def aug_etb_for_dfbasis(mol, dfbasis=DFBASIS, beta=ETB_BETA,
start_at=FIRST_ETB_ELEMENT):
'''augment weigend basis with even-tempered gaussian basis
exps = alpha*beta^i for i = 1..N
'''
nuc_start = gto.charge(start_at)
uniq_atoms = set([a[0] for a in mol._atom])
newbasis = {}
for symb in uniq_atoms:
nuc_charge = gto.charge(symb)
if nuc_charge < nuc_start:
newbasis[symb] = dfbasis
#?elif symb in mol._ecp:
else:
conf = elements.CONFIGURATION[nuc_charge]
max_shells = 4 - conf.count(0)
emin_by_l = [1e99] * 8
emax_by_l = [0] * 8
l_max = 0
for b in mol._basis[symb]:
l = b[0]
l_max = max(l_max, l)
if l >= max_shells+1:
continue
if isinstance(b[1], int):
e_c = numpy.array(b[2:])
else:
e_c = numpy.array(b[1:])
es = e_c[:,0]
cs = e_c[:,1:]
es = es[abs(cs).max(axis=1) > 1e-3]
emax_by_l[l] = max(es.max(), emax_by_l[l])
emin_by_l[l] = min(es.min(), emin_by_l[l])
l_max1 = l_max + 1
emin_by_l = numpy.array(emin_by_l[:l_max1])
emax_by_l = numpy.array(emax_by_l[:l_max1])
# Estimate the exponents ranges by geometric average
emax = numpy.sqrt(numpy.einsum('i,j->ij', emax_by_l, emax_by_l))
emin = numpy.sqrt(numpy.einsum('i,j->ij', emin_by_l, emin_by_l))
liljsum = numpy.arange(l_max1)[:,None] + numpy.arange(l_max1)
emax_by_l = [emax[liljsum==ll].max() for ll in range(l_max1*2-1)]
emin_by_l = [emin[liljsum==ll].min() for ll in range(l_max1*2-1)]
# Tune emin and emax
emin_by_l = numpy.array(emin_by_l) * 2 # *2 for alpha+alpha on same center
emax_by_l = numpy.array(emax_by_l) * 2 #/ (numpy.arange(l_max1*2-1)*.5+1)
ns = numpy.log((emax_by_l+emin_by_l)/emin_by_l) / numpy.log(beta)
etb = []
for l, n in enumerate(numpy.ceil(ns).astype(int)):
if n > 0:
etb.append((l, n, emin_by_l[l], beta))
newbasis[symb] = gto.expand_etbs(etb)
return newbasis
def get_atm_nrhf(mol):
if mol.has_ecp():
raise NotImplementedError('Atomic calculation with ECP is not implemented')
atm_scf_result = {}
for a, b in mol._basis.items():
atm = gto.Mole()
atm.stdout = mol.stdout
atm.atom = atm._atom = [[a, (0, 0, 0)]]
atm._basis = {a: b}
atm.nelectron = gto.charge(a)
atm.spin = atm.nelectron % 2
atm._atm, atm._bas, atm._env = \
atm.make_env(atm._atom, atm._basis, atm._env)
atm._built = True
if atm.nelectron == 0: # GHOST
nao = atm.nao_nr()
mo_occ = mo_energy = numpy.zeros(nao)
mo_coeff = numpy.zeros((nao,nao))
atm_scf_result[a] = (0, mo_energy, mo_coeff, mo_occ)
else:
atm_hf = AtomSphericAverageRHF(atm)
atm_hf.verbose = 0
atm_scf_result[a] = atm_hf.scf()[1:]
atm_hf._eri = None
mol.stdout.flush()
return atm_scf_result
def print_geometry_header(self):
''' Atoms written in order of increasing ia
'''
#Write number of atom types, number of atoms
self.out_file.write('\' * Geometry section\'\n')
self.out_file.write('3\t\t\tndim\n')
self.out_file.write('%d %d\t\t\tnctypes, ncent\n' %
(len(self.atoms), self.mol.natm))
#For each atom, write the atom type
ia2species = [
self.atoms.index(self.mol.atom_symbol(ia)) + 1
for ia in range(self.mol.natm)
]
self.out_file.write(' '.join([str(species) for species in ia2species]))
self.out_file.write('\t\t\t(iwctype(i), i= 1,ncent)\n')
#For each atom type, write Z
self.out_file.write(' '.join(
[str(gto.charge(atom)) for atom in self.atoms]))
self.out_file.write('\t\t\t(znuc(i), i=1, nctype)\n')
#For each atom, write the coordinates/atom type
for ia in range(self.mol.natm):
self.out_file.write('%E\t%E\t%E\t%d\n' %
(tuple(self.mol.atom_coord(ia)) +
(ia2species[ia], )))
self.out_file.write('\n')
return
def get_atm_nrhf(mol, atomic_configuration=elements.NRSRHF_CONFIGURATION):
atm_scf_result = {}
for a, b in mol._basis.items():
atm = gto.Mole()
atm.stdout = mol.stdout
atm.atom = atm._atom = [[a, (0, 0, 0)]]
atm._basis = {a: b}
atm.nelectron = gto.charge(a)
atm.spin = atm.nelectron % 2
atm._atm, atm._bas, atm._env = \
atm.make_env(atm._atom, atm._basis, atm._env)
if a in mol._ecp:
atm._ecp[a] = mol._ecp[a]
atm._atm, atm._ecpbas, atm._env = \
atm.make_ecp_env(atm._atm, atm._ecp, atm._env)
atm._built = True
if atm.nelectron == 0: # GHOST
nao = atm.nao_nr()
mo_occ = mo_energy = numpy.zeros(nao)
mo_coeff = numpy.zeros((nao, nao))
atm_scf_result[a] = (0, mo_energy, mo_coeff, mo_occ)
else:
atm_hf = AtomSphericAverageRHF(atm)
atm_hf.atomic_configuration = atomic_configuration
atm_hf.verbose = 0
atm_hf.run()
atm_scf_result[a] = (atm_hf.e_tot, atm_hf.mo_energy,
atm_hf.mo_coeff, atm_hf.mo_occ)
atm_hf._eri = None
mol.stdout.flush()
return atm_scf_result
def kernel(self):
mol = self.mol
basis_type = _get_basis_type(mol)
if self.xc in FUNC_CODE:
func, supported_versions = FUNC_CODE[self.xc]
if func == 'b3lyp' and basis_type == '6-31gd':
func, supported_versions = FUNC_CODE['B3LYP/631GD']
elif func == 'hf' and basis_type == 'sv':
func, supported_versions = FUNC_CODE['HF/SV']
else:
raise RuntimeError('Functional %s not found' % self.xc)
assert (self.version in supported_versions)
# dft-d3 has special treatment for def2-TZ basis
tz = (basis_type == 'def2-TZ')
coords = mol.atom_coords()
nuc_types = [gto.charge(mol.atom_symbol(ia)) for ia in range(mol.natm)]
nuc_types = numpy.asarray(nuc_types, dtype=numpy.int32)
edisp = ctypes.c_double(0)
grads = numpy.zeros((mol.natm, 3))
drv = self.libdftd3.wrapper
drv(ctypes.c_int(mol.natm), coords.ctypes.data_as(ctypes.c_void_p),
nuc_types.ctypes.data_as(ctypes.c_void_p), ctypes.c_char_p(func),
ctypes.c_int(self.version), ctypes.c_int(tz), ctypes.byref(edisp),
grads.ctypes.data_as(ctypes.c_void_p))
self.edisp = edisp.value
self.grads = grads
return edisp.value, grads
def write(self, field, fname, comment=None):
""" Result: .cube file with the field in the file fname. """
assert (field.ndim == 3)
assert (field.shape == (self.nx, self.ny, self.nz))
if comment is None:
comment = 'Generic field? Supply the optional argument "comment" to define this line'
mol = self.mol
coord = mol.atom_coords()
with open(fname, 'w') as f:
f.write(comment + '\n')
f.write('PySCF Version: %s Date: %s\n' %
(pyscf.__version__, time.ctime()))
f.write('%5d' % mol.natm)
f.write('%12.6f%12.6f%12.6f\n' % tuple(self.boxorig.tolist()))
f.write('%5d%12.6f%12.6f%12.6f\n' % (self.nx, self.xs[1], 0, 0))
f.write('%5d%12.6f%12.6f%12.6f\n' % (self.ny, 0, self.ys[1], 0))
f.write('%5d%12.6f%12.6f%12.6f\n' % (self.nz, 0, 0, self.zs[1]))
for ia in range(mol.natm):
atmsymb = mol.atom_symbol(ia)
f.write('%5d%12.6f' % (gto.charge(atmsymb), 0.))
f.write('%12.6f%12.6f%12.6f\n' % tuple(coord[ia]))
for ix in range(self.nx):
for iy in range(self.ny):
for iz0, iz1 in lib.prange(0, self.nz, 6):
fmt = '%13.5E' * (iz1 - iz0) + '\n'
f.write(fmt % tuple(field[ix, iy, iz0:iz1].tolist()))
def get_atm_nrhf(mol):
if mol.has_ecp():
raise NotImplementedError('Atomic calculation with ECP is not implemented')
atm_scf_result = {}
for a, b in mol._basis.items():
atm = gto.Mole()
atm.stdout = mol.stdout
atm.atom = atm._atom = [[a, (0, 0, 0)]]
atm._basis = {a: b}
atm.nelectron = gto.charge(a)
atm.spin = atm.nelectron % 2
atm._atm, atm._bas, atm._env = \
atm.make_env(atm._atom, atm._basis, atm._env)
atm._built = True
if atm.nelectron == 0: # GHOST
nao = atm.nao_nr()
mo_occ = mo_energy = numpy.zeros(nao)
mo_coeff = numpy.zeros((nao,nao))
atm_scf_result[a] = (0, mo_energy, mo_coeff, mo_occ)
else:
atm_hf = AtomSphericAverageRHF(atm)
atm_hf.verbose = 0
atm_scf_result[a] = atm_hf.scf()[1:]
atm_hf._eri = None
mol.stdout.flush()
return atm_scf_result
def write_header(self, filename, dset_ids=None):
"""Write header of cube-file."""
if self.nfields > 1 and dset_ids is None:
dset_ids = range(1, self.nfields + 1)
with open(filename, 'w') as f:
f.write('%s\n' % self.title)
f.write('%s\n' % self.comment)
if self.nfields > 1:
f.write('%5d' % -self.cell.natm)
else:
f.write('%5d' % self.cell.natm)
f.write('%12.6f%12.6f%12.6f' % tuple(self.origin))
if self.nfields > 1:
f.write('%5d' % self.nfields)
f.write('\n')
# Lattice vectors
f.write('%5d%12.6f%12.6f%12.6f\n' % (self.nx, *(self.a[0] /
(self.nx - 1))))
f.write('%5d%12.6f%12.6f%12.6f\n' % (self.ny, *(self.a[1] /
(self.ny - 1))))
f.write('%5d%12.6f%12.6f%12.6f\n' % (self.nz, *(self.a[2] /
(self.nz - 1))))
# Atoms
for atm in range(self.cell.natm):
sym = self.cell.atom_symbol(atm)
f.write('%5d%12.6f' % (gto.charge(sym), 0.0))
f.write('%12.6f%12.6f%12.6f\n' %
tuple(self.cell.atom_coords()[atm]))
# Data set indices
if self.nfields > 1:
f.write('%5d' % self.nfields)
for i in range(self.nfields):
f.write('%5d' % dset_ids[i])
f.write('\n')
def gen_atomic_grids(mol, atom_grid={}, radi_method=radi.gauss_chebyshev,
level=3, prune=nwchem_prune, **kwargs):
'''Generate number of radial grids and angular grids for the given molecule.
