def multipoles1(r, lmax, reorder_dipole=True):
ngrid = r.shape[0]
xs = numpy.ones((lmax+1,ngrid))
ys = numpy.ones((lmax+1,ngrid))
zs = numpy.ones((lmax+1,ngrid))
for i in range(1,lmax+1):
xs[i] = xs[i-1] * r[:,0]
ys[i] = ys[i-1] * r[:,1]
zs[i] = zs[i-1] * r[:,2]
ylms = []
for l in range(lmax+1):
nd = (l+1)*(l+2)//2
c = numpy.empty((nd,3,ngrid))
k = 0
for lx in reversed(range(0, l+1)):
for ly in reversed(range(0, l-lx+1)):
lz = l - lx - ly
c[k,0] = lx * xs[lx-1] * ys[ly] * zs[lz]
c[k,1] = ly * xs[lx] * ys[ly-1] * zs[lz]
c[k,2] = lz * xs[lx] * ys[ly] * zs[lz-1]
k += 1
ylm = gto.cart2sph(l, c.reshape(nd,3*ngrid).T)
ylm = ylm.reshape(3,ngrid,l*2+1).transpose(0,2,1)
ylms.append(ylm)
# when call libcint, p functions are ordered as px,py,pz
# reorder px,py,pz to p(-1),p(0),p(1)
if (not reorder_dipole) and lmax >= 1:
ylms[1] = ylms[1][:,[1,2,0]]
return ylms
def write_mo(fout, mol, mo_coeff, mo_energy=None, mo_occ=None):
nmo = mo_coeff.shape[1]
mo_cart = []
centers = []
types = []
exps = []
p0 = 0
for ib in range(mol.nbas):
ia = mol.bas_atom(ib)
l = mol.bas_angular(ib)
es = mol.bas_exp(ib)
c = mol.bas_ctr_coeff(ib)
np, nc = c.shape
nd = nc * (2 * l + 1)
mosub = mo_coeff[p0:p0 + nd].reshape(-1, nc, nmo)
c2s = gto.cart2sph(l)
mosub = numpy.einsum('yki,cy,pk->pci', mosub, c2s, c)
mo_cart.append(mosub.reshape(-1, nmo))
for t in TYPE_MAP[l]:
types.append([t] * np)
ncart = gto.len_cart(l)
exps.extend([es] * ncart)
centers.extend([ia + 1] * (np * ncart))
p0 += nd
mo_cart = numpy.vstack(mo_cart)
centers = numpy.hstack(centers)
types = numpy.hstack(types)
exps = numpy.hstack(exps)
nprim, nmo = mo_cart.shape
fout.write('title line\n')
fout.write(
'GAUSSIAN %3d MOL ORBITALS %3d PRIMITIVES %3d NUCLEI\n'
% (mo_cart.shape[1], mo_cart.shape[0], mol.natm))
for ia in range(mol.natm):
x, y, z = mol.atom_coord(ia)
fout.write(
'%-4s %-4d (CENTRE%3d) %12.8f %12.8f %12.8f CHARGE = %.1f\n' %
(mol.atom_pure_symbol(ia), ia, ia, x, y, z, mol.atom_charge(ia)))
for i0, i1 in lib.prange(0, nprim, 20):
fout.write('CENTRE ASSIGNMENTS %s\n' %
''.join('%3d' % x for x in centers[i0:i1]))
for i0, i1 in lib.prange(0, nprim, 20):
fout.write('TYPE ASSIGNMENTS %s\n' % ''.join('%3d' % x
for x in types[i0:i1]))
for i0, i1 in lib.prange(0, nprim, 5):
fout.write('EXPONENTS %s\n' % ' '.join('%14.7E' % x
for x in exps[i0:i1]))
for k in range(nmo):
mo = mo_cart[:, k]
if mo_energy is None or mo_occ is None:
fout.write('CANMO %d\n' (k, mo_occ[k], mo_energy[k]))
else:
fout.write(
'MO %-4d OCC NO = %12.8f ORB. ENERGY = %12.8f\n'
% (k, mo_occ[k], mo_energy[k]))
for i0, i1 in lib.prange(0, nprim, 5):
fout.write('%s\n' % ' '.join('%15.8E' % x for x in mo[i0:i1]))
def multipoles1(r, lmax, reorder_dipole=True):
ngrid = r.shape[0]
xs = numpy.ones((lmax+1,ngrid))
ys = numpy.ones((lmax+1,ngrid))
zs = numpy.ones((lmax+1,ngrid))
for i in range(1,lmax+1):
xs[i] = xs[i-1] * r[:,0]
ys[i] = ys[i-1] * r[:,1]
zs[i] = zs[i-1] * r[:,2]
ylms = []
for l in range(lmax+1):
nd = (l+1)*(l+2)//2
c = numpy.empty((nd,3,ngrid))
k = 0
for lx in reversed(range(0, l+1)):
for ly in reversed(range(0, l-lx+1)):
lz = l - lx - ly
c[k,0] = lx * xs[lx-1] * ys[ly] * zs[lz]
c[k,1] = ly * xs[lx] * ys[ly-1] * zs[lz]
c[k,2] = lz * xs[lx] * ys[ly] * zs[lz-1]
k += 1
ylm = gto.cart2sph(l, c.reshape(nd,3*ngrid).T)
ylm = ylm.reshape(3,ngrid,l*2+1).transpose(0,2,1)
ylms.append(ylm)
# when call libcint, p functions are ordered as px,py,pz
# reorder px,py,pz to p(-1),p(0),p(1)
if (not reorder_dipole) and lmax >= 1:
ylms[1] = ylms[1][:,[1,2,0]]
return ylms
def write_mo(fout, mol, mo_coeff, mo_energy=None, mo_occ=None):
nmo = mo_coeff.shape[1]
mo_cart = []
centers = []
types = []
exps = []
p0 = 0
for ib in range(mol.nbas):
ia = mol.bas_atom(ib)
l = mol.bas_angular(ib)
es = mol.bas_exp(ib)
c = mol.bas_ctr_coeff(ib)
np, nc = c.shape
nd = nc*(2*l+1)
mosub = mo_coeff[p0:p0+nd].reshape(-1,nc,nmo)
c2s = gto.cart2sph(l)
mosub = numpy.einsum('yki,cy,pk->pci', mosub, c2s, c)
mo_cart.append(mosub.reshape(-1,nmo))
for t in TYPE_MAP[l]:
types.append([t]*np)
ncart = gto.len_cart(l)
exps.extend([es]*ncart)
centers.extend([ia+1]*(np*ncart))
p0 += nd
mo_cart = numpy.vstack(mo_cart)
centers = numpy.hstack(centers)
types = numpy.hstack(types)
exps = numpy.hstack(exps)
nprim, nmo = mo_cart.shape
fout.write('title line\n')
fout.write('GAUSSIAN %3d MOL ORBITALS %3d PRIMITIVES %3d NUCLEI\n'
% (mo_cart.shape[1], mo_cart.shape[0], mol.natm))
for ia in range(mol.natm):
x, y, z = mol.atom_coord(ia)
fout.write('%-4s %-4d (CENTRE%3d) %12.8f %12.8f %12.8f CHARGE = %.1f\n'
% (mol.atom_pure_symbol(ia), ia, ia, x, y, z,
mol.atom_charge(ia)))
for i0, i1 in lib.prange(0, nprim, 20):
fout.write('CENTRE ASSIGNMENTS %s\n' % ''.join('%3d'%x for x in centers[i0:i1]))
for i0, i1 in lib.prange(0, nprim, 20):
fout.write('TYPE ASSIGNMENTS %s\n' % ''.join('%3d'%x for x in types[i0:i1]))
for i0, i1 in lib.prange(0, nprim, 5):
fout.write('EXPONENTS %s\n' % ' '.join('%14.7E'%x for x in exps[i0:i1]))
for k in range(nmo):
mo = mo_cart[:,k]
if mo_energy is None or mo_occ is None:
fout.write('CANMO %d\n'
(k, mo_occ[k], mo_energy[k]))
else:
fout.write('MO %-4d OCC NO = %12.8f ORB. ENERGY = %12.8f\n' %
(k, mo_occ[k], mo_energy[k]))
for i0, i1 in lib.prange(0, nprim, 5):
fout.write('%s\n' % ' '.join('%15.8E'%x for x in mo[i0:i1]))
def multipoles(r, lmax, reorder_dipole=True):
'''
Compute all multipoles upto lmax
rad = numpy.linalg.norm(r, axis=1)
ylms = real_ylm(r/rad.reshape(-1,1), lmax)
pol = [rad**l*y for l, y in enumerate(ylms)]
Kwargs:
reorder_p : bool
sort dipole to the order (x,y,z)
'''
from pyscf import gto
# libcint cart2sph transformation provide the capability to compute
# multipole directly. cart2sph function is fast for low angular moment.
ngrid = r.shape[0]
xs = numpy.ones((lmax + 1, ngrid))
ys = numpy.ones((lmax + 1, ngrid))
zs = numpy.ones((lmax + 1, ngrid))
for i in range(1, lmax + 1):
xs[i] = xs[i - 1] * r[:, 0]
ys[i] = ys[i - 1] * r[:, 1]
zs[i] = zs[i - 1] * r[:, 2]
ylms = []
for l in range(lmax + 1):
nd = (l + 1) * (l + 2) // 2
c = numpy.empty((nd, ngrid))
k = 0
for lx in reversed(range(0, l + 1)):
for ly in reversed(range(0, l - lx + 1)):
lz = l - lx - ly
c[k] = xs[lx] * ys[ly] * zs[lz]
k += 1
ylm = gto.cart2sph(l, c.T).T
ylms.append(ylm)
# when call libcint, p functions are ordered as px,py,pz
# reorder px,py,pz to p(-1),p(0),p(1)
if (not reorder_dipole) and lmax >= 1:
ylms[1] = ylms[1][[1, 2, 0]]
return ylms
def write_coeff(fout, mol, mo_coeff):
#fout.write('ALDET\n')
nmo = mo_coeff.shape[1]
mo_cart = []
centers = []
types = []
exps = []
p0 = 0
for ib in range(mol.nbas):
ia = mol.bas_atom(ib)
l = mol.bas_angular(ib)
es = mol.bas_exp(ib)
c = mol._libcint_ctr_coeff(ib)
#c = mol.bas_ctr_coeff(ib)
np, nc = c.shape
nd = nc*(2*l+1)
mosub = mo_coeff[p0:p0+nd].reshape(-1,nc,nmo)
c2s = gto.cart2sph(l)
mosub = numpy.einsum('yki,cy,pk->pci', mosub, c2s, c)
mo_cart.append(mosub.transpose(1,0,2).reshape(-1,nmo))
for t in TYPE_MAP[l]:
types.append([t]*np)
ncart = gto.len_cart(l)
exps.extend([es]*ncart)
centers.extend([ia+1]*(np*ncart))
p0 += nd
mo_cart = numpy.vstack(mo_cart)
centers = numpy.hstack(centers)
types = numpy.hstack(types)
exps = numpy.hstack(exps)
nprim, nmo = mo_cart.shape
fout.write('From PySCF\n')
for k in range(nmo):
mo = mo_cart[:,k]
fout.write('CANMO %d\n' % (k+1))
for i0, i1 in lib.prange(0, nprim, 5):
fout.write(' %s\n' % ' '.join('%15.8E'%x for x in mo[i0:i1]))
fout.write('END DATA\n')
def mo_comps(test, mol, mo_coeff, cart=False, orth_method='meta_lowdin'):
'''Pick particular AOs based on the given test function
compute the AO components
'''
if cart:
s = mol.intor_symmetric('cint1e_ovlp_cart')
preao = lo.orth.pre_orth_ao(mol)
tc2s = []
for ib in range(mol.nbas):
l = mol.bas_angular(ib)
tc2s.append(gto.cart2sph(l))
tc2s = scipy.linalg.block_diag(*tc2s)
lao = lo.orth.orth_ao(mol, orth_method)
lao = numpy.dot(tc2s, lao)
else:
s = mol.intor_symmetric('cint1e_ovlp_sph')
lao = lo.orth.orth_ao(mol, orth_method)
idx = [i for i,x in enumerate(mol.spheric_labels(1)) if test(x)]
idx = numpy.array(idx)
mo1 = reduce(numpy.dot, (lao[:,idx].T, s, mo_coeff))
s1 = numpy.einsum('ki,ki->i', mo1, mo1)
return s1
def write_mo(fout, mol, mo_coeff, mo_energy=None, mo_occ=None):
if mol.cart:
raise NotImplementedError('Cartesian basis not available')
