Introduction
The relax_dynamic calculation style dynamically relaxes an atomic configuration for a specified number of timesteps. Upon completion, the mean, \(\langle X \rangle\), and standard deviation, \(\sigma_X\), of all thermo properties, \(X\), are computed for a specified range of times. This method is meant to measure equilibrium properties of bulk materials, both at zero K and at various temperatures.
Version notes
2018-07-09: Notebook added.
2019-07-30: Description updated and small changes due to iprPy version.
2020-05-22: Version 0.10 update - potentials now loaded from database.
2020-09-22: Setup and parameter definition streamlined.
Disclaimers
The calculation reports the standard deviation, \(\sigma_X\) of the measured properties not the standard error of the mean, \(\sigma_{\langle X \rangle}\). The two are related to each other according to \(\sigma_{\langle X \rangle} = \sigma_X \sqrt{\frac{C}{N}}\), where \(N\) is the number of samples taken of \(X\), and \(C\) is a statistical inefficiency due to the autocorrelation of the measurements with time. Obtaining a proper estimate of \(\sigma_{\langle X \rangle}\) requires either estimating \(C\) from the raw thermo data (not done here), or only taking measurements sporadically to ensure the samples are independent.
Good (low error) results requires running large simulations for a long time. The reasons for this are:
Systems have to be large enough to avoid issues with fluctuations across the periodic boundaries.
Runs must first let the systems equilibrate before meaningful measurements can be taken.
The standard deviation, \(\sigma\), of thermo properties is proportional to the number of atoms, \(N_a\) as \(\sigma \propto \frac{1}{\sqrt{N_a}}\).
The standard error, \(\sigma_x\) of thermo properties is proportional to the number of samples taken, \(N\) as \(\sigma_x \propto \frac{1}{\sqrt{N}}\).