Ionic conductivity from ams.rkf trajectory¶
First, an ams.rkf trajectory with ions in the system needs to be calculated, as is done, for example, in the ionic conductivity Tutorial. Next, the ions in the system and their respective charges need to be identified.
Example usage: (Download get_charged_ions.py)
$AMSBIN/amspython get_charged_ions.py /path/to/ams.rkf
import sys
import os
import numpy
from scm.plams import AMSJob, Settings, Units, AMSAnalysisJob
from scm.plams import to_rdmol, init, finish
def main(filename):
"""
Main functionality (charge assignment to ions)
"""
# Get the molecular system
job = AMSJob.load_external(filename)
mol = job.molecule
elements = [at.symbol for at in mol.atoms]
# Assign atomic charges
charges = mol.guess_atomic_charges(adjust_to_systemcharge=False)
charges = add_metal_charges(mol, charges)
# Find ions
molindices = mol.get_molecule_indices()
ions = {}
ioncharges = {}
nions = {}
formulas = {}
for imol, atoms in enumerate(molindices):
submol = mol.get_fragment(atoms)
label = submol.label()
q = sum([charges[i] for i in atoms])
if abs(q) > 1e-10:
if not label in ions.keys():
ions[label] = []
ioncharges[label] = q
nions[label] = 0
formulas[label] = submol.get_formula()
ions[label] += atoms
nions[label] += 1
for k, q in ioncharges.items():
print(formulas[k], q, nions[k])
return ions, ioncharges
def add_metal_charges(mol, charges):
"""
Assign charges to the metal ions
"""
system_charge = mol.properties.charge if not isinstance(mol.properties.charge, Settings) else 0.0
if system_charge == sum(charges):
return charges
dq = system_charge - sum(charges)
# print ('Charge difference: ',dq)
elements = [at.symbol for at in mol.atoms]
metals = [i for i, at in enumerate(mol.atoms) if at.is_metallic]
# print ('Metals: ',metals)
electron_affinities, ionization_energies = read_ea_ie()
chi0 = {iat: 0.5 * (electron_affinities[elements[iat]] + ionization_energies[elements[iat]]) for iat in metals}
J0 = {iat: ionization_energies[elements[iat]] - electron_affinities[elements[iat]] for iat in metals}
Jc = 1.0
# Set up the matrix (A) and vector b, to then solve Ax = b
# The last element of the vector (and last row of A) hold the constraint sum(x_i) = Q_tot
matrix = numpy.zeros((len(metals) + 1, len(metals) + 1))
b = numpy.ones(len(metals) + 1)
for i, iat in enumerate(metals):
matrix[i, i] = J0[iat]
b[i] = chi0[iat]
matrix[-1, :-1] = 1.0
matrix[:-1, -1] = 1.0
b[-1] = dq
# print ('Matrix:')
# print (matrix)
# print ('b: ',b)
# Solve Ax+b
mcharges = numpy.linalg.solve(matrix, b)
mcharges_int = [round(q) for q in mcharges]
if sum(mcharges_int) != dq:
print([(elements[iat], mcharges[i]) for i, iat in enumerate(metals)])
raise Exception("Predicted charges non-integer!")