#FIXME: Duplicated primitives may lead to problems. x2c._uncontract_mol
# is the workaround at the moment to remove duplicated primitives.
from pyscf.x2c import x2c
mol, ctr = x2c._uncontract_mol(mol, True, 0.)
mo_coeff = numpy.dot(ctr, mo_coeff)
nmo = mo_coeff.shape[1]
mo_cart = []
centers = []
types = []
exps = []
p0 = 0
for ib in range(mol.nbas):
ia = mol.bas_atom(ib)
l = mol.bas_angular(ib)
es = mol.bas_exp(ib)
c = mol._libcint_ctr_coeff(ib)
np, nc = c.shape
nd = nc*(2*l+1)
mosub = mo_coeff[p0:p0+nd].reshape(-1,nc,nmo)
c2s = gto.cart2sph(l)
mosub = numpy.einsum('yki,cy,pk->pci', mosub, c2s, c)
mo_cart.append(mosub.transpose(1,0,2).reshape(-1,nmo))
for t in TYPE_MAP[l]:
types.append([t]*np)
ncart = mol.bas_len_cart(ib)
exps.extend([es]*ncart)
centers.extend([ia+1]*(np*ncart))
p0 += nd
mo_cart = numpy.vstack(mo_cart)
centers = numpy.hstack(centers)
types = numpy.hstack(types)
exps = numpy.hstack(exps)
nprim, nmo = mo_cart.shape
fout.write('From PySCF\n')
fout.write('GAUSSIAN %3d MOL ORBITALS %3d PRIMITIVES %3d NUCLEI\n'
% (mo_cart.shape[1], mo_cart.shape[0], mol.natm))
for ia in range(mol.natm):
x, y, z = mol.atom_coord(ia)
fout.write(' %-4s %-4d (CENTRE%3d) %11.8f %11.8f %11.8f CHARGE = %.1f\n'
% (mol.atom_pure_symbol(ia), ia+1, ia+1, x, y, z,
mol.atom_charge(ia)))
for i0, i1 in lib.prange(0, nprim, 20):
fout.write('CENTRE ASSIGNMENTS %s\n' % ''.join('%3d'%x for x in centers[i0:i1]))
for i0, i1 in lib.prange(0, nprim, 20):
fout.write('TYPE ASSIGNMENTS %s\n' % ''.join('%3d'%x for x in types[i0:i1]))
for i0, i1 in lib.prange(0, nprim, 5):
fout.write('EXPONENTS %s\n' % ' '.join('%13.7E'%x for x in exps[i0:i1]))
for k in range(nmo):
mo = mo_cart[:,k]
if mo_energy is None and mo_occ is None:
fout.write('CANMO %d\n' % (k+1))
elif mo_energy is None:
fout.write('MO %-4d OCC NO = %12.8f ORB. ENERGY = 0.0000\n' %
(k+1, mo_occ[k]))
else:
fout.write('MO %-4d OCC NO = %12.8f ORB. ENERGY = %12.8f\n' %
(k+1, mo_occ[k], mo_energy[k]))
for i0, i1 in lib.prange(0, nprim, 5):
fout.write(' %s\n' % ' '.join('%15.8E'%x for x in mo[i0:i1]))
fout.write('END DATA\n')
if mo_energy is None or mo_occ is None:
fout.write('ALDET ENERGY = 0.0000000000 VIRIAL(-V/T) = 0.00000000\n')
elif mo_energy is None and mo_occ is None:
pass
else :
fout.write('RHF ENERGY = 0.0000000000 VIRIAL(-V/T) = 0.00000000\n')
def write_wfn(fout, mol, mo_coeff, mo_energy, mo_occ, tot_ener):
from pyscf.x2c import x2c
mol, ctr = x2c._uncontract_mol(mol, True, 0.)
