def analyse(self):
for name, data in self.data.items():
if 'strains' in data:
atoms = self.create_system(name)
# use relaxed volume if present
if 'relaxed volume' in data:
volume = data['relaxed volume']
else:
volume = atoms.get_volume()
volumes = data['strains']**3 * volume
energies = data['energies']
# allow selection of eos type independent of data
if self.eos is not None:
eos = EquationOfState(volumes, energies, self.eos)
else:
eos = EquationOfState(volumes, energies)
try:
v, e, B = eos.fit()
except (RuntimeError, ValueError):
pass
else:
data['fitted energy'] = e
data['volume'] = v
data['B'] = B
if abs(v) < min(volumes) or abs(v) > max(volumes):
raise ValueError(name + ': fit outside of range! ' + \
str(abs(v)) + ' not in ' + \
str(volumes))
def fit(filename):
configs = read(filename + '@:')
volumes = [a.get_volume() for a in configs]
energies = [a.get_potential_energy() for a in configs]
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
return (4 * v0)**(1 / 3.0)
def bulk_summary(self, plot, a0):
natoms = len(self.atoms)
eos = EquationOfState(self.volumes, self.energies)
v, e, B = eos.fit()
x = (v / self.atoms.get_volume())**(1.0 / 3)
self.log('Fit using %d points:' % len(self.energies))
self.log('Volume per atom: %.3f Ang^3' % (v / natoms))
if a0:
a = a0 * x
self.log('Lattice constant: %.3f Ang' % a)
else:
a = None
self.log('Bulk modulus: %.1f GPa' % (B * 1e24 / units.kJ))
self.log('Total energy: %.3f eV (%d atom%s)' %
(e, natoms, ' s'[1:natoms]))
if plot:
import pylab as plt
plt.plot(self.volumes, self.energies, 'o')
x = np.linspace(self.volumes[0], self.volumes[-1], 50)
plt.plot(x, eos.fit0(x**-(1.0 / 3)), '-r')
plt.show()
bulk = self.atoms.copy()
bulk.set_cell(x * bulk.cell, scale_atoms=True)
self.write_optimized(bulk, e)
return e, v, B, a
def eos(self, atoms, name):
opts = self.opts
traj = PickleTrajectory(self.get_filename(name, 'traj'), 'w', atoms)
eps = 0.01
strains = np.linspace(1 - eps, 1 + eps, 5)
v1 = atoms.get_volume()
volumes = strains**3 * v1
energies = []
cell1 = atoms.cell
for s in strains:
atoms.set_cell(cell1 * s, scale_atoms=True)
energies.append(atoms.get_potential_energy())
traj.write(atoms)
traj.close()
eos = EquationOfState(volumes, energies, opts.eos_type)
v0, e0, B = eos.fit()
atoms.set_cell(cell1 * (v0 / v1)**(1 / 3), scale_atoms=True)
data = {'volumes': volumes,
'energies': energies,
'fitted_energy': e0,
'fitted_volume': v0,
'bulk_modulus': B,
'eos_type': opts.eos_type}
return data
def f(width, k, g):
filename = 'Fe-FD-%.2f-%02d-%2d.traj' % (width, k, g)
configs = read(filename + '@::2')
# Extract volumes and energies:
volumes = [a.get_volume() for a in configs]
energies = [a.get_potential_energy() for a in configs]
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
return v0, e0, B
def relax(input_atoms, ref_db):
atoms_string = input_atoms.get_chemical_symbols()
# Open connection to the database with reference data
db = connect(ref_db)
# Load our model structure which is just FCC
atoms = FaceCenteredCubic('X', latticeconstant=1.)
atoms.set_chemical_symbols(atoms_string)
# Compute the average lattice constant of the metals in this individual
# and the sum of energies of the constituent metals in the fcc lattice
# we will need this for calculating the heat of formation
a = 0
ei = 0
for m in set(atoms_string):
dct = db.get(metal=m)
count = atoms_string.count(m)
a += count * dct.latticeconstant
ei += count * dct.energy_per_atom
a /= len(atoms_string)
atoms.set_cell([a, a, a], scale_atoms=True)
# Since calculations are extremely fast with EMT we can also do a volume
# relaxation
atoms.set_calculator(EMT())
eps = 0.05
volumes = (a * np.linspace(1 - eps, 1 + eps, 9))**3
energies = []
for v in volumes:
atoms.set_cell([v**(1. / 3)] * 3, scale_atoms=True)
energies.append(atoms.get_potential_energy())
eos = EquationOfState(volumes, energies)
v1, ef, B = eos.fit()
latticeconstant = v1**(1. / 3)
# Calculate the heat of formation by subtracting ef with ei
hof = (ef - ei) / len(atoms)
# Place the calculated parameters in the info dictionary of the
# input_atoms object
input_atoms.info['key_value_pairs']['hof'] = hof
# Raw score must always be set
input_atoms.info['key_value_pairs']['raw_score'] = -hof
input_atoms.info['key_value_pairs']['latticeconstant'] = latticeconstant
# Setting the atoms_string directly for easier analysis
atoms_string = ''.join(input_atoms.get_chemical_symbols())
input_atoms.info['key_value_pairs']['atoms_string'] = atoms_string
def analyse(self):
for name, data in self.data.items():
if 'strains' in data:
atoms = self.create_system(name)
volumes = data['strains']**3 * atoms.get_volume()
energies = data['energies']
eos = EquationOfState(volumes, energies)
try:
v, e, B = eos.fit()
except ValueError:
pass
else:
data['fitted energy'] = e
data['volume'] = v
data['B'] = B
def analyse(self):
OptimizeTask.analyse(self)
for name, data in self.data.items():
if 'strains' in data:
atoms = self.create_system(name)
volumes = data['strains']**3 * atoms.get_volume()
energies = data['energies']
eos = EquationOfState(volumes, energies)
try:
v, e, B = eos.fit()
except ValueError:
self.results[name].extend([None, None])
else:
self.results[name][1:] = [energies[2] - e, v,
B * 1e24 / units.kJ]
else:
self.results[name].extend([None, None])
def test_calculator():
"""
Take ASE structure, PySCF object,
and run through ASE calculator interface.
