def __init__(self,
tar_img,
ref_img,
src_pts,
dst_pts,
grid_size=100,
scale_factor=15):
'''
The image stitching engine usings APAP algorithm.
tar_img : Target image that will be warped to be stitched to reference image.
ref_img : Reference image that will not be warped.
src_pts : Paired key points' coordinates in target image.
dst_pts : Paired key points' coordinates in reference image.
grid_size : The grid size is grid_size by grid_size.
scale_factor : Scale factor used in matching pairs' weight adjustment.
'''
self.src_pts = src_pts
self.dst_pts = dst_pts
self.scale_factor = scale_factor
self.grids = Grids(grid_size, tar_img.shape[0], tar_img.shape[1])
self.mask = None
self.homoMat = HomoMatrix()
def main():
grids = Grids()
grid = grids.grid5
path = eval(grid, 15)
print("---- Path is of length: {}".format(len(path)))
astar_animation(path, grid)
def set_grid(self, h=0.2, cutoff=3.0):
if self.calculation_required(self.el.atoms, ['energy']):
raise AssertionError('Electronic structure is not solved yet!')
if self.flags['grid'] == False:
self.gd = Grids(self, h, cutoff)
self.flags['grid'] = True
class Hotbit(Output):
def __init__(self,
parameters=None,
elements=None,
tables=None,
verbose=False,
charge=0.0,
SCC=True,
kpts=(1, 1, 1),
rs='kappa',
physical_k=True,
maxiter=50,
gamma_cut=None,
txt=None,
verbose_SCC=False,
width=0.02,
mixer=None,
coulomb_solver=None,
charge_density='Gaussian',
vdw=False,
vdw_parameters=None,
internal={}):
"""
Hotbit -- density-functional tight-binding calculator
for atomic simulation environment (ASE).
Parameters:
-----------
parameters: The directory for parametrization files.
* If parameters==None, use HOTBIT_PARAMETERS environment variable.
* Parametrizations given by 'elements' and 'tables' keywords
override parametrizations in this directory.
elements: Files for element data (*.elm).
example: {'H':'H_custom.elm','C':'/../C.elm'}
* If extension '.elm' is omitted, it is assumed.
* Items can also be elements directly: {'H':H} (H is type Element)
* If elements==None, use element info from default directory.
* If elements['rest']=='default', use default parameters for all other
elements than the ones specified. E.g. {'H':'H.elm','rest':'default'}
(otherwise all elements present have to be specified explicitly).
tables: Files for Slater-Koster tables.
example: {'CH':'C_H.par','CC':'C_C.par'}
* If extension '.par' is omitted, it is assumed.
* If tables==None, use default interactions.
* If tables['rest']='default', use default parameters for all other
interactions, e.g. {'CH':'C_H.par','rest':'default'}
* If tables['AB']==None, ignore interactions for A and B
(both chemical and repulsive)
mixer: Density mixer.
example: {'name':'Anderson','mixing_constant':0.2, 'memory':5}.
charge: Total charge for system (-1 means an additional electron)
width: Width of Fermi occupation (eV)
SCC: Self-Consistent Charge calculation
* True for SCC-DFTB, False for DFTB
kpts: Number of k-points.
* For translational symmetry points are along the directions
given by the cell vectors.
* For general symmetries, you need to look at the info
from the container used
rs: * 'kappa': use kappa-points
* 'k': use normal k-points. Only for Bravais lattices.
physical_k Use physical (realistic) k-points for generally periodic systems.
* Ignored with normal translational symmetry
* True for physically allowed k-points in periodic symmetries.
maxiter: Maximum number of self-consistent iterations
* only for SCC-DFTB
coulomb_solver: The Coulomb solver object. If None, a DirectCoulomb
object will the automatically instantiated.
* only for SCC-DFTB
charge_density: Shape of the excess charge on each atom. Possibilities
are:
* 'Gaussian': Use atom centered Gaussians. This is the
default.
* 'Slater': Slater-type exponentials as used in the
original SCC-DFTB scheme.
* only for SCC-DFTB
gamma_cut: Range for Coulomb interaction if direct summation is
selected (coulomb_solver = None).
* only for SCC-DFTB
vdw: Include van der Waals interactions
vdw_parameters: Dictionary containing the parameters for the van-der-Waals
interaction for each element.
i.e. { el: ( p, R0 ), ... }
where *el* is the element name, *p* the polarizability and
*R0* the radius where the van-der-Waals interaction starts.
Will override whatever read from .elm files.
txt: Filename for log-file.
* None: standard output
* '-': throw output to trash (/null)
verbose_SCC: Increase verbosity in SCC iterations.
internal: Dictionary for internal variables, some of which are set for
stability purposes, some for quick and dirty bug fixes.
Use these with caution! (For this reason, for the description
of these variables you are forced to look at the source code.)
"""
from copy import copy
import os
if gamma_cut != None: gamma_cut = gamma_cut / Bohr
self.__dict__ = {
'parameters': parameters,
'elements': elements,
'tables': tables,
'verbose': verbose,
'charge': charge,
'width': width / Hartree,
'SCC': SCC,
'kpts': kpts,
'rs': rs,
'physical_k': physical_k,
'maxiter': maxiter,
'gamma_cut': gamma_cut,
'vdw': vdw,
'vdw_parameters': vdw_parameters,
'txt': txt,
'verbose_SCC': verbose_SCC,
'mixer': mixer,
'coulomb_solver': coulomb_solver,
'charge_density': charge_density,
'internal': internal
}
if parameters != None:
os.environ.data['HOTBIT_PARAMETERS'] = parameters
self.init = False
self.notes = []
self.dry_run = '--dry-run' in sys.argv
internal0 = {
'sepsilon':
0., # add this to the diagonal of S to avoid LAPACK error in diagonalization
'tol_imaginary_e': 1E-13, # tolerance for imaginary band energy
'tol_mulliken':
1E-5, # tolerance for mulliken charge sum deviation from integer
'tol_eigenvector_norm':
1E-6, # tolerance for eigenvector norm for eigensolver
'symop_range': 5
} # range for the number of symmetry operations in all symmetries
internal0.update(internal)
for key in internal0:
self.set(key, internal0[key])
#self.set_text(self.txt)
#self.timer=Timer('Hotbit',txt=self.get_output())
def __del__(self):
""" Delete calculator -> timing summary. """
if self.get('SCC'):
try:
print >> self.txt, self.st.solver.get_iteration_info()
self.txt.flush()
except:
pass
if len(self.notes) > 0:
print >> self.txt, 'Notes and warnings:'
for note in self.notes:
print >> self.txt, note
if self.init:
self.timer.summary()
Output.__del__(self)
def write_electronic_data(self, filename, keys=None):
"""
Write key electronic data into a file with *general* format.
Hotbit is not needed to analyze the resulting data file.
The data will be in a dictionary with the following items:
N the number of atoms
norb the number of orbitals
nelectrons the number of electrons
charge system charge
epot potential energy
ebs band structure energy
ecoul coulomb energy
erep repulsive energy
forces atomic forces
symbols element symbols
e single-particle energies
occ occupations
nk number of k-points
k k-point vectors
wk k-point weights
dq excess Mulliken populations
gap energy gap
gap_prob certainty of the gap determination above
dose energies for density of states (all states over k-points as well)
0 = Fermi-level
dos density of states (including k-point weights)
Access to data, simply:
data = numpy.load(filename)
print data['epot']
parameters:
-----------
filename: output file name
keys: list of items (key names) to save.
If None, save all.
