def main():
args = parse_args()
fn_h5, grp_name = parse_h5(args.output, 'output')
# check if the group is already present (and not empty) in the output file
if check_output(fn_h5, grp_name, args.overwrite):
return
# Load the system
sys = System.from_file(args.wfn)
# Define a list of optional arguments for the WPartClass:
WPartClass = wpart_schemes[args.scheme]
kwargs = dict((key, val) for key, val in vars(args).iteritems() if key in WPartClass.options)
# Load the proatomdb
if args.atoms is not None:
proatomdb = ProAtomDB.from_file(args.atoms)
proatomdb.normalize()
kwargs['proatomdb'] = proatomdb
else:
proatomdb = None
# Run the partitioning
agspec = AtomicGridSpec(args.grid)
molgrid = BeckeMolGrid(sys, agspec, mode='only')
sys.update_grid(molgrid) # for the grid to be written to the output
wpart = wpart_schemes[args.scheme](sys, molgrid, **kwargs)
names = wpart.do_all()
write_part_output(fn_h5, grp_name, wpart, names, args)
def getBeckeGrid(self, resolution='fine', new=False, **kwargs):
"""
coarse, medium, fine, veryfine, ultrafine and insane
"""
if not hasattr(self, 'molecule'):
qtk.exit("no molecule structure found")
if new or not hasattr(self, 'grid'):
molecule = self.molecule
coord = np.array(np.atleast_2d(molecule.R * 1.8897261245650618))
self.grid = BeckeMolGrid(coord, molecule.Z.astype(int), molecule.Z,
resolution)
mol_str = []
for i in range(molecule.N):
atm_str = [molecule.type_list[i]]
for j in range(3):
atm_str.append(str(molecule.R[i, j]))
mol_str.append(' '.join(atm_str))
mol_str = '; '.join(mol_str)
if 'gto_kwargs' in kwargs:
mol = gto.Mole(**kwargs['gto_kwargs'])
else:
mol = gto.Mole()
#mol.build(atom=mol_str, basis=self.setting['basis_set'])
if hasattr(self, 'basis_name'):
basis = self.basis_name
self.basisFormat()
mol.build(atom=mol_str, basis=self.pybasis)
self.mol = mol
del_list = ['_phi', '_psi', '_dphi', '_dpsi', '_rho', '_drho']
for p in del_list:
if hasattr(self, p):
delattr(self, p)
def __init__(self,
coordinates,
numbers,
pseudo_numbers,
specs='medium',
k=3,
rotate=False):
"""Initialize class.
Parameters
----------
coordinates : np.ndarray, shape=(M, 3)
Cartesian coordinates of `M` atoms in the molecule.
numbers : np.ndarray, shape=(M,)
Atomic number of `M` atoms in the molecule.
pseudo_numbers : np.ndarray, shape=(M,)
Pseudo-number of `M` atoms in the molecule.
specs : str, optional
Specification of grid. Either choose from ['coarse', 'medium', 'fine', 'veryfine',
'ultrafine', 'insane'] or provide a string of 'rname:rmin:rmax:nrad:nang' format.
Here 'rname' denotes the type of radial grid and can be chosen from ['linear', 'exp',
'power'], 'rmin' and 'rmax' specify the first and last radial grid points in angstrom,
'nrad' specify the number of radial grid points, and 'nang' specify the number of
angular Lebedev-Laikov grid. The 'nang' can be chosen from (6, 14, 26, 38, 50, 74, 86,
110, 146, 170, 194, 230, 266, 302, 350, 434, 590, 770, 974, 1202, 1454, 1730, 2030,
2354, 2702, 3074, 3470, 3890, 4334, 4802, 5294, 5810).
k : int, optional
The order of the switching function in Becke's weighting scheme.
rotate : bool, optional
Whether to randomly rotate spherical grids.
