def loc_orbs(mol: gto.Mole, mo_coeff: Tuple[np.ndarray, np.ndarray], \
s: np.ndarray, ref: str, variant: str) -> np.ndarray:
"""
this function returns a set of localized MOs of a specific variant
"""
# loop over spins
for i, spin_mo in enumerate((mol.alpha, mol.beta)):
if variant == 'fb':
# foster-boys procedure
loc = lo.Boys(mol, mo_coeff[i][:, spin_mo])
loc.conv_tol = LOC_CONV
# FB MOs
mo_coeff[i][:, spin_mo] = loc.kernel()
elif variant == 'pm':
# pipek-mezey procedure
loc = lo.PM(mol, mo_coeff[i][:, spin_mo])
loc.conv_tol = LOC_CONV
# PM MOs
mo_coeff[i][:, spin_mo] = loc.kernel()
elif 'ibo' in variant:
# orthogonalized IAOs
iao = lo.iao.iao(mol, mo_coeff[i][:, spin_mo])
iao = lo.vec_lowdin(iao, s)
# IBOs
mo_coeff[i][:, spin_mo] = lo.ibo.ibo(mol, mo_coeff[i][:, spin_mo], iaos=iao, \
grad_tol = LOC_CONV, exponent=int(variant[-1]), verbose=0)
# closed-shell reference
if ref == 'restricted' and mol.spin == 0:
mo_coeff[i + 1][:, spin_mo] = mo_coeff[i][:, spin_mo]
break
return mo_coeff
def make_separate_spin_iaos(cell, mf, mos, iao_basis="minao"):
""" Make IAOs for up and down MOs separately for all k points.
Args:
cell (PySCF cell): Cell for the calculation.
mf (PySCF UKS or UHF object): Contains the MOs information.
mos (array): indices of the MOs to use to make the IAOs.
basis (basis): IAO basis desired (in PySCF format).
Returns:
iaos_all (list): each list entry is np array of IAO orbitals
in the basis of cell for a given k point.
"""
# print("Making combined spin-up and spin-dw IAOs...")
ovlp = mf.get_ovlp()
coefs = np.array(mf.mo_coeff)[:, :, mos]
iaos_up = lo.iao.iao(cell, coefs[0], minao=iao_basis)
iaos_up = lo.vec_lowdin(iaos_up, ovlp)
iaos_down = lo.iao.iao(cell, coefs[1], minao=iao_basis)
iaos_down = lo.vec_lowdin(iaos_down, ovlp)
return np.array([iaos_up, iaos_down])
def localizeValence(mf, mo_coeff, method="iao"):
if (method == "iao"):
return iao.iao(mf.mol, mo_coeff)
elif (method == "ibo"):
a = iao.iao(mf.mol, mo_coeff)
a = lo.vec_lowdin(a, mf.get_ovlp())
return ibo.ibo(mf.mol, mo_coeff, iaos=a)
elif (method == "boys"):
return boys.Boys(mf.mol).kernel(mo_coeff)
elif (method == "er"):
return edmiston.ER(mf.mol).kernel(mo_coeff)
def gen_basis(mol, mf, obdm, threshold=1e-2):
"""From an obdm, use IAOs to generate a minimal atomic basis for a given state """
n = obdm.shape[0]
obdm *= n
w, v = np.linalg.eig(obdm)
keep = np.abs(w) > threshold
a = lo.orth_ao(mol, 'lowdin')
basis = np.dot(a, v[:, keep]).real
iao = lo.iao.iao(mol, basis)
iao = lo.vec_lowdin(iao, mf.get_ovlp())
return iao
def test_pbc(li_cubic_ccecp):
from pyqmc import supercell
import scipy
mol, mf = li_cubic_ccecp
# S = np.ones((3, 3)) - np.eye(3)
S = np.identity(3)
mol = supercell.get_supercell(mol, S)
kpts = supercell.get_supercell_kpts(mol)[:2]
kdiffs = mf.kpts[np.newaxis] - kpts[:, np.newaxis]
kinds = np.nonzero(np.linalg.norm(kdiffs, axis=-1) < 1e-12)[1]
# Lowdin orthogonalized AO basis.
# lowdin = lo.orth_ao(mol, "lowdin")
loiao = lo.iao.iao(mol.original_cell, mf.mo_coeff, kpts=kpts)
occs = [mf.mo_occ[k] for k in kinds]
coefs = [mf.mo_coeff[k] for k in kinds]
ovlp = mf.get_ovlp()[kinds]
lowdin = [lo.vec_lowdin(l, o) for l, o in zip(loiao, ovlp)]
lreps = [np.linalg.multi_dot([l.T, o, c]) for l, o, c in zip(lowdin, ovlp, coefs)]
# make AO to localized orbital coefficients.
mfobdm = [np.einsum("ij,j,kj->ik", l.conj(), o, l) for l, o in zip(lreps, occs)]
### Test OBDM calculation.
nconf = 500
nsteps = 100
warmup = 6
wf = Slater(mol, mf)
configs = initial_guess(mol, nconf)
obdm_dict = dict(mol=mol, orb_coeff=lowdin, kpts=kpts, nsweeps=4, warmup=10)
obdm = OBDMAccumulator(**obdm_dict)
df, coords = vmc(
wf,
configs,
nsteps=nsteps,
accumulators={"obdm": obdm}, # , "obdm_up": obdm_up, "obdm_down": obdm_down},
verbose=True,
)
obdm_est = {}
for k in ["obdm"]: # , "obdm_up", "obdm_down"]:
avg_norm = np.mean(df[k + "norm"][warmup:], axis=0)
avg_obdm = np.mean(df[k + "value"][warmup:], axis=0)
obdm_est[k] = normalize_obdm(avg_obdm, avg_norm)
mfobdm = scipy.linalg.block_diag(*mfobdm)
mae = np.mean(np.abs(obdm_est["obdm"] - mfobdm))
assert mae < 0.05, f"mae {mae}"
def localizeAllElectron(mf, method="lowdin"):
if (method == "lowdin"):
return fractional_matrix_power(mf.get_ovlp(), -0.5).T
elif (method == "pm"):
return pipek.PM(mf.mol).kernel(mf.mo_coeff)
elif (method == "boys"):
return boys.Boys(mf.mol).kernel(mf.mo_coeff)
elif (method == "er"):
return edmiston.ER(mf.mol).kernel(mf.mo_coeff)
elif (method == "iao"):
return iao.iao(mf.mol, mf.mo_coeff)
elif (method == "ibo"):
a = iao.iao(mf.mol, mf.mo_coeff)
a = lo.vec_lowdin(a, mf.get_ovlp())
return ibo.ibo(mf.mol, mf.mo_coeff, iaos=a)
def calcIAO(cell, mf, basis, occ):
'''
input:
cell and scf (PBC SCF) objects from pyscf and basis
to calculate IAOs on
occ is MOs which IAOs should span
output:
Calculates 1RDM on orthog atomic orbitals, orthogonalized
using Lowdin S^1/2
Returns coefficient matrix for IAOs
'''
s = mf.get_ovlp()[0]
mo_occ = mf.mo_coeff[0][0][:, occ[0]]
mo_occ2 = mf.mo_coeff[1][0][:, occ[1]]
mo_occ = np.concatenate((mo_occ, mo_occ2), axis=1)
a = lo.iao.iao(cell, mo_occ, minao=basis)
a = lo.vec_lowdin(a, s)
return a
def make_combined_spin_iaos(cell, mf, mos, iao_basis="minao"):
""" Make IAOs for up and down MOs together for all k points.
Args:
cell (PySCF cell): Cell for the calculation.
mf (PySCF UKS or UHF object): Contains the MOs information.
mos (array): indices of the MOs to use to make the IAOs.
basis (basis): IAO basis desired (in PySCF format).
Returns:
iaos_all (list): each list entry is np array of IAO orbitals
in the basis of cell for a given k point.
"""
# print("Making combined spin-up and spin-dw IAOs...")
ovlp = mf.get_ovlp()
# Concatenates the spin-up and the spin-down chosen MOs
coefs = np.array(mf.mo_coeff)[
:, :, mos
] # Notice that, unlike the KUHF case, here we do not need to transpose the matrix
coefs = np.concatenate([coefs[0].T, coefs[1].T]).T
iaos = lo.iao.iao(cell, coefs, minao=iao_basis)
iaos = lo.vec_lowdin(iaos, ovlp)
return np.array([iaos, iaos])
def make_minao_lo(ks, minao_ref):
"""
Construct minao local orbitals.
"""
cell = ks.cell
nao = cell.nao_nr()
kpts = ks.kpts
nkpts = len(kpts)
ovlp = ks.get_ovlp()
C_ao_minao, labels = proj_ref_ao(cell, minao=minao_ref, kpts=kpts,
return_labels=True)
for k in range(nkpts):
C_ao_minao[k] = lo.vec_lowdin(C_ao_minao[k], ovlp[k])
labels = np.asarray(labels)
C_ao_lo = np.zeros((nkpts, nao, nao), dtype=np.complex128)
for idx, lab in zip(ks.U_idx, ks.U_lab):
idx_minao = [i for i, l in enumerate(labels) if l in lab]
assert len(idx_minao) == len(idx)
C_ao_sub = C_ao_minao[:, :, idx_minao]
C_ao_lo[:, :, idx] = C_ao_sub
return C_ao_lo
cell.build()
cell.rcut *= 2
print("running intial DFT calc to generate IAOs")
mf = dft.RKS(cell)
mf.chkfile = 'graphene.chk'
mf.init_guess = 'chkfile'
mf.xc = 'pbe,pbe'
mf.kernel()
#we need to makVe the IAOs out of a converged calculation
print("generating IAOs")
mo_occ = mf.mo_coeff[:, mf.mo_occ > 0]
a = lo.iao.iao(cell, mo_occ)
# Orthogonalize IAO
a = lo.vec_lowdin(a, mf.get_ovlp())
#arbitrary parameters
offset = 0.0001
orbital = 4
print("running constrained dft")
mf = cdft(mf, mf.cell, offset, orbital, basis=a)
population = fast_iao_mullikan_pop(mf, a=a)
result = numpy.zeros(3)
result[0] = offset
result[1] = mf.e_tot
result[2] = population[0][4]
scaled_kpts = cell.get_scaled_kpts(abs_kpts)
kmf = pscf.KRHF(cell, abs_kpts).density_fit()
gdf = df.GDF(cell, abs_kpts)
kmf.with_df = gdf
kmf.checkfile = './ch4.chk'
kmf.verbose = 5
#kmf = pscf.KRHF(cell, abs_kpts)
#kmf.__dict__.update(scf.chkfile.load('ch4.chk', 'scf')) # test
ekpt = kmf.run()
kmf_sc = k2gamma(kmf, abs_kpts, kmesh, realize = False, tol_deg = 5e-5, real_split = False)
c_g_ao = kmf_sc.mo_coeff[0]
print "Supercell gamma MO in AO basis from conversion:"
print c_g_ao
mo_coeff_occ = kmf_sc.mo_coeff[0][:,kmf_sc.mo_occ[0]>0]
lo_iao = lo.iao.iao(kmf_sc.cell, mo_coeff_occ)
# Orthogonalize IAO
lo_iao = lo.vec_lowdin(lo_iao, kmf_sc.get_ovlp()[0])
# transform mo_occ to IAO representation. Note the AO dimension is reduced
mo_coeff_occ = reduce(np.dot, (lo_iao.conj().T, kmf_sc.get_ovlp()[0], mo_coeff_occ))
dm = np.dot(mo_coeff_occ, mo_coeff_occ.conj().T) * 2
pmol = kmf_sc.cell.copy()
pmol.build(False, False, basis='minao')
kmf_sc.mulliken_pop(pmol, dm, s=np.eye(pmol.nao_nr()))
cell.build()
cell.rcut*=2
print("running intial DFT calc to generate IAOs")
mf = dft.RKS(cell)
mf.chkfile = 'graphene.chk'
mf.init_guess = 'chkfile'
mf.xc = 'pbe,pbe'
mf.kernel()
#we need to makVe the IAOs out of a converged calculation
print("generating IAOs")
mo_occ = mf.mo_coeff[:,mf.mo_occ>0]
a = lo.iao.iao(cell, mo_occ)
# Orthogonalize IAO
a = lo.vec_lowdin(a, mf.get_ovlp())
#arbitrary parameters
offset = 0.0001
orbital =4
print("running constrained dft")
mf = cdft(mf,mf.cell,offset,orbital,basis=a)
population = fast_iao_mullikan_pop(mf,a=a)
result = numpy.zeros(3)
result[0] = offset
result[1] = mf.e_tot
result[2] = population[0][4]
def init(self,molecule,charge,spin,basis_set,orb_basis='scf',cas=False,cas_nstart=None,cas_nstop=None,cas_nel=None,loc_nstart=None,loc_nstop=None,
scf_conv_tol=1e-14):
# {{{
import pyscf
from pyscf import gto, scf, ao2mo, molden, lo
pyscf.lib.num_threads(1) #with degenerate states and multiple processors there can be issues
#PYSCF inputs
print(" ---------------------------------------------------------")
print(" Using Pyscf:")
print(" ---------------------------------------------------------")
print(" ")
mol = gto.Mole()
mol.atom = molecule
mol.max_memory = 1000 # MB
mol.symmetry = True
mol.charge = charge
mol.spin = spin
mol.basis = basis_set
mol.build()
print("symmertry")
print(mol.topgroup)
#SCF
#mf = scf.RHF(mol).run(init_guess='atom')
