def fit(symbol: str) -> Tuple[float, float, float, float]:
V = []
E = []
for atoms in read('{}.traj@:'.format(symbol)):
V.append(atoms.get_volume() / len(atoms))
E.append(atoms.get_potential_energy() / len(atoms))
eos = EOS(V, E, 'birchmurnaghan')
eos.fit()
e0, B, Bp, v0 = eos.eos_parameters
return e0, v0, B, Bp
def test_eos():
import numpy as np
import scipy # skip test early if no scipy
from ase.build import bulk
from ase.calculators.emt import EMT
from ase.eos import EquationOfState as EOS, eos_names
scipy # silence pyflakes
b = bulk('Al', 'fcc', a=4.0, orthorhombic=True)
b.set_calculator(EMT())
cell = b.get_cell()
volumes = []
energies = []
for x in np.linspace(0.98, 1.01, 5):
b.set_cell(cell * x, scale_atoms=True)
volumes.append(b.get_volume())
energies.append(b.get_potential_energy())
results = []
for name in eos_names:
if name == 'antonschmidt':
# Someone should fix this!
continue
eos = EOS(volumes, energies, name)
v, e, b = eos.fit()
print('{0:20} {1:.8f} {2:.8f} {3:.8f} '.format(name, v, e, b))
assert abs(v - 3.18658700e+01) < 4e-4
assert abs(e - -9.76187802e-03) < 5e-7
assert abs(b - 2.46812688e-01) < 2e-4
results.append((v, e, b))
print(np.ptp(results, 0))
print(np.mean(results, 0))
def calc_lattice_parameter_al(atom_set, A, lmbd, D, mu2):
global n_sets, cells
q = 0.2
n_points = 10
lattice_param_set = np.zeros(n_sets)
calc = get_calc((A, lmbd, D, mu2))
for index, atoms in enumerate(atom_set):
# # # Find lattice constant with lowest energy # # #
cell_0 = atoms.cells[index] # Unit cell object of the Al bulk
atoms.set_calculator(calc)
energies = []
volumes = []
inval = np.linspace(-q, q, n_points)
for eps in inval:
atoms.cell = (1 + eps) * cell_0 # Adjust lattice constant of unit cell
# Calculate the potential energy for the Al bulk
energies.append(atoms.get_potential_energy())
volumes.append(atoms.get_volume())
# Plot energies as a function of unit cell volume (directly related to latt. const.)
eos = EquationOfState(volumes, energies)
v0, E, B = eos.fit()
# Latt. const. acc. to ASE doc., but why is this correct?
a_calc = v0**(1 / 3.0)
n_min = np.argmin(energies)
atoms.cell = (1 + inval[n_min]) * cell_0
lattice_param_set[index] = a_calc
return lattice_param_set
def calc_lattice_parameter(al_bulk_ASE, A, lmbd, D, mu2):
q = 0.2
n_points = 15
calc = get_calc((A, lmbd, D, mu2))
# # # Find lattice constant with lowest energy # # #
cell_0 = al_bulk_ASE.get_cell() # Unit cell object of the Al bulk
al_bulk_ASE.set_calculator(calc)
energies = []
volumes = []
for eps in np.linspace(-q, q, n_points):
al_bulk_ASE.set_cell(
(1 + eps) * cell_0) # Adjust lattice constant of unit cell
# Calculate the potential energy for the Al bulk
energies.append(al_bulk_ASE.get_potential_energy())
volumes.append(al_bulk_ASE.get_volume())
#plt.plot(np.asarray(volumes)**(1 / 3), energies)
# plt.show()
# Plot energies as a function of unit cell volume (directly related to latt. const.)
eos = EquationOfState(volumes, energies)
v0, E, B = eos.fit()
# Latt. const. acc. to ASE doc., but why is this correct?
a_calc = v0**(1 / 3.0)
print('a=' + str(a_calc))
al_bulk_ASE.set_cell(cell_0)
return a_calc
def eosfit_spec(atoms, calc, rg, method="birchmurnaghan"):
from ase.eos import EquationOfState
from numpy import linspace
rootdir = os.getcwd()
if not os.path.exists('eosfit'):
os.mkdir('eosfit')
os.chdir('eosfit')
cell = atoms.get_cell()
atoms.set_calculator(calc)
traj = Trajectory('eosfit.traj', 'w')
for x in rg:
print(str(x))
atoms.set_cell(cell * x, scale_atoms=True)
atoms.get_potential_energy()
traj.write(atoms)
configs = Trajectory('eosfit.traj', 'r')
volumes = [at.get_volume() for at in configs]
energies = [at.get_potential_energy() for at in configs]
eos = EquationOfState(volumes, energies, eos=method)
v0, e0, B = eos.fit()
eos.plot('eosfit.svg')
fp = open('eosdata.dat', 'w')
fp.write('Volume\t\tEnergy')
for i in range(len(configs)):
fp.write(str(volumes[i]) + '\t' + str(energies[i]) + '\n')
os.chdir(rootdir)
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 calc_lattice_parameter_al(al_bulk, A, lmbd, D, mu2):
q = 0.03
n_points = 14
calc = get_calc((A, lmbd, D, mu2))
# # # Find lattice constant with lowest energy # # #
cell_0 = al_bulk.cell # Unit cell object of the Al bulk
al_bulk.set_calculator(calc)
energies = []
volumes = []
for eps in np.linspace(-q, q, n_points):
al_bulk.cell = (1 + eps) * cell_0 # Adjust lattice constant of unit cell
# Calculate the potential energy for the Al bulk
energies.append(al_bulk.get_potential_energy())
volumes.append(al_bulk.get_volume())