"""
self._coordinates = coordinates
self._numbers = numbers
self._pseudo_numbers = pseudo_numbers
self._k = k
self._rotate = rotate
self.specs = specs
self._grid = BeckeMolGrid(self.coordinates,
self.numbers,
self.pseudo_numbers,
agspec=self.specs,
k=k,
random_rotate=rotate,
mode='keep')
def from_molecule(cls, mol, scheme=None, grid=None, spin="ab", **kwargs):
if grid is None:
grid = BeckeMolGrid(mol.coordinates, mol.numbers, mol.pseudo_numbers,
agspec="fine", random_rotate=False, mode='keep')
else:
check_molecule_grid(mol, grid)
# compute molecular electron density
dens = mol.compute_density(grid.points, spin=spin)
if mol.pesudo_numbers is None:
pesudo_numbers = mol.numbers
else:
pesudo_numbers = mol.pesudo_numbers
return cls(mol.coordinates, mol.numbers, pesudo_numbers, dens, grid, scheme, **kwargs)
def main():
args = parse_args()
fn_h5, grp_name = parse_h5(args.output, 'output')
# check if the group is already present (and not empty) in the output file
if check_output(fn_h5, grp_name, args.overwrite):
return
# Load the system
mol = IOData.from_file(args.wfn)
# Define a list of optional arguments for the WPartClass:
WPartClass = wpart_schemes[args.scheme]
kwargs = dict((key, val) for key, val in vars(args).iteritems()
if key in WPartClass.options)
# Load the proatomdb
if args.atoms is not None:
proatomdb = ProAtomDB.from_file(args.atoms)
proatomdb.normalize()
kwargs['proatomdb'] = proatomdb
else:
proatomdb = None
# Run the partitioning
agspec = AtomicGridSpec(args.grid)
grid = BeckeMolGrid(mol.coordinates,
mol.numbers,
mol.pseudo_numbers,
agspec,
mode='only')
dm_full = mol.get_dm_full()
moldens = mol.obasis.compute_grid_density_dm(dm_full,
grid.points,
epsilon=args.epsilon)
dm_spin = mol.get_dm_spin()
if dm_spin is not None:
kwargs['spindens'] = mol.obasis.compute_grid_density_dm(
dm_spin, grid.points, epsilon=args.epsilon)
wpart = wpart_schemes[args.scheme](mol.coordinates, mol.numbers,
mol.pseudo_numbers, grid, moldens,
**kwargs)
keys = wpart.do_all()
if args.slow:
# ugly hack for the slow analysis involving the AIM overlap operators.
wpart_slow_analysis(wpart, mol)
keys = list(wpart.cache.iterkeys(tags='o'))
write_part_output(fn_h5, grp_name, wpart, keys, args)
def getBeckeGrid(self, resolution='fine', new=False, **kwargs):
"""
coarse, medium, fine, veryfine, ultrafine and insane
"""
if not hasattr(self, 'molecule'):
qtk.exit("no molecule structure found")
if new or not hasattr(self, 'grid'):
molecule = self.molecule
coord = np.array(np.atleast_2d(molecule.R*1.8897261245650618))
self.grid = BeckeMolGrid(coord,
molecule.Z.astype(int),
molecule.Z,
resolution)
mol_str = []
for i in range(molecule.N):
atm_str = [molecule.type_list[i]]
for j in range(3):
atm_str.append(str(molecule.R[i,j]))
mol_str.append(' '.join(atm_str))
mol_str = '; '.join(mol_str)
if 'gto_kwargs' in kwargs:
mol = gto.Mole(**kwargs['gto_kwargs'])
else:
mol = gto.Mole()
#mol.build(atom=mol_str, basis=self.setting['basis_set'])
if hasattr(self, 'basis_name'):
basis = self.basis_name
self.basisFormat()
mol.build(atom=mol_str, basis=self.pybasis)
self.mol = mol
del_list = ['_phi', '_psi', '_dphi', '_dpsi', '_rho', '_drho']
for p in del_list:
if hasattr(self, p):
delattr(self, p)
def __init__(self, molecule, **kwargs):
if not ht_found:
qtk.exit("horton module not found.")
