def show_symmetry_species(self):
if msym is None:
raise ImportError('no libmsym installation found')
bs = self.basis_set
elements = [msym.Element(coordinates = Coord, charge = int(Charge))
for Coord, Charge in zip(bs.center_coordinates, bs.center_charges)]
basis_functions = [msym.RealSphericalHarmonic(element = elements[element_id-1], n = n + l, l = l, m = m)
for [element_id, n, l, m] in bs.contracted_ids]
with msym.Context(elements = elements, basis_functions = basis_functions) as ctx:
point_group = ctx.find_symmetry()
species_names = [s.name for s in ctx.character_table.symmetry_species]
coefficients = np.asarray(self.coefficients)
for offset in range(0,self.n_orb):
mo = coefficients[:,offset]
#mo /= np.linalg.norm(mo)
species_components = ctx.symmetry_species_components(mo)
print(offset,': ',' + '.join(['%f %s' % k for k in zip(species_components, species_names) if k[0] > 1.0e-6]))
def symmetrize(self):
""" Symmetrizes the wavefunction """
if msym is None:
raise ImportError('no libmsym installation found')
bs = self.basis_set
elements = [msym.Element(coordinates = Coord, charge = int(Charge))
for Coord, Charge in zip(bs.center_coordinates, bs.center_charges)]
basis_functions = [msym.RealSphericalHarmonic(element = elements[element_id-1], n = n + l, l = l, m = m)
for [element_id, n, l, m] in bs.contracted_ids]
Smat_ao = np.asmatrix(self.basis_set.overlap)
symorb = {}
with msym.Context(elements = elements, basis_functions = basis_functions) as ctx:
point_group = ctx.find_symmetry()
species = ctx.character_table.symmetry_species
species_names = [s.name for s in species]
for kind in self.mo.keys():
# remove overlap
C_mo = np.asmatrix(self.mo[kind].coefficients)
s,U = np.linalg.eigh(C_mo.T*C_mo)
U_lowdin = U * np.diag(1/np.sqrt(s)) * U.T
C_mo = C_mo * U_lowdin
(salcs, species, partner_functions) = ctx.symmetrize_wavefunctions(C_mo.T)
# orthonormalize
s,U = np.linalg.eigh(salcs * Smat_ao * salcs.T)
U_lowdin = U * np.diag(1/np.sqrt(s)) * U.T
C_mo = C_mo * U_lowdin
symorb[kind] = OrbitalSet(C_mo,
energies=self.mo[kind].energies,
irreps=self.mo[kind].irreps,
basis_set=self.mo[kind].basis_set)
return Wavefunction(symorb, self.basis_set, n_sym=self.n_sym, n_bas=self.n_bas)
def set_basis(element, name="1s"):
basis_function = msym.RealSphericalHarmonic(element=element, name=name)
element.basis_functions = [basis_function]
return basis_function
def salcorb(self, kind='restricted'):
"""
generate a set of initial molecular orbitals from SALCs
"""
if msym is None:
raise ImportError('no libmsym installation found')
symorb = {}
Smat_ao = np.asmatrix(self.basis_set.overlap)
Fmat_ao = np.asmatrix(self.basis_set.fockint)
bs = self.basis_set
elements = [msym.Element(coordinates = Coord, charge = int(Charge))
for Coord, Charge in zip(bs.center_coordinates, bs.center_charges)]
basis_functions = [msym.RealSphericalHarmonic(element = elements[element_id-1], n = n + l, l = l, m = m)
for [element_id, n, l, m] in bs.contracted_ids]
E_salcs = np.empty(len(basis_functions))
supsym = np.empty(len(basis_functions), dtype=np.int_)
with msym.Context(elements = elements, basis_functions = basis_functions) as ctx:
point_group = ctx.find_symmetry()
species_names = [s.name for s in ctx.character_table.symmetry_species]
(C_salcs, salc_species, partner_functions) = ctx.salcs
C_salcs = C_salcs.T
salc_components = np.array([pf.dim for pf in partner_functions])
salc_sc = [(s, np.sort(np.unique(salc_components[salc_species == s]))) for s in np.unique(salc_species)]
salc_sci = {}
for (species, components) in salc_sc:
salc_sci.update({(species,c):len(salc_sci) + i for i, c in enumerate(components)})
comp_head, *comp_tail = components
select_species = species == salc_species
select_comp = {c:np.where(np.all([select_species, salc_components == c], axis=0))[0] for c in components}
Cmat = {c:C_salcs[:,select_comp[c]] for c in components}
Smat_mo = Cmat[comp_head].T * Smat_ao * Cmat[comp_head]
# average out symmetry breaking in overlap
for component in comp_tail:
Smat_mo += Cmat[component].T * Smat_ao * Cmat[component]
Smat_mo /= len(components)
# orthonormalize overlap
s,U = np.linalg.eigh(Smat_mo)
U_lowdin = U * np.diag(1/np.sqrt(s)) * U.T
for component in components:
Cmat[component] = Cmat[component] * U_lowdin
# average out symmetry breaking in metric Fock
Fmat_mo = Cmat[comp_head].T * Smat_ao.T * Fmat_ao * Smat_ao * Cmat[comp_head]
for component in comp_tail:
Fmat_mo += Cmat[component].T * Smat_ao.T * Fmat_ao * Smat_ao * Cmat[component]
Fmat_mo /= len(components)
# diagonalize metric Fock
f,U = np.linalg.eigh(Fmat_mo)
for component in components:
Cmat[component] = Cmat[component] * U
# update components, energies and supsym
select = select_comp[component]
supsym[select] = salc_sci[(species,component)]
C_salcs[:,select] = Cmat[component]
E_salcs[select] = f
salc_order = np.argsort(E_salcs)
for kind in self.mo.keys():
symorb[kind] = OrbitalSet(C_salcs[:,salc_order],
energies=E_salcs[salc_order],
irreps=supsym[salc_order],
basis_set=self.mo[kind].basis_set)
return Wavefunction(symorb, self.basis_set, n_sym=self.n_sym, n_bas=self.n_bas)