mf = scf.RHF(mol).run(conv_tol=scf_conv_tol)
#C = mf.mo_coeff #MO coeffs
enu = mf.energy_nuc()
print(" SCF Total energy: %12.8f" %mf.e_tot)
print(" SCF Elec energy: %12.8f" %(mf.e_tot-enu))
print(mf.get_fock())
print(np.linalg.eig(mf.get_fock())[0])
if mol.symmetry == True:
from pyscf import symm
mo = symm.symmetrize_orb(mol, mf.mo_coeff)
osym = symm.label_orb_symm(mol, mol.irrep_name, mol.symm_orb, mo)
#symm.addons.symmetrize_space(mol, mo, s=None, check=True, tol=1e-07)
for i in range(len(osym)):
print("%4d %8s %16.8f"%(i+1,osym[i],mf.mo_energy[i]))
#orbitals and lectrons
n_orb = mol.nao_nr()
n_b , n_a = mol.nelec
nel = n_a + n_b
self.n_orb = mol.nao_nr()
if cas == True:
cas_norb = cas_nstop - cas_nstart
from pyscf import mcscf
assert(cas_nstart != None)
assert(cas_nstop != None)
assert(cas_nel != None)
else:
cas_nstart = 0
cas_nstop = n_orb
cas_nel = nel
##AO 2 MO Transformation: orb_basis or scf
if orb_basis == 'scf':
print("\nUsing Canonical Hartree Fock orbitals...\n")
C = cp.deepcopy(mf.mo_coeff)
print("C shape")
print(C.shape)
elif orb_basis == 'lowdin':
assert(cas == False)
S = mol.intor('int1e_ovlp_sph')
print("Using lowdin orthogonalized orbitals")
C = lowdin(S)
#end
elif orb_basis == 'boys':
pyscf.lib.num_threads(1) #with degenerate states and multiple processors there can be issues
cl_c = mf.mo_coeff[:, :cas_nstart]
cl_a = lo.Boys(mol, mf.mo_coeff[:, cas_nstart:cas_nstop]).kernel(verbose=4)
cl_v = mf.mo_coeff[:, cas_nstop:]
C = np.column_stack((cl_c, cl_a, cl_v))
elif orb_basis == 'boys2':
pyscf.lib.num_threads(1) #with degenerate states and multiple processors there can be issues
cl_c = mf.mo_coeff[:, :loc_nstart]
cl_a = lo.Boys(mol, mf.mo_coeff[:, loc_nstart:loc_nstop]).kernel(verbose=4)
cl_v = mf.mo_coeff[:, loc_nstop:]
C = np.column_stack((cl_c, cl_a, cl_v))
elif orb_basis == 'PM':
pyscf.lib.num_threads(1) #with degenerate states and multiple processors there can be issues
cl_c = mf.mo_coeff[:, :cas_nstart]
cl_a = lo.PM(mol, mf.mo_coeff[:, cas_nstart:cas_nstop]).kernel(verbose=4)
cl_v = mf.mo_coeff[:, cas_nstop:]
C = np.column_stack((cl_c, cl_a, cl_v))
elif orb_basis == 'PM2':
pyscf.lib.num_threads(1) #with degenerate states and multiple processors there can be issues
cl_c = mf.mo_coeff[:, :loc_nstart]
cl_a = lo.PM(mol, mf.mo_coeff[:, loc_nstart:loc_nstop]).kernel(verbose=4)
cl_v = mf.mo_coeff[:, loc_nstop:]
C = np.column_stack((cl_c, cl_a, cl_v))
elif orb_basis == 'ER':
pyscf.lib.num_threads(1) #with degenerate states and multiple processors there can be issues
cl_c = mf.mo_coeff[:, :cas_nstart]
cl_a = lo.PM(mol, mf.mo_coeff[:, cas_nstart:cas_nstop]).kernel(verbose=4)
cl_v = mf.mo_coeff[:, cas_nstop:]
C = np.column_stack((cl_c, cl_a, cl_v))
elif orb_basis == 'ER2':
pyscf.lib.num_threads(1) #with degenerate states and multiple processors there can be issues
cl_c = mf.mo_coeff[:, :loc_nstart]
cl_a = lo.ER(mol, mf.mo_coeff[:, loc_nstart:loc_nstop]).kernel(verbose=4)
cl_v = mf.mo_coeff[:, loc_nstop:]
C = np.column_stack((cl_c, cl_a, cl_v))
elif orb_basis == 'ibmo':
loc_vstop = loc_nstop - n_a
print(loc_vstop)
mo_occ = mf.mo_coeff[:,mf.mo_occ>0]
mo_vir = mf.mo_coeff[:,mf.mo_occ==0]
c_core = mo_occ[:,:loc_nstart]
iao_occ = lo.iao.iao(mol, mo_occ[:,loc_nstart:])
iao_vir = lo.iao.iao(mol, mo_vir[:,:loc_vstop])
c_out = mo_vir[:,loc_vstop:]
# Orthogonalize IAO
iao_occ = lo.vec_lowdin(iao_occ, mf.get_ovlp())
iao_vir = lo.vec_lowdin(iao_vir, mf.get_ovlp())
#
# Method 1, using Knizia's alogrithm to localize IAO orbitals
#
'''
Generate IBOS from orthogonal IAOs
'''
ibo_occ = lo.ibo.ibo(mol, mo_occ[:,loc_nstart:], iaos = iao_occ)
ibo_vir = lo.ibo.ibo(mol, mo_vir[:,:loc_vstop], iaos = iao_vir)
C = np.column_stack((c_core,ibo_occ,ibo_vir,c_out))
else:
print("Error:NO orbital basis defined")
molden.from_mo(mol, 'orbitals.molden', C)
if cas == True:
print(C.shape)
print(cas_norb)
print(cas_nel)
mycas = mcscf.CASSCF(mf, cas_norb, cas_nel)
h1e_cas, ecore = mycas.get_h1eff(mo_coeff = C) #core core orbs to form ecore and eff
h2e_cas = ao2mo.kernel(mol, C[:,cas_nstart:cas_nstop], aosym='s4',compact=False).reshape(4 * ((cas_norb), ))
print(h1e_cas)
print(h1e_cas.shape)
#return h1e_cas,h2e_cas,ecore,C,mol,mf
self.h = h1e_cas
self.g = h2e_cas
self.ecore = ecore
self.mf = mf
self.mol = mol
self.C = cp.deepcopy(C[:,cas_nstart:cas_nstop])
J,K = mf.get_jk()
self.J = self.C.T @ J @ self.C
self.K = self.C.T @ J @ self.C
#HF density
if orb_basis == 'scf':
#C = C[:,cas_nstart:cas_nstop]
D = mf.make_rdm1(mo_coeff=C)
S = mf.get_ovlp()
sal, svec = np.linalg.eigh(S)
idx = sal.argsort()[::-1]
sal = sal[idx]
svec = svec[:, idx]
sal = sal**-0.5
sal = np.diagflat(sal)
X = svec @ sal @ svec.T
C_ao2mo = np.linalg.inv(X) @ C
Cocc = C_ao2mo[:, :n_a]
D = Cocc @ Cocc.T
DMO = C_ao2mo.T @ D @ C_ao2mo
#only for cas space
DMO = DMO[cas_nstart:cas_nstop,cas_nstart:cas_nstop]
self.dm_aa = DMO
self.dm_bb = DMO
print("DENSITY")
print(self.dm_aa.shape)
if 0:
h = C.T.dot(mf.get_hcore()).dot(C)
g = ao2mo.kernel(mol,C,aosym='s4',compact=False).reshape(4*((n_orb),))
const,heff = get_eff_for_casci(cas_nstart,cas_nstop,h,g)
print(heff)
print("const",const)
print("ecore",ecore)
idx = range(cas_nstart,cas_nstop)
h = h[:,idx]
h = h[idx,:]
g = g[:,:,:,idx]
g = g[:,:,idx,:]
g = g[:,idx,:,:]
g = g[idx,:,:,:]
self.ecore = const
self.h = h + heff
self.g = g
elif cas==False:
h = C.T.dot(mf.get_hcore()).dot(C)
g = ao2mo.kernel(mol,C,aosym='s4',compact=False).reshape(4*((n_orb),))
print(h)
#return h, g, enu, C,mol,mf
self.h = h
self.g = g
self.ecore = enu
self.mf = mf
self.mol = mol
self.C = C
J,K = mf.get_jk()
self.J = self.C.T @ J @ self.C
self.K = self.C.T @ J @ self.C
#HF density
if orb_basis == 'scf':
D = mf.make_rdm1(mo_coeff=None)
S = mf.get_ovlp()
sal, svec = np.linalg.eigh(S)
idx = sal.argsort()[::-1]
sal = sal[idx]
svec = svec[:, idx]
sal = sal**-0.5
sal = np.diagflat(sal)
X = svec @ sal @ svec.T
C_ao2mo = np.linalg.inv(X) @ C
Cocc = C_ao2mo[:, :n_a]
D = Cocc @ Cocc.T
DMO = C_ao2mo.T @ D @ C_ao2mo
self.dm_aa = DMO
self.dm_bb = DMO
print("DENSITY")
print(self.dm_aa)
def assign_rdm1s(mol: gto.Mole, s: np.ndarray, mo_coeff: Tuple[np.ndarray, np.ndarray], \
mo_occ: np.ndarray, ref: str, pop: str, part: str, multiproc: bool, verbose: int, \
**kwargs: float) -> Tuple[Union[List[np.ndarray], List[List[np.ndarray]]], Union[None, np.ndarray]]:
"""
this function returns a list of population weights of each spin-orbital on the individual atoms
"""
# declare nested kernel function in global scope
global get_weights
# max number of occupied spin-orbs
n_spin = max(mol.alpha.size, mol.beta.size)
# mol object projected into minao basis
if pop == 'iao':
pmol = lo.iao.reference_mol(mol)
else:
pmol = mol
# number of atoms
natm = pmol.natm
# AO labels
ao_labels = pmol.ao_labels(fmt=None)
# overlap matrix
if pop == 'mulliken':
ovlp = s
else:
ovlp = np.eye(pmol.nao_nr())
def get_weights(orb_idx: int):
"""
this function computes the full set of population weights
"""
# get orbital
orb = mo[:, orb_idx].reshape(mo.shape[0], 1)
# orbital-specific rdm1
rdm1_orb = make_rdm1(orb, mocc[orb_idx])
# population weights of rdm1_orb
return _population(natm, ao_labels, ovlp, rdm1_orb)
# init population weights array
weights = [
np.zeros([n_spin, pmol.natm], dtype=np.float64),