if not ps_found:
qtk.exit("pyscf module not found.")
if not xc_found:
print xcpath
print xc_found
qtk.exit("libxc not found.")
if 'wf_convergence' not in kwargs:
kwargs['wf_convergence'] = 1e-06
if 'kinetic_functional' not in kwargs:
kwargs['kinetic_functional'] = 'LLP'
if 'aufbau' in kwargs and kwargs['aufbau']:
self.aufbau = True
self.orbitals = []
else:
self.aufbau = False
GaussianBasisInput.__init__(self, molecule, **kwargs)
self.setting.update(kwargs)
self.backup()
if 'dft_setting' not in kwargs:
if not self.aufbau:
kf = self.setting['kinetic_functional']
if kf == 'LLP':
self.setting['dft_setting'] = {
'K': {
1.0: 'XC_GGA_K_LLP'
},
}
else:
self.setting['dft_setting'] = {'K': {1.0: 'XC_GGA_K_VW'}}
ss = self.setting['theory']
sdft = self.setting['dft_setting']
if ss == 'pbe':
sdft['X'] = 'XC_GGA_X_PBE'
sdft['C'] = 'XC_GGA_C_PBE'
elif ss == 'blyp':
sdft['X'] = 'XC_GGA_X_B88'
sdft['C'] = 'XC_GGA_C_LYP'
dft = self.setting['dft_setting']
for k, v in dft.iteritems():
if type(dft[k]) is str:
dft[k] = xc_dict[v]
elif type(dft[k]) is dict:
for key, value in dft[k].iteritems():
if type(value) is str:
dft[k][key] = xc_dict[value]
mol_str = []
for i in range(molecule.N):
atm_str = [molecule.type_list[i]]
for j in range(3):
atm_str.append(str(molecule.R[i, j]))
mol_str.append(' '.join(atm_str))
mol_str = '; '.join(mol_str)
mol = gto.Mole()
mol.build(atom=mol_str, basis=self.setting['basis_set'])
ig = ps.scf.hf.get_init_guess(mol, key='atom')
ovl = mol.intor_symmetric("cint1e_ovlp_sph")
kin = mol.intor_symmetric("cint1e_kin_sph")
ext = mol.intor_symmetric("cint1e_nuc_sph")
# 4D array, can be contracted by numpy.tensordot (td)
# nao x nao integrated density Coulomb kernel can be computed via
# int_vee_rho = td(dm, vee, axes=([0,1], [0,1]))
# the final electron-electron cam be computed via
# Vee = 0.5 * trace(dm, int_vee_rho)
nao = mol.nao_nr()
vee = mol.intor(
"cint2e_sph",
comp=1,
hermi=1,
).reshape(nao, nao, nao, nao)
coord = np.array(np.atleast_2d(molecule.R * 1.8897261245650618))
grid = BeckeMolGrid(coord, molecule.Z.astype(int), molecule.Z)
self.molecule = molecule
self.mol = mol
self.ovl = ovl
self.kin = kin
self.ext = ext
self.vee = vee
self.nao = nao
self.dv = self.normalize(sqrt(diag(ig)))
self.initial_guess = copy.deepcopy(self.dv)
self.ig = ig
self.grid = grid
self.update(self.dv)
self.old_deltadv = None
self.new_deltadv = None
self.old_E = None
self.dv_list = []
self.psi_list = []
self.dpsi_list = []
self.optimizers = {
'tnc': opt.fmin_tnc,
'ncg': opt.fmin_ncg,
'cg': opt.fmin_cg,
'bfgs': opt.fmin_bfgs,
'l_bfgs_b': opt.fmin_l_bfgs_b,
'simplex': opt.fmin,
}
self.optimizer_settings = {
'tnc': {
'xtol': 0.0,
'pgtol': 0.0,
'maxfun': 1000
},
'simplex': {
'xtol': 1E-10,
'ftol': 1E-10,
'maxfun': 1000
},
}
self.orbitals = []
class MolecularGrid(object):
"""Becke-Lebedev molecular grid for numerical integrations."""
def __init__(self,
coordinates,
numbers,
pseudo_numbers,
specs='medium',
k=3,
rotate=False):
"""Initialize class.
