def residue(self, X, so_prop_ints):
prop_a = [
core.triplet(self.Co[0], x, self.Cv[0], True, False, False)
for x in so_prop_ints
]
prop_b = [
core.triplet(self.Co[1], x, self.Cv[1], True, False, False)
for x in so_prop_ints
]
return np.array([
X[0].vector_dot(u[0]) + X[1].vector_dot(u[1])
for u in zip(prop_a, prop_b)
])
def residue(self, X, so_prop_ints):
# return zeros if spin multiplicity of GS and ES differ
if not self.singlet and (self.mult_gs == 1):
return np.zeros(len(so_prop_ints))
prop = [core.triplet(self.Co, x, self.Cv, True, False, False) for x in so_prop_ints]
return np.sqrt(2.0) * np.array([X.vector_dot(u) for u in prop])
def _compute_fxc(PQrho, half_Saux, halfp_Saux, x_alpha, rho_thresh=1.e-8):
"""
Computes the gridless (P|fxc|Q) ALDA tensor.
"""
naux = PQrho.shape[0]
# Level it out
PQrho_lvl = core.triplet(half_Saux, PQrho, half_Saux, False, False, False)
# Rotate into a diagonal basis
rho = core.Vector("rho eigenvalues", naux)
U = core.Matrix("rho eigenvectors", naux, naux)
PQrho_lvl.diagonalize(U, rho, core.DiagonalizeOrder.Ascending)
# "Gridless DFT"
mask = rho.np < rho_thresh # Values too small cause singularities
rho.np[mask] = rho_thresh
dft_size = rho.shape[0]
inp = {"RHO_A": rho}
out = {
"V": core.Vector(dft_size),
"V_RHO_A": core.Vector(dft_size),
"V_RHO_A_RHO_A": core.Vector(dft_size)
}
func_x = core.LibXCFunctional('XC_LDA_X', True)
func_x.compute_functional(inp, out, dft_size, 2)
out["V_RHO_A_RHO_A"].scale(1.0 - x_alpha)
func_c = core.LibXCFunctional('XC_LDA_C_VWN', True)
func_c.compute_functional(inp, out, dft_size, 2)
out["V_RHO_A_RHO_A"].np[mask] = 0
# Rotate back
Ul = U.clone()
Ul.np[:] *= out["V_RHO_A_RHO_A"].np
tmp = core.doublet(Ul, U, False, True)
# Undo the leveling
return core.triplet(halfp_Saux, tmp, halfp_Saux, False, False, False)
def _compute_fxc(PQrho, half_Saux, halfp_Saux, rho_thresh=1.e-8):
"""
Computes the gridless (P|fxc|Q) ALDA tensor.
"""
naux = PQrho.shape[0]
# Level it out
PQrho_lvl = core.triplet(half_Saux, PQrho, half_Saux, False, False, False)
# Rotate into a diagonal basis
rho = core.Vector("rho eigenvalues", naux)
U = core.Matrix("rho eigenvectors", naux, naux)
PQrho_lvl.diagonalize(U, rho, core.DiagonalizeOrder.Ascending)
# "Gridless DFT"
mask = rho.np < rho_thresh # Values too small cause singularities
rho.np[mask] = rho_thresh
dft_size = rho.shape[0]
inp = {"RHO_A": rho}
out = {"V": core.Vector(dft_size),
"V_RHO_A": core.Vector(dft_size),
"V_RHO_A_RHO_A": core.Vector(dft_size)}
func_x = core.LibXCFunctional('XC_LDA_X', True)
func_x.compute_functional(inp, out, dft_size, 2)
func_c = core.LibXCFunctional('XC_LDA_C_VWN', True)
func_c.compute_functional(inp, out, dft_size, 2)
out["V_RHO_A_RHO_A"].np[mask] = 0
# Rotate back
Ul = U.clone()
Ul.np[:] *= out["V_RHO_A_RHO_A"].np
tmp = core.doublet(Ul, U, False, True)
# Undo the leveling
return core.triplet(halfp_Saux, tmp, halfp_Saux, False, False, False)
def _core_triplet(A, B, C, transA, transB, transC):
"""Multiply three matrices together.