Returns:
A dict, with the atom symbol for the dict key. For each atom type,
the dict value has two items: one is the meshgrid coordinates wrt the
atom center; the second is the volume of that grid.
'''
if isinstance(atom_grid, (list, tuple)):
atom_grid = dict([(mol.atom_symbol(ia), atom_grid)
for ia in range(mol.natm)])
atom_grids_tab = {}
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
if symb not in atom_grids_tab:
chg = gto.charge(symb)
if symb in atom_grid:
n_rad, n_ang = atom_grid[symb]
if n_ang not in LEBEDEV_NGRID:
if n_ang in LEBEDEV_ORDER:
logger.warn(mol, 'n_ang %d for atom %d %s is not '
'the supported Lebedev angular grids. '
'Set n_ang to %d', n_ang, ia, symb,
LEBEDEV_ORDER[n_ang])
n_ang = LEBEDEV_ORDER[n_ang]
else:
raise ValueError('Unsupported angular grids %d' % n_ang)
else:
n_rad = _default_rad(chg, level)
n_ang = _default_ang(chg, level)
rad, dr = radi_method(n_rad, chg, ia, **kwargs)
rad_weight = 4*numpy.pi * rad**2 * dr
if callable(prune):
angs = prune(chg, rad, n_ang)
else:
angs = [n_ang] * n_rad
logger.debug(mol, 'atom %s rad-grids = %d, ang-grids = %s',
symb, n_rad, angs)
angs = numpy.array(angs)
coords = []
vol = []
for n in sorted(set(angs)):
grid = numpy.empty((n,4))
libdft.MakeAngularGrid(grid.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(n))
idx = numpy.where(angs==n)[0]
for i0, i1 in prange(0, len(idx), 12): # 12 radi-grids as a group
coords.append(numpy.einsum('i,jk->jik',rad[idx[i0:i1]],
grid[:,:3]).reshape(-1,3))
vol.append(numpy.einsum('i,j->ji', rad_weight[idx[i0:i1]],
grid[:,3]).ravel())
atom_grids_tab[symb] = (numpy.vstack(coords), numpy.hstack(vol))
return atom_grids_tab
def gen_atomic_grids(mol, atom_grid={}, radi_method=radi.gauss_chebyshev,
level=3, prune=nwchem_prune, **kwargs):
'''Generate number of radial grids and angular grids for the given molecule.
Returns:
A dict, with the atom symbol for the dict key. For each atom type,
the dict value has two items: one is the meshgrid coordinates wrt the
atom center; the second is the volume of that grid.
'''
if isinstance(atom_grid, (list, tuple)):
atom_grid = dict([(mol.atom_symbol(ia), atom_grid)
for ia in range(mol.natm)])
atom_grids_tab = {}
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
if symb not in atom_grids_tab:
chg = gto.charge(symb)
if symb in atom_grid:
n_rad, n_ang = atom_grid[symb]
if n_ang not in LEBEDEV_NGRID:
if n_ang in LEBEDEV_ORDER:
logger.warn(mol, 'n_ang %d for atom %d %s is not '
'the supported Lebedev angular grids. '
'Set n_ang to %d', n_ang, ia, symb,
LEBEDEV_ORDER[n_ang])
n_ang = LEBEDEV_ORDER[n_ang]
else:
raise ValueError('Unsupported angular grids %d' % n_ang)
else:
n_rad = _default_rad(chg, level)
n_ang = _default_ang(chg, level)
rad, dr = radi_method(n_rad, chg, ia, **kwargs)
rad_weight = 4*numpy.pi * rad**2 * dr
if callable(prune):
angs = prune(chg, rad, n_ang)
else:
angs = [n_ang] * n_rad
logger.debug(mol, 'atom %s rad-grids = %d, ang-grids = %s',
symb, n_rad, angs)
angs = numpy.array(angs)
coords = []
vol = []
for n in sorted(set(angs)):
grid = numpy.empty((n,4))
libdft.MakeAngularGrid(grid.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(n))
idx = numpy.where(angs==n)[0]
for i0, i1 in prange(0, len(idx), 12): # 12 radi-grids as a group
coords.append(numpy.einsum('i,jk->jik',rad[idx[i0:i1]],
grid[:,:3]).reshape(-1,3))
vol.append(numpy.einsum('i,j->ji', rad_weight[idx[i0:i1]],
grid[:,3]).ravel())
atom_grids_tab[symb] = (numpy.vstack(coords), numpy.hstack(vol))
return atom_grids_tab
def frac_occ(symb, l):
nuc = gto.charge(symb)
if l < 4 and elements.CONFIGURATION[nuc][l] > 0:
ne = elements.CONFIGURATION[nuc][l]
nd = (l * 2 + 1) * 2
ndocc = ne.__floordiv__(nd)
frac = (float(ne) / nd - ndocc) * 2
else:
ndocc = frac = 0
return ndocc, frac
def frac_occ(symb, l):
nuc = gto.charge(symb)
if l < 4 and elements.CONFIGURATION[nuc][l] > 0:
ne = elements.CONFIGURATION[nuc][l]
nd = (l * 2 + 1) * 2
ndocc = ne.__floordiv__(nd)
frac = (float(ne) / nd - ndocc) * 2
else:
ndocc = frac = 0
return ndocc, frac
def frac_occ(symb, l, atomic_configuration=elements.NRSRHF_CONFIGURATION):
nuc = gto.charge(symb)
if l < 4 and atomic_configuration[nuc][l] > 0:
ne = atomic_configuration[nuc][l]
nd = (l * 2 + 1) * 2
ndocc = ne.__floordiv__(nd)
frac = (float(ne) / nd - ndocc) * 2
else:
ndocc = frac = 0
return ndocc, frac
def plot_mesh_3d(mesh, weight=False, **kwargs):
'''Plot atoms and grid points in a 3d plot.
Args:
mesh :
Object of class :class:`Grids`.
Kwargs:
weight : bool or int
Scale grid points by their weights when set to ``True``. Integers
will scale grid points.
'''
# Initialize logger
verbose = mesh.verbose
log = logger.Logger(stdout, verbose)
# Handle user inputs
if not isinstance(mesh, Grids):
log.error('The mesh parameter has to be a Grids object.')
if not isinstance(weight, bool) and not isinstance(weight, int):
log.error('The weight parameter has to be a boolean or an integer.')
mol = mesh.mol
coords = mesh.coords
atoms = mol.atom_coords()
if weight and isinstance(weight, bool):
weights = abs(mesh.weights)
elif weight and isinstance(weight, int):
weights = weight
else:
weights = 2
# Get the atom colors and radii (scale with 100 to make it look good)
colors = []
radii = []
for ia in range(mol.natm):
colors.append(cpk_colors.get(mol.atom_symbol(ia), 'magenta'))
radii.append(BRAGG_RADII[charge(mol.atom_symbol(ia))] * 100)
fig = plt.figure()
ax = fig.add_subplot(111, projection=Axes3D.name)
# Plot atoms
ax.scatter(atoms[:, 0],
atoms[:, 1],
atoms[:, 2],
s=radii,
c=colors,
edgecolors='k',
depthshade=0)
# Plot mesh points
ax.scatter(coords[:, 0], coords[:, 1], coords[:, 2], s=weights, c='g')
ax.set_xlabel('x-axis', fontsize=12)
ax.set_ylabel('y-axis', fontsize=12)
ax.set_zlabel('z-axis', fontsize=12)
plt.tight_layout()
plt.show()
return
def get_atomic_radii(pcmobj):
mol = pcmobj.mol
vdw_radii = pcmobj.radii_table
atom_radii = pcmobj.atom_radii
atom_symb = [mol.atom_symbol(i) for i in range(mol.natm)]
r_vdw = [vdw_radii[gto.charge(x)] for x in atom_symb]
if atom_radii is not None:
for i in range(mol.natm):
if atom_symb[i] in atom_radii:
r_vdw[i] = atom_radii[atom_symb[i]]
return numpy.asarray(r_vdw)
def project_mol(mol, dual_basis={}):
from pyscf import df
uniq_atoms = set([a[0] for a in mol._atom])
newbasis = {}
for symb in uniq_atoms:
if gto.charge(symb) <= 10:
newbasis[symb] = '321g'
elif gto.charge(symb) <= 12:
newbasis[symb] = 'dzp'
elif gto.charge(symb) <= 18:
newbasis[symb] = 'dz'
elif gto.charge(symb) <= 86:
newbasis[symb] = 'dzp'
else:
newbasis[symb] = 'sto3g'
if isinstance(dual_basis, (dict, tuple, list)):
newbasis.update(dual_basis)
elif isinstance(dual_basis, str):
for k in newbasis:
newbasis[k] = dual_basis
return df.addons.make_auxmol(mol, newbasis)
def get_atomic_radii(pcmobj):
mol = pcmobj.mol
vdw_radii = pcmobj.radii_table
atom_radii = pcmobj.atom_radii
atom_symb = [mol.atom_symbol(i) for i in range(mol.natm)]
r_vdw = [vdw_radii[gto.charge(x)] for x in atom_symb]
if atom_radii is not None:
for i in range(mol.natm):
if atom_symb[i] in atom_radii:
r_vdw[i] = atom_radii[atom_symb[i]]
return numpy.asarray(r_vdw)
def project_mol(mol, dual_basis={}):
from pyscf import df
uniq_atoms = set([a[0] for a in mol._atom])
newbasis = {}
for symb in uniq_atoms:
if gto.charge(symb) <= 10:
newbasis[symb] = '321g'
elif gto.charge(symb) <= 12:
newbasis[symb] = 'dzp'
elif gto.charge(symb) <= 18:
newbasis[symb] = 'dz'
elif gto.charge(symb) <= 86:
newbasis[symb] = 'dzp'
else:
newbasis[symb] = 'sto3g'
if isinstance(dual_basis, (dict, tuple, list)):
newbasis.update(dual_basis)
elif isinstance(dual_basis, str):
for k in newbasis:
newbasis[k] = dual_basis
return df.addons.make_auxmol(mol, newbasis)
def ecp_ano_det_ovlp(atm_ecp, atm_ano, ecpcore):
ecp_ao_loc = atm_ecp.ao_loc_nr()
ano_ao_loc = atm_ano.ao_loc_nr()
ecp_ao_dim = ecp_ao_loc[1:] - ecp_ao_loc[:-1]
ano_ao_dim = ano_ao_loc[1:] - ano_ao_loc[:-1]
ecp_bas_l = [[atm_ecp.bas_angular(i)] * d
for i, d in enumerate(ecp_ao_dim)]
ano_bas_l = [[atm_ano.bas_angular(i)] * d
for i, d in enumerate(ano_ao_dim)]
ecp_bas_l = numpy.hstack(ecp_bas_l)
ano_bas_l = numpy.hstack(ano_bas_l)
nelec_core = 0
ecp_occ_tmp = []
ecp_idx = []
ano_idx = []
for l in range(4):
nocc, frac = atom_hf.frac_occ(stdsymb, l)
l_occ = [2] * ((nocc - ecpcore[l]) * (2 * l + 1))
if frac > 1e-15:
l_occ.extend([frac] * (2 * l + 1))
nocc += 1
if nocc == 0:
break
nelec_core += 2 * ecpcore[l] * (2 * l + 1)
i0 = ecpcore[l] * (2 * l + 1)
i1 = nocc * (2 * l + 1)
ecp_idx.append(numpy.where(ecp_bas_l == l)[0][:i1 - i0])
ano_idx.append(numpy.where(ano_bas_l == l)[0][i0:i1])
ecp_occ_tmp.append(l_occ[:i1 - i0])
ecp_idx = numpy.hstack(ecp_idx)
ano_idx = numpy.hstack(ano_idx)
ecp_occ = numpy.zeros(atm_ecp.nao_nr())
ecp_occ[ecp_idx] = numpy.hstack(ecp_occ_tmp)
nelec_valence_left = int(
gto.charge(stdsymb) - nelec_core - sum(ecp_occ[ecp_idx]))
if nelec_valence_left > 0:
logger.warn(
mol, 'Characters of %d valence electrons are not identified.\n'
'It can affect the "meta-lowdin" localization method '
'and the population analysis of SCF method.\n'
'Adjustment to the core/valence partition may be needed '
'(see function lo.nao.set_atom_conf)\nto get reasonable '
'local orbitals or Mulliken population.\n', nelec_valence_left)
# Return 0 to force the projection to ANO basis
return 0
else:
s12 = gto.intor_cross('int1e_ovlp', atm_ecp,
atm_ano)[ecp_idx][:, ano_idx]
return numpy.linalg.det(s12)
def get_ang(symb, level):
'''Get angular grids.