"""
data = {}
data['N'] = self.el.N
data['norb'] = self.st.norb
data['charge'] = self.get('charge')
data['nelectrons'] = self.el.get_number_of_electrons()
data['erep'] = self.rep.get_repulsive_energy()
data['ecoul'] = self.get_coulomb_energy(self.el.atoms)
data['ebs'] = self.get_band_structure_energy(self.el.atoms)
data['epot'] = self.get_potential_energy(self.el.atoms)
data['forces'] = self.get_forces(self.el.atoms)
data['symbols'] = self.el.symbols
data['e'] = self.st.e
data['occ'] = self.st.f
data['nk'] = self.st.nk
data['k'] = self.st.k
data['wk'] = self.st.wk
data['dq'] = self.st.mulliken()
data['gap'], data['gap_prob'] = self.get_energy_gap()
data['dose'], data['dos'] = self.get_density_of_states(False)
for key in data.keys():
if keys != None and key not in keys:
del data[key]
import pickle
f = open(filename, 'w')
pickle.dump(data, f)
f.close()
def set(self, key, value):
if key == 'txt':
self.set_text(value)
elif self.init == True and key not in ['charge']:
raise AssertionError(
'Parameters cannot be set after initialization.')
else:
self.__dict__[key] = value
def get_atoms(self):
""" Return the current atoms object. """
atoms = self.el.atoms.copy()
atoms.set_calculator(self)
return atoms
def add_note(self, note):
""" Add warning (etc) note to be printed in log file end. """
self.notes.append(note)
def greetings(self):
""" Simple greetings text """
from time import asctime
from os import uname
from os.path import abspath, curdir
from os import environ
self.version = hotbit_version
print >> self.txt, '\n\n\n\n\n'
print >> self.txt, ' _ _ _ _ _'
print >> self.txt, '| |__ ___ | |_ | |__ |_| |_'
print >> self.txt, '| _ \ / _ \| _|| _ \| | _|'
print >> self.txt, '| | | | ( ) | |_ | ( ) | | |_'
print >> self.txt, '|_| |_|\___/ \__|\____/|_|\__| ver.', self.version
print >> self.txt, 'Distributed under GNU GPL; see %s' % environ.get(
'HOTBIT_DIR') + '/LICENSE'
print >> self.txt, 'Date:', asctime()
dat = uname()
print >> self.txt, 'Nodename:', dat[1]
print >> self.txt, 'Arch:', dat[4]
print >> self.txt, 'Dir:', abspath(curdir)
print >> self.txt, 'System:', self.el.get_name()
print >> self.txt, ' Charge=%4.1f' % self.charge
print >> self.txt, ' Container', self.el.container_info()
print >> self.txt, 'Symmetry operations (if any):'
rs = self.get('rs')
kpts = self.get('kpts')
M = self.el.get_number_of_transformations()
for i in range(3):
print >> self.txt, ' %i: pbc=' % i, self.el.atoms.get_pbc(
)[i],
if type(kpts) == type([]):
print >> self.txt, ', %s-points=%i, M=%.f' % (rs, len(kpts),
M[i])
else:
print >> self.txt, ', %s-points=%i, M=%.f' % (rs, kpts[i],
M[i])
print >> self.txt, 'Electronic temperature:', self.width * Hartree, 'eV'
mixer = self.st.solver.mixer
print >> self.txt, 'Mixer:', mixer.get(
'name'), 'with memory =', mixer.get(
'memory'), ', mixing parameter =', mixer.get('beta')
print >> self.txt, self.el.greetings()
print >> self.txt, self.ia.greetings()
print >> self.txt, self.rep.greetings()
if self.pp.exists():
print >> self.txt, self.pp.greetings()
def out(self, text):
print >> self.txt, text
self.txt.flush()
def set_text(self, txt):
""" Set up the output file. """
if txt == '-' or txt == 'null':
self.txt = open('/dev/null', 'w')
elif hasattr(txt, 'write'):
self.txt = txt
elif txt is None:
from sys import stdout
self.txt = stdout
else:
self.txt = open(txt, 'a')
# check if the output of timer must be changed also
if 'timer' in self.__dict__:
self.timer.txt = self.get_output()
def get(self, arg=None):
"""
Get calculator input parameters.
arg: 'kpts','width',...
"""
if arg == None:
return self.__dict__
else:
return self.__dict__[arg]
def memory_estimate(self):
"""
Print an estimate for memory consumption in GB.
If script run with --dry-run, exit.
"""
if self.st.nk > 1:
number = 16. #complex
else:
number = 8. #real
M = self.st.nk * self.st.norb**2 * number
# H S dH0 dS wf H1 dH rho rhoe
mem = M + M + 3 * M + 3 * M + M + M + 3 * M + M + M
print >> self.txt, 'Memory consumption estimate: > %.2f GB' % (mem /
1E9)
self.txt.flush()
if self.dry_run:
raise SystemExit
def solve_ground_state(self, atoms):
""" If atoms moved, solve electronic structure. """
if not self.init:
assert type(atoms) != type(None)
self._initialize(atoms)
if type(atoms) == type(None):
pass
elif self.calculation_required(atoms, 'ground state'):
self.el.update_geometry(atoms)
t0 = time()
self.st.solve()
self.el.set_solved('ground state')
t1 = time()
self.flags['Mulliken'] = False
self.flags['DOS'] = False
self.flags['bonds'] = False
if self.verbose:
print >> self.get_output(), "Solved in %0.2f seconds" % (t1 -
t0)
#if self.get('SCC'):
# atoms.set_charges(-self.st.get_dq())
else:
pass
def _initialize(self, atoms):
""" Initialization of hotbit. """
if not self.init:
self.set_text(self.txt)
self.timer = Timer('Hotbit', txt=self.get_output())
self.start_timing('initialization')
self.el = Elements(self, atoms)
self.ia = Interactions(self)
self.st = States(self)
self.rep = Repulsion(self)
self.pp = PairPotential(self)
if self.get('vdw'):
if self.get('vdw_parameters') is not None:
self.el.update_vdw(self.get('vdw_parameters'))
setup_vdw(self)
self.env = Environment(self)
pbc = atoms.get_pbc()
# FIXME: gamma_cut -stuff
#if self.get('SCC') and np.any(pbc) and self.get('gamma_cut')==None:
# raise NotImplementedError('SCC not implemented for periodic systems yet (see parameter gamma_cut).')
if np.any(pbc) and abs(
self.get('charge')) > 0.0 and self.get('SCC'):
raise AssertionError('Charged system cannot be periodic.')
self.flush()
self.flags = {}
self.flags['Mulliken'] = False
self.flags['DOS'] = False
self.flags['bonds'] = False
self.flags['grid'] = False
self.stop_timing('initialization')
self.el.set_atoms(atoms)
if not self.init:
self.init = True
self.greetings()
def calculation_required(self, atoms, quantities):
""" Check if a calculation is required.
Check if the quantities in the quantities list have already been calculated
for the atomic configuration atoms. The quantities can be one or more of:
'ground state', 'energy', 'forces', 'magmoms', and 'stress'.
"""
return self.el.calculation_required(atoms, quantities)
def get_potential_energy(self, atoms):
""" Return the potential energy of present system. """
if self.calculation_required(atoms, ['energy']):
self.solve_ground_state(atoms)
self.start_timing('energy')
ebs = self.get_band_structure_energy(atoms)
ecoul = self.get_coulomb_energy(atoms)
erep = self.rep.get_repulsive_energy()
epp = self.pp.get_energy()
self.epot = ebs + ecoul + erep + epp - self.el.efree * Hartree
self.stop_timing('energy')
self.el.set_solved('energy')
return self.epot.copy()
def get_forces(self, atoms):
"""
Return forces (in eV/Angstrom)
Ftot = F(band structure) + F(coulomb) + F(repulsion).
"""
if self.calculation_required(atoms, ['forces']):
self.solve_ground_state(atoms)
self.start_timing('forces')
fbs = self.st.get_band_structure_forces()
frep = self.rep.get_repulsive_forces()
fcoul = self.st.es.gamma_forces() #zero for non-SCC
fpp = self.pp.get_forces()
self.stop_timing('forces')
self.f = (fbs + frep + fcoul + fpp) * (Hartree / Bohr)
self.el.set_solved('forces')
return self.f.copy()
def get_band_energies(self, kpts=None, shift=True, rs='kappa', h1=False):
'''
Return band energies for explicitly given list of k-points.
parameters:
===========
kpts: list of k-points; e.g. kpts=[(0,0,0),(pi/2,0,0),(pi,0,0)]
k- or kappa-points, depending on parameter rs.
if None, return for all k-points in the calculation
shift: shift zero to the Fermi-level
rs: use 'kappa'- or 'k'-points in reciprocal space
h1: Add Coulomb part to hamiltonian matrix. Required for consistent use of SCC.