This allows other ASE methods to be used with PySCF;
here we try to compute an equation of state.
"""
ase_atom=Diamond(symbol='C', latticeconstant=3.5668)
# Set up a cell; everything except atom; the ASE calculator will
# set the atom variable
cell = pbcgto.Cell()
cell.h=ase_atom.cell
cell.basis = 'gth-szv'
cell.pseudo = 'gth-pade'
cell.gs=np.array([8,8,8])
cell.verbose = 0
# Set up the kind of calculation to be done
# Additional variables for mf_class are passed through mf_dict
mf_class=pbcdft.RKS
mf_dict = { 'xc' : 'lda,vwn' }
# Once this is setup, ASE is used for everything from this point on
ase_atom.set_calculator(pyscf_ase.PySCF(molcell=cell, mf_class=mf_class, mf_dict=mf_dict))
print "ASE energy", ase_atom.get_potential_energy()
print "ASE energy (should avoid re-evaluation)", ase_atom.get_potential_energy()
# Compute equation of state
ase_cell=ase_atom.cell
volumes = []
energies = []
for x in np.linspace(0.95, 1.2, 5):
ase_atom.set_cell(ase_cell * x, scale_atoms = True)
print "[x: %f, E: %f]" % (x, ase_atom.get_potential_energy())
volumes.append(ase_atom.get_volume())
energies.append(ase_atom.get_potential_energy())
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
print(B / kJ * 1.0e24, 'GPa')
eos.plot('eos.png')
def analyse(self):
for name, data in self.data.items():
if 'strains' in data:
atoms = self.create_system(name)
volumes = data['strains']**3 * atoms.get_volume()
energies = data['energies']
eos = EquationOfState(volumes, energies)
try:
v, e, B = eos.fit()
except ValueError:
pass
else:
data['fitted energy'] = e
data['volume'] = v
data['B'] = B
if abs(v) < min(volumes) or abs(v) > max(volumes):
raise ValueError(name + ': fit outside of range! ' + \
str(abs(v)) + ' not in ' + \
str(volumes))
def eosanal(volumes,energies,CI):
eos=EquationOfState(volumes,energies) #Performs the EOS calcs
v0,e0,B0=eos.fit() #Gives us the values at minimum energy
def func(x): #sets up the function to be solved
return CI-erf(.701707*x)
#Proposes the function dictating the normal random variable
z=fsolve(func,0) #solves for the normal random variable
v=np.power(volumes,-.3333333) #sets up the variable as the one in the EOS
fit3=np.polyder(((np.poly1d(np.polyfit(v,energies,3)))),2)
#Creates an equation that solves for the bulk modulus in the same manner as the EOS
BM=fit3(v)/9*v**5
#solves for the bulk modulus corresponding to each volume value
var=[np.std(volumes),np.std(energies),np.std(BM)]
#solves for the standard deviation of each set of data of interest
SS=[np.count_nonzero(volumes),np.count_nonzero(energies),np.count_nonzero(BM)]
#determines the sample size of each set of data of interest.
R=[z*var[0]*SS[0]**-.5,z*var[1]*SS[1]**-.5,z*var[2]*SS[2]**-.5]
#Determines the radius of the confidence interval
Limits=[v0-R[0],v0+R[0],e0-R[1],e0+R[1],B0-R[2],B0+R[2]]
#sets up each confidence interval
print 'The {0} confidence interval around the volume at minimum energy of the selected structure is between {1} and {2} A^3.The {0} confidence interval around the minimum energy of the selected structure is between {3} and {4} eV.The {0} confidence interval around the bulk modulus of the selected structure is between {5} and {6} eV/A^3 '.format(CI,Limits[0],Limits[1],Limits[2],Limits[3],Limits[4],Limits[5]) #displays the results
return;
from ase.calculators.emt import EMT
from ase.utils.eos import EquationOfState
from ase.db import connect
db = connect('refs.db')
metals = ['Al', 'Au', 'Cu', 'Ag', 'Pd', 'Pt', 'Ni']
for m in metals:
atoms = FaceCenteredCubic(m)
atoms.set_calculator(EMT())
e0 = atoms.get_potential_energy()
a = atoms.cell[0][0]
eps = 0.05
volumes = (a * np.linspace(1 - eps, 1 + eps, 9))**3
energies = []
for v in volumes:
atoms.set_cell([v**(1. / 3)] * 3, scale_atoms=True)
energies.append(atoms.get_potential_energy())
eos = EquationOfState(volumes, energies)
v1, e1, B = eos.fit()
atoms.set_cell([v1**(1. / 3)] * 3, scale_atoms=True)
ef = atoms.get_potential_energy()
db.write(atoms,
metal=m,
latticeconstant=v1**(1. / 3),
energy_per_atom=ef / len(atoms))
e = atoms.get_potential_energy()
energies.append(e)
ones.append(1)
except (VaspSubmitted, VaspQueued):
ready = False
if not ready:
import sys
sys.exit()
for m in LC:
with jasp("bulk/Cl-{0}".format(m)) as calc:
atoms = calc.get_atoms()
volumes.append(atoms.get_volume())
eos = EquationOfState(volumes, energies)
v0, e0, B0 = eos.fit()
CI = 0.95
def func(x):
return CI - erf(0.701707 * x)
z = fsolve(func, 0)
v = np.power(volumes, -0.3333333)
fit3 = np.polyder(((np.poly1d(np.polyfit(v, energies, 3)))), 2)
BM = fit3(v) / 9 * v ** 5
var = [np.std(volumes), np.std(energies), np.std(BM)]
SS = [np.count_nonzero(volumes), np.count_nonzero(energies), np.count_nonzero(BM)]
R = [z * var[0] * SS[0] ** -0.5, z * var[1] * SS[1] ** -0.5, z * var[2] * SS[2] ** -0.5]
from vasp import Vasp
from ase.utils.eos import EquationOfState
LC = [3.5, 3.55, 3.6, 3.65, 3.7, 3.75]
energies = []
volumes = []
for a in LC:
calc = Vasp('bulk/Cu-{0}'.format(a))
atoms = calc.get_atoms()
volumes.append(atoms.get_volume())
energies.append(atoms.get_potential_energy())
calc.stop_if(None in energies)
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
print '''
v0 = {0} A^3
E0 = {1} eV
B = {2} eV/A^3'''.format(v0, e0, B)
eos.plot('images/Cu-fcc-eos.png')