.. deprecated:: 1.4
Use :py:func:`psi4.core.triplet` instead.
"""
warnings.warn(
"Using `psi4.core.Matrix.triplet` instead of `psi4.core.triplet` is deprecated, and in 1.4 it will stop working\n",
category=FutureWarning,
stacklevel=2)
return core.triplet(A, B, C, transA, transB, transC)
def orthogonalize(C, S):
nbf, nocc = C.shape
eigenvectors = core.Matrix(nocc, nocc)
eigvals = core.Vector(nocc)
sqrt_eigvals = core.Vector(nocc)
CTSC = core.triplet(C, S, C, True, False, False)
CTSC.diagonalize(eigenvectors, eigvals, core.DiagonalizeOrder.Ascending)
orthonormal = core.doublet(C, eigenvectors, False, False)
sqrt_eigvals.np[:] = np.sqrt(eigvals.np)
orthonormal.np[:, :] /= sqrt_eigvals.np[np.newaxis, :]
return orthonormal
def _ROHF_orbital_gradient(self, save_fock: bool,
max_diis_vectors: int) -> float:
# Only the inact-act, inact-vir, and act-vir rotations are non-redundant
dim_zero = core.Dimension(self.nirrep(), "Zero Dim")
noccpi = self.doccpi() + self.soccpi()
row_slice = core.Slice(dim_zero, noccpi)
col_slice = core.Slice(self.doccpi(), self.nmopi())
MOgradient = self.moFeff().get_block(row_slice, col_slice)
# Zero the active-active block
for h in range(MOgradient.nirrep()):
socc = self.soccpi()[h]
docc = self.doccpi()[h]
MOgradient.nph[h][docc:docc + socc, 0:socc] = 0
# Grab inact-act and act-vir orbs
# Ct is (nmo x nmo), not the (nso x nmo) you would expect
row_slice = core.Slice(dim_zero, self.nmopi())
col_slice = core.Slice(dim_zero, noccpi)
Cia = self.Ct().get_block(row_slice, col_slice)
col_slice = core.Slice(self.doccpi(), self.nmopi())
Cav = self.Ct().get_block(row_slice, col_slice)
# Back transform MOgradient
gradient = core.triplet(Cia, MOgradient, Cav, False, False, True)
if save_fock:
if not self.initialized_diis_manager_:
self.diis_manager_ = core.DIISManager(max_diis_vectors,
"HF DIIS vector",
RemovalPolicy.LargestError,
StoragePolicy.OnDisk)
self.diis_manager_.set_error_vector_size(gradient)
self.diis_manager_.set_vector_size(self.soFeff())
self.initialized_diis_manager_ = True
self.diis_manager_.add_entry(gradient, self.soFeff())
if self.options().get_bool("DIIS_RMS_ERROR"):
return gradient.rms()
else:
return gradient.absmax()
def __call__(self, mol1_wfn, mol2_wfn):
nbf = self.p.dimer_basis.nbf()
nocc = mol1_wfn.nalpha() + mol2_wfn.nalpha()