# Plot energies as a function of unit cell volume (directly related to latt. const.)
eos = EquationOfState(volumes, energies)
v0, E, B = eos.fit()
# Latt. const. acc. to ASE doc., but why is this correct?
a_calc = (4 * v0)**(1 / 3.0)
al_bulk.cell = cell_0
print('Lattice_parameter:', a_calc)
return a_calc
def eos(self, atoms, name):
args = self.args
traj = Trajectory(self.get_filename(name, 'traj'), 'w', atoms)
N, eps = args.equation_of_state.split(',')
N = int(N)
eps = float(eps) / 100
strains = np.linspace(1 - eps, 1 + eps, N)
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, args.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': args.eos_type}
return data
def eos(self, atoms, name):
args = self.args
traj = Trajectory(self.get_filename(name, 'traj'), 'w', atoms)
N, eps = args.equation_of_state.split(',')
N = int(N)
eps = float(eps) / 100
strains = np.linspace(1 - eps, 1 + eps, N)
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, args.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': args.eos_type
}
return data
def eos(self, atoms, name):
args = self.args
traj = Trajectory(self.get_filename(name, 'traj'), 'w', atoms)
N, eps = args.equation_of_state.split(',')
N = int(N)
eps = float(eps) / 100
strains = np.linspace(1 - eps, 1 + eps, N)
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, args.eos_type)
v0, e0, B = eos.fit()
atoms.set_cell(cell1 * (v0 / v1)**(1 / 3), scale_atoms=True)
from ase.parallel import parprint as p
p('volumes:', volumes)
p('energies:', energies)
p('fitted energy:', e0)
p('fitted volume:', v0)
p('bulk modulus:', B)
p('eos type:', args.eos_type)
def do_autotune_volume(self,start_scan=0.90,end_scan=1.10,num_scan=25,exclude_type=None,only_type=None):
# Load system and calculator
system = self.system.copy()
calc = self.system.calc
system.set_calculator(calc)
# Scale volumes and collect energy & volume measurements
ens = []
vols = []
start_cell = system.get_cell()
print("Performing volume scan.")
for i,x in enumerate(np.linspace(start_scan,end_scan,num_scan)):
#print(i)
scale = x**(1./3.)
system.set_cell(scale*start_cell,scale_atoms=True)
vols.append(system.get_volume())
ens.append(system.get_potential_energy())
self.volume_vs_energy = [vols,ens]
# Fit to Equations of States
print("Fitting data to equations of state.")
eos_types = "sjeos taylor murnaghan birch birchmurnaghan pouriertarantola p3 antonschmidt".split()
if exclude_type != None:
_ = [eos_types.remove(i) for i in exclude_type]
elif only_type != None:
eos_types = only_type
eos_fits = {}
errors = []
for typ in eos_types:
try:
eos = EquationOfState(vols,ens,eos=typ)
v, e, B = eos.fit()
eos_fits[typ] = {'volume':v,'energy':e,'buld_modulus':B}
except:
errors.append(typ)
self.eos_fits = eos_fits
self.eos_errors = errors if len(errors)>0 else None
if len(errors) > 0:
print("WARNING: Was not able to fit equation of state for the following: {}".format(errors))
# Rescale initial cell to optimized volume
print("Rescaling with optimized volume.")
vol_avg = np.average([eos_fits[key]['volume'] for key in eos_fits.keys()])
system.set_cell(start_cell,scale_atoms=True)
scale = (vol_avg/system.get_volume())**(1./3.)
print("Optimized volume: {}".format(vol_avg))
del self.system
self.system = system
self.system.set_cell(scale*start_cell,scale_atoms=True)
print("Performing second relaxation.")
self.system.get_potential_energy()
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
# Use one of the following two; they are equivalent
input_atoms.info['key_value_pairs']['raw_score'] = -hof
# set_raw_score(input_atoms, -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 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
# Use one of the following two; they are equivalent
input_atoms.info['key_value_pairs']['raw_score'] = -hof
# set_raw_score(input_atoms, -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 run_task(self,fw_spec):
jobID,latticeParams = fw_spec['jobID'],fw_spec['latticeParams'] # WHY IS LATTICEPARAMS [[FLOAT]] INSTEAD OF [FLOAT]?