'''
if kpts == None:
e = self.st.e * Hartree
else:
if rs == 'k':
klist = k_to_kappa_points(kpts, self.el.atoms)
elif rs == 'kappa':
klist = kpts
e = self.st.get_band_energies(klist, h1) * Hartree
if shift:
return e - self.get_fermi_level()
else:
return e
def get_stress(self, atoms):
self.solve_ground_state(atoms)
# TODO: ASE needs an array from this method, would it be proper to
# somehow inform that the stresses are not calculated?
return np.zeros((6, ))
def get_charge(self):
""" Return system's total charge. """
return self.get('charge')
def get_eigenvalues(self):
""" Return eigenvalues without shifts.
For alternative, look at method get_band_energies.
"""
return self.st.get_eigenvalues() * Hartree
def get_energy_gap(self):
"""
Return the energy gap. (in eV)
Gap is the energy difference between the first states
above and below Fermi-level. Return also the probability
of having returned the gap; it is the difference
in the occupations of these states, divided by 2.
"""
eigs = (self.get_eigenvalues() - self.get_fermi_level()).flatten()
occ = self.get_occupations().flatten()
ehi, elo = 1E10, -1E10
for e, f in zip(eigs, occ):
if elo < e <= 0.0:
elo = e
flo = f
elif 0.0 < e < ehi:
ehi = e
fhi = f
return ehi - elo, (flo - fhi) / 2
def get_state_indices(self, state):
"""
Return the k-point index and band index of given state.
parameters:
-----------
state: 'H**O', or 'LUMO'
H**O is the first state below Fermi-level.
LUMO is the first state above Fermi-level.
"""
eigs = (self.get_eigenvalues() - self.get_fermi_level()).flatten()
if state == 'H**O':
k, a = np.unravel_index(
np.ma.masked_array(eigs, eigs > 0.0).argmax(),
(self.st.nk, self.st.norb))
if state == 'LUMO':
k, a = np.unravel_index(
np.ma.masked_array(eigs, eigs < 0.0).argmin(),
(self.st.nk, self.st.norb))
return k, a
def get_occupations(self):
#self.solve_ground_state(atoms)
return self.st.get_occupations()
def get_band_structure_energy(self, atoms):
if self.calculation_required(atoms, ['ebs']):
self.solve_ground_state(atoms)
self.ebs = self.st.get_band_structure_energy() * Hartree
self.el.set_solved('ebs')
return self.ebs
def get_coulomb_energy(self, atoms):
if self.calculation_required(atoms, ['ecoul']):
self.solve_ground_state(atoms)
self.ecoul = self.st.es.coulomb_energy() * Hartree
self.st
return self.ecoul
# some not implemented ASE-assumed methods
def get_fermi_level(self):
"""
Return the Fermi-energy (chemical potential) in eV.
"""
return self.st.occu.get_mu() * Hartree
def set_atoms(self, atoms):
""" Initialize the calculator for given atomic system. """
if self.init == True and atoms.get_chemical_symbols(
) != self.el.atoms.get_chemical_symbols():
raise RuntimeError(
'Calculator initialized for %s. Create new calculator for %s.'
% (self.el.get_name(), mix.parse_name_for_atoms(atoms)))
else:
self._initialize(atoms)
def get_occupation_numbers(self, kpt=0):
""" Return occupation numbers for given k-point index. """
return self.st.f[kpt].copy()
def get_number_of_bands(self):
""" Return the total number of orbitals. """
return self.st.norb
def start_timing(self, label):
self.timer.start(label)
def stop_timing(self, label):
self.timer.stop(label)
#
# various analysis methods
#
def get_dielectric_function(self, width=0.05, cutoff=None, N=400):
"""
Return the imaginary part of the dielectric function for non-SCC.
Note: Uses approximation that requires that the orientation of
neighboring unit cells does not change much.
(Exact for Bravais lattice.)
See, e.g., Marder, Condensed Matter Physics, or
Popov New J. Phys 6, 17 (2004)
parameters:
-----------
width: energy broadening in eV
cutoff: cutoff energy in eV
N: number of points in energy grid
return:
-------
e[:], d[:,0:2]
"""
self.start_timing('dielectric function')
width = width / Hartree
otol = 0.05 # tolerance for occupations
if cutoff == None:
cutoff = 1E10
else:
cutoff = cutoff / Hartree
st = self.st
nk, e, f, wk = st.nk, st.e, st.f, st.wk
ex, wt = [], []
for k in range(nk):
wf = st.wf[k]
wfc = wf.conjugate()
dS = st.dS[k].transpose((0, 2, 1))
ek = e[k]
fk = f[k]
kweight = wk[k]
# electron excitation ka-->kb; restrict the search:
bmin = list(fk < 2 - otol).index(True)
amin = list(ek > ek[bmin] - cutoff).index(True)
amax = list(fk < otol).index(True)
for a in xrange(amin, amax + 1):
bmax = list(ek > ek[a] + cutoff).index(True)
for b in range(max(a + 1, bmin), bmax + 1):
de = ek[b] - ek[a]
df = fk[a] - fk[b]
if df < otol:
continue
# P = < ka | P | kb >
P = 1j * hbar * np.dot(wfc[a], np.dot(dS, wf[b]))
ex.append(de)
wt.append(kweight * df * np.abs(P)**2)
ex, wt = np.array(ex), np.array(wt)
cutoff = min(ex.max(), cutoff)
y = np.zeros((N, 3))
for d in range(3):
# Lorenzian should be used, but long tail would bring divergence at zero energy
x, y[:, d] = broaden(ex,
wt[:, d],
width,
'gaussian',
N=N,
a=width,
b=cutoff)
y[:, d] = y[:, d] / x**2
const = (4 * np.pi**2 / hbar)
self.stop_timing('dielectric function')
return x * Hartree, y * const #y also in eV, Ang
#
# grid stuff
#
def set_grid(self, h=0.2, cutoff=3.0):
if self.calculation_required(self.el.atoms, ['energy']):
raise AssertionError('Electronic structure is not solved yet!')
if self.flags['grid'] == False:
self.gd = Grids(self, h, cutoff)
self.flags['grid'] = True
def get_grid_basis_orbital(self, I, otype, k=0, pad=True):
"""
Return basis orbital on grid.
parameters:
===========
I: atom index
otype: orbital type ('s','px','py',...)
k: k-point index (basis functions are really the extended
Bloch functions for periodic systems)
pad: padded edges in the array
"""
if self.flags['grid'] == False:
raise AssertionError(
'Grid needs to be set first by method "set_grid".')
return self.gd.get_grid_basis_orbital(I, otype, k, pad)
def get_grid_wf(self, a, k=0, pad=True):
"""
Return eigenfunction on a grid.
parameters:
===========
a: state (band) index
k: k-vector index
pad: padded edges
"""
if self.flags['grid'] == False:
raise AssertionError(
'Grid needs to be set first by method "set_grid".')
return self.gd.get_grid_wf(a, k, pad)
def get_grid_wf_density(self, a, k=0, pad=True):
"""
Return eigenfunction density.
Density is not normalized; accurate quantitative analysis
on this density are best avoided.
parameters:
===========
a: state (band) index
k: k-vector index
pad: padded edges
"""
if self.flags['grid'] == False:
raise AssertionError(
'Grid needs to be set first by method "set_grid".')
return self.gd.get_grid_wf_density(a, k, pad)
def get_grid_density(self, pad=True):
"""
Return electron density on grid.
Do not perform accurate analysis on this density.
Integrated density differs from the total number of electrons.
Bader analysis inaccurate.
parameters:
pad: padded edges
"""
if self.flags['grid'] == False:
raise AssertionError(
'Grid needs to be set first by method "set_grid".')
return self.gd.get_grid_density(pad)
def get_grid_LDOS(self, bias=None, window=None, pad=True):
"""
Return electron density over selected states around the Fermi-level.
parameters:
-----------
bias: bias voltage (eV) with respect to Fermi-level.
