def make_rdm2(self, t2=None, ao_repr=False):
if t2 is None:
t2 = self.t2
assert t2 is not None
return make_rdm2(self, t2, ao_repr=ao_repr)
def solve (mol, nel, cf_core, cf_gs, ImpOrbs, chempot=0., n_orth=0, FrozenPot=None, mf_tot=None):
# 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
print("cfx shape", cfx.shape)
Sf = mol.intor_symmetric('cint1e_ovlp_sph')
Hc = mol.intor_symmetric('cint1e_kin_sph') \
+ mol.intor_symmetric('cint1e_nuc_sph') \
+ FrozenPot
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))
# density fitting ============================================================
# mf = scf.RHF(mol).density_fit() # this should be moved out of to the parent directory, to avoid repetition
# mf.with_df._cderi_to_save = 'saved_cderi.h5' # rank-3 decomposition
# mf.kernel() ### moved these three lines to orbital_selection_fc
auxmol = df.incore.format_aux_basis(mol, auxbasis='weigend')
j3c = df.incore.aux_e2(mol, auxmol, intor='cint3c2e_sph', aosym='s1')
nao = mol.nao_nr()
naoaux = auxmol.nao_nr()
j3c = j3c.reshape(nao,nao,naoaux) # (ij|L)
print("j3c shape", j3c.shape)
j2c = df.incore.fill_2c2e(mol, auxmol) #(L|M) overlap matrix between auxiliary basis functions
#the eri is (ij|kl) = \sum_LM (ij|L) (L|M) (M|kl)
omega = sla.inv(j2c)
eps,U = sla.eigh(omega)
#after this transformation the eri is (ij|kl) = \sum_L (ij|L) (L|kl)
j3c = np.dot(np.dot(j3c,U),np.diag(np.sqrt(eps)))
#this part is slow, as we again store the whole eri_df
# conv = np.einsum('prl,pi,rj->ijl', j3c, cfx, cfx)
conv = np.einsum('prl,pi->irl',j3c,cfx)
conv = np.einsum('irl,rj->ijl',conv,cfx)
df_eri = np.einsum('ijm,klm->ijkl',conv,conv)
intsp_df = ao2mo.restore(4, df_eri, cfx.shape[1])
print("DF instp", intsp_df.shape)
# =============================================================================
# intsp = ao2mo.outcore.full_iofree (mol, cfx) #TODO: this we need to calculate on the fly using generator f'n
# print("intsp shape", intsp.shape)
# 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
mf1 = scf.RHF(mol_) #.density_fit()
#mf.verbose = 4
mf1.mo_coeff = cf
mf1.mo_occ = occ
mf1.get_ovlp = lambda *args: Sp
mf1.get_hcore = lambda *args: Hp + jkp - 0.5*chempot*(Np + Np.T)
mf1._eri = ao2mo.restore (8, intsp_df, cfx.shape[1]) #trying something
nt = scf.newton(mf1)
#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')
mo_coeff = nt.mo_coeff
mo_energy = nt.mo_energy
mo_occ = nt.mo_occ
print("mo_coeff", mo_coeff)
# dfMP2 solution
nocc = nel//2
# mp2solver = dfmp2_testing.MP2(mf_tot) #(work) #we just pass the mf for the full molecule to dfmp2
mp2solver = dfmp2.DFMP2(mf_tot) #(work) #we just pass the mf for the full molecule to dfmp2
# mp2solver = dfmp2.MP2(mf) #(home)
mp2solver.verbose = 5
mp2solver.kernel(mo_energy=mo_energy, mo_coeff=mo_coeff, nocc=nocc)
mp2solver.mo_occ=mo_occ.copy() # this is DIRTY
def get_t2(mp):
'''basically identical to the DFMP2 kernel, returns t2'''
from pyscf.mp import mp2
mo_coeff = mp2._mo_without_core(mp, mp.mo_coeff)
# print("mo_coeff rdms", mo_coeff)
mo_energy = mp2._mo_energy_without_core(mp, mp.mo_energy)
nocc = mp.nocc
