def get_gap(gs, es, fnal):
e0 = mcpdft.CASSCF(gs._scf, fnal, gs.ncas, gs.nelecas,
grids_level=9).set(fcisolver=gs.fcisolver,
conv_tol=1e-10).kernel(
gs.mo_coeff, gs.ci)[0]
e1 = mcpdft.CASSCF(es._scf, fnal, es.ncas, es.nelecas,
grids_level=9).set(fcisolver=es.fcisolver,
conv_tol=1e-10).kernel(
es.mo_coeff, es.ci)[0]
return (e1 - e0) * 27.2114
def test_molgrad (otxc):
mc = mcpdft.CASSCF (mf, otxc, 6, 6).set (conv_tol=1e-10).run ().as_scanner ()
mc_grad = mc.nuc_grad_method ().run ()
de_an = (mc_grad.de[1,0]-mc_grad.de[0,0])/2
de_num = (mc (N2_xyz (1.601)) - mc (N2_xyz (1.599)))*lib.param.BOHR/0.002
print (otxc, "Numeric gradient:", de_num)
print (otxc, "Analytical gradient:", de_an)
print (otxc, "Gradient error:", de_an-de_num)
def get_mc_ref(mol, ri=False, sa2=False):
mf = scf.RHF(mol)
if ri: mf = mf.density_fit(auxbasis=df.aug_etb(mol))
mc = mcpdft.CASSCF(mf.run(), 'tPBE', 6, 6, grids_level=6)
if sa2:
fcisolvers = [csf_solver(mol, smult=((2 * i) + 1)) for i in (0, 1)]
if mol.symmetry:
fcisolvers[0].wfnsym = 'A1'
fcisolvers[1].wfnsym = 'A2'
mc = mc.state_average_mix_(fcisolvers, [0.5, 0.5])
ref = np.load('h2co_sa2_tpbe66_631g_grad_num.npy').reshape(2, 2, 4,
3)[int(ri)]
else:
ref = np.load('h2co_tpbe66_631g_grad_num.npy')[int(ri)]
return mc.run(), ref
def get_mc_ref(mol, ri=False, sa2=False):
mf = scf.RHF(mol)
# if ri: mf = mf.density_fit (auxbasis = df.aug_etb (mol))
mc = mcpdft.CASSCF(mf.run(), 'tPBE', 6, 6, grids_level=9)
# if sa2:
# fcisolvers = [csf_solver (mol, smult=((2*i)+1)) for i in (0,1)]
# if mol.symmetry:
# fcisolvers[0].wfnsym = 'A1'
# fcisolvers[1].wfnsym = 'A2'
# mc = mc.state_average_mix_(fcisolvers, [0.5,0.5])
# ref = np.load ('h2co_sa2_tpbe66_631g_grad_num.npy').reshape (2,2,4,3)[int(ri)]
# else:
# ref = np.load ('h2co_tpbe66_631g_grad_num.npy')[int(ri)]
#this refernce is obtained by mcpdft numerical differentiation in pyscf
#using central differences with a second order accuracy and step size of 1e-4
ref = np.load('h2co_tpbe66_631g_edipole_num.npy')[int(ri)]
return mc.run(), ref
def test_densgrad (otxc):
# throat-clearing
mc = mcpdft.CASSCF (mf, otxc, 6, 6).set (conv_tol=1e-10).run ().as_scanner ()
ncore, ncas = mc.ncore, mc.ncas
nocc, nao = ncore + ncas, mc.mol.nao_nr ()
mo_coeff = mc.mo_coeff
mo_core = mc.mo_coeff[:,:ncore]
mo_cas = mc.mo_coeff[:,ncore:nocc]
ot = mc.otfnal
if ot.grids.coords is None:
ot.grids.build(with_non0tab=True)
ngrids = ot.grids.coords.shape[0]
ni = ot._numint
dens_deriv = ot.dens_deriv
def get_dens (d1, d2):
make_rho, nset, nao = ni._gen_rho_evaluator (ot.mol, d1, 1)
for ao, mask, weight, coords in ni.block_loop (ot.mol, ot.grids, nao, ot.dens_deriv, mc.max_memory, blksize=ngrids):
rho = np.asarray ([make_rho (i, ao, mask, ot.xctype) for i in range(2)])
Pi = get_ontop_pair_density (ot, rho, ao, d1, d2, mo_cas, ot.dens_deriv, mask)
return rho, Pi, weight
# densities and potentials for the wave function
dm1s, dm2s = mc.fcisolver.make_rdm12s (mc.ci, mc.ncas, mc.nelecas)
dm1 = dm1s[0] + dm1s[1]
dm2 = dm2s[0] + dm2s[1] + dm2s[1].transpose (2,3,0,1) + dm2s[2]
dm2 -= np.multiply.outer (dm1, dm1)