Negative means probing occupied states.
window: 2-tuple for lower and upper bounds wrt. Fermi-level
pad: padded edges
"""
if self.flags['grid'] == False:
raise AssertionError(
'Grid needs to be set first by method "set_grid".')
return self.gd.get_grid_LDOS(bias, window, pad)
#
# Mulliken population analysis tools
#
def _init_mulliken(self):
""" Initialize Mulliken analysis. """
if self.calculation_required(self.el.atoms, ['energy']):
raise AssertionError('Electronic structure is not solved yet!')
if self.flags['Mulliken'] == False:
self.MA = MullikenAnalysis(self)
self.flags['Mulliken'] = True
def get_dq(self, atoms=None):
""" Return atoms' excess Mulliken populations.
The total populations subtracted by
the numbers of valence electrons.
"""
self.solve_ground_state(atoms)
return self.st.get_dq()
def get_charges(self, atoms=None):
""" Return atoms' electric charges (Mulliken). """
return -self.get_dq(atoms)
def get_atom_mulliken(self, I):
"""
Return Mulliken population for atom I.
This is the total population, without the number
of valence electrons subtracted.
parameters:
===========
I: atom index
"""
self._init_mulliken()
return self.MA.get_atom_mulliken(I)
def get_basis_mulliken(self, mu):
"""
Return Mulliken population of given basis state.
parameters:
===========
mu: orbital index (see Elements' methods for indices)
"""
self._init_mulliken()
return self.MA.get_basis_mulliken(mu)
def get_basis_wf_mulliken(self, mu, k, a, wk=True):
"""
Return Mulliken population for given basis state and wavefunction.
parameters:
===========
mu: basis state index
k: k-vector index
a: eigenstate index
wk: include k-point weight in the population?
"""
self._init_mulliken()
return self.MA.get_basis_wf_mulliken(mu, k, a, wk)
def get_atom_wf_mulliken(self, I, k, a, wk=True):
"""
Return Mulliken population for given atom and wavefunction.
parameters:
===========
I: atom index (if None, return an array for all atoms)
k: k-vector index
a: eigenstate index
wk: embed k-point weight in population
"""
self._init_mulliken()
return self.MA.get_atom_wf_mulliken(I, k, a, wk)
def get_atom_wf_all_orbital_mulliken(self, I, k, a):
"""
Return orbitals' Mulliken populations for given atom and wavefunction.
parameters:
===========
I: atom index (returned array size = number of orbitals on I)
k: k-vector index
a: eigenstate index
"""
self._init_mulliken()
return self.MA.get_atom_wf_all_orbital_mulliken(I, k, a)
def get_atom_wf_all_angmom_mulliken(self, I, k, a, wk=True):
"""
Return atom's Mulliken populations for all angmom for given wavefunction.
parameters:
===========
I: atom index
k: k-vector index
a: eigenstate index
wk: embed k-point weight into population
return: array (length 3) containing s,p and d-populations
"""
self._init_mulliken()
return self.MA.get_atom_wf_all_angmom_mulliken(I, k, a, wk)
#
# Densities of states methods
#
def _init_DOS(self):
""" Initialize Density of states analysis. """
if self.calculation_required(self.el.atoms, ['energy']):
raise AssertionError('Electronic structure is not solved yet!')
if self.flags['DOS'] == False:
self.DOS = DensityOfStates(self)
self.flags['DOS'] = True
def get_local_density_of_states(self,
projected=False,
width=0.05,
window=None,
npts=501):
"""
Return state density for all atoms as a function of energy.
parameters:
===========
projected: return local density of states projected for
angular momenta 0,1 and 2 (s,p and d)
width: energy broadening (in eV)
window: energy window around Fermi-energy; 2-tuple (eV)
npts: number of grid points for energy
return: projected==False:
energy grid, ldos[atom,grid]
projected==True:
energy grid,
ldos[atom, grid],
pldos[atom, angmom, grid]
"""
self._init_DOS()
return self.DOS.get_local_density_of_states(projected, width, window,
npts)
def get_density_of_states(self,
broaden=False,
projected=False,
occu=False,
width=0.05,
window=None,
npts=501):
"""
Return the full density of states.
Sum of states over k-points. Zero is the Fermi-level.
Spin-degeneracy is NOT counted.
parameters:
===========
broaden: * If True, return broadened DOS in regular grid
in given energy window.
* If False, return energies of all states, followed
by their k-point weights.
projected: project DOS for angular momenta
occu: for not broadened case, return also state occupations
width: Gaussian broadening (eV)
window: energy window around Fermi-energy; 2-tuple (eV)
npts: number of data points in output
return: * if projected: e[:],dos[:],pdos[l,:] (angmom l=0,1,2)
* if not projected: e[:],dos[:]
* if broaden: e[:] is on regular grid, otherwise e[:] are
eigenvalues and dos[...] corresponding weights
* if occu: e[:],dos[:],occu[:]
"""
self._init_DOS()
return self.DOS.get_density_of_states(broaden, projected, occu, width,
window, npts)
# Bonding analysis
def _init_bonds(self):
""" Initialize Mulliken bonding analysis. """
if self.calculation_required(self.el.atoms, ['energy']):
raise AssertionError('Electronic structure is not solved yet!')
if self.flags['bonds'] == False:
self.bonds = MullikenBondAnalysis(self)
self.flags['bonds'] = True
def get_atom_energy(self, I=None):
"""
Return the energy of atom I (in eV).
Warning: bonding & atom energy analysis less clear for
systems where orbitals overlap with own periodic images.
parameters:
===========
I: atom index. If None, return all atoms' energies
as an array.
"""
self._init_bonds()
return self.bonds.get_atom_energy(I)
def get_mayer_bond_order(self, i, j):
"""
Return Mayer bond-order between two atoms.
Warning: bonding & atom energy analysis less clear for
systems where orbitals overlap with own periodic images.
parameters:
===========
I: first atom index
J: second atom index
"""
self._init_bonds()
return self.bonds.get_mayer_bond_order(i, j)
def get_promotion_energy(self, I=None):
"""
Return atom's promotion energy (in eV).
Defined as:
E_prom,I = sum_(mu in I) [q_(mu) - q_(mu)^0] epsilon_mu
parameters:
===========
I: atom index. If None, return all atoms' energies
as an array.
"""
self._init_bonds()
return self.bonds.get_promotion_energy(I)
def get_bond_energy(self, i, j):
"""
Return the absolute bond energy between atoms (in eV).
Warning: bonding & atom energy analysis less clear for
systems where orbitals overlap with own periodic images.
parameters:
===========
i,j: atom indices
"""
self._init_bonds()
return self.bonds.get_bond_energy(i, j)
def get_atom_and_bond_energy(self, i=None):
"""
Return given atom's contribution to cohesion.
parameters:
===========
i: atom index. If None, return all atoms' energies
as an array.
"""
self._init_bonds()
return self.bonds.get_atom_and_bond_energy(i)
def get_covalent_energy(self,
mode='default',
i=None,
j=None,
width=None,
window=None,
npts=501):
"""
Return covalent bond energies in different modes. (eV)
ecov is described in
Bornsen, Meyer, Grotheer, Fahnle, J. Phys.:Condens. Matter 11, L287 (1999) and
Koskinen, Makinen Comput. Mat. Sci. 47, 237 (2009)
parameters:
===========
mode: 'default' total covalent energy
'orbitals' covalent energy for orbital pairs
'atoms' covalent energy for atom pairs
'angmom' covalent energy for angular momentum components
i,j: atom or orbital indices, or angular momentum pairs
width: * energy broadening (in eV) for ecov
* if None, return energy eigenvalues and corresponding
covalent energies in arrays, directly
window: energy window (in eV wrt Fermi-level) for broadened ecov
npts: number of points in energy grid (only with broadening)
return:
=======
x,y: * if width==None, x is list of energy eigenvalues (including k-points)
and y covalent energies of those eigenstates
* if width!=None, x is energy grid for ecov.
* energies (both energy grid and ecov) are in eV.
Note: energies are always shifted so that Fermi-level is at zero.