mo_coeff = numpy.dot(ctr, mo_coeff)
nmo = mo_coeff.shape[1]
mo_cart = []
from pyscf import gto
centers = []
types = []
exps = []
p0 = 0
for ib in range(mol.nbas):
ia = mol.bas_atom(ib)
l = mol.bas_angular(ib)
es = mol.bas_exp(ib)
c = mol._libcint_ctr_coeff(ib)
np, nc = c.shape
nd = nc * (2 * l + 1)
mosub = mo_coeff[p0:p0 + nd].reshape(-1, nc, nmo)
c2s = gto.cart2sph(l)
mosub = numpy.einsum('yki,cy,pk->pci', mosub, c2s, c)
mo_cart.append(mosub.transpose(1, 0, 2).reshape(-1, nmo))
for t in TYPE_MAP[l]:
types.append([t] * np)
ncart = mol.bas_len_cart(ib)
exps.extend([es] * ncart)
centers.extend([ia + 1] * (np * ncart))
p0 += nd
mo_cart = numpy.vstack(mo_cart)
centers = numpy.hstack(centers)
types = numpy.hstack(types)
exps = numpy.hstack(exps)
nprim, nmo = mo_cart.shape
fout.write('From PySCF\\n')
fout.write('GAUSSIAN %14d MOL ORBITALS %6d PRIMITIVES %8d NUCLEI\\n' %
(mo_cart.shape[1], mo_cart.shape[0], mol.natm))
for ia in range(mol.natm):
x, y, z = mol.atom_coord(ia)
fout.write('%3s%8d (CENTRE%3d) %12.8f%12.8f%12.8f CHARGE = %4.1f\\n' %
(mol.atom_pure_symbol(ia), ia + 1, ia + 1, x, y, z,
mol.atom_charge(ia)))
for i0, i1 in lib.prange(0, nprim, 20):
fout.write('CENTRE ASSIGNMENTS %s\\n' %
''.join('%3d' % x for x in centers[i0:i1]))
for i0, i1 in lib.prange(0, nprim, 20):
fout.write('TYPE ASSIGNMENTS %s\\n' %
''.join('%3d' % x for x in types[i0:i1]))
for i0, i1 in lib.prange(0, nprim, 5):
fout.write('EXPONENTS %s\\n' % ' '.join('%13.7E' % x
for x in exps[i0:i1]))
for k in range(nmo):
mo = mo_cart[:, k]
fout.write(
'MO %-12d OCC NO = %12.8f ORB. ENERGY = %12.8f\\n' %
(k + 1, mo_occ[k], mo_energy[k]))
for i0, i1 in lib.prange(0, nprim, 5):
fout.write(' %s\\n' % ' '.join('%15.8E' % x for x in mo[i0:i1]))
fout.write('END DATA\\n')
fout.write(' THE SCF ENERGY =%20.12f THE VIRIAL(-V/T)= 0.00000000\\n' %
tot_ener)
def mo_comps(test_or_idx,
mol,
mo_coeff,
cart=False,
orth_method='meta_lowdin'):
'''Pick particular AOs based on the given test function to compute the AO
contributions for each MO
Args:
test_or_idx : filter function or list
If test_or_idx is a list, it is considered as the AO indices.
If it's a function, the AO indices are the items for which the
function value is true.
Kwargs:
cart : bool
whether the orbital coefficients are based on cartesian basis.
orth_method : str
The localization method to generated orthogonal AO upon which the AO
contribution are computed. It can be one of 'meta_lowdin',
'lowdin' or 'nao'.
