4.7.2.1. Radial Distribution Functions — MDAnalysis.analysis.rdf
This module contains two classes to calculate radial pair distribution functions (radial distribution functions or “RDF”). The RDF \(g_{ab}(r)\) between types of particles \(a\) and \(b\) is
which is normalized so that the RDF becomes 1 for large separations in a homogenous system. The RDF effectively counts the average number of \(b\) neighbours in a shell at distance \(r\) around a \(a\) particle and represents it as a density.
The radial cumulative distribution function is
and the average number of \(b\) particles within radius \(r\)
(with the appropriate density \(\rho\)). The latter function can be used to compute, for instance, coordination numbers such as the number of neighbors in the first solvation shell \(N(r_1)\) where \(r_1\) is the position of the first minimum in \(g(r)\).
In InterRDF_s
, we provide an option density. When density is
False
, it will return the RDF \(g_{ab}(r)\); when density is
True
, it will return the density of particle \(b\) in a shell at
distance \(r\) around a \(a\) particle, which is
4.7.2.1.1. Average radial distribution function
InterRDF
is a tool to calculate average radial distribution functions
between two groups of atoms. Suppose we have two AtomGroups A
and
B
. A
contains atom A1
, A2
, and B
contains B1
,
B2
. Given A
and B
to InterRDF
, the output will be the
average of RDFs between A1
and B1
, A1
and B2
, A2
and
B1
, A2
and B2
. A typical application is to calculate the RDF of
solvent with itself or with another solute.
- class MDAnalysis.analysis.rdf.InterRDF(g1, g2, nbins=75, range=(0.0, 15.0), exclusion_block=None, **kwargs)[source]
Intermolecular pair distribution function
The radial distribution function is calculated by histogramming distances between all particles in g1 and g2 while taking periodic boundary conditions into account via the minimum image convention.
The exclusion_block keyword may be used to exclude a set of distances from the calculations.
Results are available in the attributes
rdf
andcount
.- Parameters
g1 (AtomGroup) – First AtomGroup
g2 (AtomGroup) – Second AtomGroup
nbins (int (optional)) – Number of bins in the histogram
exclusion_block (tuple (optional)) – A tuple representing the tile to exclude from the distance array.
verbose (bool (optional)) – Show detailed progress of the calculation if set to
True
Example
First create the
InterRDF
object, by supplying two AtomGroups then use therun()
methodrdf = InterRDF(ag1, ag2) rdf.run()
Results are available through the
results.bins
andresults.rdf
attributes:plt.plot(rdf.results.bins, rdf.results.rdf)
The exclusion_block keyword allows the masking of pairs from within the same molecule. For example, if there are 7 of each atom in each molecule, the exclusion mask (7, 7) can be used.
New in version 0.13.0.
Changed in version 1.0.0: Support for the
start
,stop
, andstep
keywords has been removed. These should instead be passed toInterRDF.run()
.Changed in version 2.0.0: Store results as attributes
bins
,edges
,rdf
andcount
of theresults
attribute ofAnalysisBase
.- results.bins
numpy.ndarray
of the centers of the nbins histogram bins.New in version 2.0.0.
- bins
Alias to the
results.bins
attribute.Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use
results.bins
instead.
- results.edges
numpy.ndarray
of the nbins + 1 edges of the histogram bins.New in version 2.0.0.
- edges
Alias to the
results.edges
attribute.Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use
results.edges
instead.
- results.rdf
numpy.ndarray
of the radial distribution function values for theresults.bins
.New in version 2.0.0.
- rdf
Alias to the
results.rdf
attribute.Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use
results.rdf
instead.
- results.count
numpy.ndarray
representing the radial histogram, i.e., the raw counts, for allresults.bins
.New in version 2.0.0.
- count
Alias to the
results.count
attribute.Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use
results.count
instead.
- run(start=None, stop=None, step=None, verbose=None)
Perform the calculation
4.7.2.1.2. Site-specific radial distribution function
InterRDF_s
calculates site-specific radial distribution
functions. Instead of two groups of atoms it takes as input a list of pairs of
AtomGroup, [[A, B], [C, D], ...]
. Given the same A
and B
to
InterRDF_s
, the output will be a list of individual RDFs between
A1
and B1
, A1
and B2
, A2
and B1
, A2
and B2
(and
similarly for C
and D
). These site-specific radial distribution
functions are typically calculated if one is interested in the solvation shells
of a ligand in a binding site or the solvation of specific residues in a
protein.