Occupations are not otherwise take into account (while k-point weights are)
"""
self._init_bonds()
return self.bonds.get_covalent_energy(mode, i, j, width, window, npts)
def add_pair_potential(self, i, j, v, eVA=True):
"""
Add pair interaction potential function for elements or atoms
parameters:
===========
i,j: * atom indices, if integers (0,1,2,...)
* elements, if strings ('C','H',...)
v: Pair potential function.
Only one potential per element and atom pair allowed.
Syntax: v(r,der=0), v(r=None) returning the
interaction range in Bohr or Angstrom.
eVA: True for v in eV and Angstrom
False for v in Hartree and Bohr
"""
self.pp.add_pair_potential(i, j, v, eVA)
def set_grid(self, h=0.2, cutoff=3.0):
if self.calculation_required(self.el.atoms, ["energy"]):
raise AssertionError("Electronic structure is not solved yet!")
if self.flags["grid"] == False:
self.gd = Grids(self, h, cutoff)
self.flags["grid"] = True
class Hotbit(Output):
def __init__(
self,
parameters=None,
elements=None,
tables=None,
verbose=False,
charge=0.0,
SCC=True,
kpts=(1, 1, 1),
rs="kappa",
physical_k=True,
maxiter=50,
gamma_cut=None,
txt=None,
verbose_SCC=False,
width=0.02,
mixer=None,
coulomb_solver=None,
charge_density="Gaussian",
vdw=False,
vdw_parameters=None,
internal={},
):
"""
Hotbit -- density-functional tight-binding calculator
for atomic simulation environment (ASE).
Parameters:
-----------
parameters: The directory for parametrization files.
* If parameters==None, use HOTBIT_PARAMETERS environment variable.
* Parametrizations given by 'elements' and 'tables' keywords
override parametrizations in this directory.
elements: Files for element data (*.elm).
example: {'H':'H_custom.elm','C':'/../C.elm'}
* If extension '.elm' is omitted, it is assumed.
* Items can also be elements directly: {'H':H} (H is type Element)
* If elements==None, use element info from default directory.
* If elements['rest']=='default', use default parameters for all other
elements than the ones specified. E.g. {'H':'H.elm','rest':'default'}
(otherwise all elements present have to be specified explicitly).
tables: Files for Slater-Koster tables.
example: {'CH':'C_H.par','CC':'C_C.par'}
* If extension '.par' is omitted, it is assumed.
* If tables==None, use default interactions.
* If tables['rest']='default', use default parameters for all other
interactions, e.g. {'CH':'C_H.par','rest':'default'}
* If tables['AB']==None, ignore interactions for A and B
(both chemical and repulsive)
mixer: Density mixer.
example: {'name':'Anderson','mixing_constant':0.2, 'memory':5}.
charge: Total charge for system (-1 means an additional electron)
width: Width of Fermi occupation (eV)
SCC: Self-Consistent Charge calculation
* True for SCC-DFTB, False for DFTB
kpts: Number of k-points.
* For translational symmetry points are along the directions
given by the cell vectors.
* For general symmetries, you need to look at the info
from the container used
rs: * 'kappa': use kappa-points
* 'k': use normal k-points. Only for Bravais lattices.
physical_k Use physical (realistic) k-points for generally periodic systems.
* Ignored with normal translational symmetry
* True for physically allowed k-points in periodic symmetries.
maxiter: Maximum number of self-consistent iterations
* only for SCC-DFTB
coulomb_solver: The Coulomb solver object. If None, a DirectCoulomb
object will the automatically instantiated.
* only for SCC-DFTB
charge_density: Shape of the excess charge on each atom. Possibilities
are:
* 'Gaussian': Use atom centered Gaussians. This is the
default.
* 'Slater': Slater-type exponentials as used in the
original SCC-DFTB scheme.
* only for SCC-DFTB
gamma_cut: Range for Coulomb interaction if direct summation is
selected (coulomb_solver = None).
* only for SCC-DFTB
vdw: Include van der Waals interactions
vdw_parameters: Dictionary containing the parameters for the van-der-Waals
interaction for each element.
i.e. { el: ( p, R0 ), ... }
where *el* is the element name, *p* the polarizability and
*R0* the radius where the van-der-Waals interaction starts.
Will override whatever read from .elm files.
txt: Filename for log-file.
* None: standard output
* '-': throw output to trash (/null)
verbose_SCC: Increase verbosity in SCC iterations.
internal: Dictionary for internal variables, some of which are set for
stability purposes, some for quick and dirty bug fixes.
Use these with caution! (For this reason, for the description
of these variables you are forced to look at the source code.)
"""
from copy import copy
import os
if gamma_cut != None:
gamma_cut = gamma_cut / Bohr
self.__dict__ = {
"parameters": parameters,
"elements": elements,
"tables": tables,
"verbose": verbose,
"charge": charge,
"width": width / Hartree,
"SCC": SCC,
"kpts": kpts,
"rs": rs,
"physical_k": physical_k,
"maxiter": maxiter,
"gamma_cut": gamma_cut,
"vdw": vdw,
"vdw_parameters": vdw_parameters,
"txt": txt,
"verbose_SCC": verbose_SCC,
"mixer": mixer,
"coulomb_solver": coulomb_solver,
"charge_density": charge_density,
"internal": internal,
}
if parameters != None:
os.environ.data["HOTBIT_PARAMETERS"] = parameters
self.init = False
self.notes = []
self.dry_run = "--dry-run" in sys.argv
internal0 = {
"sepsilon": 0.0, # add this to the diagonal of S to avoid LAPACK error in diagonalization
"tol_imaginary_e": 1e-13, # tolerance for imaginary band energy
"tol_mulliken": 1e-5, # tolerance for mulliken charge sum deviation from integer
"tol_eigenvector_norm": 1e-6, # tolerance for eigenvector norm for eigensolver
"symop_range": 5,
} # range for the number of symmetry operations in all symmetries
internal0.update(internal)
for key in internal0:
self.set(key, internal0[key])
# self.set_text(self.txt)
# self.timer=Timer('Hotbit',txt=self.get_output())
def __del__(self):
""" Delete calculator -> timing summary. """
if self.get("SCC"):
try:
print >>self.txt, self.st.solver.get_iteration_info()
self.txt.flush()
except:
pass
if len(self.notes) > 0:
print >>self.txt, "Notes and warnings:"
for note in self.notes:
print >>self.txt, note
if self.init:
self.timer.summary()
Output.__del__(self)
def write_electronic_data(self, filename, keys=None):
"""
Write key electronic data into a file with *general* format.
Hotbit is not needed to analyze the resulting data file.
The data will be in a dictionary with the following items:
N the number of atoms
norb the number of orbitals
nelectrons the number of electrons
charge system charge
epot potential energy
ebs band structure energy
ecoul coulomb energy
erep repulsive energy
forces atomic forces
symbols element symbols
e single-particle energies
occ occupations
nk number of k-points
k k-point vectors
wk k-point weights
dq excess Mulliken populations
gap energy gap
gap_prob certainty of the gap determination above
dose energies for density of states (all states over k-points as well)
0 = Fermi-level
dos density of states (including k-point weights)
Access to data, simply:
data = numpy.load(filename)
print data['epot']
parameters:
-----------
filename: output file name
keys: list of items (key names) to save.
If None, save all.