# Take the occupied orbitals from the two HF monomer wavefunctions
# and pack them (block diagonal) into the dimer basis set.
m1_OCC = mol1_wfn.Ca_subset('SO', 'OCC')
m2_OCC = mol2_wfn.Ca_subset('SO', 'OCC')
C = core.Matrix(nbf, nocc)
C.np[:mol1_wfn.nso(), :mol1_wfn.nalpha()] = m1_OCC.np[:, :]
C.np[-mol2_wfn.nso():, -mol2_wfn.nalpha():] = m2_OCC.np[:, :]
C = orthogonalize(C, self.p.dimer_S)
# At this point, it should be the case that
# C.T * S * C == I
np.testing.assert_array_almost_equal(
core.triplet(C, self.p.dimer_S, C, True, False, False),
np.eye(nocc))
self.jk.C_clear()
self.jk.C_left_add(C)
self.jk.compute()
J = self.jk.J()[0]
K = self.jk.K()[0]
D = self.jk.D()[0]
# 2T + 2V + 2J - K
FH = J.clone()
FH.zero()
FH.axpy(2, self.p.dimer_T)
FH.axpy(2, self.p.dimer_V)
FH.axpy(2, J)
FH.axpy(-1, K)
energy = FH.vector_dot(D) + self.p.dimer_basis.molecule().nuclear_repulsion_energy()
hl = energy - (mol1_wfn.energy() + mol2_wfn.energy())
return hl
def build_sapt_jk_cache(wfn_A, wfn_B, jk, do_print=True):
"""
Constructs the DCBS cache data required to compute ELST/EXCH/IND
"""
core.print_out("\n ==> Preparing SAPT Data Cache <== \n\n")
jk.print_header()
cache = {}
cache["wfn_A"] = wfn_A
cache["wfn_B"] = wfn_B
# First grab the orbitals
cache["Cocc_A"] = wfn_A.Ca_subset("AO", "OCC")
cache["Cvir_A"] = wfn_A.Ca_subset("AO", "VIR")
cache["Cocc_B"] = wfn_B.Ca_subset("AO", "OCC")
cache["Cvir_B"] = wfn_B.Ca_subset("AO", "VIR")
cache["eps_occ_A"] = wfn_A.epsilon_a_subset("AO", "OCC")
cache["eps_vir_A"] = wfn_A.epsilon_a_subset("AO", "VIR")
cache["eps_occ_B"] = wfn_B.epsilon_a_subset("AO", "OCC")
cache["eps_vir_B"] = wfn_B.epsilon_a_subset("AO", "VIR")
# Build the densities as HF takes an extra "step"
cache["D_A"] = core.doublet(cache["Cocc_A"], cache["Cocc_A"], False, True)
cache["D_B"] = core.doublet(cache["Cocc_B"], cache["Cocc_B"], False, True)
cache["P_A"] = core.doublet(cache["Cvir_A"], cache["Cvir_A"], False, True)
cache["P_B"] = core.doublet(cache["Cvir_B"], cache["Cvir_B"], False, True)
# Potential ints
mints = core.MintsHelper(wfn_A.basisset())
cache["V_A"] = mints.ao_potential()
# cache["V_A"].axpy(1.0, wfn_A.Va())
mints = core.MintsHelper(wfn_B.basisset())
cache["V_B"] = mints.ao_potential()
# cache["V_B"].axpy(1.0, wfn_B.Va())
# Anything else we might need
cache["S"] = wfn_A.S().clone()
# J and K matrices
jk.C_clear()
# Normal J/K for Monomer A
jk.C_left_add(wfn_A.Ca_subset("SO", "OCC"))
jk.C_right_add(wfn_A.Ca_subset("SO", "OCC"))
# Normal J/K for Monomer B
jk.C_left_add(wfn_B.Ca_subset("SO", "OCC"))
jk.C_right_add(wfn_B.Ca_subset("SO", "OCC"))
# K_O J/K
C_O_A = core.triplet(cache["D_B"], cache["S"], cache["Cocc_A"], False,
False, False)
jk.C_left_add(C_O_A)
jk.C_right_add(cache["Cocc_A"])
jk.compute()
# Clone them as the JK object will overwrite.
cache["J_A"] = jk.J()[0].clone()
cache["K_A"] = jk.K()[0].clone()
cache["J_B"] = jk.J()[1].clone()
cache["K_B"] = jk.K()[1].clone()
cache["J_O"] = jk.J()[2].clone()
cache["K_O"] = jk.K()[2].clone()
cache["K_O"].transpose_this()
monA_nr = wfn_A.molecule().nuclear_repulsion_energy()
monB_nr = wfn_B.molecule().nuclear_repulsion_energy()
dimer_nr = wfn_A.molecule().extract_subsets([1, 2
]).nuclear_repulsion_energy()
cache["nuclear_repulsion_energy"] = dimer_nr - monA_nr - monB_nr
return cache
def induction(cache,
jk,
do_print=True,
maxiter=12,
conv=1.e-8,
do_response=True,
Sinf=False,
sapt_jk_B=None):
"""
Compute Ind20 and Exch-Ind20 quantities from a SAPT cache and JK object.