v = atoms.get_volume()
volumes.append(v)
f.write('{0:1.3f} {1:1.5f} {2:1.5f}'.format(a, v, e))
except:
print('aims failed when a = {0:1.3f}'.format(a))
ready = False
if not ready:
import sys; sys.exit()
print '#+tblname: pt-bcc-latt'
print r'| lattice constant ($\AA$) | Total Energy (eV) |'
for lc, e in zip(LC, energies):
print '| {0} | {1} |'.format(lc, e)
import matplotlib.pyplot as plt
plt.plot(LC, energies)
plt.xlabel('Lattice constant ($\AA$)')
plt.ylabel('Total energy (eV)')
plt.savefig('images/pt-bcc-latt.png')
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
print '''
v0 = {0} A^3
E0 = {1} eV
B = {2} eV/A^3'''.format(v0, e0, B)
f.write('v0 = {0} A^3 \n E0 = {1} eV \n B = {2} eV/A^3'.format(v0, e0, B))
eos.plot('images/pt-bcc-eos.png')
f.close()
def analyse(self, atomsfile=None):
try:
BulkTask.analyse(self)
except ValueError: # allow fit outside of range
pass
for name, data in self.data.items():
if 'strains' in data:
atoms = self.create_system(name)
# use relaxed volume if present
if 'relaxed volume' in data:
volume = data['relaxed volume']
else:
volume = atoms.get_volume()
volumes = data['strains']**3 * volume
energies = data['energies']
# allow selection of eos type independent of data
if self.eos is not None:
eos = EquationOfState(volumes, energies, self.eos)
else:
eos = EquationOfState(volumes, energies)
try:
v, e, B = eos.fit()
except ValueError:
pass
else:
data['fitted energy'] = e
data['volume'] = v
data['B'] = B
# with respect tot the reference volume
data['volume error [%]'] = (data['volume'] / atoms.get_volume() - 1) * 100
if self.collection.B:
i = self.collection.labels.index(self.collection.xc) - 1
B = self.collection.B[name][i] * units.kJ * 1e-24
data['B error [%]'] = (data['B'] / B - 1) * 100
else:
data['B error [%]'] = None
data['strukturbericht'] = self.collection.data[name][0]
data['crystal structure'] = strukturbericht[data['strukturbericht']]
# calculate lattice constant from volume
cs = data['crystal structure']
if cs == 'bcc':
a0 = (volume*2)**(1/3.)
a = (data['volume']*2)**(1/3.)
elif cs == 'cesiumchloride':
a0 = (volume)**(1/3.)
a = (data['volume'])**(1/3.)
elif cs in ['fcc',
'diamond',
'zincblende',
'rocksalt',
'fluorite']:
a0 = (volume*4)**(1/3.)
a = (data['volume']*4)**(1/3.)
i = self.collection.labels.index(self.collection.xc) - 1
a0_ref = self.collection.data[name][i]
if 'relaxed volume' not in data:
# no volume relaxation performed - volume equals the reference one
assert abs(a0 - a0_ref) < 1.e-4
data['lattice constant'] = a
data['lattice constant error [%]'] = (a - a0_ref) / a0_ref * 100
if atomsfile:
# MDTMP: TODO
atomdata = read_json(atomsfile)
for name, data in self.data.items():
atoms = self.create_system(name)
e = -data['energy']
for atom in atoms:
e += atomdata[atom.symbol]['energy']
e /= len(atoms)
data['cohesive energy'] = e
if self.collection.xc == 'PBE':
eref = self.collection.data[name][7]
else:
eref = self.collection.data[name][9]
data['cohesive energy error [%]'] = (e / eref - 1) * 100
self.summary_keys += ['cohesive energy',
'cohesive energy error [%]']
cell.basis = 'gth-szv'
cell.pseudo = 'gth-pade'
cell.verbose = 0
# Set up the kind of calculation to be done
# Additional variables for mf_class are passed through mf_dict
mf_class = pbcdft.RKS
mf_dict = {'xc': 'lda,vwn'}
# Once this is setup, ASE is used for everything from this point on
ase_atom.set_calculator(
pyscf_ase.PySCF(molcell=cell, mf_class=mf_class, mf_dict=mf_dict))
print("ASE energy", ase_atom.get_potential_energy())
print("ASE energy (should avoid re-evaluation)",
ase_atom.get_potential_energy())
# Compute equation of state
ase_cell = ase_atom.cell
volumes = []
energies = []
for x in np.linspace(0.95, 1.2, 5):
ase_atom.set_cell(ase_cell * x, scale_atoms=True)
print "[x: %f, E: %f]" % (x, ase_atom.get_potential_energy())
volumes.append(ase_atom.get_volume())
energies.append(ase_atom.get_potential_energy())
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
print(B / kJ * 1.0e24, 'GPa')
eos.plot('eos.png')
from jasp import *
from ase.utils.eos import EquationOfState
LC = [3.5, 3.55, 3.6, 3.65, 3.7, 3.75]
energies = []
volumes = []
for a in LC:
with jasp('bulk/Cu-{0}'.format(a)) as calc:
atoms = calc.get_atoms()
volumes.append(atoms.get_volume())
energies.append(atoms.get_potential_energy())
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
print '''
v0 = {0} A^3
E0 = {1} eV
B = {2} eV/A^3'''.format(v0, e0, B)
eos.plot('images/Cu-fcc-eos.png')
xc='PBE',
encut=350,
kpts=(6,6,6),
isym=2,
atoms=newatoms)
calculators.append(calc)
# now we set up the Pool of processes
pool = multiprocessing.Pool(processes=NCORES)
# get the output from running each calculation
out = pool.map(do_calculation, calculators)
pool.close()
pool.join() # this makes the script wait here until all jobs are done
# now proceed with analysis
V = [x[0] for x in out]
E = [x[1] for x in out]
eos = EquationOfState(V, E)
v1, e1, B = eos.fit()
print 'step1: v1 = {v1}'.format(**locals())
### ################################################################
## STEP 2, eos around the minimum
## #################################################################
factors = [-0.06, -0.04, -0.02,
0.0,
0.02, 0.04, 0.06]
calculators = [] # reset list
for f in factors:
newatoms = atoms.copy()
