4.7.3. 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
4.7.3.1. 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 [75]
 range (tuple or list (optional)) – The size of the RDF [0.0, 15.0]
 exclusion_block (tuple (optional)) – A tuple representing the tile to exclude from the distance array. [None]
 verbose (bool (optional)) – Show detailed progress of the calculation if set to
True
; the default isFalse
.
Example
First create the
InterRDF
object, by supplying two AtomGroups then use therun()
methodrdf = InterRDF(ag1, ag2) rdf.run()
Results are available through the
bins
andrdf
attributes:plt.plot(rdf.bins, rdf.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()
.
bins
¶ numpy.ndarray
of the centers of the nbins histogram bins.

edges
¶ numpy.ndarray
of the nbins + 1 edges of the histogram bins.

rdf
¶ numpy.ndarray
of the radial distribution function values for thebins
.

count
¶ numpy.ndarray
representing the radial histogram, i.e., the raw counts, for allbins
.

run
(start=None, stop=None, step=None, verbose=None)¶ Perform the calculation
Parameters:
4.7.3.2. Sitespecific radial distribution function¶
InterRDF_s
calculates sitespecific 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 sitespecific 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]¶ Sitespecific intermolecular pair distribution function
Parameters:  u (Universe) – a Universe that contains atoms in ags
 ags (list) – a list of pairs of
AtomGroup
instances  nbins (int (optional)) – Number of bins in the histogram [75]
 range (tuple or list (optional)) – The size of the RDF [0.0, 15.0]
 density (bool (optional)) –
False
: calculate \(g_{ab}(r)\);True
: calculate the true single particle density \(n_{ab}(r)\). The default isFalse
.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
bins
andrdf
attributes:plt.plot(rdf.bins, rdf.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
cdf
attribute:plt.plot(rdf.bins, rdf.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()
.
bins
¶ numpy.ndarray
of the centers of the nbins histogram bins; all individual sitespecific RDFs have the same bins.

edges
¶ numpy.ndarray
of the nbins + 1 edges of the histogram bins; all individual sitespecific RDFs have the same bins.

rdf
¶ list
of the sitespecific 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,rdf[i][0, 2]
is the RDF between atomsA[0]
andB[2]
.

count
¶ list
of the sitespecific radial histograms, i.e., the raw counts, for allbins
. The data have the same structure asrdf
except that the arrays contain the raw counts.

cdf
¶ list
of the sitespecific cumulative counts, for allbins
. The data have the same structure asrdf
except that the arrays contain the cumulative counts.This attribute only exists after
get_cdf()
has been run.

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
cdf
.Returns: cdf – list of arrays with the same structure as rdf
Return type: list

run
(start=None, stop=None, step=None, verbose=None)¶ Perform the calculation
Parameters: