many iterations). I need small time step to properly simulate, but
    not too short otherwise I would have a too short total time of the
     simulation. 
     

Velocity Verlet has the problem of assigning initial velocity (just look at
 the expression, it is not known). How do we assign? We link it to the
  concept of temperature (tricky because we are in microcanonical). We use
   equipartition theorem to define temperature as proportional to the total
    kinetic energy. Will fluctuate because we are not in canonical. There is
     a thermalization time, you can estimate it but we start from a given
      value. The thermalization temperature will oscillate aroung 1/2 the
       initial (if temperature not too big to use harmonic approx, and we
        start from a energy minimum configuration, otherwise you have to
         find by trials and errors the initial temperature to have the final
          you want). I can use Boltzmann dist to extract, but since it 
          thermalizes anyway I use uniform distribution. 
           

With PBC I cant' describe thermal expansion of a solid. Can't describe a
 distortion because it would replicate it.