np.zeros([n_spin, pmol.natm], dtype=np.float64)
]
# loop over spin
for i, spin_mo in enumerate((mol.alpha, mol.beta)):
# get mo coefficients and occupation
if pop == 'mulliken':
mo = mo_coeff[i][:, spin_mo]
elif pop == 'iao':
iao = lo.iao.iao(mol, mo_coeff[i][:, spin_mo])
iao = lo.vec_lowdin(iao, s)
mo = contract('ki,kl,lj->ij', iao, s, mo_coeff[i][:, spin_mo])
mocc = mo_occ[i][spin_mo]
# domain
domain = np.arange(spin_mo.size)
# execute kernel
if multiproc:
n_threads = min(domain.size, lib.num_threads())
with mp.Pool(processes=n_threads) as pool:
weights[i] = pool.map(get_weights, domain) # type:ignore
else:
weights[i] = list(map(get_weights, domain)) # type:ignore
# closed-shell reference
if ref == 'restricted' and mol.spin == 0:
weights[i + 1] = weights[i]
break
# verbose print
if 0 < verbose:
symbols = [pmol.atom_pure_symbol(i) for i in range(pmol.natm)]
print('\n *** partial population weights: ***')
print(' spin ' + 'MO ' +
' '.join(['{:}'.format(i) for i in symbols]))
for i, spin_mo in enumerate((mol.alpha, mol.beta)):
for j in domain:
with np.printoptions(suppress=True,
linewidth=200,
formatter={'float': '{:6.3f}'.format}):
print(' {:s} {:>2d} {:}'.format(
'a' if i == 0 else 'b', spin_mo[j], weights[i][j]))
# bond-wise partitioning
if part == 'bonds':
# init population centres array and get threshold
centres = [
np.zeros([mol.alpha.size, 2], dtype=np.int),
np.zeros([mol.beta.size, 2], dtype=np.int)
]
thres = kwargs['thres']
# loop over spin
for i, spin_mo in enumerate((mol.alpha, mol.beta)):
# loop over orbitals
for j in domain:
# get sorted indices
max_idx = np.argsort(weights[i][j])[::-1]
# compute population centres
if np.abs(weights[i][j][max_idx[0]]) > thres:
# core orbital or lone pair
centres[i][j] = np.array([max_idx[0], max_idx[0]],
dtype=np.int)
else:
# valence orbitals
centres[i][j] = np.sort(
np.array([max_idx[0], max_idx[1]], dtype=np.int))
# closed-shell reference
if ref == 'restricted' and mol.spin == 0:
centres[i + 1] = centres[i]
break
# unique and repetitive centres
centres_unique = np.array(
[np.unique(centres[i], axis=0) for i in range(2)])
rep_idx = [[
np.where((centres[i] == j).all(axis=1))[0]
for j in centres_unique[i]
] for i in range(2)]
if part in ['atoms', 'eda']:
return weights, None
else:
return rep_idx, centres_unique
def get_localized_orbitals(mf, lo_method, mo=None):
if mo is None:
mo = mf.mo_coeff
if not isinstance(mf, khf.KSCF):
mol = mf.mol
s1e = mf.get_ovlp()
if lo_method.lower() == 'lowdin' or lo_method.lower() == 'meta_lowdin':
C = lo.orth_ao(mf, 'meta_lowdin', s=s1e)
C_inv = np.dot(C.conj().T, s1e)
if isinstance(mf, scf.hf.RHF):
C_inv_spin = C_inv
else:
C_inv_spin = np.array([C_inv] * 2)
elif lo_method == 'iao':
s1e = mf.get_ovlp()
pmol = mf.mol.copy()
pmol.build(False, False, basis='minao')
if isinstance(mf, scf.hf.RHF):
mo_coeff_occ = mf.mo_coeff[:, mf.mo_occ > 0]
C = lo.iao.iao(mf.mol, mo_coeff_occ)
# Orthogonalize IAO
C = lo.vec_lowdin(C, s1e)
C_inv = np.dot(C.conj().T, s1e)
C_inv_spin = C_inv
else:
mo_coeff_occ_a = mf.mo_coeff[0][:, mf.mo_occ[0] > 0]
mo_coeff_occ_b = mf.mo_coeff[1][:, mf.mo_occ[1] > 0]
C_a = lo.iao.iao(mf.mol, mo_coeff_occ_a)
C_b = lo.iao.iao(mf.mol, mo_coeff_occ_b)
C_a = lo.vec_lowdin(C_a, s1e)
C_b = lo.vec_lowdin(C_b, s1e)
C_inv_a = np.dot(C_a.T, s1e)
C_inv_b = np.dot(C_b.T, s1e)
C_inv_spin = np.array([C_inv_a, C_inv_b])
elif lo_method == 'nao':
C = lo.orth_ao(mf, 'nao')
C_inv = np.dot(C.conj().T, s1e)
if isinstance(mf, scf.hf.RHF):
C_inv_spin = C_inv
else:
C_inv_spin = np.array([C_inv] * 2)
else:
raise NotImplementedError("UNDEFINED LOCAL ORBITAL TYPE, EXIT...")
