md2011-02-notes 1.3

md2011-02-notes 1.3 - Typically, the first few hundred...

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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 Θ 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 Carlo course. 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 molecular systems. 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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md2011-02-notes 1.3 - Typically, the first few hundred...

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