newatoms.set_volume(v1*(1 + f))
label = 'bulk/cu-mp/step2-{0}'.format(COUNTER)
COUNTER += 1
calc = jasp(label,
from __future__ import print_function
import pickle
import numpy as np
import matplotlib.pyplot as plt
from ase.utils.eos import EquationOfState
import ase.units as units
results = []
K = range(3, 13)
for k in K:
A, data = pickle.load(open('eos-%d.pckl' % k))
for energies, xcname in zip(data, ['PBE', 'LDA', 'PBE0']):
eos = EquationOfState(A**3 / 4, energies)
v0, e0, B = eos.fit()
a = (v0 * 4)**(1 / 3.0)
B *= 1.0e24 / units.kJ
print(('%-4s %2d %.3f %.3f %.2f' % (xcname, k, a, e0, B)))
results.append((a, B))
results = np.array(results).reshape((-1, 3, 2))
LDA = dict(a=5.4037, B=95.1, eGX=0.52)
PBE = dict(
a=5.469,
B=87.8,
eGG=2.56,
eGX=0.71,
eGL=1.54,
eI=0.47, # indirect
ea=4.556)
PBE0 = dict(a=5.433, B=99.0, eGG=3.96, eGX=1.93, eGL=2.87, eI=1.74, ea=4.555)
def get_e_v(fname):
data = np.loadtxt(fname, usecols=(1, 3, 5, 6, 7))
volumes = data[:, 1]
energies = data[:, 4]
return volumes, energies
def custom_plot(volumes, energies, eos):
plot.plot(volumes, energies, 'ro')
x = np.linspace(min(eos.v), max(eos.v), 100)
y = eval(eos.eos_string)(x, eos.eos_parameters[0], eos.eos_parameters[1],
eos.eos_parameters[2], eos.eos_parameters[3])
plot.plot(x, y, label='fit')
plot.xlabel('Volume ($\AA^3$)')
plot.ylabel('Energy (eV)')
plot.legend(loc='best')
plot.savefig('eos.png')
plot.show()
if __name__ == '__main__':
volumes, energies = get_e_v('test_bulk.txt')
# eos = 'sjeos', 'murnaghan', 'birch', 'taylor', 'vinet' etc.
eos = EquationOfState(volumes, energies, eos='murnaghan')
v0, e0, B = eos.fit()
# the ASE units for the bulk modulus is eV/Angstrom^3
print('optimum volume, energy and bulk moduls', v0, e0, B)
# plot
# eos.plot(filename= "eos_fit")
custom_plot(volumes, energies, eos)
# reoptimize/check volume
#
volumes = []
energies = []
for x in np.linspace(0.98, 1.02, 5):
atoms.set_cell(init_cell * x, scale_atoms=True)
volumes.append(atoms.get_volume() / atoms.get_number_of_atoms())
energies.append(atoms.get_potential_energy() / atoms.get_number_of_atoms())
print "per atom volumes:", volumes
print "per atom energies:", energies
# fit EOS
#
from ase.utils.eos import EquationOfState
eos = EquationOfState(volumes, energies)
vpaf, epaf, B1 = eos.fit()
print "vpaf:", vpaf, "A^3"
print "epaf:", epaf, "eV"
print "B1:", B1 / kJ * 1.0e24, "GPa"
# get optimal lattice parameter from optimal volume
#
volrc = abs(np.linalg.det(refcell))
optlp = pow(vpaf * atoms.get_number_of_atoms() / volrc, 1. / 3.)
print "optlp:", optlp, "\n"
# get actual energy at optimal volume
#
opt_cell = optlp * refcell
atoms.set_cell(opt_cell, scale_atoms=True)
def fit_a(conv, n, description_for_archive, analysis_type, show, push2archive):
"""Fit equation of state for bulk systems.
The following equation is used::
sjeos (default)
A third order inverse polynomial fit 10.1103/PhysRevB.67.026103
2 3 -1/3
E(V) = c + c t + c t + c t , t = V
0 1 2 3
taylor
A third order Taylor series expansion about the minimum volume
murnaghan
PRB 28, 5480 (1983)
birch
Intermetallic compounds: Principles and Practice,
Vol I: Principles. pages 195-210
birchmurnaghan
PRB 70, 224107
pouriertarantola
PRB 70, 224107
vinet
PRB 70, 224107
antonschmidt
Intermetallics 11, 23-32 (2003)
p3
A third order polynomial fit
Use::
eos = EquationOfState(volumes, energies, eos='sjeos')
v0, e0, B = eos.fit()
eos.plot()
"""
# e, v, emin, vmin = plot_conv( conv[n], calc, "fit_gb_volume2")
from picture_functions import fit_and_plot
alist = []
vlist = []
etotlist = []
magn1 = []
magn2 = []
alphas= []
for id in conv[n]:
cl = db[id]
st = cl.end
alist.append(cl.end.rprimd[0][0])
etotlist.append(cl.energy_sigma0)
vlist.append(cl.end.vol)
magn1.append(cl.magn1)
magn2.append(cl.magn2)
alpha, beta, gamma = st.get_angles()
alphas.append(alpha)
print('alpha, energy: {:4.2f}, {:6.3f}'.format(alpha, cl.energy_sigma0))
fit_and_plot(U1 = (alphas, etotlist, 'o-r'),
image_name = 'figs/angle', ylabel = 'Total energy, eV', xlabel = 'Angle, deg', xlim = (89, 92.6))
if ase_flag:
if 'angle' in analysis_type:
eos = EquationOfState(alphas, etotlist, eos = 'sjeos')
else:
eos = EquationOfState(vlist, etotlist, eos = 'sjeos')
# import inspect
# print (inspect.getfile(EquationOfState))
v0, e0, B = eos.fit()
#print "c = ", clist[2]
printlog( '''
v0 = {0} A^3
a0 = {1} A
E0 = {2} eV
B = {3} eV/A^3'''.format(v0, v0**(1./3), e0, B), imp = 'Y' )
savedpath = 'figs/'+cl.name+'.png'
makedir(savedpath)
cl.B = B*160.218
# plt.close()
# plt.clf()
# plt.close('all')
if 'fit' in show:
mpl.rcParams.update({'font.size': 14})
eos.plot(savedpath, show = True)
printlog('fit results are saved in ',savedpath, imp = 'y')
else:
printlog('To use fitting install ase: pip install ase')
# plt.clf()
if push2archive:
push_figure_to_archive(local_figure_path = savedpath, caption = description_for_archive)
return
try:
e=atoms.get_potential_energy()
energies.append(e)
ones.append(1)
except (VaspSubmitted,VaspQueued):
ready=False
if not ready:
import sys; sys.exit()
for m in LC:
with jasp('bulk/Cl-{0}'.format(m)) as calc:
atoms=calc.get_atoms()
volumes.append(atoms.get_volume())
# all of the above sets up the problem for the code below. It simply creates an FCC Cl. Changing the above can easily make a different structure.