dm2 += np.multiply.outer (dm1s[0], dm1s[0]).transpose (0,3,2,1)
dm2 += np.multiply.outer (dm1s[1], dm1s[1]).transpose (0,3,2,1)
dm1s = [(mo_core @ mo_core.T) + (mo_cas @ d @ mo_cas.T) for d in dm1s]
rho0, Pi0, weight = get_dens (dm1s, dm2)
eot0, vot0, fot0 = ot.eval_ot (rho0, Pi0, dderiv=2, weights=weight)
vrho0, vPi0 = vot0
# Perturbed densities
ddm1s = np.zeros ((2,nao,nao), dtype = dm1s[0].dtype)
ddm1s[:,ncore:,:nocc] = 0.0001
ddm1s += ddm1s.transpose (0,2,1)
ddm1s = [mo_coeff @ d @ mo_coeff.T for d in ddm1s]
ddm2 = np.ones_like (dm2) / 10000
ddm2[:3,:,:,:] *= -1
rhoD, PiD = get_dens (ddm1s, ddm2)[:2]
def sector (rhoT, PiT):
# Evaluate energy and potential at dens0 + densD = dens1
rho1 = rho0 + rhoT
Pi1 = Pi0 + PiT
eot1 = ot.eval_ot (rho1, Pi1, weights=weight)[0]
eotD = eot1 - eot0
vot1 = contract_fot (ot, fot0, rho0.sum (0), Pi0, rhoT.sum (0), PiT)
# Polynomial expansion
if PiT.ndim == 1: PiT = PiT[None,:]
nPi = min (PiT.shape[0], vPi0.shape[0])
vrho = vrho0# + vot1[0]
vPi = vPi0# + vot1[1]
eotD_lin = (vrho*rhoT.sum (0)).sum (0) + (vPi[:nPi]*PiT[:nPi]).sum (0)
E = np.dot (eot0, weight)
dE_num = np.dot (eotD, weight)
dE_lin = np.dot (eotD_lin, weight)
eotD_quad = (vot1[0]*rhoT.sum (0)).sum (0) + (vot1[1][:nPi]*PiT[:nPi]).sum (0)
dE_quad = np.dot (eotD_quad, weight) / 2 # Taylor series!!!
return dE_num, dE_lin, dE_quad
rhoT, PiT = np.zeros_like (rhoD), np.zeros_like (PiD)
if rhoT.ndim > 2:
rhoT[:,0,:] = rhoD[:,0,:]
else:
rhoT[:] = rhoD[:]
num, lin, quad = sector (rhoT, PiT)
rho_rat = (lin-num)/num
rho2_rat = (lin+quad-num)/num
rhoT[:] = PiT[:] = 0.0
if PiT.ndim > 1:
PiT[0,:] = PiD[0,:]
else:
PiT[:] = PiD[:]
num, lin, quad = sector (rhoT, PiT)
Pi_rat = (lin-num)/num
Pi2_rat = (lin+quad-num)/num
rhoT[:] = PiT[:] = 0.0
if rhoT.ndim > 2:
rhoT[:,1:4,:] = rhoD[:,1:4,:]
num, lin, quad = sector (rhoT, PiT)
rhop_rat = (lin-num)/num
rhop2_rat = (lin+quad-num)/num
else:
rhop_rat = rhop2_rat = 0.0
rhoT[:] = PiT[:] = 0.0
if PiT.ndim > 1 and vPi0.shape[0] > 1:
PiT[1:4,:] = PiD[1:4,:]
num, lin, quad = sector (rhoT, PiT)
Pip_rat = (lin-num)/num
Pip2_rat = (lin+quad-num)/num
else:
Pip_rat = Pip2_rat = 0.0
print (("{:>8s} " + ' '.join (['{:8.5f}',]*8)).format (otxc, rho_rat, rho2_rat, Pi_rat, Pi2_rat, rhop_rat, rhop2_rat, Pip_rat, Pip2_rat))
print("tHCH = {:.2f} degrees".format(bond_angle(carts, 3, 0, 2)))
print("eta = {:.2f} degrees".format(out_of_plane_angle(carts, 0, 2, 3, 1)))
# Energy calculation at initial geometry
h2co_casscf66_631g_xyz = '''C 0.534004 0.000000 0.000000
O -0.676110 0.000000 0.000000
H 1.102430 0.000000 0.920125
H 1.102430 0.000000 -0.920125'''
mol = gto.M(atom=h2co_casscf66_631g_xyz,
basis='6-31g',
symmetry=False,
verbose=logger.INFO,
output='h2co_sa2_tpbe66_631g_opt0.log')
mf = scf.RHF(mol).run()
mc = mcpdft.CASSCF(mf, 'tPBE', 6, 6, grids_level=9)
mc.fcisolver = csf_solver(mol, smult=1)
mc.state_average_([0.5, 0.5])
mc.kernel()
# Geometry optimization (my_call is optional; it just prints the geometry in internal coordinates every iteration)
print("Initial geometry: ")
h2co_geom_analysis(mol.atom_coords() * BOHR)