- class MDAnalysis.analysis.rdf.InterRDF_s(u, ags, nbins=75, range=(0.0, 15.0), density=False, **kwargs)[source]
Site-specific intermolecular pair distribution function
- Parameters
u (Universe) – a Universe that contains atoms in ags
nbins (int (optional)) – Number of bins in the histogram
density (bool (optional)) –
False
: calculate \(g_{ab}(r)\);True
: calculate the true single particle density \(n_{ab}(r)\).New in version 1.0.1: This keyword was available since 0.19.0 but was not documented. Furthermore, it had the opposite meaning. Since 1.0.1 it is officially supported as documented.
Example
First create the
InterRDF_s
object, by supplying one Universe and one list of pairs of AtomGroups, then use therun()
method:from MDAnalysisTests.datafiles import GRO_MEMPROT, XTC_MEMPROT u = mda.Universe(GRO_MEMPROT, XTC_MEMPROT) s1 = u.select_atoms('name ZND and resid 289') s2 = u.select_atoms('(name OD1 or name OD2) and resid 51 and sphzone 5.0 (resid 289)') s3 = u.select_atoms('name ZND and (resid 291 or resid 292)') s4 = u.select_atoms('(name OD1 or name OD2) and sphzone 5.0 (resid 291)') ags = [[s1, s2], [s3, s4]] rdf = InterRDF_s(u, ags) rdf.run()
Results are available through the
results.bins
andresults.rdf
attributes:plt.plot(rdf.results.bins, rdf.results.rdf[0][0, 0])
(Which plots the rdf between the first atom in
s1
and the first atom ins2
)To generate the cumulative distribution function (cdf) in the sense of “particles within radius \(r\)”, i.e., \(N_{ab}(r)\), use the
get_cdf()
methodcdf = rdf.get_cdf()
Results are available through the
results.cdf
attribute:plt.plot(rdf.results.bins, rdf.results.cdf[0][0, 0])
(Which plots the cdf between the first atom in
s1
and the first atom ins2
)New in version 0.19.0.
Changed in version 1.0.0: Support for the
start
,stop
, andstep
keywords has been removed. These should instead be passed toInterRDF_s.run()
.Changed in version 2.0.0: Store results as attributes
bins
,edges
,rdf
,count
andcdf
of theresults
attribute ofAnalysisBase
.- results.bins
numpy.ndarray
of the centers of the nbins histogram bins; all individual site-specific RDFs have the same bins.New in version 2.0.0.
- bins
Alias to the
results.bins
attribute.Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use
results.bins
instead.
- results.edges
numpy.ndarray
of the nbins + 1 edges of the histogram bins; all individual site-specific RDFs have the same bins.New in version 2.0.0.
- edges
Alias to the
results.edges
attribute.Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use
results.edges
instead.
- results.rdf
list
of the site-specific radial distribution functions or density functions for thebins
. The list containslen(ags)
entries. Each entry for thei
-th pair[A, B] = ags[i]
in ags is anumpy.ndarray
with shape(len(A), len(B))
, i.e., a stack of RDFs. For example,results.rdf[i][0, 2]
is the RDF between atomsA[0]
andB[2]
.New in version 2.0.0.
- rdf
Alias to the
results.rdf
attribute.Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use
results.rdf
instead.
- results.count
list
of the site-specific radial histograms, i.e., the raw counts, for allresults.bins
. The data have the same structure asresults.rdf
except that the arrays contain the raw counts.New in version 2.0.0.
- count
Alias to the
results.count
attribute.Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use
results.count
instead.
- results.cdf
list
of the site-specific cumulative counts, for allresults.bins
. The data have the same structure asresults.rdf
except that the arrays contain the cumulative counts.This attribute only exists after
get_cdf()
has been run.New in version 2.0.0.
- cdf
Alias to the
results.cdf
attribute.Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use
results.cdf
instead.
- get_cdf()[source]
Calculate the cumulative counts for all sites.
This is the cumulative count within a given radius, i.e., \(N_{ab}(r)\).
The result is returned and also stored in the attribute
results.cdf
.- Returns
cdf – list of arrays with the same structure as
results.rdf
- Return type
- run(start=None, stop=None, step=None, verbose=None)
Perform the calculation