print volumes
print energies
eos=EquationOfState(volumes,energies) #Performs the EOS calcs
v0,e0,B0=eos.fit() #Gives us the values at minimum energy
CI=.95 #Determines the level of Confidence Interval
def func(x): #sets up the function to be solved
return CI-erf(.701707*x) #Proposes the function dictating the normal random variable
z=fsolve(func,0) #solves for the normal random variable
v=np.power(volumes,-.3333333) #sets up the variable as the one in the EOS
fit3=np.polyder(((np.poly1d(np.polyfit(v,energies,3)))),2) #Creates an equation that solves for the bulk modulus in the same manner as the EOS
BM=fit3(v)/9*v**5 #solves for the bulk modulus corresponding to each volume value
var=[np.std(volumes),np.std(energies),np.std(BM)] #solves for the standard deviation of each set of data of interest
SS=[np.count_nonzero(volumes),np.count_nonzero(energies),np.count_nonzero(BM)] #determines the sample size of each set of data of interest.
R=[z*var[0]*SS[0]**-.5,z*var[1]*SS[1]**-.5,z*var[2]*SS[2]**-.5] #Determines the radius of the confidence interval
Limits=[v0-R[0],v0+R[0],e0-R[1],e0+R[1],B0-R[2],B0+R[2]] #sets up each confidence interval
print 'The {0} confidence interval around the volume at minimum energy of the selected structure is between {1} and {2} A^3.The {0} confidence interval around the minimum energy of the selected structure is between {3} and {4} eV.The {0} confidence interval around the bulk modulus of the selected structure is between {5} and {6} eV/A^3 '.format(CI,Limits[0],Limits[1],Limits[2],Limits[3],Limits[4],Limits[5]) #displays the results#solves for the standard deviation of each set of data of interest
def custom_plot(volumes, energies, eos):
plot.plot(volumes, energies, 'ro')
x = np.linspace(min(eos.v), max(eos.v), 100)
y = eval(eos.eos_string)(x, eos.eos_parameters[0],
eos.eos_parameters[1],
eos.eos_parameters[2],
eos.eos_parameters[3])
plot.plot(x, y, label='fit')
plot.xlabel('Volume ($\AA^3$)')
plot.ylabel('Energy (eV)')
plot.legend(loc='best')
plot.savefig('eos.png')
# show()
if __name__ == '__main__':
# load from file
# volumes = np.loadtxt('filename')[:,0]
# energies = np.loadtxt('filename')[:,1]
# volumes = np.array([13.72, 14.83, 16.0, 17.23, 18.52])
# energies = np.array([-56.29, -56.41, -56.46, -56.46, -56.42])
volumes, energies = get_e_v('VOLUME')
# eos = 'sjeos', 'murnaghan', 'birch', 'taylor', 'vinet' etc.
eos = EquationOfState(volumes, energies, eos='murnaghan')
v0, e0, B = eos.fit()
# the ASE units for the bulk modulus is eV/Angstrom^3
print('optimum volume, energy and bulk moduls', v0, e0, B)
# plot
eos.plot(filename="eos_fit")
# custom_plot(volumes, energies, eos)
def custom_plot(volumes, energies, eos):
plot.plot(volumes, energies, 'ro')
x = np.linspace(min(eos.v), max(eos.v), 100)
y = eval(eos.eos_string)(x, eos.eos_parameters[0], eos.eos_parameters[1],
eos.eos_parameters[2], eos.eos_parameters[3])
plot.plot(x, y, label='fit')
plot.xlabel('Volume ($\AA^3$)')
plot.ylabel('Energy (eV)')
plot.legend(loc='best')
plot.savefig('eos.png')
#show()
if __name__ == '__main__':
#load from file
#volumes = np.loadtxt('filename')[:,0]
#energies = np.loadtxt('filename')[:,1]
#volumes = np.array([13.72, 14.83, 16.0, 17.23, 18.52])
#energies = np.array([-56.29, -56.41, -56.46, -56.46, -56.42])
volumes, energies = get_e_v('VOLUME')
#eos = 'sjeos', 'murnaghan', 'birch', 'taylor', 'vinet' etc.
