Idea of Classical Molecular Dynamics Simulations
- Solve classical Newton's equations for N particles fully including all binary interaction
potentials and external forces
- Include quantum mechanical wave effects for the electrons by means of effective quantum pair potentials (Kelbg potential), see below.
Newton's second law
with the effective quantum interaction potential, the Kelbg potential
- The Kelbg potential was derived by G. Kelbg in the 1960s, see refs. in the
paper of Golubnichiy et al.
- The Kelbg potential goes over to the Coulomb potential for large distances.
- At small interparticle separation, it is finite (in contrast to the Coulomb potential)
accounting for the wave nature of microparticles
- lambda is the thermal DeBroglie wave length (\lambda=\Lambda/2\pi)
Newton's equations can be solved with the initial conditions
The result are random trajectories, so one has to average over many runs with
varying initial conditions (or over a long run time).
From these trajectories all properties of classical systems can be computed.
For quantum systems, one has to solve the Schrödinger equation instead of
Newton's equations. To find a numerical approach which is of comparable rigorousity and simplicity
to classical MD remains a challenging problem.
We use a very promising approach due to V.S. Filinov, for details look at
our recent paper and the cited references.
See MD simulation results for dense plasmas
Research Results |
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