job = db2object(jobID)
existsPrecalc = job.precalc != 'None'
optAtoms = job.fromParams(latticeParams[0])
optCell = optAtoms.get_cell()
strains = np.linspace(1-job.strain,1+job.strain,9)
calc = job.calc(restart=True) if existsPrecalc else job.calc()
vol,eng = [],[]
for i, strain in enumerate(strains):
atoms = optAtoms.copy()
atoms.set_cell(optCell*strain,scale_atoms=True)
if existsPrecalc:
preCalc = job.calc(precalc=True)
job.optimizePos(atoms,preCalc,saveWF = True)
if job.dftcode =='gpaw':
atoms,calc = job.gpawRestart()
job.optimizePos(atoms,calc)
energy = atoms.get_potential_energy()
volume = atoms.get_volume()
vol.append(deepcopy(volume))
eng.append(deepcopy(energy))
parprint('%f %f'%(strain,energy))
with paropen('bulkmod.log','a') as logfile:
logfile.write('%s\t%s\n' %(strain,energy))
parprint('%f %f'%(strain,energy))
aHat,quadR2 = quadFit(np.array(deepcopy(vol)),np.array(deepcopy(eng)))
try:
eos = EquationOfState(vol,eng)
v0, e0, b = eos.fit()
eos.plot(filename='bulk-eos.png',show=False)
b0= b/kJ*1e24 #GPa use this value if EOS doesn't fail
except ValueError: # too bad of a fit for ASE to handle
b0 = aHat*2*vol[4]*160.2 # units: eV/A^6 * A^3 * 1, where 1 === 160.2 GPa*A^3/eV
return FWAction( stored_data= {'b0':b0,'quadR2':quadR2}
,mod_spec=[{'_push': {'b0':b0,'quadR2':quadR2}}])
def Free_energy(
x, T, E0, V0, B0, Bp
): #T in K, M is molar mass, E0 in eV, V0 in A^3, B0 in eV/A^3, x is concentration in atomic fraction
try:
i = 0
M = 0
for el in elements:
M = M + mass_dict[el] * x[i]
i = i + 1
M = abs(M)
r0 = (3 * V0 / 4 / np.pi)**(1.0 / 3.0)
T_D0 = C * np.sqrt(r0 * B0 * 160.21766208 / M)
g = 1 - (np.tanh(4 * (T - T_D0) / T_D0) / 2.0 +
0.5) / 3.0 #2/3 for high T, 1 for low T
gamma = -g + 0.5 * (1 + Bp)
x = np.array(x)
V = np.linspace(V0 - 0.1 * V0, V0 + 0.1 * V0, NUM_VOL_POINTS)
F_temp = []
for Vi in V:
E = E0 + 9 * V0 * B0 / 16 * (((V0 / Vi)**(2.0 / 3.0) - 1)**3 * Bp +
((V0 / Vi)**(2.0 / 3.0) - 1)**2 *
(6 - 4 * (V0 / Vi)**(2.0 / 3.0)))
T_D = T_D0 * (V0 / Vi)**gamma
x = T_D / T
#t = np.linspace(0.000001,x,10000)
#Deb_func = 3.0 / x**3 * np.trapz(t**3 / (np.exp(t) - 1), t)
F_vib = 9.0 / 8.0 * kB * T_D - kB * T * Debye(
x) + 3 * kB * T * np.log(1 - np.exp(-(T_D / T)))
F = E + F_vib
F_temp.append(F)
eos = EquationOfState(V, F_temp)
vol_eq, F_eq, B_eq = eos.fit()
return F_eq
except KeyboardInterrupt:
raise
except Exception as e:
print(x)
raise
def ev_bulk(volumes, energies, plot_name):
"""Plot volume energy curve and calculates bulk modulus
Args:
volumes (list of float): The volumes correlated to the energies calculated.
energies (list of float): The energies the cell calculated by gfn0 xtb.
plot_name (str): The file name the plot is saved to.
Returns:
v0 (float): The volume of minimum energy.
e0 (float): The fitted minimum energy of the V/E curve.
B (float): The calculated bulk modulus.
"""
volumes = np.array(volumes)
energies = np.array(energies) * Hartree / eV
eos = EquationOfState(volumes, energies, eos="murnaghan")
v0, e0, B = eos.fit()
print(B / kJ * 1.0e24, "GPa") # Converts into GPa
ax = eos.plot()
fig = plt.gcf()
fig.set_size_inches(8, 5)
fig.savefig(plot_name)
return v0, e0, B
import pandas as pd
from glob import glob
from ase.eos import EquationOfState
eos_name = 'birch'
for f in glob('AutoCrossfilts_VASP/*.csv'):
dat = pd.read_csv(f)
dat.dropna(inplace=True)
#if dat:
print(f)
try:
if max(dat['kpts']) > 100000:
Eos = EquationOfState(dat['volume'], dat['energy'], eos=eos_name)
E0, E0_err, V0, V0_err, B, B_err, BP, BP_err, y_pred = Eos.fit()
pd.DataFrame({
'E0': [E0],
'V0': [V0],
'B': [B],
'BP': [BP]
}).to_csv('Init_files/{}_Rdata_init.csv'.format(
f.replace('.csv', '').replace('AutoCrossfilts_VASP/', '')),
index=False)
except:
print('Issue with {}'.format(f))
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")
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
from ase.units import kJ, Bohr, Hartree
from ase.eos import EquationOfState
import numpy as np
filename = "TEMP_EOS_data.dat"
dat = np.loadtxt(filename)
# dont forget to convert to Angstrom and eV
volumes = dat[:,0]**3/2.0 * Bohr**3 # only for bcc
energies = dat[:,1]*Hartree
energies_abinit = dat[:,2]*Hartree
energies_pwscf = dat[:,3]*Hartree
eos = EquationOfState(volumes, energies)
v0, e0, B = eos.fit()
print("PWDFT.jl: B = %18.10f GPa" % (B/kJ * 1.0e24))
eos.plot("pwdft-eos-ase.pdf")
eos = EquationOfState(volumes, energies_abinit)
v0, e0, B = eos.fit()
print("ABINIT : B = %18.10f GPa" % (B/kJ * 1.0e24))
eos.plot("abinit-eos-ase.pdf")
eos = EquationOfState(volumes, energies_pwscf)
v0, e0, B = eos.fit()
print("PWSCF : B = %18.10f GPa" % (B/kJ * 1.0e24))
eos.plot("pwscf-eos-ase.pdf")
else:
f = open('volumes_energies.txt', 'rU')
energies = []
volumes = []
lines = f.readlines()
for i in range(len(lines) - 1):
volumes.append(float(lines[i + 1].split()[0]))
energies.append(float(lines[i + 1].split()[1]))
f.close()
eos = EquationOfState(volumes, energies, eos='birchmurnaghan')
volume, energy, bulkmodulus = eos.fit()
latticeconstant = volume**(1. / 3.)