Args:
symb : str
Atom type identifier.
level : int
Grid level of atom type.
Returns: int
Amount of angular grids.
'''
try:
return ang[symb][level]
except (KeyError, TypeError):
return dft.gen_grid._default_ang(gto.charge(symb), level)
def symm_identical_atoms(gpname, atoms):
''' Requires '''
from pyscf import gto
# Dooh Coov for linear molecule
if gpname == 'Dooh':
coords = numpy.array([a[1] for a in atoms], dtype=float)
idx0 = argsort_coords(coords)
coords0 = coords[idx0]
opdic = symm_ops(gpname)
newc = numpy.dot(coords, opdic['sz'])
idx1 = argsort_coords(newc)
dup_atom_ids = numpy.sort((idx0,idx1), axis=0).T
uniq_idx = numpy.unique(dup_atom_ids[:,0], return_index=True)[1]
eql_atom_ids = dup_atom_ids[uniq_idx]
eql_atom_ids = [list(sorted(set(i))) for i in eql_atom_ids]
return eql_atom_ids
elif gpname == 'Coov':
eql_atom_ids = [[i] for i,a in enumerate(atoms)]
return eql_atom_ids
charges = numpy.array([gto.charge(a[0]) for a in atoms])
coords = numpy.array([a[1] for a in atoms])
center = numpy.einsum('z,zr->r', charges, coords)/charges.sum()
# if not numpy.allclose(center, 0, atol=TOLERANCE):
# sys.stderr.write('WARN: Molecular charge center %s is not on (0,0,0)\n'
# % center)
opdic = symm_ops(gpname)
ops = [opdic[op] for op in OPERATOR_TABLE[gpname]]
idx = argsort_coords(coords)
coords0 = coords[idx]
dup_atom_ids = []
for op in ops:
newc = numpy.dot(coords, op)
idx = argsort_coords(newc)
if not numpy.allclose(coords0, newc[idx], atol=TOLERANCE):
raise RuntimeError('Symmetry identical atoms not found')
dup_atom_ids.append(idx)
dup_atom_ids = numpy.sort(dup_atom_ids, axis=0).T
uniq_idx = numpy.unique(dup_atom_ids[:,0], return_index=True)[1]
eql_atom_ids = dup_atom_ids[uniq_idx]
eql_atom_ids = [list(sorted(set(i))) for i in eql_atom_ids]
return eql_atom_ids
def symm_identical_atoms(gpname, atoms):
''' Requires '''
from pyscf import gto
# Dooh Coov for linear molecule
if gpname == 'Dooh':
coords = numpy.array([a[1] for a in atoms], dtype=float)
idx0 = argsort_coords(coords)
coords0 = coords[idx0]
opdic = symm_ops(gpname)
newc = numpy.dot(coords, opdic['sz'])
idx1 = argsort_coords(newc)
dup_atom_ids = numpy.sort((idx0, idx1), axis=0).T
uniq_idx = numpy.unique(dup_atom_ids[:, 0], return_index=True)[1]
eql_atom_ids = dup_atom_ids[uniq_idx]
eql_atom_ids = [list(sorted(set(i))) for i in eql_atom_ids]
return eql_atom_ids
elif gpname == 'Coov':
eql_atom_ids = [[i] for i, a in enumerate(atoms)]
return eql_atom_ids
charges = numpy.array([gto.charge(a[0]) for a in atoms])
coords = numpy.array([a[1] for a in atoms])
center = numpy.einsum('z,zr->r', charges, coords) / charges.sum()
# if not numpy.allclose(center, 0, atol=TOLERANCE):
# sys.stderr.write('WARN: Molecular charge center %s is not on (0,0,0)\n'
# % center)
opdic = symm_ops(gpname)
ops = [opdic[op] for op in OPERATOR_TABLE[gpname]]
idx = argsort_coords(coords)
coords0 = coords[idx]
dup_atom_ids = []
for op in ops:
newc = numpy.dot(coords, op)
idx = argsort_coords(newc)
if not numpy.allclose(coords0, newc[idx], atol=TOLERANCE):
raise RuntimeError('Symmetry identical atoms not found')
dup_atom_ids.append(idx)
dup_atom_ids = numpy.sort(dup_atom_ids, axis=0).T
uniq_idx = numpy.unique(dup_atom_ids[:, 0], return_index=True)[1]
eql_atom_ids = dup_atom_ids[uniq_idx]
eql_atom_ids = [list(sorted(set(i))) for i in eql_atom_ids]
return eql_atom_ids
def get_atomic_radii(pcmobj):
'''
get atomic radii for QM and MM
'''
mol = pcmobj.mol
mm_mol = pcmobj.mm_mol
vdw_radii = pcmobj.radii_table
atom_radii = pcmobj.atom_radii
atom_symb = [mol.atom_symbol(i) for i in range(mol.natm)]
if mm_mol is not None:
atom_symb += [mm_mol.atom_symbol(i) for i in range(mm_mol.natm)]
