Category:Ensemble properties: Difference between revisions

In a molecular-dynamics calculation, VASP simulates a specific ensemble. In principle, any property of the system can be monitored, and then one can take the ensemble average of this property. For some observables, VASP provides convenient tags, articles, and files that help evaluate these so-called ensemble properties.

Theory

For any property ${\displaystyle {\mathcal {A}}}$ of the system, we can define the observable macroscopic property ${\displaystyle {\mathcal {A}}_{\mathrm {obs} }}$ by taking the ensemble average:

${\displaystyle {\mathcal {A}}_{\mathrm {obs} }=\left\langle {\mathcal {A}}\left(p(t),q(t)\right)\right\rangle _{\mathrm {time} }=\lim _{t_{\mathrm {obs} }\to \infty }{\frac {1}{t_{\mathrm {obs} }}}\int _{0}^{t_{\mathrm {obs} }}\,{\mathcal {A}}\left(p(t),q(t)\right)\,\mathrm {d} t.}$

Here, ${\displaystyle t_{\mathrm {obs} }}$ corresponds to the simulation time, ${\displaystyle p(t)}$ and ${\displaystyle q(t)}$ are the canonical momenta and positions, and an average of ${\displaystyle {\mathcal {A}}\left(p(t),q(t)\right)}$ is taken over time ${\displaystyle t}$.

How to

References