eos = EquationOfState(volumes, energies, eos='murnaghan')
v0, e0, B = eos.fit()
#the ASE units for the bulk modulus is eV/Angstrom^3
print('optimum volume, energy and bulk moduls', v0, e0, B)
#plot
eos.plot(filename="eos_fit")
#custom_plot(volumes, energies, eos)
atoms.set_calculator(calc)
nm_e = 0
nm_e = atoms.get_potential_energy() / atoms.get_number_of_atoms()
nm_v = atoms.get_volume() / atoms.get_number_of_atoms()
if nm_e < -0.001:
volumes.append(nm_v)
energies.append(nm_e)
save(result, '{3} result : {0} {1} {2}'.format(opt, nm_v, nm_e, name))
print volumes, energies
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
eos.plot('{0}/graph/{1}.png'.format(temp_dir, name))
save(result, '{0} {1} {2} {3}'.format(v0, e0, B/kJ*1.0e24, (4.0 * v0) ** (1.0 / 3.0)))
save(result, OPTIONS)
save(result, volumes)
save(result, energies)
save(result, '------------------------')
save(result_sum, '{0}, {1}, {2}, {3}, {4}, {5}'.format(name, e0, v0, B, volumes, energies))
def get_e_v(fname):
data = np.loadtxt(fname, usecols=(1, 3, 5, 6, 7))
volumes = data[:, 1]
energies = data[:, 4]
return volumes, energies
def custom_plot(volumes, energies, eos):
plot.plot(volumes, energies, 'ro')
x = np.linspace(min(eos.v), max(eos.v), 100)
y = eval(eos.eos_string)(x, eos.eos_parameters[0], eos.eos_parameters[1],
eos.eos_parameters[2], eos.eos_parameters[3])
plot.plot(x, y, label='fit')
plot.xlabel('Volume ($\AA^3$)')
plot.ylabel('Energy (eV)')
plot.legend(loc='best')
plot.savefig('eos.png')
plot.show()
if __name__ == '__main__':
volumes, energies = get_e_v('test_bulk.txt')
#eos = 'sjeos', 'murnaghan', 'birch', 'taylor', 'vinet' etc.
eos = EquationOfState(volumes, energies, eos='murnaghan')
v0, e0, B = eos.fit()
#the ASE units for the bulk modulus is eV/Angstrom^3
print('optimum volume, energy and bulk moduls', v0, e0, B)
#plot
#eos.plot(filename= "eos_fit")
custom_plot(volumes, energies, eos)
from vasp import Vasp
from ase import Atom, Atoms
from ase.utils.eos import EquationOfState
import numpy as np
LC = [3.75, 3.80, 3.85, 3.90, 3.95, 4.0, 4.05, 4.1]
volumes, energies = [], []
for a in LC:
atoms = Atoms(
[Atom('Pd', (0, 0, 0))],
cell=0.5 * a *
np.array([[1.0, 1.0, 0.0], [0.0, 1.0, 1.0], [1.0, 0.0, 1.0]]))
calc = Vasp('bulk/Pd-LDA-{0}'.format(a),
encut=350,
kpts=[12, 12, 12],
xc='LDA',
atoms=atoms)
e = atoms.get_potential_energy()
energies.append(e)
volumes.append(atoms.get_volume())
calc.stop_if(None in energies)
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
print('LDA lattice constant is {0:1.3f} Ang^3'.format((4 * v0)**(1. / 3.)))
from ase.units import kJ
from ase.utils.eos import EquationOfState
lestim = lat0
volumes = []
energies = []
elstr=el1+el2+'-'+str
for x in np.linspace(0.98, 1.02, 5):
mys.set_cell(lestim * x, scale_atoms=True)
volumes.append(mys.get_volume()/mys.get_number_of_atoms())
energies.append(mys.get_potential_energy()/mys.get_number_of_atoms())
print "Volumespa:", volumes
print "Energiespa:", energies
eos = EquationOfState(volumes, energies)
vpa1, epa1, B1 = eos.fit()
lpopt1 = pow(vpa1*(n1+n2)/vpc, 1/3.)
print 'vpa1:', vpa1, 'A^3'
print 'epa1:', epa1, 'eV'
print 'B1:', B1 / kJ * 1.0e24, 'GPa'
print 'lpopt1:', lpopt1
#eos.plot(elstr+'-eos.pdf')#,show=True)
if binary == 1:
hof = epa1+esub1*n1/(n1+n2)+esub2*n2/(n1+n2)
else:
hof = epa1/n1-esub1
print "hof1:", hof*1000, "meV/atom\n"
def get_eos(self, static=False):
'''calculate the equation of state for the attached atoms.
Returns a dictionary of data for each step. You do not need to
specify any relaxation parameters, only the base parameters for the
calculations. Writes to eos.org with a report of output.
if static is True, then run a final static calculation at high
precision, with ismear=-5.
'''
# this returns if the data exists.
if os.path.exists('eos.json'):
with open('eos.json') as f:
return json.loads(f.read())
# we need an initial calculation to get us going.
self.calculate()
cwd = os.getcwd()
data = {'cwd': os.getcwd()} # dictionary to store results in
org = [] # list of strings to make the org-file report
org += ['#+STARTUP: showeverything']
org += ['* Initial guess']
org += [str(self)]
org += ['',
'[[shell:jaspsum -p {0}][view initial guess]]'.format(cwd)]
with open('eos.org', 'w') as f:
f.write('\n'.join(org))
atoms = self.get_atoms()
original_atoms = atoms.copy() # save for comparison later.
v_init = atoms.get_volume()
# ############################################################
# ## Step 1
# ############################################################
org += ['* step 1 - relax ions and shape']
volumes1, energies1 = [], []
ready = True
factors = [-0.15, -0.07, 0.0, 0.07, 0.15]
for i, f in enumerate(factors):
wd = cwd + '/step-1/f-{0}'.format(i)
self.clone(wd)
with jasp(wd,
isif=4,
ibrion=2,
ediffg=-0.05, ediff=1e-6,
nsw=50,
atoms=atoms) as calc:
try:
# add org-link to calculation
org += ['[[shell:jaspsum {0}][{0}]]'.format(wd)]
atoms.set_volume(v_init * (1 + f))
volumes1.append(atoms.get_volume())
energies1.append(atoms.get_potential_energy())
calc.strip()
except (VaspSubmitted, VaspQueued):
ready = False
if not ready:
log.info('Step 1 is still running')
raise VaspRunning
data['step1'] = {}
data['step1']['volumes'] = volumes1
data['step1']['energies'] = energies1
with open('eos.json', 'w') as f:
f.write(json.dumps(data))