Parameters
----------
coordinates : np.ndarray, shape=(M, 3)
Cartesian coordinates of `M` atoms in the molecule.
numbers : np.ndarray, shape=(M,)
Atomic number of `M` atoms in the molecule.
pseudo_numbers : np.ndarray, shape=(M,)
Pseudo-number of `M` atoms in the molecule.
specs : str, optional
Specification of grid. Either choose from ['coarse', 'medium', 'fine', 'veryfine',
'ultrafine', 'insane'] or provide a string of 'rname:rmin:rmax:nrad:nang' format.
Here 'rname' denotes the type of radial grid and can be chosen from ['linear', 'exp',
'power'], 'rmin' and 'rmax' specify the first and last radial grid points in angstrom,
'nrad' specify the number of radial grid points, and 'nang' specify the number of
angular Lebedev-Laikov grid. The 'nang' can be chosen from (6, 14, 26, 38, 50, 74, 86,
110, 146, 170, 194, 230, 266, 302, 350, 434, 590, 770, 974, 1202, 1454, 1730, 2030,
2354, 2702, 3074, 3470, 3890, 4334, 4802, 5294, 5810).
k : int, optional
The order of the switching function in Becke's weighting scheme.
rotate : bool, optional
Whether to randomly rotate spherical grids.
"""
self._coordinates = coordinates
self._numbers = numbers
self._pseudo_numbers = pseudo_numbers
self._k = k
self._rotate = rotate
self.specs = specs
self._grid = BeckeMolGrid(self.coordinates,
self.numbers,
self.pseudo_numbers,
agspec=self.specs,
k=k,
random_rotate=rotate,
mode='keep')
@classmethod
def from_molecule(cls, molecule, specs='medium', k=3, rotate=False):
"""Initialize the class given an instance of Molecule.
Parameters
----------
molecule : instance of Molecule
Instance of Molecule class.
specs : str, optional
Specification of grid. Either choose from ['coarse', 'medium', 'fine', 'veryfine',
'ultrafine', 'insane'] or provide a string of 'rname:rmin:rmax:nrad:nang' format.
Here 'rname' denotes the type of radial grid and can be chosen from ['linear', 'exp',
'power'], 'rmin' and 'rmax' specify the first and last radial grid points in angstrom,
'nrad' specify the number of radial grid points, and 'nang' specify the number of
angular Lebedev-Laikov grid. The 'nang' can be chosen from (6, 14, 26, 38, 50, 74, 86,
110, 146, 170, 194, 230, 266, 302, 350, 434, 590, 770, 974, 1202, 1454, 1730, 2030,
2354, 2702, 3074, 3470, 3890, 4334, 4802, 5294, 5810).
k : int, optional
The order of the switching function in Becke's weighting scheme.
rotate : bool, optional
Whether to randomly rotate spherical grids.
"""
if not isinstance(molecule, Molecule):
raise TypeError(
'Argument molecule should be an instance of Molecule class.')
coords, nums, pnums = molecule.coordinates, molecule.numbers, molecule.pseudo_numbers
return cls(coords, nums, pnums, specs, k, rotate)
@classmethod
def from_file(cls, fname, specs='medium', k=3, rotate=False):
"""Initialize the class given an instance of Molecule.
Parameters
----------
fname : str
Path to molecule's files.
specs : str, optional
Specification of grid. Either choose from ['coarse', 'medium', 'fine', 'veryfine',
'ultrafine', 'insane'] or provide a string of 'rname:rmin:rmax:nrad:nang' format.