nvir = mp.nmo - nocc
eia = mo_energy[:nocc,None] - mo_energy[None,nocc:]
emp2 = 0
t2 = []
for istep, qov in enumerate(mp.loop_ao2mo(mo_coeff, nocc)):
for i in range(nocc):
buf = np.dot(qov[:,i*nvir:(i+1)*nvir].T,qov).reshape(nvir,nocc,nvir)
gi = np.array(buf,copy=False)
gi = gi.reshape(nvir,nocc,nvir).transpose(1,0,2)
t2i = gi.conj()/lib.direct_sum('jb+a->jba',eia,eia[i])
t2.append(t2i)
emp2 += np.einsum('jab,jab',t2i,gi) * 2
emp2 -= np.einsum('jab,jba',t2i,gi)
return emp2,t2
def make_rdm1(mp2solver):
'''rdm1 in the MO basis'''
from pyscf.cc import ccsd_rdm
doo, dvv = _gamma1_intermediates(mp2solver)
nocc = doo.shape[0]
nvir = dvv.shape[0]
print('nocc', nocc)
print('nvir', nvir)
dov = np.zeros((nocc,nvir), dtype=doo.dtype)
dvo = dov.T
return ccsd_rdm._make_rdm1(mp,(doo,dov,dvo,dvv),with_frozen=False)
def _gamma1_intermediates(mp,t2=None):
nmo = mp.nmo
nocc = mp.nocc
nvir = nmo - nocc
from pyscf.mp import mp2
mo_coeff = mp2._mo_without_core(mp, mp.mo_coeff)
print("mo coeff rdms", mo_coeff)
print('nmo, nocc, nvir, mo_coeff shape')
print(nmo, nocc, nvir, mp.mo_coeff.shape)
mo_energy = mp2._mo_energy_without_core(mp, mp.mo_energy)
eia = mo_energy[:nocc,None] - mo_energy[None,nocc:]
if(t2 is None):
for istep, qov in enumerate(mp.loop_ao2mo(mo_coeff, nocc)):
if(istep==0):
dtype = qov.dtype
dm1occ = np.zeros((nocc,nocc), dtype=dtype)
dm1vir = np.zeros((nvir,nvir), dtype=dtype)
for i in range(nocc):
buf = np.dot(qov[:,i*nvir:(i+1)*nvir].T,
qov).reshape(nvir,nocc,nvir)
gi = np.array(buf, copy=False)
gi = gi.reshape(nvir,nocc,nvir).transpose(1,0,2)
t2i = gi/lib.direct_sum('jb+a->jba', eia, eia[i])
l2i = t2i.conj()
dm1vir += np.einsum('jca,jcb->ba', l2i, t2i) * 2 \
- np.einsum('jca,jbc->ba', l2i, t2i)
dm1occ += np.einsum('iab,jab->ij', l2i, t2i) * 2 \
- np.einsum('iab,jba->ij', l2i, t2i)
else:
dtype = t2[0].dtype
dm1occ = np.zeros((nocc,nocc), dtype=dtype)
dm1vir = np.zeros((nvir,nvir), dtype=dtype)
for i in range(nocc):
t2i = t2[i]
l2i = t2i.conj()
dm1vir += np.einsum('jca,jcb->ba', l2i, t2i) * 2 \
- np.einsum('jca,jbc->ba', l2i, t2i)
dm1occ += np.einsum('iab,jab->ij', l2i, t2i) * 2 \
- np.einsum('iab,jba->ij', l2i, t2i)
return -dm1occ, dm1vir
def make_rdm2(mp2solver):
nmo = nmo0 = mp2solver.nmo
nocc = nocc0 = mp2solver.nocc
nvir = nmo - nocc
from pyscf.mp import mp2
mo_coeff = mp2._mo_without_core(mp2solver, mp2solver.mo_coeff)
mo_energy = mp2._mo_energy_without_core(mp2solver, mp2solver.mo_energy)
eia = mo_energy[:nocc,None] - mo_energy[None,nocc:]
moidx = oidx = vidx = None
dm1 = make_rdm1(mp2solver)
dm1[np.diag_indices(nocc0)] -= 2
dm2 = np.zeros((nmo0,nmo0,nmo0,nmo0), dtype=dm1.dtype)
if(t2 is None):
for istep, qov in enumerate(mp2solver.loop_ao2mo(mo_coeff, nocc)):
for i in range(nocc):
buf = np.dot(qov[:,i*nvir:(i+1)*nvir].T,qov).reshape(nvir,nocc,nvir)
gi = np.array(buf,copy=False)
gi = gi.reshape(nvir,nocc,nvir).transpose(1,0,2)
t2i = gi.conj()/lib.direct_sum('jb+a->jba',eia,eia[i])
dovov = t2i.transpose(1,0,2)*2 - t2i.transpose(2,0,1)
dovov *= 2
if moidx is None:
dm2[i,nocc:,:nocc,nocc:] = dovov
dm2[nocc:,i,nocc:,:nocc] = dovov.conj().transpose(0,2,1)