r_vdw = [vdw_radii[gto.charge(x)] for x in atom_symb]
if atom_radii is not None:
for i in range(len(atom_symb)):
if atom_symb[i] in atom_radii:
r_vdw[i] = atom_radii[atom_symb[i]]
return numpy.asarray(r_vdw)
def write(self, field, fname, comment=None):
""" Result: .cube file with the field in the file fname. """
assert (field.ndim == 3)
assert (field.shape == (self.nx, self.ny, self.nz))
if comment is None:
comment = 'Generic field? Supply the optional argument "comment" to define this line'
mol = self.mol
coord = mol.atom_coords()
with open(fname, 'w') as f:
f.write(comment + '\n')
f.write(
f'PySCF Version: {pyscf.__version__} Date: {time.ctime()}\n')
f.write(f'{mol.natm:5d}')
f.write('%12.6f%12.6f%12.6f\n' % tuple(self.boxorig.tolist()))
dx = self.xs[-1] if len(self.xs) == 1 else self.xs[1]
dy = self.ys[-1] if len(self.ys) == 1 else self.ys[1]
dz = self.zs[-1] if len(self.zs) == 1 else self.zs[1]
delta = (self.box.T * [dx, dy, dz]).T
f.write(
f'{self.nx:5d}{delta[0,0]:12.6f}{delta[0,1]:12.6f}{delta[0,2]:12.6f}\n'
)
f.write(
f'{self.ny:5d}{delta[1,0]:12.6f}{delta[1,1]:12.6f}{delta[1,2]:12.6f}\n'
)
f.write(
f'{self.nz:5d}{delta[2,0]:12.6f}{delta[2,1]:12.6f}{delta[2,2]:12.6f}\n'
)
for ia in range(mol.natm):
atmsymb = mol.atom_symbol(ia)
f.write('%5d%12.6f' % (gto.charge(atmsymb), 0.))
f.write('%12.6f%12.6f%12.6f\n' % tuple(coord[ia]))
for ix in range(self.nx):
for iy in range(self.ny):
for iz0, iz1 in lib.prange(0, self.nz, 6):
fmt = '%13.5E' * (iz1 - iz0) + '\n'
f.write(fmt % tuple(field[ix, iy, iz0:iz1].tolist()))
def kernel(self):
mol = self.mol
basis_type = _get_basis_type(mol)
if self.xc in FUNC_CODE:
func, supported_versions = FUNC_CODE[self.xc]
if func == 'b3lyp' and basis_type == '6-31gd':
func, supported_versions = FUNC_CODE['B3LYP/631GD']
elif func == 'hf' and basis_type == 'sv':
func, supported_versions = FUNC_CODE['HF/SV']
else:
raise RuntimeError('Functional %s not found' % self.xc)
assert(self.version in supported_versions)
# dft-d3 has special treatment for def2-TZ basis
tz = (basis_type == 'def2-TZ')
coords = mol.atom_coords()
nuc_types = [gto.charge(mol.atom_symbol(ia))
for ia in range(mol.natm)]
nuc_types = numpy.asarray(nuc_types, dtype=numpy.int32)
edisp = ctypes.c_double(0)
grads = numpy.zeros((mol.natm,3))
drv = self.libdftd3.wrapper
drv(ctypes.c_int(mol.natm),
coords.ctypes.data_as(ctypes.c_void_p),
nuc_types.ctypes.data_as(ctypes.c_void_p),
ctypes.c_char_p(func),
ctypes.c_int(self.version),
ctypes.c_int(tz),
ctypes.byref(edisp),
grads.ctypes.data_as(ctypes.c_void_p))
self.edisp = edisp.value
self.grads = grads
return edisp.value, grads
energy = energy
gen_solver = as_solver = gen_ddcosmo_solver
get_atomic_radii = get_atomic_radii
def regularize_xt(self, t, eta, scale=1):
# scale = eta*scale, is it correct?
return regularize_xt(t, eta*scale)
if __name__ == '__main__':
from pyscf import scf
from pyscf import mcscf
from pyscf import cc
mol = gto.M(atom='H 0 0 0; H 0 1 1.2; H 1. .1 0; H .5 .5 1')
natm = mol.natm
r_vdw = [radii.VDW[gto.charge(mol.atom_symbol(i))]
for i in range(natm)]
r_vdw = numpy.asarray(r_vdw)
pcmobj = DDCOSMO(mol)
pcmobj.regularize_xt = lambda t, eta, scale: regularize_xt(t, eta)
pcmobj.lebedev_order = 7
pcmobj.lmax = 6
pcmobj.eta = 0.1
nlm = (pcmobj.lmax+1)**2
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
fi = make_fi(pcmobj, r_vdw)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
L = make_L(pcmobj, r_vdw, ylm_1sph, fi)
print(lib.finger(L) - 6.2823493771037473)
mol = gto.Mole()
energy = energy
gen_solver = as_solver = gen_ddcosmo_solver
get_atomic_radii = get_atomic_radii
def regularize_xt(self, t, eta, scale=1):