Here 'rname' denotes the type of radial grid and can be chosen from ['linear', 'exp',
'power'], 'rmin' and 'rmax' specify the first and last radial grid points in angstrom,
'nrad' specify the number of radial grid points, and 'nang' specify the number of
angular Lebedev-Laikov grid. The 'nang' can be chosen from (6, 14, 26, 38, 50, 74, 86,
110, 146, 170, 194, 230, 266, 302, 350, 434, 590, 770, 974, 1202, 1454, 1730, 2030,
2354, 2702, 3074, 3470, 3890, 4334, 4802, 5294, 5810).
k : int, optional
The order of the switching function in Becke's weighting scheme.
rotate : bool, optional
Whether to randomly rotate spherical grids.
"""
mol = Molecule.from_file(fname)
return cls.from_molecule(mol, specs, k, rotate)
def __getattr__(self, item):
return getattr(self._grid, item)
@property
def center(self):
"""Cartesian coordinates of atomic centers."""
return self._coordinates
@property
def coordinates(self):
"""Cartesian coordinates of atomic centers."""
return self._coordinates
@property
def numbers(self):
"""Atomic number of atomic centers."""
return self._numbers
@property
def pseudo_numbers(self):
"""Pseudo atomic number of atomic centers."""
return self._pseudo_numbers
@property
def npoints(self):
"""Number of grid points."""
return self._grid.points.shape[0]
@property
def points(self):
"""Cartesian coordinates of grid points."""
return self._grid.points
@property
def weights(self):
"""Integration weight of grid points."""
return self._grid.weights
def integrate(self, *value):
"""Integrate the property evaluated on the grid points.
Parameters
----------
value : np.ndarray
Property value evaluated on the grid points.
"""
# temporary hack because of HORTON
if not isinstance(value, np.ndarray):
temp = value[0]
for item in value[1:]:
if item is not None:
temp = temp * item
value = temp
if value.ndim != 1:
raise ValueError('Argument value should be a 1D array.')
if value.shape != (self.npoints, ):
raise ValueError('Argument value should have ({0},) shape!'.format(
self.npoints))
return self._grid.integrate(value)
def compute_spherical_average(self, value):
"""Compute spherical average of given value evaluated on the grid points.
Note: This method only works for atomic systems with one nuclear center.
Parameters
----------
value : np.ndarray
Property value evaluated on the grid points.
"""
if len(self.numbers) != 1:
raise NotImplementedError(
'This method only works for systems with one atom!')
if value.ndim != 1:
raise ValueError('Argument value should be a 1D array.')
if value.shape != (self.npoints, ):
raise ValueError('Argument value should have ({0},) shape!'.format(
self.npoints))
return self._grid.get_spherical_average(value)
class GaussianBasisOutput(GenericQMOutput):
def __init__(self, output=None, **kwargs):
GenericQMOutput.__init__(self, output, **kwargs)
def copy(self):
if hasattr(self, 'mol'):
del self.mol
if hasattr(self, 'grid'):
del self.grid
return copy.deepcopy(self)
def mo_g09_nwchem(self):
mo = self.mo_vectors
ind = np.arange(len(mo[0]))
itr = 0
# hard coded reordering for d and f orbitals
order = {
'd': [0, 3, 4, 1, 5, 2],
'f': [0, 4, 5, 3, 9, 6, 1, 8, 7, 2],
}
while itr < len(mo[0]):
bStr = self.basis[itr]['type']
if len(bStr) > 2:
key = bStr[0]