mo_lo = np.einsum('...jk,...kl->...jl', C_inv_spin, mo)
return C_inv_spin, mo_lo
else:
cell = mf.cell
s1e = mf.get_ovlp()
if lo_method.lower() == 'lowdin' or lo_method.lower() == 'meta_lowdin':
nkpt = len(mf.kpts)
C_arr = []
C_inv_arr = []
for i in range(nkpt):
C_curr = lo.orth_ao(mf, 'meta_lowdin', s=s1e[i])
C_inv_arr.append(np.dot(C_curr.conj().T, s1e[i]))
C_inv_arr = np.array(C_inv_arr)
if isinstance(mf, scf.hf.RHF):
C_inv_spin = C_inv_arr
else:
C_inv_spin = np.array([C_inv_arr] * 2)
else:
raise NotImplementedError("CONSTRUCTING...EXIT")
mo_lo = np.einsum('...jk,...kl->...jl', C_inv_spin, mo)
return C_inv_spin, mo_lo
def setuph2(r, obdm_steps=5):
from pyscf import gto, scf, lo
from pyqmc.accumulators import LinearTransform, EnergyAccumulator
from pyqmc.obdm import OBDMAccumulator
from pyqmc.cvmc import DescriptorFromOBDM, PGradDescriptor
import itertools
# ccECP from A. Annaberdiyev et al. Journal of Chemical Physics 149, 134108 (2018)
basis = {
"H":
gto.basis.parse("""
H S
23.843185 0.00411490
10.212443 0.01046440
4.374164 0.02801110
1.873529 0.07588620
0.802465 0.18210620
0.343709 0.34852140
0.147217 0.37823130
0.063055 0.11642410
""")
}
"""
H S
0.040680 1.00000000
H S
0.139013 1.00000000
H P
0.166430 1.00000000
H P
0.740212 1.00000000
"""
ecp = {
"H":
gto.basis.parse_ecp("""
H nelec 0
H ul
1 21.24359508259891 1.00000000000000
3 21.24359508259891 21.24359508259891
2 21.77696655044365 -10.85192405303825
""")
}
mol = gto.M(atom=f"H 0. 0. 0.; H 0. 0. {r}",
unit="bohr",
basis=basis,
ecp=ecp,
verbose=5)
mf = scf.RHF(mol).run()
mo_occ = mf.mo_coeff[:, mf.mo_occ > 0]
a = lo.iao.iao(mol, mo_occ)
a = lo.vec_lowdin(a, mf.get_ovlp())
obdm_up = OBDMAccumulator(mol=mol, orb_coeff=a, nstep=obdm_steps, spin=0)
obdm_down = OBDMAccumulator(mol=mol, orb_coeff=a, nstep=obdm_steps, spin=1)
wf = pyqmc.slater_jastrow(mol, mf)
freeze = {}
for k in wf.parameters:
freeze[k] = np.zeros(wf.parameters[k].shape, dtype='bool')
print(freeze.keys())
print(wf.parameters['wf1mo_coeff_alpha'])