"""
if do_print:
core.print_out("\n ==> E20 Induction <== \n\n")
# Build Induction and Exchange-Induction potentials
S = cache["S"]
D_A = cache["D_A"]
V_A = cache["V_A"]
J_A = cache["J_A"]
K_A = cache["K_A"]
D_B = cache["D_B"]
V_B = cache["V_B"]
J_B = cache["J_B"]
K_B = cache["K_B"]
K_O = cache["K_O"]
J_O = cache["J_O"]
jk.C_clear()
jk.C_left_add(core.Matrix.chain_dot(D_B, S, cache["Cocc_A"]))
jk.C_right_add(cache["Cocc_A"])
jk.C_left_add(core.Matrix.chain_dot(D_B, S, D_A, S, cache["Cocc_B"]))
jk.C_right_add(cache["Cocc_B"])
jk.C_left_add(core.Matrix.chain_dot(D_A, S, D_B, S, cache["Cocc_A"]))
jk.C_right_add(cache["Cocc_A"])
jk.compute()
J_Ot, J_P_B, J_P_A = jk.J()
K_Ot, K_P_B, K_P_A = jk.K()
# Exch-Ind Potential A
EX_A = K_B.clone()
EX_A.scale(-1.0)
EX_A.axpy(-2.0, J_O)
EX_A.axpy(1.0, K_O)
EX_A.axpy(2.0, J_P_B)
EX_A.axpy(-1.0, core.Matrix.chain_dot(S, D_B, V_A))
EX_A.axpy(-2.0, core.Matrix.chain_dot(S, D_B, J_A))
EX_A.axpy(1.0, core.Matrix.chain_dot(S, D_B, K_A))
EX_A.axpy(1.0, core.Matrix.chain_dot(S, D_B, S, D_A, V_B))
EX_A.axpy(2.0, core.Matrix.chain_dot(S, D_B, S, D_A, J_B))
EX_A.axpy(1.0, core.Matrix.chain_dot(S, D_B, V_A, D_B, S))
EX_A.axpy(2.0, core.Matrix.chain_dot(S, D_B, J_A, D_B, S))
EX_A.axpy(-1.0,
core.Matrix.chain_dot(S, D_B, K_O, trans=[False, False, True]))
EX_A.axpy(-1.0, core.Matrix.chain_dot(V_B, D_B, S))
EX_A.axpy(-2.0, core.Matrix.chain_dot(J_B, D_B, S))
EX_A.axpy(1.0, core.Matrix.chain_dot(K_B, D_B, S))
EX_A.axpy(1.0, core.Matrix.chain_dot(V_B, D_A, S, D_B, S))
EX_A.axpy(2.0, core.Matrix.chain_dot(J_B, D_A, S, D_B, S))
EX_A.axpy(-1.0, core.Matrix.chain_dot(K_O, D_B, S))
EX_A = core.Matrix.chain_dot(cache["Cocc_A"],
EX_A,
cache["Cvir_A"],
trans=[True, False, False])
# Exch-Ind Potential B
EX_B = K_A.clone()
EX_B.scale(-1.0)
EX_B.axpy(-2.0, J_O)
EX_B.axpy(1.0, K_O.transpose())
EX_B.axpy(2.0, J_P_A)
EX_B.axpy(-1.0, core.Matrix.chain_dot(S, D_A, V_B))
EX_B.axpy(-2.0, core.Matrix.chain_dot(S, D_A, J_B))
EX_B.axpy(1.0, core.Matrix.chain_dot(S, D_A, K_B))
EX_B.axpy(1.0, core.Matrix.chain_dot(S, D_A, S, D_B, V_A))
EX_B.axpy(2.0, core.Matrix.chain_dot(S, D_A, S, D_B, J_A))
EX_B.axpy(1.0, core.Matrix.chain_dot(S, D_A, V_B, D_A, S))
EX_B.axpy(2.0, core.Matrix.chain_dot(S, D_A, J_B, D_A, S))
EX_B.axpy(-1.0, core.Matrix.chain_dot(S, D_A, K_O))
EX_B.axpy(-1.0, core.Matrix.chain_dot(V_A, D_A, S))
EX_B.axpy(-2.0, core.Matrix.chain_dot(J_A, D_A, S))
EX_B.axpy(1.0, core.Matrix.chain_dot(K_A, D_A, S))
EX_B.axpy(1.0, core.Matrix.chain_dot(V_A, D_B, S, D_A, S))