# create an org-table of the data.
org += ['',
'#+tblname: step1',
'| volume (A^3) | Energy (eV) |',
'|-']
for v, e in zip(volumes1, energies1):
org += ['|{0}|{1}|'.format(v, e)]
org += ['']
with open('eos.org', 'w') as f:
f.write('\n'.join(org))
eos1 = EquationOfState(volumes1, energies1)
try:
v1, e1, B1 = eos1.fit()
except:
with open('error', 'w') as f:
f.write('Error fitting the equation of state')
data['step1']['eos'] = (v1, e1, B1)
with open('eos.json', 'w') as f:
f.write(json.dumps(data))
# create a plot
f = eos1.plot(show=False)
f.subplots_adjust(left=0.18, right=0.9, top=0.9, bottom=0.15)
plt.xlabel(u'volume ($\AA^3$)')
plt.ylabel(u'energy (eV)')
plt.title(u'E: %.3f eV, V: %.3f $\AA^3$, B: %.3f GPa' %
(e1, v1, B1 / GPa))
plt.text(eos1.v0, max(eos1.e), 'EOS: %s' % eos1.eos_string)
f.savefig('eos-step1.png')
org += ['[[./eos-step1.png]]',
'']
min_energy_index = np.argmin(energies1)
if min_energy_index in [0, -1]:
log.warn('Your minimum energy is at an endpoint.'
'This indicates something is wrong.')
with open('eos.org', 'w') as f:
f.write('\n'.join(org))
# ########################################################
# # STEP 2
# ########################################################
# step 2 - isif=4, ibrion=1. now we allow the shape of each cell to
# change, and we use the best guess from step 1 for minimum volume.
ready = True
volumes2, energies2 = [], []
factors = [-0.09, -0.06, -0.03, 0.0, 0.03, 0.06, 0.09]
org += ['* step 2 - relax ions and shape with improved minimum estimate']
for i, f in enumerate(factors):
wd = cwd + '/step-2/f-{0}'.format(i)
# clone closest result from above.
with jasp('step-1/f-{0}'.format(min_energy_index)) as calc:
calc.clone(wd)
with jasp(wd,
isif=4,
ibrion=1,
nsw=50) as calc:
try:
atoms = calc.get_atoms()
atoms.set_volume(v1 * (1 + f))
volumes2 += [atoms.get_volume()]
energies2 += [atoms.get_potential_energy()]
calc.strip()
except (VaspSubmitted, VaspQueued):
ready = False
if not ready:
log.info('Step 2 is still running')
raise VaspRunning
# update org and json files.
data['step2'] = {}
data['step2']['volumes'] = volumes2
data['step2']['energies'] = energies2
with open('eos.json', 'w') as f:
f.write(json.dumps(data))
# create an org-table of the data.
org += ['',
'#+tblname: step2',
'| volume (A^3) | Energy (eV) |',
'|-']
for v, e in zip(volumes2, energies2):
org += ['|{0}|{1}|'.format(v, e)]
org += ['']
with open('eos.org', 'w') as f:
f.write('\n'.join(org))
eos2 = EquationOfState(volumes2, energies2)
try:
v2, e2, B2 = eos2.fit()
except:
with open('error', 'w') as f:
f.write('Error fitting the equation of state')
data['step2']['eos'] = (v2, e2, B2)
with open('eos.json', 'w') as f:
f.write(json.dumps(data))
f = eos2.plot(show=False)
f.subplots_adjust(left=0.18, right=0.9, top=0.9, bottom=0.15)
plt.xlabel(u'volume ($\AA^3$)')
plt.ylabel(u'energy (eV)')
plt.title(u'E: %.3f eV, V: %.3f $\AA^3$, B: %.3f GPa' %
(e2, v2, B2 / GPa))
plt.text(eos2.v0, max(eos2.e), 'EOS: %s' % eos2.eos_string)
f.savefig('eos-step2.png')
org += [
'[[./eos-step2.png]]',
'']
with open('eos.org', 'w') as f:
f.write('\n'.join(org))
# statistical analysis of the equation of state
EOS = ['sjeos',
'taylor',
'murnaghan',
'birch',
'birchmurnaghan',
'pouriertarantola',
'vinet']
from ase.units import kJ
Vs, Es, Bs = [], [], []
for label in EOS:
eos = EquationOfState(volumes2, energies2, eos=label)
try:
v, e, B = eos.fit()
Vs += [v]
Es += [e]
Bs += [B / kJ * 1.0e24] # GPa
except:
with open('error', 'w') as f:
f.write('Error fitting the '
'equation of state {0}'.format(label))
avgV = np.mean(Vs)
stdV = np.std(Vs)
avgE = np.mean(Es)
stdE = np.std(Es)
avgB = np.mean(Bs)
stdB = np.std(Bs)
from scipy.stats.distributions import t
n = len(Vs)
dof = n - 1
alpha = 0.05
Vconf = t.ppf(1 - alpha/2., dof) * stdV * np.sqrt(1 + 1./n)
Bconf = t.ppf(1 - alpha/2., dof) * stdB * np.sqrt(1 + 1./n)
data['step2']['avgV'] = avgV
data['step2']['Vconf95'] = Vconf
data['step2']['avgB'] = avgB
data['step2']['Bconf95'] = Bconf
org += ['** Statistical analysis',
'''
Volume = {avgV:1.3f} \pm {Vconf:1.3f} \AA^3 at the 95% confidence level
B = {avgB:1.0f} \pm {Bconf:1.0f} GPa at the 95% confidence level
'''.format(**locals())]
with open('eos.org', 'w') as f:
f.write('\n'.join(org))
with open('eos.json', 'w') as f:
f.write(json.dumps(data))
# step 3 should be isif = 3 where we let the volume change too
# start from the minimum in step2
org += ['* step 3 - relax volume']
emin_ind = np.argmin(energies2)
log.info('Minimum energy found in factor={0}.'.format(factors[emin_ind]))
with jasp('step-2/f-{0}'.format(emin_ind)) as calc:
calc.clone('step-3')
with jasp('step-3',
isif=3, # vol, shape and internal degrees of freedom
ibrion=1,
prec='high',
nsw=50) as calc:
atoms = calc.get_atoms()
atoms.set_volume(avgV)
calc.calculate()
calc.strip()
org += [str(calc)]
atoms = calc.get_atoms()
data['step3'] = {}