"""
data = {}
data["N"] = self.el.N
data["norb"] = self.st.norb
data["charge"] = self.get("charge")
data["nelectrons"] = self.el.get_number_of_electrons()
data["erep"] = self.rep.get_repulsive_energy()
data["ecoul"] = self.get_coulomb_energy(self.el.atoms)
data["ebs"] = self.get_band_structure_energy(self.el.atoms)
data["epot"] = self.get_potential_energy(self.el.atoms)
data["forces"] = self.get_forces(self.el.atoms)
data["symbols"] = self.el.symbols
data["e"] = self.st.e
data["occ"] = self.st.f
data["nk"] = self.st.nk
data["k"] = self.st.k
data["wk"] = self.st.wk
data["dq"] = self.st.mulliken()
data["gap"], data["gap_prob"] = self.get_energy_gap()
data["dose"], data["dos"] = self.get_density_of_states(False)
for key in data.keys():
if keys != None and key not in keys:
del data[key]
import pickle
f = open(filename, "w")
pickle.dump(data, f)
f.close()
def set(self, key, value):
if key == "txt":
self.set_text(value)
elif self.init == True and key not in ["charge"]:
raise AssertionError("Parameters cannot be set after initialization.")
else:
self.__dict__[key] = value
def get_atoms(self):
""" Return the current atoms object. """
atoms = self.el.atoms.copy()
atoms.set_calculator(self)
return atoms
def add_note(self, note):
""" Add warning (etc) note to be printed in log file end. """
self.notes.append(note)
def greetings(self):
""" Simple greetings text """
from time import asctime
from os import uname
from os.path import abspath, curdir
from os import environ
self.version = hotbit_version
print >>self.txt, "\n\n\n\n\n"
print >>self.txt, " _ _ _ _ _"
print >>self.txt, "| |__ ___ | |_ | |__ |_| |_"
print >>self.txt, "| _ \ / _ \| _|| _ \| | _|"
print >>self.txt, "| | | | ( ) | |_ | ( ) | | |_"
print >>self.txt, "|_| |_|\___/ \__|\____/|_|\__| ver.", self.version
print >>self.txt, "Distributed under GNU GPL; see %s" % environ.get("HOTBIT_DIR") + "/LICENSE"
print >>self.txt, "Date:", asctime()
dat = uname()
print >>self.txt, "Nodename:", dat[1]
print >>self.txt, "Arch:", dat[4]
print >>self.txt, "Dir:", abspath(curdir)
print >>self.txt, "System:", self.el.get_name()
print >>self.txt, " Charge=%4.1f" % self.charge
print >>self.txt, " Container", self.el.container_info()
print >>self.txt, "Symmetry operations (if any):"
rs = self.get("rs")
kpts = self.get("kpts")
M = self.el.get_number_of_transformations()
for i in range(3):
print >>self.txt, " %i: pbc=" % i, self.el.atoms.get_pbc()[i],
if type(kpts) == type([]):
print >>self.txt, ", %s-points=%i, M=%.f" % (rs, len(kpts), M[i])
else:
print >>self.txt, ", %s-points=%i, M=%.f" % (rs, kpts[i], M[i])
print >>self.txt, "Electronic temperature:", self.width * Hartree, "eV"
mixer = self.st.solver.mixer
print >>self.txt, "Mixer:", mixer.get("name"), "with memory =", mixer.get(
"memory"
), ", mixing parameter =", mixer.get("beta")
print >>self.txt, self.el.greetings()
print >>self.txt, self.ia.greetings()
print >>self.txt, self.rep.greetings()
if self.pp.exists():
print >>self.txt, self.pp.greetings()
def out(self, text):
print >>self.txt, text
self.txt.flush()
def set_text(self, txt):
""" Set up the output file. """
if txt == "-" or txt == "null":
self.txt = open("/dev/null", "w")
elif hasattr(txt, "write"):
self.txt = txt
elif txt is None:
from sys import stdout
self.txt = stdout
else:
self.txt = open(txt, "a")
# check if the output of timer must be changed also
if "timer" in self.__dict__:
self.timer.txt = self.get_output()
def get(self, arg=None):
"""
Get calculator input parameters.
arg: 'kpts','width',...
"""
if arg == None:
return self.__dict__
else:
return self.__dict__[arg]
def memory_estimate(self):
"""
Print an estimate for memory consumption in GB.
If script run with --dry-run, exit.
"""
if self.st.nk > 1:
number = 16.0 # complex
else:
number = 8.0 # real
M = self.st.nk * self.st.norb ** 2 * number
# H S dH0 dS wf H1 dH rho rhoe
mem = M + M + 3 * M + 3 * M + M + M + 3 * M + M + M
print >>self.txt, "Memory consumption estimate: > %.2f GB" % (mem / 1e9)
self.txt.flush()
if self.dry_run:
raise SystemExit
def solve_ground_state(self, atoms):
""" If atoms moved, solve electronic structure. """
if not self.init:
assert type(atoms) != type(None)
self._initialize(atoms)
if type(atoms) == type(None):
pass
elif self.calculation_required(atoms, "ground state"):
self.el.update_geometry(atoms)
t0 = time()
self.st.solve()
self.el.set_solved("ground state")
t1 = time()
self.flags["Mulliken"] = False
self.flags["DOS"] = False
self.flags["bonds"] = False
if self.verbose:
print >>self.get_output(), "Solved in %0.2f seconds" % (t1 - t0)
# if self.get('SCC'):
# atoms.set_charges(-self.st.get_dq())
else:
pass
def _initialize(self, atoms):
""" Initialization of hotbit. """
if not self.init:
self.set_text(self.txt)
self.timer = Timer("Hotbit", txt=self.get_output())
self.start_timing("initialization")
self.el = Elements(self, atoms)
self.ia = Interactions(self)
self.st = States(self)
self.rep = Repulsion(self)
self.pp = PairPotential(self)
if self.get("vdw"):
if self.get("vdw_parameters") is not None:
self.el.update_vdw(self.get("vdw_parameters"))
setup_vdw(self)
self.env = Environment(self)
pbc = atoms.get_pbc()
# FIXME: gamma_cut -stuff
# if self.get('SCC') and np.any(pbc) and self.get('gamma_cut')==None:
# raise NotImplementedError('SCC not implemented for periodic systems yet (see parameter gamma_cut).')
if np.any(pbc) and abs(self.get("charge")) > 0.0 and self.get("SCC"):
raise AssertionError("Charged system cannot be periodic.")
self.flush()
self.flags = {}
self.flags["Mulliken"] = False
self.flags["DOS"] = False
self.flags["bonds"] = False
self.flags["grid"] = False
self.stop_timing("initialization")
self.el.set_atoms(atoms)
if not self.init:
self.init = True
self.greetings()
def calculation_required(self, atoms, quantities):
""" Check if a calculation is required.
Check if the quantities in the quantities list have already been calculated
for the atomic configuration atoms. The quantities can be one or more of:
'ground state', 'energy', 'forces', 'magmoms', and 'stress'.
"""
return self.el.calculation_required(atoms, quantities)
def get_potential_energy(self, atoms):
""" Return the potential energy of present system. """
if self.calculation_required(atoms, ["energy"]):
self.solve_ground_state(atoms)
self.start_timing("energy")
ebs = self.get_band_structure_energy(atoms)
ecoul = self.get_coulomb_energy(atoms)
erep = self.rep.get_repulsive_energy()
epp = self.pp.get_energy()
self.epot = ebs + ecoul + erep + epp - self.el.efree * Hartree
self.stop_timing("energy")
self.el.set_solved("energy")
return self.epot.copy()
def get_forces(self, atoms):
"""
Return forces (in eV/Angstrom)
Ftot = F(band structure) + F(coulomb) + F(repulsion).
"""
if self.calculation_required(atoms, ["forces"]):
self.solve_ground_state(atoms)
self.start_timing("forces")
fbs = self.st.get_band_structure_forces()
frep = self.rep.get_repulsive_forces()
fcoul = self.st.es.gamma_forces() # zero for non-SCC
fpp = self.pp.get_forces()
self.stop_timing("forces")
self.f = (fbs + frep + fcoul + fpp) * (Hartree / Bohr)
self.el.set_solved("forces")
return self.f.copy()
def get_band_energies(self, kpts=None, shift=True, rs="kappa", h1=False):
"""
Return band energies for explicitly given list of k-points.
parameters:
===========
kpts: list of k-points; e.g. kpts=[(0,0,0),(pi/2,0,0),(pi,0,0)]
k- or kappa-points, depending on parameter rs.
if None, return for all k-points in the calculation
shift: shift zero to the Fermi-level
rs: use 'kappa'- or 'k'-points in reciprocal space
h1: Add Coulomb part to hamiltonian matrix. Required for consistent use of SCC.
"""
if kpts == None:
e = self.st.e * Hartree
else:
if rs == "k":
klist = k_to_kappa_points(kpts, self.el.atoms)
elif rs == "kappa":
klist = kpts
e = self.st.get_band_energies(klist, h1) * Hartree
if shift:
return e - self.get_fermi_level()
else:
return e
def get_stress(self, atoms):
self.solve_ground_state(atoms)
# TODO: ASE needs an array from this method, would it be proper to
# somehow inform that the stresses are not calculated?
return np.zeros((6,))
def get_charge(self):
""" Return system's total charge. """
return self.get("charge")
def get_eigenvalues(self):
""" Return eigenvalues without shifts.