else:
dm2[oidx[i],vidx[:,None,None],oidx[:,None],vidx] = dovov
dm2[vidx[:,None,None],oidx[i],vidx[:,None],oidx] = dovov.conj().transpose(0,2,1)
else:
for i in range(nocc):
t2i = t2[i]
dovov = t2i.transpose(1,0,2)*2 - t2i.transpose(2,0,1)
dovov *= 2
if moidx is None:
dm2[i,nocc:,:nocc,nocc:] = dovov
dm2[nocc:,i,nocc:,:nocc] = dovov.conj().transpose(0,2,1)
else:
dm2[oidx[i],vidx[:,None,None],oidx[:,None],vidx] = dovov
dm2[vidx[:,None,None],oidx[i],vidx[:,None],oidx] = dovov.conj().transpose(0,2,1)
for i in range(nocc0):
dm2[i,i,:,:] += dm1.T * 2
dm2[:,:,i,i] += dm1.T * 2
dm2[:,i,i,:] -= dm1.T
dm2[i,:,:,i] -= dm1
for i in range(nocc0):
for j in range(nocc0):
dm2[i,i,j,j] += 4
dm2[i,j,j,i] -= 2
return dm2
t2 = None
rdm1 = make_rdm1(mp2solver)
rdm2 = make_rdm2(mp2solver)
# # -------------------------------------
# TEST: compare rdm dmet with dfmp2 rdms
# atoms_test=\
# [['C',( 0.0000, 0.0000, 0.7680)],\
# ['C',( 0.0000, 0.0000,-0.7680)],\
# ['H',(-1.0192, 0.0000, 1.1573)],\
# ['H',( 0.5096, 0.8826, 1.1573)],\
# ['H',( 0.5096,-0.8826, 1.1573)],\
# ['H',( 1.0192, 0.0000,-1.1573)],\
# ['H',(-0.5096,-0.8826,-1.1573)],\
# ['H',(-0.5096, 0.8826,-1.1573)]]
atoms_test = [
['O' , (0. , 0. , 0.)],\
['H' , (0. , -0.757 , 0.587)],\
['H' , (0. , 0.757 , 0.587)]]
mol_test = gto.M(atom=atoms_test,basis='cc-pvdz')
m_test = scf.RHF(mol_test).density_fit()
m_test.kernel()
mm_test = dfmp2.DFMP2(m_test)
mm_test.kernel()
from pyscf.mp import mp2
rdm1_test = mp2.make_rdm1(mm_test)
rdm2_test = mp2.make_rdm2(mm_test)
# Plot sorted rdm1 values
x1 = rdm1
y1 = x1.flatten()
y1 = np.sort(y1)
import matplotlib.pyplot as plt
plt.plot(y1, 'r', label='rdm1 from dmet')
plt.ylabel('rdm1')
x2 = rdm1_test
y2 = x2.flatten()
print("rdm1", y2)
print(type(y2))
y2 = np.sort(y2)
plt.plot(y2, 'b', label='rdm1 for dfmp2')
plt.ylabel('rdm1 sorted values')
# Place a legend above this subplot, expanding itself to
# fully use the given bounding box.
plt.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,
ncol=2, mode="expand", borderaxespad=0.)
plt.show()
plt.close()
print("deviations between sorted 1rdm in MO basis ")
print(np.abs(y1-y2).max())
# Plot sorted rdm2 values
x1 = rdm2
y1 = x1.flatten()
y1 = np.sort(y1)
import matplotlib.pyplot as plt
plt.plot(y1, 'r', label='rdm2 from dmet')
plt.ylabel('rdm2')
x2 = rdm2_test
y2 = x2.flatten()
print("rdm1", y2)
print(type(y2))
y2 = np.sort(y2)
plt.plot(y2, 'b', label='rdm2 for dfmp2')
plt.ylabel('rdm1 sorted values')
# Place a legend above this subplot, expanding itself to
# fully use the given bounding box.
plt.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,
ncol=2, mode="expand", borderaxespad=0.)
plt.show()
plt.close()
print("deviations between sorted 1rdm in MO basis ")
print(np.abs(y1-y2).max())
print("deviations between 1rdm,2rdm in MO basis ")
print(np.abs(rdm1-rdm1_test).max())
print(np.abs(rdm2-rdm2_test).max())
# # ----------------------------------
# transform rdm's to original basis
tei = ao2mo.restore(1, intsp_df, cfx.shape[1])
print("tei shape", tei.shape)
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