f = open('log.txt', 'w+')
f.write('lattice constant = {0:18.7f} A\n'.format(latticeconstant))
f.write('bulk energy = {0:18.7f} eV\n'.format(energy))
f.write('bulk modulus = {0:18.7f} eV/A^3\n'.format(bulkmodulus))
f.close()
if plot_eos is True:
eos.plot(show=True)
################################################################################
# END
################################################################################
def test_rescaled_calculator():
"""
Test rescaled RescaledCalculator() by computing lattice constant
and bulk modulus using fit to equation of state
and comparing it to the desired values
"""
from ase.calculators.eam import EAM
from ase.units import GPa
# A simple empirical N-body potential for
# transition metals by M. W. Finnis & J.E. Sinclair
# https://www.tandfonline.com/doi/abs/10.1080/01418618408244210
# using analytical formulation in order to avoid extra file dependence
# All the constants are taken from the paper.
# Please refer to the paper for more details
def pair_potential(r):
"""
returns the pair potential as a equation 27 in pair_potential
r - numpy array with the values of distance to compute the pair function
"""
# parameters for W
c = 3.25
c0 = 47.1346499
c1 = -33.7665655
c2 = 6.2541999
energy = (c0 + c1 * r + c2 * r**2.0) * (r - c)**2.0
energy[r > c] = 0.0
return energy
def cohesive_potential(r):
"""
returns the cohesive potential as a equation 28 in pair_potential
r - numpy array with the values of distance to compute the pair function
"""
# parameters for W
d = 4.400224
rho = (r - d)**2.0
rho[r > d] = 0.0
return rho
def embedding_function(rho):
"""
returns energy as a function of electronic density from eq 3
"""
A = 1.896373
energy = -A * np.sqrt(rho)
return energy
cutoff = 4.400224
W_FS = EAM(elements=['W'],
embedded_energy=np.array([embedding_function]),
electron_density=np.array([[cohesive_potential]]),
phi=np.array([[pair_potential]]),
cutoff=cutoff,
form='fs')
# compute MM and QM equations of state
def strain(at, e, calc):
at = at.copy()
at.set_cell((1.0 + e) * at.cell, scale_atoms=True)
at.calc = calc
v = at.get_volume()
e = at.get_potential_energy()
return v, e
# desired DFT values
a0_qm = 3.18556
C11_qm = 522 # pm 15 GPa
C12_qm = 193 # pm 5 GPa
B_qm = (C11_qm + 2.0 * C12_qm) / 3.0
bulk_at = bulk("W", cubic=True)
mm_calc = W_FS
eps = np.linspace(-0.01, 0.01, 13)
v_mm, E_mm = zip(*[strain(bulk_at, e, mm_calc) for e in eps])
eos_mm = EquationOfState(v_mm, E_mm)
v0_mm, E0_mm, B_mm = eos_mm.fit()
B_mm /= GPa
a0_mm = v0_mm**(1.0 / 3.0)
mm_r = RescaledCalculator(mm_calc, a0_qm, B_qm, a0_mm, B_mm)
bulk_at = bulk("W", cubic=True, a=a0_qm)
v_mm_r, E_mm_r = zip(*[strain(bulk_at, e, mm_r) for e in eps])
eos_mm_r = EquationOfState(v_mm_r, E_mm_r)
v0_mm_r, E0_mm_r, B_mm_r = eos_mm_r.fit()
B_mm_r /= GPa
a0_mm_r = v0_mm_r**(1.0 / 3)
# check match of a0 and B after rescaling is adequate
# 0.1% error in lattice constant and bulk modulus
assert abs((a0_mm_r - a0_qm) / a0_qm) < 1e-3
assert abs((B_mm_r - B_qm) / B_qm) < 1e-3
# compute MM and QM equations of state
def strain(at, e, calc):
at = at.copy()
at.set_cell((1.0 + e) * at.cell, scale_atoms=True)
at.set_calculator(calc)
v = at.get_volume()
e = at.get_potential_energy()
return v, e
eps = np.linspace(-0.01, 0.01, 13)
v_qm, E_qm = zip(*[strain(bulk_at, e, qm) for e in eps])
v_mm, E_mm = zip(*[strain(bulk_at, e, mm) for e in eps])
eos_qm = EquationOfState(v_qm, E_qm)
v0_qm, E0_qm, B_qm = eos_qm.fit()
a0_qm = v0_qm**(1.0 / 3.0)
eos_mm = EquationOfState(v_mm, E_mm)
v0_mm, E0_mm, B_mm = eos_mm.fit()
a0_mm = v0_mm**(1.0 / 3.0)
mm_r = RescaledCalculator(mm, a0_qm, B_qm, a0_mm, B_mm)