For alternative, look at method get_band_energies.
"""
return self.st.get_eigenvalues() * Hartree
def get_energy_gap(self):
"""
Return the energy gap. (in eV)
Gap is the energy difference between the first states
above and below Fermi-level. Return also the probability
of having returned the gap; it is the difference
in the occupations of these states, divided by 2.
"""
eigs = (self.get_eigenvalues() - self.get_fermi_level()).flatten()
occ = self.get_occupations().flatten()
ehi, elo = 1e10, -1e10
for e, f in zip(eigs, occ):
if elo < e <= 0.0:
elo = e
flo = f
elif 0.0 < e < ehi:
ehi = e
fhi = f
return ehi - elo, (flo - fhi) / 2
def get_state_indices(self, state):
"""
Return the k-point index and band index of given state.
parameters:
-----------
state: 'H**O', or 'LUMO'
H**O is the first state below Fermi-level.
LUMO is the first state above Fermi-level.
"""
eigs = (self.get_eigenvalues() - self.get_fermi_level()).flatten()
if state == "H**O":
k, a = np.unravel_index(np.ma.masked_array(eigs, eigs > 0.0).argmax(), (self.st.nk, self.st.norb))
if state == "LUMO":
k, a = np.unravel_index(np.ma.masked_array(eigs, eigs < 0.0).argmin(), (self.st.nk, self.st.norb))
return k, a
def get_occupations(self):
# self.solve_ground_state(atoms)
return self.st.get_occupations()
def get_band_structure_energy(self, atoms):
if self.calculation_required(atoms, ["ebs"]):
self.solve_ground_state(atoms)
self.ebs = self.st.get_band_structure_energy() * Hartree
self.el.set_solved("ebs")
return self.ebs
def get_coulomb_energy(self, atoms):
if self.calculation_required(atoms, ["ecoul"]):
self.solve_ground_state(atoms)
self.ecoul = self.st.es.coulomb_energy() * Hartree
self.st
return self.ecoul
# some not implemented ASE-assumed methods
def get_fermi_level(self):
"""
Return the Fermi-energy (chemical potential) in eV.
"""
return self.st.occu.get_mu() * Hartree
def set_atoms(self, atoms):
""" Initialize the calculator for given atomic system. """
if self.init == True and atoms.get_chemical_symbols() != self.el.atoms.get_chemical_symbols():
raise RuntimeError(
"Calculator initialized for %s. Create new calculator for %s."
% (self.el.get_name(), mix.parse_name_for_atoms(atoms))
)
else:
self._initialize(atoms)
def get_occupation_numbers(self, kpt=0):
""" Return occupation numbers for given k-point index. """
return self.st.f[kpt].copy()
def get_number_of_bands(self):
""" Return the total number of orbitals. """
return self.st.norb
def start_timing(self, label):
self.timer.start(label)
def stop_timing(self, label):
self.timer.stop(label)
#
# various analysis methods
#
def get_dielectric_function(self, width=0.05, cutoff=None, N=400):
"""
Return the imaginary part of the dielectric function for non-SCC.
Note: Uses approximation that requires that the orientation of
neighboring unit cells does not change much.
(Exact for Bravais lattice.)
See, e.g., Marder, Condensed Matter Physics, or
Popov New J. Phys 6, 17 (2004)
parameters:
-----------
width: energy broadening in eV
cutoff: cutoff energy in eV
N: number of points in energy grid
return:
-------
e[:], d[:,0:2]
"""
self.start_timing("dielectric function")
width = width / Hartree
otol = 0.05 # tolerance for occupations
if cutoff == None:
cutoff = 1e10
else:
cutoff = cutoff / Hartree
st = self.st
nk, e, f, wk = st.nk, st.e, st.f, st.wk
ex, wt = [], []
for k in range(nk):
wf = st.wf[k]
wfc = wf.conjugate()
dS = st.dS[k].transpose((0, 2, 1))
ek = e[k]
fk = f[k]
kweight = wk[k]
# electron excitation ka-->kb; restrict the search:
bmin = list(fk < 2 - otol).index(True)
amin = list(ek > ek[bmin] - cutoff).index(True)
amax = list(fk < otol).index(True)
for a in xrange(amin, amax + 1):
bmax = list(ek > ek[a] + cutoff).index(True)
for b in range(max(a + 1, bmin), bmax + 1):
de = ek[b] - ek[a]
df = fk[a] - fk[b]
if df < otol:
continue
# P = < ka | P | kb >
P = 1j * hbar * np.dot(wfc[a], np.dot(dS, wf[b]))
ex.append(de)
wt.append(kweight * df * np.abs(P) ** 2)
ex, wt = np.array(ex), np.array(wt)
cutoff = min(ex.max(), cutoff)
y = np.zeros((N, 3))
for d in range(3):
# Lorenzian should be used, but long tail would bring divergence at zero energy
x, y[:, d] = broaden(ex, wt[:, d], width, "gaussian", N=N, a=width, b=cutoff)
y[:, d] = y[:, d] / x ** 2
const = 4 * np.pi ** 2 / hbar
self.stop_timing("dielectric function")
return x * Hartree, y * const # y also in eV, Ang
#
# grid stuff
#
def set_grid(self, h=0.2, cutoff=3.0):
if self.calculation_required(self.el.atoms, ["energy"]):
raise AssertionError("Electronic structure is not solved yet!")
if self.flags["grid"] == False:
self.gd = Grids(self, h, cutoff)
self.flags["grid"] = True
def get_grid_basis_orbital(self, I, otype, k=0, pad=True):
"""
Return basis orbital on grid.
parameters:
===========
I: atom index
otype: orbital type ('s','px','py',...)
k: k-point index (basis functions are really the extended
Bloch functions for periodic systems)
pad: padded edges in the array
"""
if self.flags["grid"] == False:
raise AssertionError('Grid needs to be set first by method "set_grid".')
return self.gd.get_grid_basis_orbital(I, otype, k, pad)
def get_grid_wf(self, a, k=0, pad=True):
"""
Return eigenfunction on a grid.
parameters:
===========
a: state (band) index
k: k-vector index
pad: padded edges
"""
if self.flags["grid"] == False:
raise AssertionError('Grid needs to be set first by method "set_grid".')
return self.gd.get_grid_wf(a, k, pad)
def get_grid_wf_density(self, a, k=0, pad=True):
"""
Return eigenfunction density.
Density is not normalized; accurate quantitative analysis
on this density are best avoided.
parameters:
===========
a: state (band) index
k: k-vector index
pad: padded edges
"""
if self.flags["grid"] == False:
raise AssertionError('Grid needs to be set first by method "set_grid".')
return self.gd.get_grid_wf_density(a, k, pad)
def get_grid_density(self, pad=True):
"""
Return electron density on grid.
Do not perform accurate analysis on this density.
Integrated density differs from the total number of electrons.
Bader analysis inaccurate.
parameters:
pad: padded edges
"""
if self.flags["grid"] == False:
raise AssertionError('Grid needs to be set first by method "set_grid".')
return self.gd.get_grid_density(pad)
def get_grid_LDOS(self, bias=None, window=None, pad=True):
"""
Return electron density over selected states around the Fermi-level.
parameters:
-----------
bias: bias voltage (eV) with respect to Fermi-level.
Negative means probing occupied states.
window: 2-tuple for lower and upper bounds wrt. Fermi-level
pad: padded edges
"""
if self.flags["grid"] == False:
raise AssertionError('Grid needs to be set first by method "set_grid".')
return self.gd.get_grid_LDOS(bias, window, pad)
#
# Mulliken population analysis tools
#
def _init_mulliken(self):
""" Initialize Mulliken analysis. """
if self.calculation_required(self.el.atoms, ["energy"]):
raise AssertionError("Electronic structure is not solved yet!")
if self.flags["Mulliken"] == False:
self.MA = MullikenAnalysis(self)
self.flags["Mulliken"] = True
def get_dq(self, atoms=None):
""" Return atoms' excess Mulliken populations.