Returns:
A list of float to indicate the total contributions (normalized to 1) of
localized AOs
Examples:
>>> from pyscf import gto, scf
>>> from pyscf.tools import mo_mapping
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='6-31g')
>>> mf = scf.RHF(mol).run()
>>> comp = mo_mapping.mo_comps(lambda x: 'F 2s' in x, mol, mf.mo_coeff)
>>> print('MO-id components')
>>> for i in enumerate(comp):
... print('%-3d %.10f' % (i, comp[i]))
MO-id components
0 0.0000066344
1 0.8796915532
2 0.0590259826
3 0.0000000000
4 0.0000000000
5 0.0435028851
6 0.0155889103
7 0.0000000000
8 0.0000000000
9 0.0000822361
10 0.0021017982
'''
if cart:
s = mol.intor_symmetric('cint1e_ovlp_cart')
preao = lo.orth.pre_orth_ao(mol)
tc2s = []
for ib in range(mol.nbas):
l = mol.bas_angular(ib)
t = gto.cart2sph(l)
for i in range(mol.bas_nctr(ib)):
tc2s.append(t)
tc2s = scipy.linalg.block_diag(*tc2s)
lao = lo.orth.orth_ao(mol, orth_method)
lao = numpy.dot(tc2s, lao)
else:
s = mol.intor_symmetric('cint1e_ovlp_sph')
lao = lo.orth.orth_ao(mol, orth_method)
if callable(test_or_idx):
idx = [
i for i, x in enumerate(mol.spheric_labels(1)) if test_or_idx(x)
]
else:
idx = numpy.asarray(test_or_idx, dtype=int)
if len(idx) == 0:
logger.warn(mol, 'Required orbitals are not found')
mo1 = reduce(numpy.dot, (lao[:, idx].T, s, mo_coeff))
s1 = numpy.einsum('ki,ki->i', mo1, mo1)
return s1
def mo_comps(test_or_idx, mol, mo_coeff, cart=False, orth_method='meta_lowdin'):
'''Pick particular AOs based on the given test function to compute the AO
contributions for each MO
Args:
test_or_idx : filter function or 1D array
If test_or_idx is a list, it is considered as the AO indices.
If it's a function, the AO indices are the items for which the
function value is true.
Kwargs:
cart : bool
whether the orbital coefficients are based on cartesian basis.
orth_method : str
The localization method to generated orthogonal AO upon which the AO
contribution are computed. It can be one of 'meta_lowdin',
'lowdin' or 'nao'.
Returns:
A list of float to indicate the total contributions (normalized to 1) of
localized AOs
Examples:
>>> from pyscf import gto, scf
>>> from pyscf.tools import mo_mapping
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='6-31g')
>>> mf = scf.RHF(mol).run()
>>> comp = mo_mapping.mo_comps(lambda x: 'F 2s' in x, mol, mf.mo_coeff)
>>> print('MO-id components')
>>> for i in enumerate(comp):
... print('%-3d %.10f' % (i, comp[i]))
MO-id components
0 0.0000066344
1 0.8796915532
2 0.0590259826
3 0.0000000000
4 0.0000000000
5 0.0435028851
6 0.0155889103
7 0.0000000000
8 0.0000000000
9 0.0000822361
10 0.0021017982
'''
if cart:
s = mol.intor_symmetric('cint1e_ovlp_cart')
preao = lo.orth.pre_orth_ao(mol)
tc2s = []
for ib in range(mol.nbas):
l = mol.bas_angular(ib)
tc2s.append(gto.cart2sph(l))
tc2s = scipy.linalg.block_diag(*tc2s)
lao = lo.orth.orth_ao(mol, orth_method)
lao = numpy.dot(tc2s, lao)
else:
s = mol.intor_symmetric('cint1e_ovlp_sph')
lao = lo.orth.orth_ao(mol, orth_method)
if callable(test):
idx = [i for i,x in enumerate(mol.spheric_labels(1)) if test(x)]
else:
idx = test
idx = numpy.asarray(idx)
mo1 = reduce(numpy.dot, (lao[:,idx].T, s, mo_coeff))
s1 = numpy.einsum('ki,ki->i', mo1, mo1)
return s1