#this freezing allows us to easily go between bonding and
# AFM configurations.
freeze['wf1mo_coeff_alpha'][0, 0] = True
freeze['wf1mo_coeff_beta'][1, 0] = True
descriptors = {
"t": [[(1.0, (0, 1)), (1.0, (1, 0))], [(1.0, (0, 1)), (1.0, (1, 0))]],
"trace": [[(1.0, (0, 0)), (1.0, (1, 1))], [(1.0, (0, 0)),
(1.0, (1, 1))]],
}
for i in [0, 1]:
descriptors[f"nup{i}"] = [[(1.0, (i, i))], []]
descriptors[f"ndown{i}"] = [[], [(1.0, (i, i))]]
acc = PGradDescriptor(
EnergyAccumulator(mol),
LinearTransform(wf.parameters, freeze=freeze),
[obdm_up, obdm_down],
DescriptorFromOBDM(descriptors, norm=2.0),
)
return {
"wf": wf,
"acc": acc,
"mol": mol,
"mf": mf,
"descriptors": descriptors
}
m.__dict__.update(lib.chkfile.load('rohf/Cuvtz_r1.725_s1_ROHF_0.chk', 'scf'))
for i in (mol.basis["Cu"]):
if (len(cu_basis) < 2):
if (i[0] == 0): cu_basis.append(i)
elif (len(cu_basis) == 2):
if (i[0] == 1): cu_basis.append(i)
elif (len(cu_basis) == 3):
if (i[0] == 2): cu_basis.append(i)
else:
pass
o_basis = []
for i in (mol.basis["O"]):
if (len(o_basis) == 0):
if (i[0] == 0): o_basis.append(i)
elif (len(o_basis) == 1):
if (i[0] == 1): o_basis.append(i)
else:
pass
minbasis = {'Cu': cu_basis, 'O': o_basis}
#Build IAOs
s = m.get_ovlp()
a = lo.iao.iao(mol, mo_coeff, minao=minbasis)
a = lo.vec_lowdin(a, s)
a.dump('b3lyp_iao_b.pickle')
#Plot IAOs
m.mo_coeff[:, :a.shape[1]] = a
print_qwalk_mol(mol, m, method='scf', basename='qwalk/b3lyp_iao_b')
def test_pbc():
from pyscf.pbc import gto, scf
from pyqmc import PySCFSlaterUHF, PySCFSlaterPBC
from pyqmc import slaterpbc
import scipy
lvecs = (np.ones((3, 3)) - np.eye(3)) * 2.0
mol = gto.M(
atom="H 0. 0. -{0}; H 0. 0. {0}".format(0.7),
basis="sto-3g",
unit="bohr",
verbose=0,
a=lvecs,
)
mf = scf.KRHF(mol, kpts=mol.make_kpts((2, 2, 2)))
mf = mf.run()
S = np.ones((3, 3)) - 2 * np.eye(3)
mol = slaterpbc.get_supercell(mol, S)
kpts = slaterpbc.get_supercell_kpts(mol)[:2]
kdiffs = mf.kpts[np.newaxis] - kpts[:, np.newaxis]
kinds = np.nonzero(np.linalg.norm(kdiffs, axis=-1) < 1e-12)[1]
# Lowdin orthogonalized AO basis.
# lowdin = lo.orth_ao(mol, "lowdin")
loiao = lo.iao.iao(mol.original_cell, mf.mo_coeff, kpts=kpts)
occs = [mf.mo_occ[k] for k in kinds]
coefs = [mf.mo_coeff[k] for k in kinds]
ovlp = mf.get_ovlp()[kinds]
lowdin = [lo.vec_lowdin(l, o) for l, o in zip(loiao, ovlp)]
lreps = [np.linalg.multi_dot([l.T, o, c]) for l, o, c in zip(lowdin, ovlp, coefs)]
# make AO to localized orbital coefficients.
mfobdm = [np.einsum("ij,j,kj->ik", l.conj(), o, l) for l, o in zip(lreps, occs)]
### Test OBDM calculation.
nconf = 800
nsteps = 50
warmup = 6
wf = PySCFSlaterPBC(mol, mf)
configs = initial_guess(mol, nconf)
obdm_dict = dict(mol=mol, orb_coeff=lowdin, kpts=kpts, nsweeps=4, warmup=10)
obdm = OBDMAccumulator(**obdm_dict)
obdm_up = OBDMAccumulator(**obdm_dict, spin=0)
obdm_down = OBDMAccumulator(**obdm_dict, spin=1)
df, coords = vmc(
wf,
configs,
nsteps=nsteps,
accumulators={"obdm": obdm, "obdm_up": obdm_up, "obdm_down": obdm_down},
verbose=True,
)
df = DataFrame(df)
obdm_est = {}
for k in ["obdm", "obdm_up", "obdm_down"]:
avg_norm = np.array(df.loc[warmup:, k + "norm"].values.tolist()).mean(axis=0)
avg_obdm = np.array(df.loc[warmup:, k + "value"].values.tolist()).mean(axis=0)
obdm_est[k] = normalize_obdm(avg_obdm, avg_norm)
print("Average OBDM(orb,orb)", obdm_est["obdm"].round(3))
mfobdm = scipy.linalg.block_diag(*mfobdm)
print("mf obdm", mfobdm.round(3))
max_abs_err = np.max(np.abs(obdm_est["obdm"] - mfobdm))
assert max_abs_err < 0.05, "max abs err {0}".format(max_abs_err)
print(obdm_est["obdm_up"].diagonal().round(3))
print(obdm_est["obdm_down"].diagonal().round(3))
mae = np.mean(np.abs(obdm_est["obdm_up"] + obdm_est["obdm_down"] - mfobdm))
maup = np.mean(np.abs(obdm_est["obdm_up"]))
madn = np.mean(np.abs(obdm_est["obdm_down"]))
mamf = np.mean(np.abs(mfobdm))
assert mae < 0.05, "mae {0}\n maup {1}\n madn {2}\n mamf {3}".format(
mae, maup, madn, mamf
)