print("Initial energy: {:.8e}".format(mc.e_states[0]))
def my_call(env):
carts = env['mol'].atom_coords() * BOHR
h2co_geom_analysis(carts)
'convergence_drms': 1.0e-4, # Angstrom
'convergence_dmax': 1.5e-4, # Angstrom
}
lib.logger.TIMER_LEVEL = lib.logger.INFO
h2co_casscf66_631g_xyz = '''C 0.534004 0.000000 0.000000
O -0.676110 0.000000 0.000000
H 1.102430 0.000000 0.920125
H 1.102430 0.000000 -0.920125'''
mol = gto.M(atom=h2co_casscf66_631g_xyz,
basis='6-31g',
symmetry=False,
verbose=lib.logger.INFO,
output='h2co_sa2_tpbe66_631g_grad.log')
mf_conv = scf.RHF(mol).run()
mc_conv = mcpdft.CASSCF(mf_conv, 'tPBE', 6, 6, grids_level=6)
mc_conv.fcisolver = csf_solver(mol, smult=1)
mc_conv = mc_conv.state_average_([0.5, 0.5])
mc_conv.conv_tol = 1e-10
mc_conv.kernel()
mf = scf.RHF(mol).density_fit(auxbasis=df.aug_etb(mol)).run()
mc_df = mcpdft.CASSCF(mf, 'tPBE', 6, 6, grids_level=6)
mc_df.fcisolver = csf_solver(mol, smult=1)
mc_df = mc_df.state_average_([0.5, 0.5])
mc_df.conv_tol = 1e-10
mc_df.kernel()
try:
de_num = np.load('h2co_sa2_tpbe66_631g_grad_num.npy')
de_conv_0_num, de_conv_1_num, de_df_0_num, de_df_1_num = list(de_num)
denom[np.abs(dg_ref)<1e-8] = 1.0
dg_err /= denom
fmt_str = ' '.join (['{:10.3e}',]*hop.nmo)
print ("dg_test:")
for row in hop.unpack_uniq_var (dg_test): print (fmt_str.format (*row))
print ("dg_ref:")
for row in hop.unpack_uniq_var (dg_ref): print (fmt_str.format (*row))
fmt_str = ' '.join (['{:6.2f}',]*hop.nmo)
print ("dg_err (relative):")
for row in hop.unpack_uniq_var (dg_err): print (fmt_str.format (*row))
print ("")
from mrh.my_pyscf.tools import molden
for nelecas, lbl in zip ((2, (2,0)), ('Singlet','Triplet')):
#if nelecas is not 2: continue
print (lbl,'case\n')
for fnal in 'LDA,VWN3', 'PBE':
ks = dft.RKS (mol).set (xc=fnal).run ()
print ("H2 {} energy:".format (fnal),ks.e_tot)
exc_hop = ExcOrbitalHessianOperator (ks)
debug_hess (exc_hop)
for fnal in 'tLDA,VWN3', 'ftLDA,VWN3', 'tPBE':
#if fnal[:2] != 'ft': continue
mc = mcpdft.CASSCF (mf, fnal, 2, nelecas).run ()
mc.canonicalize_(cas_natorb=True)
molden.from_mcscf (mc, lbl + '.molden')
print ("H2 {} energy:".format (fnal),mc.e_tot)
eot_hop = EotOrbitalHessianOperator (mc, incl_d2rho=True)
debug_hess (eot_hop)
print ("")
idx_h0_1s = mol.search_ao_label ('0 H 1s')[0]
idx_h1_1s = mol.search_ao_label ('1 H 1s')[0]
idx_h0_2s = mol.search_ao_label ('0 H 2s')[0]
idx_h1_2s = mol.search_ao_label ('1 H 2s')[0]
dma = np.zeros ((nao, nao))
dmb = np.zeros ((nao, nao))
dma[idx_h0_1s,idx_h0_1s] = dmb[idx_h1_1s,idx_h1_1s] = dma[idx_h0_2s,idx_h0_2s] = dmb[idx_h1_2s,idx_h1_2s] = 1
dm0 = [dma, dmb]
# Restricted mean-field base of MC-SCF objects
mf = scf.RHF (mol).run ()
# MC-PDFT objects
if gsbasis:
gsmo = np.load (gsmofile)
mc = mcpdft.CASSCF (mf, transl_type + fnal, ncas, nelecas, grids_level = 3)
mo = mcscf.project_init_guess (mc, gsmo, prev_mol=gsmol)
molden.from_mo (mol, 'check_projection.molden', mo)
mc.kernel (mo)
mc = mc.as_scanner ()
else:
mc = mcpdft.CASSCF (mf, transl_type + fnal, ncas, nelecas, grids_level = 3).run ().as_scanner ()
np.save (mofile, mc.mo_coeff)
# Do MCSCF scan forwards
table = np.zeros ((HHrange.size, 9))