# scale = eta*scale, is it correct?
return regularize_xt(t, eta*scale)
if __name__ == '__main__':
from pyscf import scf
from pyscf import mcscf
from pyscf import cc
mol = gto.M(atom='H 0 0 0; H 0 1 1.2; H 1. .1 0; H .5 .5 1')
natm = mol.natm
r_vdw = [radii.VDW[gto.charge(mol.atom_symbol(i))]
for i in range(natm)]
r_vdw = numpy.asarray(r_vdw)
pcmobj = DDCOSMO(mol)
pcmobj.regularize_xt = lambda t, eta, scale: regularize_xt(t, eta)
pcmobj.lebedev_order = 7
pcmobj.lmax = 6
pcmobj.eta = 0.1
nlm = (pcmobj.lmax+1)**2
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
fi = make_fi(pcmobj, r_vdw)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
L = make_L(pcmobj, r_vdw, ylm_1sph, fi)
print(lib.finger(L) - 6.2823493771037473)
mol = gto.Mole()
def plot_mesh_2d(mesh, weight=False, plane='xy'):
'''Project atoms and grid points to a given plane in a 2d plot.
Args:
mesh :
Object of class :class:`Grids`.
Kwargs:
weight : bool or int
Scale grid points by their weights when set to ``True``. Integers
will scale grid points.
plane : str
Contains the plane to project on to. Needs two elements of ``'x'``,
``'y'``, and ``'z'``.
'''
# Dictionary to map input axes to their coordinates
ax = {'x': 0, 'y': 1, 'z': 2}
# Initialize logger
verbose = mesh.verbose
log = logger.Logger(stdout, verbose)
# Handle user inputs
if not isinstance(mesh, Grids):
log.error('The mesh parameter has to be a Grids object.')
if not isinstance(weight, bool) and not isinstance(weight, int):
log.error('The weight parameter has to be a boolean or an integer.')
if not isinstance(plane, str):
log.error('The plane parameter has to be a string.')
if len(plane) != 2:
log.error('The plane parameter has to be a string of length 2.')
if not set(plane).issubset(ax.keys()):
log.error('The plane parameter only accepts combinations of \'%s\'.',
'\', \''.join(ax.keys()))
ax1, ax2 = list(plane.lower())
mol = mesh.mol
coords = mesh.coords
atoms = mol.atom_coords()
if weight and isinstance(weight, bool):
weights = abs(mesh.weights)
elif weight and isinstance(weight, int):
weights = weight
else:
weights = 2
# Get the atom colors and radii (scale with 100 to make it look good)
colors = []
radii = []
for ia in range(mol.natm):
colors.append(cpk_colors.get(mol.atom_symbol(ia), 'magenta'))
radii.append(BRAGG_RADII[charge(mol.atom_symbol(ia))] * 100)
# Project atoms
plt.scatter(atoms[:, ax[ax1]],
atoms[:, ax[ax2]],
s=radii,
c=colors,
edgecolors='k')
# Project mesh points
plt.scatter(coords[:, ax[ax1]], coords[:, ax[ax2]], s=weights, c='g')
plt.xlabel(ax1 + '-axis', fontsize=12)
plt.ylabel(ax2 + '-axis', fontsize=12)
plt.tight_layout()
plt.show()
return
energy = energy
gen_solver = as_solver = gen_ddcosmo_solver
get_atomic_radii = get_atomic_radii
def regularize_xt(self, t, eta, scale=1):
# scale = eta*scale, is it correct?
return regularize_xt(t, eta * scale)
if __name__ == '__main__':
from pyscf import scf
from pyscf import mcscf
from pyscf import cc
mol = gto.M(atom='H 0 0 0; H 0 1 1.2; H 1. .1 0; H .5 .5 1')
natm = mol.natm
r_vdw = [radii.VDW[gto.charge(mol.atom_symbol(i))] for i in range(natm)]
r_vdw = numpy.asarray(r_vdw)
pcmobj = DDCOSMO(mol)
pcmobj.regularize_xt = lambda t, eta, scale: regularize_xt(t, eta)
pcmobj.lebedev_order = 7
pcmobj.lmax = 6
pcmobj.eta = 0.1
nlm = (pcmobj.lmax + 1)**2
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
fi = make_fi(pcmobj, r_vdw)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
L = make_L(pcmobj, r_vdw, ylm_1sph, fi)
print(lib.finger(L) - 6.2823493771037473)
mol = gto.Mole()
mol.atom = ''' O 0.00000000 0.00000000 -0.11081188
def project_to_atomic_orbitals(mol, basname):
'''projected AO = |bas><bas|ANO>
'''
from pyscf.scf.addons import project_mo_nr2nr
from pyscf.scf import atom_hf
from pyscf.gto.ecp import core_configuration
def search_atm_l(atm, l):
bas_ang = atm._bas[:, gto.ANG_OF]
ao_loc = atm.ao_loc_nr()
idx = []
for ib in numpy.where(bas_ang == l)[0]:
idx.extend(range(ao_loc[ib], ao_loc[ib + 1]))
return idx
# Overlap of ANO and ECP basis
def ecp_ano_det_ovlp(atm_ecp, atm_ano, ecpcore):
ecp_ao_loc = atm_ecp.ao_loc_nr()
ano_ao_loc = atm_ano.ao_loc_nr()
ecp_ao_dim = ecp_ao_loc[1:] - ecp_ao_loc[:-1]
ano_ao_dim = ano_ao_loc[1:] - ano_ao_loc[:-1]
ecp_bas_l = [[atm_ecp.bas_angular(i)] * d
for i, d in enumerate(ecp_ao_dim)]
ano_bas_l = [[atm_ano.bas_angular(i)] * d
for i, d in enumerate(ano_ao_dim)]