for i, iat in enumerate(metals):
charges[iat] = mcharges_int[i]
return charges
def read_ea_ie():
"""
Read in the electron affinities and ionization energies from file
"""
electron_affinities = {}
ionization_energies = {}
for el, l in data.items():
electron_affinities[el] = data[el][0]
ionization_energies[el] = data[el][1]
return electron_affinities, ionization_energies
# Element:[ ElectronAffinity, IonizationEnergy]
data = {
"Li": [0.0227110811, 0.1981523452],
"Na": [0.0201386286, 0.1888547667],
"Al": [0.0162064511, 0.2199814425],
"Si": [0.0508978112, 0.2995804744],
"Sc": [0.0069088726, 0.2411123028],
"Ti": [0.0029031965, 0.2509243718],
"V": [0.0192933941, 0.2479109274],
"Cr": [0.0244750486, 0.2486826632],
"Fe": [0.0059901395, 0.2903931438],
"Co": [0.0242913020, 0.2896214081],
"Ni": [0.0424822164, 0.2807648214],
"Cu": [0.0451281676, 0.2839252631],
"Ga": [0.0110247967, 0.2204591837],
"Ge": [0.0496115849, 0.2903196452],
"Rb": [0.0171986828, 0.1535019187],
"Y": [0.0112820419, 0.2284705360],
"Zr": [0.0156552112, 0.2437950033],
"Nb": [0.0328171447, 0.2483886686],
"Mo": [0.0274149943, 0.2606261929],
"Tc": [0.0202121272, 0.2675350654],
"Ru": [0.0385867883, 0.2705117605],
"Rh": [0.0417839793, 0.2741131941],
"Pd": [0.0204693725, 0.3063790990],
"Ag": [0.0478476175, 0.2784128648],
"In": [0.0110247967, 0.2126315781],
"Sn": [0.0440991866, 0.2698870221],
"Sb": [0.0393217747, 0.3175141436],
"Cs": [0.0173456801, 0.1431018606],
"La": [0.0183746611, 0.2049509698],
"Ce": [0.0183746611, 0.2035544955],
"Ta": [0.0118332817, 0.2899521520],
"W": [0.0299506976, 0.2932595910],
"Re": [0.0055123983, 0.2895846587],
"Os": [0.0404242544, 0.3197191029],
"Ir": [0.0575126892, 0.3344188318],
"Au": [0.0848541849, 0.3390492464],
"Tl": [0.0073498644, 0.2244648598],
"Pb": [0.0132297560, 0.2725697226],
"Bi": [0.0347648588, 0.2678658093],
"Po": [0.0698237121, 0.3093190448],
}
if __name__ == "__main__":
if len(sys.argv) == 1:
print("Usage: amspython get_chargee_ions.py path/to/ams.rkf")
sys.exit(0)
filename = sys.argv[1]
ions, ioncharges = main(filename)
outfile = open("charges.in", "w")
for k, q in ioncharges.items():
outfile.write("%8.1f: %s\n" % (q, " ".join(["%i" % (iat) for iat in ions[k]])))
outfile.close()
Running the above script results in a small input file (charges.in) containing the ion information. This input file can be used in the next script, to compute the ionic conductivity.
Example usage: (Download get_ionic_conductivity.py)
$AMSBIN/amspython get_ionic_conductivity.py /path/to/ams.rkf <charges.in
import sys
import os
import numpy
from scm.plams import AMSJob, Settings, Units, AMSAnalysisJob
from scm.plams import to_rdmol, init, finish
def main(filename, chargelines):
"""
The main body of the script
"""
# Get the molecular system
job = AMSJob.load_external(filename)
mol = job.molecule
elements = [at.symbol for at in mol.atoms]
# Read the temperature from KF
T = job.results.readrkf("MDResults", "MeanTemperature")
kBT = Units.constants["Boltzmann"] * T
print("Average temperaturs %f K" % (T))
# Read the charges from the input file
ions = {}
ioncharges = {}
nions = {}
formulas = {}
for line in chargelines:
words = line.split()
if len(words) == 0:
continue
q = float(line.split(":")[0])
atoms = [int(iat) for iat in line.split(":")[-1].split()]
submol = mol.get_fragment(atoms)
label = submol.label()
if not label in ions.keys():
ions[label] = []
ioncharges[label] = q * Units.constants["electron_charge"]
nions[label] = 0
formulas[label] = submol.separate()[0].get_formula()
ions[label] += atoms
nions[label] += len(atoms)
# Compute diffusion coefficient for each ion
init()
diffusion_coeffs = {}
for label, atoms in ions.items():
s = Settings()
s.input.Task = "MeanSquareDisplacement"
s.input.TrajectoryInfo.Trajectory.KFFilename = filename
atsettings = [iat + 1 for iat in atoms]
s.input.MeanSquareDisplacement.Atoms.Atom = atsettings
job = AMSAnalysisJob(settings=s)
results = job.run()
D = results._kf.read("Slope(1)", "Final")
diffusion_coeffs[label] = D
units = results._kf.read("Slope(1)", "Final(units)")
print(formulas[label], D, units)
finish()
# Compute the number density for each ion
rho = {}
for label, ni in nions.items():
rho[label] = ni / mol.unit_cell_volume(unit="m")
# Compute the ionic conductivity
sigma = 0.0
for label, D in diffusion_coeffs.items():
s = ioncharges[label] ** 2 * rho[label] * D / kBT
sigma += s
return sigma
if __name__ == "__main__":
if len(sys.argv) == 1 or sys.stdin.isatty():
print("Usage: amspython get_ionic_conductivity.py path/to/ams.rkf < charges.in")
sys.exit(0)
chargelines = sys.stdin.readlines()
filename = sys.argv[1]
sigma = main(filename, chargelines)
print("Ionic conductivity: %20.10e Siemens/m" % (sigma))