RadialDistribution

class RadialDistribution(md_trajectory, start_time=None, end_time=None, cutoff_radius=None, resolution=None, pair_selection=None, time_resolution=None, info_panel=None)

Class for calculating the radial distribution from an MDTrajectory.

Parameters:
  • md_trajectory (MDTrajectory | MoleculeConfiguration | BulkConfiguration | DeviceConfiguration | SurfaceConfiguration) – The MDTrajectory or configuration the radial distribution should be calculated for.
  • cutoff_radius (PhysicalQuantity of type length) – Upper limit on sampled distances (must be positive).
    Default: Half the diagonal of the unit cell
  • start_time (PhysicalQuantity of type time) – The start time.
    Default: 0.0 * fs
  • end_time (PhysicalQuantity of type time) – The end time.
    Default: The last frame time.
  • resolution (PhysicalQuantity of type length) – The binning of the histogram.
    Default: 0.05 * Angstrom
  • pair_selection (sequence) – Only include contributions between this selection of atoms. Either None or a sequence containing two of the following types: Element, tag name, list of indices, or None.
    Default: All atoms pairs are considered.
  • time_resolution (PhysicalQuantity of type time) – The time interval between snapshots in the MD trajectory that are included in the analysis.
  • info_panel (InfoPanel (Plot2D)) – Info panel to show the calculation progress.
    Default: No info panel
data()

Return the radial distribution function.

distances()

Return the distance values associated with the radial distribution function.

Usage Examples

Load an MDTrajectory and calculate the RadialDistribution function between Al and O:

md_trajectory = nlread('alumina_trajectory.nc')[-1]

rdf = RadialDistribution(md_trajectory,
                         cutoff_radius=8.0*Angstrom,
                         pair_selection=[Aluminum, Oxygen])

# Get the bin_centers and the histogram of the radial distribution.
distances = rdf.distances().inUnitsOf(Angstrom)
histogram = rdf.data()

# Plot the data using pylab.
import pylab

pylab.plot(distances, histogram, label='Al-O RDF')
pylab.xlabel('r (Ang)')
pylab.ylabel('g(r)')
pylab.legend()

pylab.show()

radial_distribution.py

Calculate the RadialDistribution function between the first atom in the configuration and the rest of the system:

rdf = RadialDistribution(md_trajectory,
                         cutoff_radius=20.0*Angstrom,
                         pair_selection=[[0], None])

radial_distribution_2.py

Notes

The radial distribution (or pair correlation) function is calculated as

\[g(r) = \frac{1}{4\pi r^2} \frac{1}{N\rho} \sum_{i = 1}^N \sum_{j\neq i}^N \langle \delta(r - | \mathbf{r}_i - \mathbf{r}_j | ) \rangle\]

It is also possible to calculate the partial radial distribution by specifying two selections A and B (elements or index lists) in pair_selection. In that case the radial distribution is calculated as

\[g_{AB}(r) = \frac{1}{4\pi r^2} \frac{N}{\rho N_A N_B} \sum_{i \in A} \sum_{j \in B, j \neq i}^N \langle \delta(r - | \mathbf{r}_i - \mathbf{r}_j | ) \rangle\]

The normalization via the density ensures that for large distances the radial distribution approaches unity.

As the radial distribution assumes a homogeneous system, this analysis is not well-defined for trajectories of DeviceConfiguration or SurfaceConfiguration types. In that case only the radial distribution of the central region atoms is calculated, using infinite electrodes as boundary conditions.