data['step3']['potential_energy'] = atoms.get_potential_energy()
data['step3']['volume'] = atoms.get_volume()
with open('eos.org', 'w') as f:
f.write('\n'.join(org))
with open('eos.json', 'w') as f:
f.write(json.dumps(data))
# now the final step with ismear=-5 for the accurate energy. This
# is recommended by the VASP manual. We only do this if you
# specify static=True as an argument
if static:
with jasp('step-3') as calc:
calc.clone('step-4')
with jasp('step-4',
isif=None, ibrion=None, nsw=None,
icharg=2, # do not reuse charge
istart=1,
prec='high',
ismear=-5) as calc:
calc.calculate()
atoms = calc.get_atoms()
data['step4'] = {}
data['step4']['potential_energy'] = atoms.get_potential_energy()
org += ['* step-4 - static calculation',
str(calc)]
# final write out
with open('eos.org', 'w') as f:
f.write('\n'.join(org))
# dump data to a json file
with open('eos.json', 'w') as f:
f.write(json.dumps(data))
return data
from ase.io import read
from ase.units import kJ
from ase.utils.eos import EquationOfState
configs = read('Ag.traj@0:5') # read 5 configurations
# Extract volumes and energies:
volumes = [ag.get_volume() for ag in configs]
energies = [ag.get_potential_energy() for ag in configs]
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
print B / kJ * 1.0e24, 'GPa'
eos.plot('Ag-eos.png')
from ase.lattice.cubic import FaceCenteredCubic
from ase.calculators.emt import EMT
from ase.utils.eos import EquationOfState
from ase.db import connect
db = connect('refs.db')
metals = ['Al', 'Au', 'Cu', 'Ag', 'Pd', 'Pt', 'Ni']
for m in metals:
atoms = FaceCenteredCubic(m)
atoms.set_calculator(EMT())
e0 = atoms.get_potential_energy()
a = atoms.cell[0][0]
eps = 0.05
volumes = (a * np.linspace(1 - eps, 1 + eps, 9))**3
energies = []
for v in volumes:
atoms.set_cell([v**(1. / 3)] * 3, scale_atoms=True)
energies.append(atoms.get_potential_energy())
eos = EquationOfState(volumes, energies)
v1, e1, B = eos.fit()
atoms.set_cell([v1**(1. / 3)] * 3, scale_atoms=True)
ef = atoms.get_potential_energy()
db.write(atoms, metal=m,
latticeconstant=v1**(1. / 3),
energy_per_atom=ef / len(atoms))
encut=350,
kpts=(6,6,6),
isym=2,
debug=logging.DEBUG,
atoms=newatoms)
calculators.append(calc)
# now we set up the Pool of processes
pool = multiprocessing.Pool(processes=3) # ask for 6 cores but run MPI on 2 cores
# get the output from running each calculation
out = pool.map(do_calculation, calculators)
pool.close()
pool.join() # this makes the script wait here until all jobs are done
# now proceed with analysis
V = [x[0] for x in out]
E = [x[1] for x in out]
eos = EquationOfState(V, E)
v1, e1, B = eos.fit()
print('step1: v1 = {v1}'.format(**locals()))
### ################################################################
## STEP 2, eos around the minimum
## #################################################################
factors = [-0.06, -0.04, -0.02,
0.0,
0.02, 0.04, 0.06]
calculators = [] # reset list
for f in factors:
newatoms = atoms.copy()
newatoms.set_volume(v1*(1 + f))
label = 'bulk/cu-mp2/step2-{0}'.format(COUNTER)
COUNTER += 1
calc = jasp(label,
xc='PBE',
encut=350,
kpts=(6,6,6),
isym=2,
atoms=newatoms)
calculators.append(calc)
# now we set up the Pool of processes
pool = multiprocessing.Pool(processes=NCORES)
# get the output from running each calculation
out = pool.map(do_calculation, calculators)
pool.close()
pool.join() # this makes the script wait here until all jobs are done
# now proceed with analysis
V = [x[0] for x in out]
E = [x[1] for x in out]
eos = EquationOfState(V, E)
v1, e1, B = eos.fit()
print('step1: v1 = {v1}'.format(**locals()))
### ################################################################
## STEP 2, eos around the minimum
## #################################################################
factors = [-0.06, -0.04, -0.02,
0.0,
0.02, 0.04, 0.06]
calculators = [] # reset list
for f in factors:
newatoms = atoms.copy()
newatoms.set_volume(v1*(1 + f))
label = 'bulk/cu-mp/step2-{0}'.format(COUNTER)
COUNTER += 1
calc = jasp(label,
print("-----------------------------------------")
print("Calculation output for Iron (fccFe) at 0K")
print("-----------------------------------------")
print(" Volumes Energies")
for e, v in zip(v_Fe, e_Fe):
print "{:<15} {:>10}".format(e, v)
SAVE_PLOT = os.path.exists('./images') and os.path.isdir('./images')
# Fit EOS
print("----------------------------")
print("Equation of state parameters")
if not SAVE_PLOT:
print("(to save a plot, mkdir 'images')")
print("----------------------------")
print(" E0 V0 B fit")
files = []
for tag in ['vinet', 'birchmurnaghan']:
eos = EquationOfState(v_Fe, e_Fe, eos=tag)
v0, e0, B = eos.fit()
print("{:2.6f} {:2.3f} {:2.1f} {:<16} ".format(e0, v0, B/GPa, tag))
if SAVE_PLOT:
fname = 'images/fccFe-0K-eos-{0}.png'.format(tag)
eos.plot(fname)
files.append(fname)
if SAVE_PLOT:
print("Plots saved as {0}".format(", ".join([f for f in files])))