ecp_bas_l = numpy.hstack(ecp_bas_l)
ano_bas_l = numpy.hstack(ano_bas_l)
nelec_core = 0
ecp_occ_tmp = []
ecp_idx = []
ano_idx = []
for l in range(4):
nocc, frac = atom_hf.frac_occ(stdsymb, l)
l_occ = [2] * ((nocc - ecpcore[l]) * (2 * l + 1))
if frac > 1e-15:
l_occ.extend([frac] * (2 * l + 1))
nocc += 1
if nocc == 0:
break
nelec_core += 2 * ecpcore[l] * (2 * l + 1)
i0 = ecpcore[l] * (2 * l + 1)
i1 = nocc * (2 * l + 1)
ecp_idx.append(numpy.where(ecp_bas_l == l)[0][:i1 - i0])
ano_idx.append(numpy.where(ano_bas_l == l)[0][i0:i1])
ecp_occ_tmp.append(l_occ[:i1 - i0])
ecp_idx = numpy.hstack(ecp_idx)
ano_idx = numpy.hstack(ano_idx)
ecp_occ = numpy.zeros(atm_ecp.nao_nr())
ecp_occ[ecp_idx] = numpy.hstack(ecp_occ_tmp)
nelec_valence_left = int(
gto.charge(stdsymb) - nelec_core - sum(ecp_occ[ecp_idx]))
if nelec_valence_left > 0:
logger.warn(
mol, 'Characters of %d valence electrons are not identified.\n'
'It can affect the "meta-lowdin" localization method '
'and the population analysis of SCF method.\n'
'Adjustment to the core/valence partition may be needed '
'(see function lo.nao.set_atom_conf)\nto get reasonable '
'local orbitals or Mulliken population.\n', nelec_valence_left)
# Return 0 to force the projection to ANO basis
return 0
else:
s12 = gto.intor_cross('int1e_ovlp', atm_ecp,
atm_ano)[ecp_idx][:, ano_idx]
return numpy.linalg.det(s12)
nelec_ecp_dic = {}
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
if symb not in nelec_ecp_dic:
nelec_ecp_dic[symb] = mol.atom_nelec_core(ia)
aos = {}
atm = gto.Mole()
atmp = gto.Mole()
for symb in mol._basis.keys():
stdsymb = gto.mole._std_symbol(symb)
atm._atm, atm._bas, atm._env = \
atm.make_env([[stdsymb,(0,0,0)]], {stdsymb:mol._basis[symb]}, [])
atm.cart = mol.cart
atm._built = True
s0 = atm.intor_symmetric('int1e_ovlp')
if gto.is_ghost_atom(symb):
aos[symb] = numpy.diag(1. / numpy.sqrt(s0.diagonal()))
continue
basis_add = gto.basis.load(basname, stdsymb)
atmp._atm, atmp._bas, atmp._env = \
atmp.make_env([[stdsymb,(0,0,0)]], {stdsymb:basis_add}, [])
atmp.cart = mol.cart
atmp._built = True
if symb in nelec_ecp_dic and nelec_ecp_dic[symb] > 0:
# If ECP basis has good atomic character, ECP basis can be used in the
# localization/population analysis directly. Otherwise project ECP
# basis to ANO basis.
if not PROJECT_ECP_BASIS:
continue
ecpcore = core_configuration(nelec_ecp_dic[symb])
# Comparing to ANO valence basis, to check whether the ECP basis set has
# reasonable AO-character contraction. The ANO valence AO should have
# significant overlap to ECP basis if the ECP basis has AO-character.
if abs(ecp_ano_det_ovlp(atm, atmp, ecpcore)) > .1:
aos[symb] = numpy.diag(1. / numpy.sqrt(s0.diagonal()))
continue
else:
ecpcore = [0] * 4
# MINAO for heavier elements needs to be used with pseudo potential
if (basname.upper() == 'MINAO' and gto.charge(stdsymb) > 36
and symb not in nelec_ecp_dic):
raise RuntimeError(
'Basis MINAO has to be used with ecp for heavy elements')
ano = project_mo_nr2nr(atmp, numpy.eye(atmp.nao_nr()), atm)
rm_ano = numpy.eye(ano.shape[0]) - reduce(numpy.dot, (ano, ano.T, s0))
c = rm_ano.copy()
for l in range(param.L_MAX):
idx = numpy.asarray(search_atm_l(atm, l))
nbf_atm_l = len(idx)
if nbf_atm_l == 0:
break
idxp = numpy.asarray(search_atm_l(atmp, l))
if l < 4:
idxp = idxp[ecpcore[l]:]
nbf_ano_l = len(idxp)
if mol.cart:
degen = (l + 1) * (l + 2) // 2
else:
degen = l * 2 + 1
if nbf_atm_l > nbf_ano_l > 0:
# For angular l, first place the projected ANO, then the rest AOs.
sdiag = reduce(
numpy.dot,
(rm_ano[:, idx].T, s0, rm_ano[:, idx])).diagonal()
nleft = (nbf_atm_l - nbf_ano_l) // degen
shell_average = numpy.einsum('ij->i', sdiag.reshape(-1, degen))
shell_rest = numpy.argsort(-shell_average)[:nleft]
idx_rest = []
for k in shell_rest:
idx_rest.extend(idx[k * degen:(k + 1) * degen])
c[:, idx[:nbf_ano_l]] = ano[:, idxp]
c[:, idx[nbf_ano_l:]] = rm_ano[:, idx_rest]
elif nbf_ano_l >= nbf_atm_l > 0: # More ANOs than the mol basis functions
c[:, idx] = ano[:, idxp[:nbf_atm_l]]
sdiag = numpy.einsum('pi,pq,qi->i', c, s0, c)
c *= 1. / numpy.sqrt(sdiag)
aos[symb] = c
nao = mol.nao_nr()
c = numpy.zeros((nao, nao))
p1 = 0
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
if symb in mol._basis:
ano = aos[symb]
else:
ano = aos[mol.atom_pure_symbol(ia)]
p0, p1 = p1, p1 + ano.shape[1]
c[p0:p1, p0:p1] = ano
return c