atom = [
["O" , (0. , 0. , 0. )],
[1 , (0. ,-0.757 ,-0.587)],
[1 , (0. , 0.757 ,-0.587)]],
basis = '631g'
)
mf = scf.RHF(mol)
mf.conv_tol = 1e-14
ehf = mf.scf()
mycc = ccsd.CCSD(mf)
mycc.conv_tol = 1e-10
mycc.conv_tol_normt = 1e-10
ecc, t1, t2 = mycc.kernel()
eris = mycc.ao2mo()
e3ref = ccsd_t.kernel(mycc, eris, t1, t2)
print ehf+ecc+e3ref
eris = mycc.ao2mo(mf.mo_coeff)
conv, l1, l2 = ccsd_t_lambda.kernel(mycc, eris, t1, t2)
g1 = kernel(mycc, t1, t2, l1, l2, eris=eris, mf_grad=grad.RHF(mf))
print(g1 + grad.grad_nuc(mol))
#O 0.0000000000 0.0000000000 -0.0112045345
#H 0.0000000000 0.0234464201 0.0056022672
#H 0.0000000000 -0.0234464201 0.0056022672
mol = gto.M(
verbose = 0,
atom = '''
H -1.90779510 0.92319522 0.08700656
H -1.08388168 -1.61405643 -0.07315086
#mol.verbose = 5
#mol.output = 'out_h2o'
mol.atom = [[8, (0., 0., 0.)], [1, (0., -.957, .587)],
[1, (0.2, .757, .487)]]
#mol.basis = 'ccpvdz'
mol.basis = '631g'
mol.build()
mf = scf.RHF(mol)
mf.conv_tol = 1e-1
mf.scf()
mcc = ccsd.CCSD(mf)
mcc.conv_tol = 1e-14
ecc, t1, t2 = mcc.kernel()
eris = mcc.ao2mo()
e3ref = ccsd_t.kernel(mcc, eris, t1, t2)
l1, l2 = ccsd_t_lambda.kernel(mcc, eris, t1, t2)[1:]
print(ecc, e3ref)
eri_mo = ao2mo.kernel(mf._eri, mf.mo_coeff, compact=False)
nmo = mf.mo_coeff.shape[1]
eri_mo = eri_mo.reshape(nmo, nmo, nmo, nmo)
dm1 = make_rdm1(mcc, t1, t2, l1, l2, eris=eris)
dm2 = make_rdm2(mcc, t1, t2, l1, l2, eris=eris)
print(lib.finger(dm1) - 1.289951975176953)
print(lib.finger(dm2) - 6.6184784979411164)
h1 = reduce(numpy.dot, (mf.mo_coeff.T, mf.get_hcore(), mf.mo_coeff))
e3 = (numpy.einsum('ij,ji->', h1, dm1) +
numpy.einsum('ijkl,ijkl->', eri_mo, dm2) * .5 + mf.mol.energy_nuc())
print(e3ref, e3 - (mf.e_tot + ecc))
def solve(mol, nel, cf_core, cf_gs, ImpOrbs, chempot=0., n_orth=0):
# cf_core : core orbitals (in AO basis, assumed orthonormal)
# cf_gs : guess orbitals (in AO basis)
# ImpOrbs : cf_gs -> impurity orbitals transformation
# n_orth : number of orthonormal orbitals in cf_gs [1..n_orth]
mol_ = gto.Mole()
mol_.build(verbose=0)
mol_.nelectron = nel
mol_.incore_anyway = True
cfx = cf_gs
Sf = mol.intor_symmetric('cint1e_ovlp_sph')
Hc = mol.intor_symmetric('cint1e_kin_sph') \
+ mol.intor_symmetric('cint1e_nuc_sph')
occ = np.zeros((cfx.shape[1], ))
occ[:nel / 2] = 2.