v_mm_r, E_mm_r = zip(*[strain(bulk_at, e, mm_r) for e in eps])
eos_mm_r = EquationOfState(v_mm_r, E_mm_r)
v0_mm_r, E0_mm_r, B_mm_r = eos_mm_r.fit()
a0_mm_r = v0_mm_r**(1.0 / 3)
# check match of a0 and B after rescaling is adequete
assert abs((a0_mm_r - a0_qm) / a0_qm) < 1e-3 # 0.1% error in lattice constant
def lattice_constant(volumes, energies):
eos = EquationOfState(volumes, energies)
v, e, B = eos.fit()
a = (v * 4)**(1 / 3)
return a
cell_0 = al.cell # Unit cell object of the Al bulk
for eps in np.linspace(-0.02, 0.02, N_lattice_spacings):
al.cell = (
1 + eps) * cell_0 # Adjust lattice constant of unit cell
# Calculate the potential energy for the Al bulk
energies.append(al.get_potential_energy())
volumes.append(al.get_volume())
#
# confs = read('out.txt@0:' + str(N_lattice_spacings)) # Read the configurations
# # Extract volumes and energies:
# volumes = [atoms.get_volume() for atoms in confs]
# energies = [atoms.get_potential_energy() for atoms in confs]
# # if rank == 0:
# # print energies, shape(energies)
#
if rank == 0:
print 'Energies: ' + str(energies)
print 'Volumes: ' + str(volumes)
# Plot energies as a function of unit cell volume (directly related to latt. const.)
eos = EquationOfState(volumes, energies)
v0, E_bulk, B = eos.fit()
eos.plot('Al_eos.png')
# Latt. const. acc. to ASE doc., but why is this correct?
a_calc = (4 * v0)**(1 / 3.0)
print 'a_calc: ' + str(a_calc)
else:
al.get_potential_energy()
print 'a0 %f\n'% (opt_cell[0][0])
# reoptimize/check volume
#
volumes = []
energies = []
for x in np.linspace(0.98, 1.02, 5):
bulk.set_cell(opt_cell * x, scale_atoms=True)
volumes.append(bulk.get_volume() / bulk.get_number_of_atoms())
energies.append(bulk.get_potential_energy() / bulk.get_number_of_atoms())
# fit EOS
#
eos = EquationOfState(volumes, energies)
vpaf, epaf, B1 = eos.fit()
print "EOS vpaf:", vpaf, "A^3"
print "EOS epaf:", epaf, "eV"
print "EOS B1:", B1 / kJ * 1.0e24, "GPa"
strain = 0.001
diag = ([1, 0, 0],
[0, 1, 0],
[0, 0, 1])
# c44
#
defm1 = np.array([[0, strain, strain],
[strain, 0, strain],
[strain, strain, 0]])
cell1 = np.dot(opt_cell, defm1 + diag)
def calc_lattice_parameter(al_bulk_ASE, A, lmbd, D, mu2):
calc = get_calc((A, lmbd, D, mu2))
eps = 0.001
energies = []
volumes = []
al_bulk_ASE.set_calculator(calc)
# # # Find lattice constant with lowest energy # # #
cell_0 = al_bulk_ASE.get_cell() # Unit cell object of the Al bulk
# DIRECTION
cell_orig = cell_0
E1 = al_bulk_ASE.get_potential_energy()
al_bulk_ASE.set_cell((1 + eps) * cell_0)
E2 = al_bulk_ASE.get_potential_energy()
direction = (E2 - E1) / abs((E2 - E1))
print('Direction', direction)
# Go one step in the right
al_bulk_ASE.set_cell(cell_orig)
energies.append(al_bulk_ASE.get_potential_energy())
volumes.append(al_bulk_ASE.get_volume())
cell_0 = al_bulk_ASE.get_cell()
al_bulk_ASE.set_cell(
(1 - direction * eps) * cell_0) # Adjust lattice constant of unit cell
energies.append(al_bulk_ASE.get_potential_energy())
volumes.append(al_bulk_ASE.get_volume())
# Go two steps back
while (energies[-1] - energies[-2]) < 0:
cell_0 = al_bulk_ASE.get_cell()
# Adjust lattice constant of unit cell
al_bulk_ASE.set_cell((1 - direction * eps) * cell_0)
# Calculate the potential energy for the Al bulk
energies.append(al_bulk_ASE.get_potential_energy())
volumes.append(al_bulk_ASE.get_volume())
cell_0 = al_bulk_ASE.get_cell()
al_bulk_ASE.set_cell(
(1 - direction * eps) * cell_0) # Adjust lattice constant of unit cell
# Calculate the potential energy for the Al bulk
energies.append(al_bulk_ASE.get_potential_energy())
volumes.append(al_bulk_ASE.get_volume())