EX_B.axpy(2.0, core.Matrix.chain_dot(J_A, D_B, S, D_A, S))
EX_B.axpy(-1.0,
core.Matrix.chain_dot(K_O, D_A, S, trans=[True, False, False]))
EX_B = core.Matrix.chain_dot(cache["Cocc_B"],
EX_B,
cache["Cvir_B"],
trans=[True, False, False])
# Build electrostatic potenital
w_A = cache["V_A"].clone()
w_A.axpy(2.0, cache["J_A"])
w_B = cache["V_B"].clone()
w_B.axpy(2.0, cache["J_B"])
w_B_MOA = core.triplet(cache["Cocc_A"], w_B, cache["Cvir_A"], True, False,
False)
w_A_MOB = core.triplet(cache["Cocc_B"], w_A, cache["Cvir_B"], True, False,
False)
# Do uncoupled
core.print_out(" => Uncoupled Induction <= \n\n")
unc_x_B_MOA = w_B_MOA.clone()
unc_x_B_MOA.np[:] /= (cache["eps_occ_A"].np.reshape(-1, 1) -
cache["eps_vir_A"].np)
unc_x_A_MOB = w_A_MOB.clone()
unc_x_A_MOB.np[:] /= (cache["eps_occ_B"].np.reshape(-1, 1) -
cache["eps_vir_B"].np)
unc_ind_ab = 2.0 * unc_x_B_MOA.vector_dot(w_B_MOA)
unc_ind_ba = 2.0 * unc_x_A_MOB.vector_dot(w_A_MOB)
unc_indexch_ab = 2.0 * unc_x_B_MOA.vector_dot(EX_A)
unc_indexch_ba = 2.0 * unc_x_A_MOB.vector_dot(EX_B)
ret = {}
ret["Ind20,u (A<-B)"] = unc_ind_ab
ret["Ind20,u (A->B)"] = unc_ind_ba
ret["Ind20,u"] = unc_ind_ab + unc_ind_ba
ret["Exch-Ind20,u (A<-B)"] = unc_indexch_ab
ret["Exch-Ind20,u (A->B)"] = unc_indexch_ba
ret["Exch-Ind20,u"] = unc_indexch_ba + unc_indexch_ab
plist = [
"Ind20,u (A<-B)", "Ind20,u (A->B)", "Ind20,u", "Exch-Ind20,u (A<-B)",
"Exch-Ind20,u (A->B)", "Exch-Ind20,u"
]
if do_print:
for name in plist:
# core.set_variable(name, ret[name])
core.print_out(print_sapt_var(name, ret[name], short=True))
core.print_out("\n")
# Exch-Ind without S^2
if Sinf:
nocc_A = cache["Cocc_A"].shape[1]
nocc_B = cache["Cocc_B"].shape[1]
SAB = core.triplet(cache["Cocc_A"], cache["S"], cache["Cocc_B"], True,
False, False)
num_occ = nocc_A + nocc_B
Sab = core.Matrix(num_occ, num_occ)
Sab.np[:nocc_A, nocc_A:] = SAB.np
Sab.np[nocc_A:, :nocc_A] = SAB.np.T
Sab.np[np.diag_indices_from(Sab.np)] += 1
Sab.power(-1.0, 1.e-14)
Tmo_AA = core.Matrix.from_array(Sab.np[:nocc_A, :nocc_A])
Tmo_BB = core.Matrix.from_array(Sab.np[nocc_A:, nocc_A:])
Tmo_AB = core.Matrix.from_array(Sab.np[:nocc_A, nocc_A:])
T_A = core.triplet(cache["Cocc_A"], Tmo_AA, cache["Cocc_A"], False,
False, True)
T_B = core.triplet(cache["Cocc_B"], Tmo_BB, cache["Cocc_B"], False,
False, True)
T_AB = core.triplet(cache["Cocc_A"], Tmo_AB, cache["Cocc_B"], False,
False, True)
sT_A = core.Matrix.chain_dot(cache["Cvir_A"],
unc_x_B_MOA,
Tmo_AA,
cache["Cocc_A"],
trans=[False, True, False, True])
sT_B = core.Matrix.chain_dot(cache["Cvir_B"],
unc_x_A_MOB,
Tmo_BB,