if key in order.keys():
ind_itr = ind[itr: itr+len(order[key])]
ind_itr = ind_itr[order[key]]
for i in range(len(order[bStr[0]])):
ind[itr + i] = ind_itr[i]
itr += len(order[bStr[0]]) - 1
else:
qtk.exit("basis reordering for %s orbital " % key\
+ "not implemented yet")
itr += 1
return mo[:, ind]
def basisFormat():
if not hasattr(self, 'basis'):
qtk.exit("no basis found")
pass
def getBeckeGrid(self, resolution='fine', new=False, **kwargs):
"""
coarse, medium, fine, veryfine, ultrafine and insane
"""
if not hasattr(self, 'molecule'):
qtk.exit("no molecule structure found")
if new or not hasattr(self, 'grid'):
molecule = self.molecule
coord = np.array(np.atleast_2d(molecule.R*1.8897261245650618))
self.grid = BeckeMolGrid(coord,
molecule.Z.astype(int),
molecule.Z,
resolution)
mol_str = []
for i in range(molecule.N):
atm_str = [molecule.type_list[i]]
for j in range(3):
atm_str.append(str(molecule.R[i,j]))
mol_str.append(' '.join(atm_str))
mol_str = '; '.join(mol_str)
if 'gto_kwargs' in kwargs:
mol = gto.Mole(**kwargs['gto_kwargs'])
else:
mol = gto.Mole()
#mol.build(atom=mol_str, basis=self.setting['basis_set'])
if hasattr(self, 'basis_name'):
basis = self.basis_name
mol.build(atom=mol_str, basis=basis)
self.mol = mol
del_list = ['_phi', '_psi', '_dphi', '_dpsi', '_rho', '_drho']
for p in del_list:
if hasattr(self, p):
delattr(self, p)
def getPhi(self, cartesian=True, resolution='fine', new=False, **kwargs):
if 'gridpoints' in kwargs:
new = True
if new or not hasattr(self, '_phi'):
self.getBeckeGrid(resolution, new, **kwargs)
coords = self.grid.points
if 'gridpoints' not in kwargs:
grid_coords = None
else:
grid_coords = np.array(kwargs['gridpoints']).astype(float)
if cartesian:
mode = "GTOval_cart"
else:
mode = "GTOval_sph"
self._phi = self.mol.eval_gto(mode, coords).T
norm = np.dot(self._phi * self.grid.weights, self._phi.T)
if grid_coords is not None:
self._phi = self.mol.eval_gto(mode, grid_coords).T
self._phi = self._phi / np.sqrt(np.diag(norm))[:, np.newaxis]
else:
self._phi = self._phi / np.sqrt(np.diag(norm))[:, np.newaxis]
return self._phi
def getDPhi(self, cartesian=True, resolution='fine', new=False, **kwargs):
if 'gridpoints' in kwargs:
new = True
if new or not hasattr(self, '_dphi'):
self.getBeckeGrid(resolution, new, **kwargs)
if 'gridpoints' not in kwargs:
coords = self.grid.points
else:
coords = np.array(kwargs['gridpoints']).astype(float)
if cartesian:
mode = "GTOval_ip_cart"
else:
mode = "GTOval_ip_sph"
self._dphi = self.mol.eval_gto(mode, coords, comp=3).T
return self._dphi
def getPsi(self, cartesian=True, resolution='fine', new=False, **kwargs):
if 'gridpoints' in kwargs:
new = True
if new or not hasattr(self, '_psi'):
self.getPhi(cartesian, resolution, new, **kwargs)
if not hasattr(self, 'mo_vectors'):
qtk.exit('mo_vectors not found')
mo = self.mo_vectors
if hasattr(self, 'program'):
if self.program == 'gaussian':
mo = self.mo_g09_nwchem()
self._psi = np.dot(mo, self._phi)
return self._psi
def getDPsi(self, cartesian=True, resolution='fine', new=False, **kwargs):
if 'gridpoints' in kwargs:
new = True
if new or not hasattr(self, '_dpsi'):
self.getDPhi(cartesian, resolution, new, **kwargs)
if not hasattr(self, 'mo_vectors'):
qtk.exit('mo_vectors not found')
