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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Calculating radial distribution functions
Radial distribution functions can be calculated from one or more pymatgen Structure objects by using the vasppy.rdf.RadialDistributionFunction class.
Step1:  The default required arguments for creating a RadialDistributionFunction object are a list of pymatgen Structure objects, and the numerical indices of the atoms (or Site objects) that we want to compute the rdf between.
Step2:  To compute a rdf between different species, we need to pass both indices_i and indices_j.
Step3:  The Na and Cl sublattices are equivalent, so the Na–Na and Cl–Cl rdfs sit on top of each other.
A smeared rdf can be produced using the smeared_rdf() method, which applies a Gaussian kernel to the raw rdf data. The smeared_rdf() method takes on optional argument sigma, which can be used to set the width of the Gaussian (default = 0.1)
Step4:  Selecting atoms by their species strings
Atom indices can also be selected by species string with the RadialDistributionFunction.from_species_strings() method
Step5:  Calculating a RDF from a VASP XDATCAR
Step6:  Weighted RDF calculations
For calculating RDFs from Monte Carlo simulation trajectories RadialDistributionFunction can be passed an optional weights argument, which takes a list of numerical weights for each structure.
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Python Code:
# Create a pymatgen Structure for NaCl
from pymatgen import Structure, Lattice
# Create a pymatgen Structure for NaCl
from pymatgen import Structure, Lattice
a = 5.6402 # NaCl lattice parameter
lattice = Lattice.from_parameters(a, a, a, 90.0, 90.0, 90.0)
lattice
structure = Structure.from_spacegroup(sg='Fm-3m', lattice=lattice,
                          species=['Na', 'Cl'],
                          coords=[[0,0,0], [0.5, 0, 0]])
structure
from vasppy.rdf import RadialDistributionFunction
Explanation: Calculating radial distribution functions
Radial distribution functions can be calculated from one or more pymatgen Structure objects by using the vasppy.rdf.RadialDistributionFunction class.
End of explanation
indices_na = [i for i, site in enumerate(structure) if site.species_string is 'Na']
indices_cl = [i for i, site in enumerate(structure) if site.species_string is 'Cl']
print(indices_na)
print(indices_cl)
rdf_nana = RadialDistributionFunction(structures=[structure], 
                                      indices_i=indices_na)
rdf_clcl = RadialDistributionFunction(structures=[structure], 
                                      indices_i=indices_cl)
Explanation: The default required arguments for creating a RadialDistributionFunction object are a list of pymatgen Structure objects, and the numerical indices of the atoms (or Site objects) that we want to compute the rdf between.
End of explanation
rdf_nacl = RadialDistributionFunction(structures=[structure], 
                                      indices_i=indices_na, indices_j=indices_cl)
import matplotlib.pyplot as plt
plt.plot(rdf_nana.r, rdf_nana.rdf, label='Na-Na')
plt.plot(rdf_clcl.r, rdf_clcl.rdf, label='Cl-Cl')
plt.plot(rdf_nacl.r, rdf_nacl.rdf, label='Na-Cl')
plt.legend()
plt.show()
Explanation: To compute a rdf between different species, we need to pass both indices_i and indices_j.
End of explanation
plt.plot(rdf_nana.r, rdf_nana.smeared_rdf(), label='Na-Na') # default smearing of 0.1
plt.plot(rdf_clcl.r, rdf_clcl.smeared_rdf(sigma=0.050), label='Cl-Cl')
plt.plot(rdf_nacl.r, rdf_nacl.smeared_rdf(sigma=0.2), label='Na-Cl')
plt.legend()
plt.show()
Explanation: The Na and Cl sublattices are equivalent, so the Na–Na and Cl–Cl rdfs sit on top of each other.
A smeared rdf can be produced using the smeared_rdf() method, which applies a Gaussian kernel to the raw rdf data. The smeared_rdf() method takes on optional argument sigma, which can be used to set the width of the Gaussian (default = 0.1)
End of explanation
rdf_nana = RadialDistributionFunction.from_species_strings(structures=[structure], 
                                      species_i='Na')
rdf_clcl = RadialDistributionFunction.from_species_strings(structures=[structure], 
                                      species_i='Cl')
rdf_nacl = RadialDistributionFunction.from_species_strings(structures=[structure], 
                                      species_i='Na', species_j='Cl')
plt.plot(rdf_nana.r, rdf_nana.smeared_rdf(), label='Na-Na')
plt.plot(rdf_clcl.r, rdf_clcl.smeared_rdf(), label='Cl-Cl')
plt.plot(rdf_nacl.r, rdf_nacl.smeared_rdf(), label='Na-Cl')
plt.legend()
plt.show()
Explanation: Selecting atoms by their species strings
Atom indices can also be selected by species string with the RadialDistributionFunction.from_species_strings() method:
End of explanation
from pymatgen.io.vasp import Xdatcar
xd = Xdatcar('data/NaCl_800K_MD_XDATCAR')
rdf_nana_800K = RadialDistributionFunction.from_species_strings(structures=xd.structures, 
                                                                species_i='Na')
rdf_clcl_800K = RadialDistributionFunction.from_species_strings(structures=xd.structures, 
                                                                species_i='Cl')
rdf_nacl_800K = RadialDistributionFunction.from_species_strings(structures=xd.structures, 
                                                                species_i='Na', species_j='Cl')
plt.plot(rdf_nana_800K.r, rdf_nana_800K.smeared_rdf(), label='Na-Na')
plt.plot(rdf_clcl_800K.r, rdf_clcl_800K.smeared_rdf(), label='Cl-Cl')
plt.plot(rdf_nacl_800K.r, rdf_nacl_800K.smeared_rdf(), label='Na-Cl')
plt.legend()
plt.show()
Explanation: Calculating a RDF from a VASP XDATCAR
End of explanation
struct_1 = struct_2 = struct_3 = structure
rdf_nacl_mc = RadialDistributionFunction(structures=[struct_1, struct_2, struct_3],
                                         indices_i=indices_na, indices_j=indices_cl,
                                         weights=[34, 27, 146])
# structures and weights lists must be equal lengths
Explanation: Weighted RDF calculations
For calculating RDFs from Monte Carlo simulation trajectories RadialDistributionFunction can be passed an optional weights argument, which takes a list of numerical weights for each structure.
End of explanation
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