# plt.plot((4 * np.asarray(volumes))**(1 / 3), energies)
# plt.show()
# Plot energies as a function of unit cell volume (directly related to latt. const.)
eos = EquationOfState(volumes, energies)
v0, E, B = eos.fit()
# Latt. const. acc. to ASE doc., but why is this correct?
print('asdasdasdasdasd: ', E)
a_calc = (4 * v0)**(1 / 3.0)
# a_calc = v0**(1 / 3.0)
print('a=' + str(a_calc))
al_bulk_ASE.set_cell(cell_0)
return a_calc
import numpy as np
from ase.lattice.cubic import FaceCenteredCubic
from ase.calculators.emt import EMT
from ase.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 ** (1.0 / 3)] * 3, scale_atoms=True)
energies.append(atoms.get_potential_energy())
eos = EquationOfState(volumes, energies)
v1, e1, B = eos.fit()
atoms.set_cell([v1 ** (1.0 / 3)] * 3, scale_atoms=True)
ef = atoms.get_potential_energy()
db.write(atoms, metal=m, latticeconstant=v1 ** (1.0 / 3), energy_per_atom=ef / len(atoms))
from ase.calculators.emt import EMT
from ase.eos import EquationOfState as EOS, eos_names
scipy # silence pyflakes
b = bulk('Al', 'fcc', a=4.0, orthorhombic=True)
b.set_calculator(EMT())
cell = b.get_cell()
volumes = []
energies = []
for x in np.linspace(0.98, 1.01, 5):
b.set_cell(cell * x, scale_atoms=True)
volumes.append(b.get_volume())
energies.append(b.get_potential_energy())
results = []
for name in eos_names:
if name == 'antonschmidt':
# Someone should fix this!
continue
eos = EOS(volumes, energies, name)
v, e, b = eos.fit()
print('{0:20} {1:.8f} {2:.8f} {3:.8f} '.format(name, v, e, b))
assert abs(v - 3.18658700e+01) < 4e-4
assert abs(e - -9.76187802e-03) < 5e-7
assert abs(b - 2.46812688e-01) < 2e-4
results.append((v, e, b))
print(np.ptp(results, 0))
print(np.mean(results, 0))
from ase.calculators.emt import EMT
from ase.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.calc = 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))
from ase.io.trajectory import Trajectory
from ase.io import read
from ase.units import kJ
from ase.eos import EquationOfState, vinet
numberline = 0
f3 = open('e-v.dat')
for line in f3:
numberline = numberline + 1
energies = np.zeros(numberline)
volumes = np.zeros(numberline)
i = 0
with open("e-v.dat") as f3:
for line in f3:
line = line.rstrip('\n')
volumes[i], energies[i] = line.split(" ")
i = i + 1
eos = EquationOfState(volumes, energies, eos='vinet')
eos.fit()
e0, B, Bp, v0 = eos.eos_parameters
fp = open("helmholtz-volume.dat")
for i, line in enumerate(fp):
if i == 1:
a, b, Fmin, d, e, V = line.split()
fp.close()
print(float(Fmin) - vinet(float(V), e0, B, Bp, v0)),
#print eos
#v0, e0, B= eos.fit()
def main():
latoms = vf.get_list_of_atoms()
latoms2 = vf.get_list_of_outcar()
natoms = latoms[0].get_positions().shape[0]
V = np.array([])
ca = np.array([])
magtot = np.array([])
for i in np.arange(len(latoms)):
temp = latoms[i].get_volume()/natoms
V = np.append(V, temp)
temp = latoms[i].get_cell()[:]
temp = np.linalg.norm( temp[2,:] ) / np.linalg.norm( temp[0,:] )
ca = np.append(ca, temp)
try:
temp = latoms2[i].get_magnetic_moment()/natoms
except:
temp = 0
magtot = np.append(magtot, temp)
magtot = np.abs(magtot)
jobn, Etot, Eent, pres = vf.vasp_read_post_data()
a_pos = np.array([]) # scale in POSCAR
for i in jobn:
filename = './y_dir/%s/CONTCAR' %(i)
with open(filename,'r') as f:
a_pos = np.append( a_pos, float( f.readlines()[1] ) )
Etot = Etot / natoms
fitres = myfitting(V, Etot)
V1 = np.array([])
a1_pos = np.array([])
p_dft = np.array([])
for i in np.arange(len(jobn)):
p_dft = np.append( p_dft, pres[i,0:2].mean()*(0.1) ) # pressure [GPa]
if jobn[i][0] == '0' or jobn[i][0] == '1' :
V1 = np.append( V1, V[i] / float(jobn[i]))
a1_pos = np.append( a1_pos, a_pos[i] / (float(jobn[i]))**(1/3) )
if (V1.std() > 1e-8) or (a1_pos.std() > 1e-8) :
print('V1, V1.std(), a1_pos.std():')
print( V1, V1.std(), a1_pos.std() )
sys.exit('V1 or a1_pos is wrong. Abort!')