mo = self.mo_vectors
if hasattr(self, 'program'):
if self.program == 'gaussian':
mo = self.mo_g09_nwchem()
self._dpsi = np.dot(mo, np.swapaxes(self._dphi, 0, 1))
return self._dpsi
def getRho(self, cartesian=True, resolution='fine', new=False, occupation=None, **kwargs):
if 'gridpoints' in kwargs:
new = True
if new or not hasattr(self, '_rho'):
self.getPsi(cartesian, resolution, new, **kwargs)
if not hasattr(self, 'occupation'):
qtk.exit("occupation number not found")
if occupation is None:
occ = np.array(self.occupation)
else:
occ = np.array(occupation)
self._rho = np.sum(self._psi**2 * occ[:, np.newaxis], axis = 0)
return self._rho
def getDRho(self, cartesian=True, resolution='fine', new=False, occupation=None, **kwargs):
if 'gridpoints' in kwargs:
new = True
if new or not hasattr(self, '_drho'):
if not hasattr(self, '_psi'):
_psi = self.getPsi(cartesian, resolution, new, **kwargs)
if not hasattr(self, '_dpsi'):
_dpsi = self.getDPsi(cartesian, resolution, new, **kwargs)
if not hasattr(self, 'occupation'):
qtk.exit("occupation number not found")
self._psi, self._dpsi = _psi, _dpsi
if occupation is None:
occ = np.array(self.occupation)
else:
occ = np.array(occupation)
self._drho = 2 * np.sum(
self._psi[..., np.newaxis] * self._dpsi \
* occ[:, np.newaxis, np.newaxis],
axis = 0
)
return self._drho
def freeRho(self, coord, gridpoints, **kwargs):
assert self.molecule.N == 1
new = self.copy()
new.molecule.R[0] = np.array(coord) / 1.8897261245650618
if 'spin' not in kwargs:
if new.molecule.getValenceElectrons() % 2 != 0:
kw = {'gto_kwargs': {'spin': 1}}
else:
kw = {}
else:
kw = {'gto_kwargs': {'spin': kwargs['spin']}}
if type(gridpoints[0][0]) is not float:
pl = np.array(gridpoints).astype(float)
else:
pl = gridpoints
return new.getRho(gridpoints = pl, **kw)
def _e_setting(self, gridpoints, **kwargs):
new = self.copy()
kw = {}
if 'spin' not in kwargs:
if new.molecule.getValenceElectrons() % 2 != 0:
kw['gto_kwargs'] = {'spin': 1}
else:
kw['gto_kwargs'] = {'spin': spin}
if 'resolution' in kwargs:
kw['resolution'] = kwargs['resolution']
if 'cartesian' in kwargs:
kw['cartesian'] = kwargs['cartesian']
occ = np.array(new.occupation)
gridpoints = np.atleast_2d(gridpoints).astype(float)
return new, occ, kw, gridpoints
def e_kin(self, gridpoints, **kwargs):
"""
kinetic energy density
"""
new, occ, kw, gridpoints = self._e_setting(gridpoints, **kwargs)
dpsi = new.getDPsi(gridpoints = gridpoints, **kw)
dpsi2 = np.linalg.norm(dpsi, axis=-1) ** 2
return (0.5 * dpsi2 * occ[:, np.newaxis]).sum(axis=0)
def e_ext(self, gridpoints, **kwargs):
"""
external potential energy density
"""
new, occ, kw, gridpoints = self._e_setting(gridpoints, **kwargs)
ext = np.zeros(len(gridpoints))
for I in range(self.molecule.N):
RI = self.molecule.R[I] * 1.8897261245650618
ZI = self.molecule.Z[I]
R_list = gridpoints - RI
ext -= ZI / np.linalg.norm(R_list, axis=1)
psi = new.getPsi(gridpoints = gridpoints, **kw)
return (psi * occ[:, np.newaxis]).sum(axis=0) * ext
def e_xc(self, gridpoints, dft='pbe', **kwargs):
new, occ, kw, gridpoints = self._e_setting(gridpoints, **kwargs)
xc_list = [xc_dict[f] for f in qtk.setting.libxc_dict[dft]]
drho = new.getDRho(gridpoints=gridpoints, new=True, **kw)
