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Unformatted text preview: Typically, the ﬁrst few hundred simulation steps must be
discarded for the system to thermalize.
An example of T ﬂuctuation: In order to speed-up the thermalization phase, the random
diplacements can be made directly.
These displacements can be derived from the Debye model. Notes A Gaussian probability function is also found for the
displacements from statistical mechanics, now σ= 9h2 T −1
3kB uM D (in Å) (20) where ΘD is the Debye temperature of the material and M
the atomic mass.
On how to generate random numbers, check out the Monte
Note that the treatment above has been completely classical:
Quantum mechanical zero-point vibrations are neglected.
This may cause problems for materials with a high Debye
temperature, depending on the features studied. Notes Summary MD dates back to late 50’s, when it was developed for simple
The idea is to solve numerically the classical equations of
motion for the given system (3N second degree or 6N ﬁrst
degree diﬀerential equations).
Always, new atomic coordinates are evaluated and the state of
the system is calculated at t + ∆t .
For modeling a large system using only a small number of
atoms, periodic boundaries are used (when possible).
The velocities can be initialized according to
Maxwell-Boltzmann distribution, but thermalization of the
system is still needed. Notes ...
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