else:
V1 = V1.mean()
a1_pos = a1_pos.mean()
write_output(V, Etot, fitres, V1, a1_pos, p_dft)
plot_eos(V, Etot, fitres, p_dft, V1, ca, magtot)
ASE_eos = EquationOfState(V, Etot, eos='birchmurnaghan')
temp = np.array([
ASE_eos.fit()[1] - fitres[0],
ASE_eos.fit()[0] - fitres[1],
ASE_eos.fit()[2] - fitres[2] ])
print('==> check with ASE fitting, diff: {0} \n'.format(temp) )
from ase.io import read
from ase.units import kJ
from ase.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')
def test_forceqmmm():
# parameters
N_cell = 2
R_QMs = np.array([3, 7])
# setup bulk and MM region
bulk_at = bulk("Cu", cubic=True)
sigma = (bulk_at * 2).get_distance(0, 1) * (2.**(-1. / 6))
mm = LennardJones(sigma=sigma, epsilon=0.05)
qm = EMT()
# compute MM and QM equations of state
def strain(at, e, calc):
at = at.copy()
at.set_cell((1.0 + e) * at.cell, scale_atoms=True)
at.calc = calc
v = at.get_volume()
e = at.get_potential_energy()
return v, e
eps = np.linspace(-0.01, 0.01, 13)
v_qm, E_qm = zip(*[strain(bulk_at, e, qm) for e in eps])
v_mm, E_mm = zip(*[strain(bulk_at, e, mm) for e in eps])
eos_qm = EquationOfState(v_qm, E_qm)
v0_qm, E0_qm, B_qm = eos_qm.fit()
a0_qm = v0_qm**(1.0 / 3.0)
eos_mm = EquationOfState(v_mm, E_mm)
v0_mm, E0_mm, B_mm = eos_mm.fit()
a0_mm = v0_mm**(1.0 / 3.0)
mm_r = RescaledCalculator(mm, a0_qm, B_qm, a0_mm, B_mm)
v_mm_r, E_mm_r = zip(*[strain(bulk_at, e, mm_r) for e in eps])
eos_mm_r = EquationOfState(v_mm_r, E_mm_r)
v0_mm_r, E0_mm_r, B_mm_r = eos_mm_r.fit()
a0_mm_r = v0_mm_r**(1.0 / 3)
# check match of a0 and B after rescaling is adequete
assert abs(
(a0_mm_r - a0_qm) / a0_qm) < 1e-3 # 0.1% error in lattice constant
assert abs((B_mm_r - B_qm) / B_qm) < 0.05 # 5% error in bulk modulus
# plt.plot(v_mm, E_mm - np.min(E_mm), 'o-', label='MM')
# plt.plot(v_qm, E_qm - np.min(E_qm), 'o-', label='QM')
# plt.plot(v_mm_r, E_mm_r - np.min(E_mm_r), 'o-', label='MM rescaled')
# plt.legend()
at0 = bulk_at * N_cell
r = at0.get_distances(0, np.arange(1, len(at0)), mic=True)
print(len(r))
del at0[0] # introduce a vacancy
print("N_cell", N_cell, 'N_MM', len(at0))
ref_at = at0.copy()
ref_at.calc = qm
opt = FIRE(ref_at)
opt.run(fmax=1e-3)
u_ref = ref_at.positions - at0.positions
us = []
for R_QM in R_QMs:
at = at0.copy()
mask = r < R_QM
print('R_QM', R_QM, 'N_QM', mask.sum(), 'N_total', len(at))
qmmm = ForceQMMM(at, mask, qm, mm, buffer_width=2 * qm.rc)
at.calc = qmmm
opt = FIRE(at)
opt.run(fmax=1e-3)
us.append(at.positions - at0.positions)
# compute error in energy norm |\nabla u - \nabla u_ref|
def strain_error(at0, u_ref, u, cutoff, mask):
I, J = neighbor_list('ij', at0, cutoff)
I, J = np.array([(i, j) for i, j in zip(I, J) if mask[i]]).T
v = u_ref - u
dv = np.linalg.norm(v[I, :] - v[J, :], axis=1)
return np.linalg.norm(dv)
du_global = [
strain_error(at0, u_ref, u, 1.5 * sigma, np.ones(len(r))) for u in us
]
du_local = [strain_error(at0, u_ref, u, 1.5 * sigma, r < 3.0) for u in us]
print('du_local', du_local)
print('du_global', du_global)
# check local errors are monotonically decreasing
assert np.all(np.diff(du_local) < 0)
# check global errors are monotonically converging
assert np.all(np.diff(du_global) < 0)
# biggest QM/MM should match QM result
assert du_local[-1] < 1e-10
assert du_global[-1] < 1e-10
def do_volume_autotune(self,
encut=None,
start_scan=0.925,
end_scan=1.075,
num_scans=20,
exclude_type=None,
only_type=None):
if not os.path.isfile(self.poscar_vol):
encut = encut if encut != None else self.do_encut_autotune()
logging.info("Commencing volume scan...")
print("Determining optimal volume...")
start_scan, end_scan, num_scans, exclude_type, only_type, vols, ens = self.set_volume_autotune_params(
start_scan=start_scan,
end_scan=end_scan,
num_scans=num_scans,
exclude_type=exclude_type,
only_type=only_type)
# Load POSCAR
try:
sys = read(self.poscar_init)
calc = self.calc_dict['volume']
calc.set(encut=encut)
start_cell = sys.get_cell()
except:
logging.error(
"Initial POSCAR file could not be found at {}".format(
poscar_init))
print("Error: See error log for details.")
return None
logging.info("Loaded initial POSCAR file.")