cache["Cocc_B"],
trans=[False, True, False, True])
sT_AB = core.Matrix.chain_dot(cache["Cvir_A"],
unc_x_B_MOA,
Tmo_AB,
cache["Cocc_B"],
trans=[False, True, False, True])
sT_BA = core.Matrix.chain_dot(cache["Cvir_B"],
unc_x_A_MOB,
Tmo_AB,
cache["Cocc_A"],
trans=[False, True, True, True])
jk.C_clear()
jk.C_left_add(core.Matrix.chain_dot(cache["Cocc_A"], Tmo_AA))
jk.C_right_add(cache["Cocc_A"])
jk.C_left_add(core.Matrix.chain_dot(cache["Cocc_B"], Tmo_BB))
jk.C_right_add(cache["Cocc_B"])
jk.C_left_add(core.Matrix.chain_dot(cache["Cocc_A"], Tmo_AB))
jk.C_right_add(cache["Cocc_B"])
jk.compute()
J_AA_inf, J_BB_inf, J_AB_inf = jk.J()
K_AA_inf, K_BB_inf, K_AB_inf = jk.K()
# A <- B
EX_AA_inf = V_B.clone()
EX_AA_inf.axpy(
-1.00,
core.Matrix.chain_dot(S, T_AB, V_B, trans=[False, True, False]))
EX_AA_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_B, V_B))
EX_AA_inf.axpy(2.00, J_AB_inf)
EX_AA_inf.axpy(
-2.00,
core.Matrix.chain_dot(S,
T_AB,
J_AB_inf,
trans=[False, True, False]))
EX_AA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_B, J_AB_inf))
EX_AA_inf.axpy(2.00, J_BB_inf)
EX_AA_inf.axpy(
-2.00,
core.Matrix.chain_dot(S,
T_AB,
J_BB_inf,
trans=[False, True, False]))
EX_AA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_B, J_BB_inf))
EX_AA_inf.axpy(-1.00, K_AB_inf.transpose())
EX_AA_inf.axpy(
1.00,
core.Matrix.chain_dot(S, T_AB, K_AB_inf, trans=[False, True,
True]))
EX_AA_inf.axpy(
1.00,
core.Matrix.chain_dot(S, T_B, K_AB_inf, trans=[False, False,
True]))
EX_AA_inf.axpy(-1.00, K_BB_inf)
EX_AA_inf.axpy(
1.00,
core.Matrix.chain_dot(S,
T_AB,
K_BB_inf,
trans=[False, True, False]))
EX_AA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_B, K_BB_inf))
EX_AB_inf = V_A.clone()
EX_AB_inf.axpy(
-1.00,
core.Matrix.chain_dot(S, T_AB, V_A, trans=[False, True, False]))
EX_AB_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_B, V_A))
EX_AB_inf.axpy(2.00, J_AA_inf)
EX_AB_inf.axpy(
-2.00,
core.Matrix.chain_dot(S,
T_AB,
J_AA_inf,
trans=[False, True, False]))
EX_AB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_B, J_AA_inf))
EX_AB_inf.axpy(2.00, J_AB_inf)
EX_AB_inf.axpy(
-2.00,
core.Matrix.chain_dot(S,
T_AB,
J_AB_inf,
trans=[False, True, False]))
EX_AB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_B, J_AB_inf))
EX_AB_inf.axpy(-1.00, K_AA_inf)
EX_AB_inf.axpy(
1.00,
core.Matrix.chain_dot(S,
T_AB,
K_AA_inf,
trans=[False, True, False]))
EX_AB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_B, K_AA_inf))
EX_AB_inf.axpy(-1.00, K_AB_inf)
EX_AB_inf.axpy(
1.00,
core.Matrix.chain_dot(S,