table[:,0] = HHrange
for ix, HHdist in enumerate (HHrange):
geom = 'H 0 0 0; H 0 0 {:.6f}'.format (HHdist)
table[ix,1] = mc (geom)
table[ix,2] = mc.e_mcscf
# comply with return signature
dg_a = dg[ncore:nocc]
dg_c = dg[:ncore, ncore:]
return dg_a, dg_c
if __name__ == '__main__':
from pyscf import gto, scf
from mrh.my_pyscf import mcpdft
mol = gto.M(atom='H 0 0 0; H 1.2 0 0',
basis='6-31g',
verbose=lib.logger.DEBUG,
output='orb_scf.log')
mf = scf.RHF(mol).run()
mc = mcpdft.CASSCF(mf, 'tPBE', 2, 2, grids_level=9).run()
print("Ordinary H2 tPBE energy:", mc.e_tot)
nao, nmo = mc.mo_coeff.shape
ncore, ncas, nelecas = mc.ncore, mc.ncas, mc.nelecas
nocc = ncore + ncas
casdm1, casdm2 = mc.fcisolver.make_rdm12(mc.ci, ncas, nelecas)
mc.update_jk_in_ah = mc1step_update_jk_in_ah
g_orb, gorb_update, h_op, h_diag = mc1step_gen_g_hop(
mc, mc.mo_coeff, 1, casdm1, casdm2, None)
print("g_orb:", g_orb)
print("gorb_update (1,mc.ci):", gorb_update(1, mc.ci))
print("h_op(0):", h_op(np.zeros_like(g_orb)))
print("h_diag:", h_diag)
# code in this block will only execute if you run this python script as the
# input directly: "python cmspdft3.py".
from pyscf import scf
from mrh.my_pyscf.tools import molden # My version is better for MC-SCF
from mrh.my_pyscf.fci import csf_solver
xyz = '''O 0.00000000 0.08111156 0.00000000
H 0.78620605 0.66349738 0.00000000
H -0.78620605 0.66349738 0.00000000'''
mol = gto.M(atom=xyz,
basis='sto-3g',
symmetry=False,
output='cmspdft3.log',
verbose=lib.logger.DEBUG)
mf = scf.RHF(mol).run()
mc = mcpdft.CASSCF(mf, 'tPBE', 4, 4).set(fcisolver=csf_solver(mol, 1))
mc = mc.state_average([
1.0 / 3,
] * 3).run()
molden.from_sa_mcscf(mc, 'h2o_sapdft_sa.molden', cas_natorb=True)
# ^ molden file with state-averaged NOs
for i in range(3):
fname = 'h2o_sapdft_ref{}.molden'.format(i)
# ^ molden file with ith reference state NOs
molden.from_sa_mcscf(mc, fname, state=i, cas_natorb=True)
conv, E_int, ci_int = kernel(mc, 3)
print("The iteration did{} converge".format((' not', '')[int(conv)]))
print("The intermediate-state energies are", E_int)
print(("Molden files with intermediate-state NOs are in "
"h2o_sapdft_int?.molden"))
fci = ci.CISD(mf).run().as_scanner()
# UKS comparison (initial guess must break symmetry!)
pks = scf.UKS(mol)
pks.xc = fnal
pks.kernel(dm0)
pks = pks.as_scanner()
hks = scf.UKS(mol)
hks.xc = kshfnal
hks.kernel(dm0)
hks = hks.as_scanner()
# MC-PDFT objects
if gsbasis:
gsmo = np.load(gsmofile)
mc = mcpdft.CASSCF(mf, transl_type + fnal, ncas, nelecas, grids_level=3)
mo = mcscf.project_init_guess(mc, gsmo, prev_mol=gsmol)
molden.from_mo(mol, 'check_projection.molden', mo)
mc.kernel(mo)
mc = mc.as_scanner()
else:
mc = mcpdft.CASSCF(mf, transl_type + fnal, ncas, nelecas,
grids_level=3).run().as_scanner()
mc0 = mcpdft.CASSCF(mf, otfnal0, ncas, nelecas,
grids_level=3).run().as_scanner()
mc1 = mcpdft.CASSCF(mf, otfnal1, ncas, nelecas,
grids_level=3).run().as_scanner()
mc2 = mcpdft.CASSCF(mf, otfnal2, ncas, nelecas,
grids_level=3).run().as_scanner()
molden.from_mcscf(mc0, moldenfile)
np.save(mofile, mc.mo_coeff)