sigma = np.sum(drho ** 2, axis = 1)
rho = new.getRho(gridpoints = gridpoints, **kw)
x = libxc_exc(rho, sigma, len(rho), xc_list[0])
c = libxc_exc(rho, sigma, len(rho), xc_list[1])
return x, c
def e_coulomb(self, gridpoints, **kwargs):
new, occ, kw, gridpoints = self._e_setting(gridpoints, **kwargs)
kernel = self.coulombKernel(gridpoints / 1.8897261245650618, **kwargs)
rho = new.getRho(gridpoints = gridpoints, **kw)
return 0.5 * rho * kernel
def epsilon(self, gridpoints, dft='pbe', **kwargs):
new, occ, kw, gridpoints = self._e_setting(gridpoints, **kwargs)
kin = self.e_kin(gridpoints, **kw)
ext = self.e_ext(gridpoints, **kw)
x, c = self.e_xc(gridpoints, **kw)
coulomb = self.e_coulomb(gridpoints, **kw)
return kin + ext + x + c + coulomb
def getDipole(self, cartesian=True, resolution='fine', unit='debye'):
if not hasattr(self, 'molecule'):
qtk.exit('molecule structure not found')
if not hasattr(self, '_rho'):
self.getRho(cartesian, resolution)
pQ = np.array(
[sum(self.molecule.Z * self.molecule.R[:,i]) for i in range(3)]
)
pQ = pQ * 1.8897259885789
pq = np.array(
[self.grid.integrate(self._rho * self.grid.points[:,i])
for i in range(3)]
)
pq = pq
mu = pQ - pq
if unit == 'debye':
return mu / 0.393430307
else:
return mu
def keMatrix(self):
return keMatrix(self.basis)
def densityMatrix(self):
return densityMatrix(self)
def veMatrix(self, coord = None, Z = None):
if coord is None:
coord = self.molecule.R
if Z is None:
Z = self.molecule.Z
return veMatrix(self.basis, coord, Z)
def eeKernel(self, coord=None, batch_size=1):
if coord is None:
coord = self.molecule.R
else:
coord = np.atleast_2d(coord).astype(float)
out = []
itr = 1
for chunk in np.array_split(coord, batch_size):
if itr > 1:
qtk.progress("eeKernel", "processing batch: %d\n" % itr)
itr += 1
out.append(eeKernel(self.basis, chunk))
return np.concatenate(out)
def coulombKernel(self, coord = None, **kwargs):
k = self.eeKernel(coord, **kwargs)
mo = self.mo_vectors
# out = np.diagonal(
# np.einsum('is,jl,kls->kij', mo, mo, k),
# axis1=1, axis2=2,
# ).sum(1)
#
# diagonal: np.einsum('is,il, kls->ki', mo, mo, k)
# or np.einsum('ii->i', a) for diagonal
# sum diagonal: np.einsum('is,il, kls->k', mo, mo, k)
# or np.einsum('ii', a) for trace
out = np.einsum('is,il, kls->k', mo, mo, k)
return out
def eeMatrix(self):
if not hasattr(self, '_eeMatrix'):
self._eeMatrix = eeMatrix(self.basis)
return self._eeMatrix
def EJ(self):
ee = 2*self.eeMatrix()
td = np.tensordot
mo = self.mo_vectors
out = td(mo, ee, axes=(1, 0))
out = td(mo, out, axes=(1, 1))
out = td(mo, out, axes=(1, 2))
out = td(mo, out, axes=(1, 3))
occ = int(np.sum(self.occupation) / 2.)
EJ = [out[a,a,b,b] for a in range(occ) for b in range(occ)]
return sum(EJ)
def EX(self):
ex = -np.swapaxes(self.eeMatrix(), 1,2)
td = np.tensordot
mo = self.mo_vectors
out = td(mo, ex, axes=(1, 0))
out = td(mo, out, axes=(1, 1))
out = td(mo, out, axes=(1, 2))
out = td(mo, out, axes=(1, 3))
occ = int(np.sum(self.occupation) / 2.)
EX = [out[a,a,b,b] for a in range(occ) for b in range(occ)]
return sum(EX)
def EK(self):
km = self.keMatrix()
dm = self.densityMatrix()
return np.trace(np.dot(dm, km))
def Eext(self):
vext = self.veMatrix()
dm = self.densityMatrix()
return np.trace(np.dot(dm, vext))