The total populations subtracted by
the numbers of valence electrons.
"""
self.solve_ground_state(atoms)
return self.st.get_dq()
def get_charges(self, atoms=None):
""" Return atoms' electric charges (Mulliken). """
return -self.get_dq(atoms)
def get_atom_mulliken(self, I):
"""
Return Mulliken population for atom I.
This is the total population, without the number
of valence electrons subtracted.
parameters:
===========
I: atom index
"""
self._init_mulliken()
return self.MA.get_atom_mulliken(I)
def get_basis_mulliken(self, mu):
"""
Return Mulliken population of given basis state.
parameters:
===========
mu: orbital index (see Elements' methods for indices)
"""
self._init_mulliken()
return self.MA.get_basis_mulliken(mu)
def get_basis_wf_mulliken(self, mu, k, a, wk=True):
"""
Return Mulliken population for given basis state and wavefunction.
parameters:
===========
mu: basis state index
k: k-vector index
a: eigenstate index
wk: include k-point weight in the population?
"""
self._init_mulliken()
return self.MA.get_basis_wf_mulliken(mu, k, a, wk)
def get_atom_wf_mulliken(self, I, k, a, wk=True):
"""
Return Mulliken population for given atom and wavefunction.
parameters:
===========
I: atom index (if None, return an array for all atoms)
k: k-vector index
a: eigenstate index
wk: embed k-point weight in population
"""
self._init_mulliken()
return self.MA.get_atom_wf_mulliken(I, k, a, wk)
def get_atom_wf_all_orbital_mulliken(self, I, k, a):
"""
Return orbitals' Mulliken populations for given atom and wavefunction.
parameters:
===========
I: atom index (returned array size = number of orbitals on I)
k: k-vector index
a: eigenstate index
"""
self._init_mulliken()
return self.MA.get_atom_wf_all_orbital_mulliken(I, k, a)
def get_atom_wf_all_angmom_mulliken(self, I, k, a, wk=True):
"""
Return atom's Mulliken populations for all angmom for given wavefunction.
parameters:
===========
I: atom index
k: k-vector index
a: eigenstate index
wk: embed k-point weight into population
return: array (length 3) containing s,p and d-populations
"""
self._init_mulliken()
return self.MA.get_atom_wf_all_angmom_mulliken(I, k, a, wk)
#
# Densities of states methods
#
def _init_DOS(self):
""" Initialize Density of states analysis. """
if self.calculation_required(self.el.atoms, ["energy"]):
raise AssertionError("Electronic structure is not solved yet!")
if self.flags["DOS"] == False:
self.DOS = DensityOfStates(self)
self.flags["DOS"] = True
def get_local_density_of_states(self, projected=False, width=0.05, window=None, npts=501):
"""
Return state density for all atoms as a function of energy.
parameters:
===========
projected: return local density of states projected for
angular momenta 0,1 and 2 (s,p and d)
width: energy broadening (in eV)
window: energy window around Fermi-energy; 2-tuple (eV)
npts: number of grid points for energy
return: projected==False:
energy grid, ldos[atom,grid]
projected==True:
energy grid,
ldos[atom, grid],
pldos[atom, angmom, grid]
"""
self._init_DOS()
return self.DOS.get_local_density_of_states(projected, width, window, npts)
def get_density_of_states(self, broaden=False, projected=False, occu=False, width=0.05, window=None, npts=501):
"""
Return the full density of states.
Sum of states over k-points. Zero is the Fermi-level.
Spin-degeneracy is NOT counted.
parameters:
===========
broaden: * If True, return broadened DOS in regular grid
in given energy window.
* If False, return energies of all states, followed
by their k-point weights.
projected: project DOS for angular momenta
occu: for not broadened case, return also state occupations
width: Gaussian broadening (eV)
window: energy window around Fermi-energy; 2-tuple (eV)
npts: number of data points in output
return: * if projected: e[:],dos[:],pdos[l,:] (angmom l=0,1,2)
* if not projected: e[:],dos[:]
* if broaden: e[:] is on regular grid, otherwise e[:] are
eigenvalues and dos[...] corresponding weights
* if occu: e[:],dos[:],occu[:]
"""
self._init_DOS()
return self.DOS.get_density_of_states(broaden, projected, occu, width, window, npts)
# Bonding analysis
def _init_bonds(self):
""" Initialize Mulliken bonding analysis. """
if self.calculation_required(self.el.atoms, ["energy"]):
raise AssertionError("Electronic structure is not solved yet!")
if self.flags["bonds"] == False:
self.bonds = MullikenBondAnalysis(self)
self.flags["bonds"] = True
def get_atom_energy(self, I=None):
"""
Return the energy of atom I (in eV).
Warning: bonding & atom energy analysis less clear for
systems where orbitals overlap with own periodic images.
parameters:
===========
I: atom index. If None, return all atoms' energies
as an array.
"""
self._init_bonds()
return self.bonds.get_atom_energy(I)
def get_mayer_bond_order(self, i, j):
"""
Return Mayer bond-order between two atoms.
Warning: bonding & atom energy analysis less clear for
systems where orbitals overlap with own periodic images.
parameters:
===========
I: first atom index
J: second atom index
"""
self._init_bonds()
return self.bonds.get_mayer_bond_order(i, j)
def get_promotion_energy(self, I=None):
"""
Return atom's promotion energy (in eV).
Defined as:
E_prom,I = sum_(mu in I) [q_(mu) - q_(mu)^0] epsilon_mu
parameters:
===========
I: atom index. If None, return all atoms' energies
as an array.
"""
self._init_bonds()
return self.bonds.get_promotion_energy(I)
def get_bond_energy(self, i, j):
"""
Return the absolute bond energy between atoms (in eV).
Warning: bonding & atom energy analysis less clear for
systems where orbitals overlap with own periodic images.
parameters:
===========
i,j: atom indices
"""
self._init_bonds()
return self.bonds.get_bond_energy(i, j)
def get_atom_and_bond_energy(self, i=None):
"""
Return given atom's contribution to cohesion.
parameters:
===========
i: atom index. If None, return all atoms' energies
as an array.
"""
self._init_bonds()
return self.bonds.get_atom_and_bond_energy(i)
def get_covalent_energy(self, mode="default", i=None, j=None, width=None, window=None, npts=501):
"""
Return covalent bond energies in different modes. (eV)
ecov is described in
Bornsen, Meyer, Grotheer, Fahnle, J. Phys.:Condens. Matter 11, L287 (1999) and
Koskinen, Makinen Comput. Mat. Sci. 47, 237 (2009)
parameters:
===========
mode: 'default' total covalent energy
'orbitals' covalent energy for orbital pairs
'atoms' covalent energy for atom pairs
'angmom' covalent energy for angular momentum components
i,j: atom or orbital indices, or angular momentum pairs
width: * energy broadening (in eV) for ecov
* if None, return energy eigenvalues and corresponding
covalent energies in arrays, directly
window: energy window (in eV wrt Fermi-level) for broadened ecov
npts: number of points in energy grid (only with broadening)
return:
=======
x,y: * if width==None, x is list of energy eigenvalues (including k-points)
and y covalent energies of those eigenstates
* if width!=None, x is energy grid for ecov.
* energies (both energy grid and ecov) are in eV.
Note: energies are always shifted so that Fermi-level is at zero.
Occupations are not otherwise take into account (while k-point weights are)
"""
self._init_bonds()
return self.bonds.get_covalent_energy(mode, i, j, width, window, npts)
def add_pair_potential(self, i, j, v, eVA=True):
"""
Add pair interaction potential function for elements or atoms
parameters:
===========
i,j: * atom indices, if integers (0,1,2,...)
* elements, if strings ('C','H',...)
v: Pair potential function.
Only one potential per element and atom pair allowed.
Syntax: v(r,der=0), v(r=None) returning the
interaction range in Bohr or Angstrom.
eVA: True for v in eV and Angstrom
False for v in Hartree and Bohr
"""
self.pp.add_pair_potential(i, j, v, eVA)