# core contributions
dm_core = np.dot(cf_core, cf_core.T) * 2
jk_core = scf.hf.get_veff(mol, dm_core)
e_core = np.trace(np.dot(Hc, dm_core)) \
+ 0.5*np.trace(np.dot(jk_core, dm_core))
# transform integrals
Sp = np.dot(cfx.T, np.dot(Sf, cfx))
Hp = np.dot(cfx.T, np.dot(Hc, cfx))
jkp = np.dot(cfx.T, np.dot(jk_core, cfx))
intsp = ao2mo.outcore.full_iofree(mol, cfx)
# orthogonalize cf [virtuals]
cf = np.zeros((cfx.shape[1], ) * 2, )
if n_orth > 0:
assert (n_orth <= cfx.shape[1])
assert (np.allclose(np.eye(n_orth), Sp[:n_orth, :n_orth]))
else:
n_orth = 0
cf[:n_orth, :n_orth] = np.eye(n_orth)
if n_orth < cfx.shape[1]:
val, vec = sla.eigh(-Sp[n_orth:, n_orth:])
idx = -val > 1.e-12
U = np.dot(vec[:,idx]*1./(np.sqrt(-val[idx])), \
vec[:,idx].T)
cf[n_orth:, n_orth:] = U
# define ImpOrbs projection
Xp = np.dot(ImpOrbs, ImpOrbs.T)
# Si = np.dot(ImpOrbs.T, np.dot(Sp, ImpOrbs))
# Mp = np.dot(ImpOrbs, np.dot(sla.inv(Si), ImpOrbs.T))
Np = np.dot(Sp, Xp)
# print ( np.allclose(Np, np.dot(Np, np.dot(Mp, Np))) )
# HF calculation
mol_.energy_nuc = lambda *args: mol.energy_nuc() + e_core
mf = scf.RHF(mol_)
#mf.verbose = 4
mf.mo_coeff = cf
mf.mo_occ = occ
mf.get_ovlp = lambda *args: Sp
mf.get_hcore = lambda *args: Hp + jkp - 0.5 * chempot * (Np + Np.T)
mf._eri = ao2mo.restore(8, intsp, cfx.shape[1])
nt = scf.newton(mf)
#nt.verbose = 4
nt.max_cycle_inner = 1
nt.max_stepsize = 0.25
nt.ah_max_cycle = 32
nt.ah_start_tol = 1.0e-12
nt.ah_grad_trust_region = 1.0e8
nt.conv_tol_grad = 1.0e-6
nt.kernel()
cf = nt.mo_coeff
if not nt.converged:
raise RuntimeError('hf failed to converge')
mf.mo_coeff = nt.mo_coeff
mf.mo_energy = nt.mo_energy
mf.mo_occ = nt.mo_occ
#CCSD(T) only implementation available is slow.
from pyscf.cc import ccsd_t_slow as ccsd_t
from pyscf.cc import ccsd_t_lambda_slow as ccsd_t_lambda
from pyscf.cc import ccsd_t_rdm_slow as ccsd_t_rdm
# CC solution
ccsolver = cc.CCSD(mf)
ccsolver.verbose = 5
ecc, t1, t2 = ccsolver.kernel()
# CCSD(T) solution
eris = ccsolver.ao2mo()
e3ref = ccsd_t.kernel(ccsolver, eris, t1, t2)
l1, l2 = ccsd_t_lambda.kernel(ccsolver, eris, t1, t2)[1:]
print("CCSD(T) energy ", ecc + e3ref)
rdm1 = ccsd_t_rdm.make_rdm1(ccsolver, t1, t2, l1, l2, eris=eris)
rdm2 = ccsd_t_rdm.make_rdm2(ccsolver, t1, t2, l1, l2, eris=eris)
# transform rdm's to original basis
tei = ao2mo.restore(1, intsp, cfx.shape[1])
rdm1 = np.dot(cf, np.dot(rdm1, cf.T))
rdm2 = np.einsum('ai,ijkl->ajkl', cf, rdm2)
rdm2 = np.einsum('bj,ajkl->abkl', cf, rdm2)
rdm2 = np.einsum('ck,abkl->abcl', cf, rdm2)
rdm2 = np.einsum('dl,abcl->abcd', cf, rdm2)
ImpEnergy = +0.25 *np.einsum('ij,jk,ki->', 2*Hp+jkp, rdm1, Xp) \
+0.25 *np.einsum('ij,jk,ki->', 2*Hp+jkp, Xp, rdm1) \
+0.125*np.einsum('ijkl,ijkm,ml->', tei, rdm2, Xp) \
+0.125*np.einsum('ijkl,ijml,mk->', tei, rdm2, Xp) \
+0.125*np.einsum('ijkl,imkl,mj->', tei, rdm2, Xp) \
+0.125*np.einsum('ijkl,mjkl,mi->', tei, rdm2, Xp)
Nel = np.trace(np.dot(np.dot(rdm1, Sp), Xp))
return Nel, ImpEnergy