# Do volume scan
logging.info("Performing volume scan.")
for x in np.linspace(start_scan, end_scan, num_scans):
sys.set_cell(x * start_cell, scale_atoms=True)
sys.set_calculator(calc)
ens.append(sys.get_potential_energy())
vols.append(sys.get_volume())
logging.info("Volume scan complete.")
# Fit EoS
logging.info("Fitting equations of state.")
eos_types = "sjeos taylor murnaghan birch birchmurnaghan pouriertarantola p3 antonschmidt".split(
)
if exclude_type != None:
_ = [eos_types.remove(i) for i in exclude]
elif only_type != None:
eos_types = only_type
eos_fits = {}
for typ in eos_types:
eos = EquationOfState(vols, ens, eos=typ)
try:
v, e, B = eos.fit()
eos_fits[typ] = {
'volume': v,
'energy': e,
'buld_modulus': B
}
except:
print("Unable to fit type {}.".format(typ))
# Rescale initial cell to optimized volume
logging.info("Optimal volume found. Rescaling original cell.")
vol_avg = np.average(
[eos_fits[key]['volume'] for key in eos_fits.keys()])
sys.set_cell(start_cell, scale_atoms=True)
scale = sys.get_volume() / vol_avg
sys.set_cell(scale * start_cell, scale_atoms=True)
# Perform sc-step
logging.info("Performing self-consistent step.")
print("Second relaxation")
#calc.set(isif=3) # Everything can relax
sys.set_calculator(calc)
en = sys.get_potential_energy()
# Set relaxed structure as active structure
print("Setting relaxed structure to active structure.")
self.system = sys
# Save structure
logging.info("Saving self-consistent calculator.")
write(self.poscar_vol, sys)
print("Done.")
logging.info("Volume scan complete.")
self.clean_up()
else:
sys = read(self.poscar_vol)
print("Volume optimized system ready.")
def getBulkModulus(jobID, latticeParams):
"""
Use optimized lattice parameters from fmin(getEnergy). Calculate energies around the minimum.
Returns optimized atomic positions, energy of minimum, calculated bulk modulus, and writes wavefunctions to file inp.gpw
"""
### INITIALIZE
vol, eng = [], []
jobObject, bulkObject, calcObject, dft, preCalcObject, preCalcObject, existsPrecalc, optAtoms, magmoms = initialize(
jobID, latticeParams)
with open('lattice_opt.log', 'r') as f:
nIter = len(f.readlines()) + 9 #count number of ionic steps taken
optCell = optAtoms.get_cell()
strains = np.linspace(0.99, 1.01, 9)
### GENERATE dE/dV plot
for i, strain in enumerate(strains):
atoms = deepcopy(optAtoms)
atoms.set_cell(optCell * strain, scale_atoms=True)
### PRECALCULATE
if existsPrecalc:
optimizePos(atoms,
dft,
preCalcObject,
magmoms,
restart=False,
saveWF=True)
### CALCULATE
optimizePos(atoms,
dft,
calcObject,
magmoms,
restart=existsPrecalc,
saveWF=False)
### COLLECT RESULTS
energy = atoms.get_potential_energy()
volume = atoms.get_volume()
vol.append(deepcopy(volume))
eng.append(deepcopy(energy))
parprint('%f %f' % (strain, energy))
### COLLECT DETAILED DATA ABOUT MINIMUM ENERGY STATE
if i == 4:
pos = atoms.get_scaled_positions()
vMin = deepcopy(volume)
io.write('optimized.traj', atoms)
magmom = atoms.get_magnetic_moments(
) if calcObject.magmom > 0 else np.zeros(len(atoms))
if dft == 'gpaw':
atoms.calc.write('inp.gpw',
mode='all') #for use in getXCContribs
aHat, quadR2 = quadFit(np.array(deepcopy(vol)), np.array(deepcopy(eng)))
b0 = aHat * 2 * vMin * 160.2 # units: eV/A^6 * A^3 * 1, where 1 === 160.2 GPa*A^3/eV
parprint('quadR2 = ' + str(quadR2))
try:
eos = EquationOfState(vol, eng)
v0, e0, b = eos.fit()
eos.plot(filename='bulk-eos.png', show=False)
b0 = b / kJ * 1e24 #GPa use this value if EOS doesn't fail
except ValueError:
e0 = eng[4]
return (optCell, nIter, pos, magmom, e0, b0, quadR2) #GPa