T_AB,
K_AB_inf,
trans=[False, True, False]))
EX_AB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_B, K_AB_inf))
# B <- A
EX_BB_inf = V_A.clone()
EX_BB_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_AB, V_A))
EX_BB_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_A, V_A))
EX_BB_inf.axpy(2.00, J_AB_inf)
EX_BB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_AB_inf))
EX_BB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_A, J_AB_inf))
EX_BB_inf.axpy(2.00, J_AA_inf)
EX_BB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_AA_inf))
EX_BB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_A, J_AA_inf))
EX_BB_inf.axpy(-1.00, K_AB_inf)
EX_BB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_AB_inf))
EX_BB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_A, K_AB_inf))
EX_BB_inf.axpy(-1.00, K_AA_inf)
EX_BB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_AA_inf))
EX_BB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_A, K_AA_inf))
EX_BA_inf = V_B.clone()
EX_BA_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_AB, V_B))
EX_BA_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_A, V_B))
EX_BA_inf.axpy(2.00, J_BB_inf)
EX_BA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_BB_inf))
EX_BA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_A, J_BB_inf))
EX_BA_inf.axpy(2.00, J_AB_inf)
EX_BA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_AB_inf))
EX_BA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_A, J_AB_inf))
EX_BA_inf.axpy(-1.00, K_BB_inf)
EX_BA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_BB_inf))
EX_BA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_A, K_BB_inf))
EX_BA_inf.axpy(-1.00, K_AB_inf.transpose())
EX_BA_inf.axpy(
1.00,
core.Matrix.chain_dot(S,
T_AB,
K_AB_inf,
trans=[False, False, True]))
EX_BA_inf.axpy(
1.00,
core.Matrix.chain_dot(S, T_A, K_AB_inf, trans=[False, False,
True]))
unc_ind_ab_total = 2.0 * (sT_A.vector_dot(EX_AA_inf) +
sT_AB.vector_dot(EX_AB_inf))
unc_ind_ba_total = 2.0 * (sT_B.vector_dot(EX_BB_inf) +
sT_BA.vector_dot(EX_BA_inf))
unc_indexch_ab_inf = unc_ind_ab_total - unc_ind_ab
unc_indexch_ba_inf = unc_ind_ba_total - unc_ind_ba
ret["Exch-Ind20,u (A<-B) (S^inf)"] = unc_indexch_ab_inf
ret["Exch-Ind20,u (A->B) (S^inf)"] = unc_indexch_ba_inf
ret["Exch-Ind20,u (S^inf)"] = unc_indexch_ba_inf + unc_indexch_ab_inf
if do_print:
for name in plist[3:]:
name = name + ' (S^inf)'
core.print_out(print_sapt_var(name, ret[name], short=True))
core.print_out("\n")
# Do coupled
if do_response:
core.print_out("\n => Coupled Induction <= \n\n")
x_B_MOA, x_A_MOB = _sapt_cpscf_solve(cache,
jk,
w_B_MOA,
w_A_MOB,
20,
1.e-6,
sapt_jk_B=sapt_jk_B)
ind_ab = 2.0 * x_B_MOA.vector_dot(w_B_MOA)
ind_ba = 2.0 * x_A_MOB.vector_dot(w_A_MOB)
indexch_ab = 2.0 * x_B_MOA.vector_dot(EX_A)
indexch_ba = 2.0 * x_A_MOB.vector_dot(EX_B)
ret["Ind20,r (A<-B)"] = ind_ab
ret["Ind20,r (A->B)"] = ind_ba
ret["Ind20,r"] = ind_ab + ind_ba
ret["Exch-Ind20,r (A<-B)"] = indexch_ab
ret["Exch-Ind20,r (A->B)"] = indexch_ba
ret["Exch-Ind20,r"] = indexch_ba + indexch_ab
if do_print:
core.print_out("\n")
for name in plist:
name = name.replace(",u", ",r")
# core.set_variable(name, ret[name])
core.print_out(print_sapt_var(name, ret[name], short=True))
core.print_out("\n")
# Exch-Ind without S^2
if Sinf:
cT_A = core.Matrix.chain_dot(cache["Cvir_A"],
x_B_MOA,
Tmo_AA,
cache["Cocc_A"],
trans=[False, True, False, True])
cT_B = core.Matrix.chain_dot(cache["Cvir_B"],
x_A_MOB,
Tmo_BB,
cache["Cocc_B"],
trans=[False, True, False, True])
cT_AB = core.Matrix.chain_dot(cache["Cvir_A"],
x_B_MOA,
Tmo_AB,
cache["Cocc_B"],
trans=[False, True, False, True])
cT_BA = core.Matrix.chain_dot(cache["Cvir_B"],
x_A_MOB,
Tmo_AB,
cache["Cocc_A"],
trans=[False, True, True, True])
ind_ab_total = 2.0 * (cT_A.vector_dot(EX_AA_inf) +
cT_AB.vector_dot(EX_AB_inf))
ind_ba_total = 2.0 * (cT_B.vector_dot(EX_BB_inf) +
cT_BA.vector_dot(EX_BA_inf))
indexch_ab_inf = ind_ab_total - ind_ab
indexch_ba_inf = ind_ba_total - ind_ba
ret["Exch-Ind20,r (A<-B) (S^inf)"] = indexch_ab_inf
ret["Exch-Ind20,r (A->B) (S^inf)"] = indexch_ba_inf
ret["Exch-Ind20,r (S^inf)"] = indexch_ba_inf + indexch_ab_inf
if do_print:
for name in plist[3:]:
name = name.replace(",u", ",r") + ' (S^inf)'
core.print_out(print_sapt_var(name, ret[name], short=True))
core.print_out("\n")
return ret
def exchange(cache, jk, do_print=True):
"""
Computes the E10 exchange (S^2 and S^inf) from a build_sapt_jk_cache datacache.
"""
if do_print:
core.print_out("\n ==> E10 Exchange <== \n\n")
# Build potenitals
h_A = cache["V_A"].clone()
h_A.axpy(2.0, cache["J_A"])
h_A.axpy(-1.0, cache["K_A"])
h_B = cache["V_B"].clone()
h_B.axpy(2.0, cache["J_B"])
h_B.axpy(-1.0, cache["K_B"])
w_A = cache["V_A"].clone()
w_A.axpy(2.0, cache["J_A"])
w_B = cache["V_B"].clone()
w_B.axpy(2.0, cache["J_B"])
# Build inverse exchange metric
nocc_A = cache["Cocc_A"].shape[1]
nocc_B = cache["Cocc_B"].shape[1]
SAB = core.triplet(cache["Cocc_A"], cache["S"], cache["Cocc_B"], True,
False, False)
num_occ = nocc_A + nocc_B
Sab = core.Matrix(num_occ, num_occ)
Sab.np[:nocc_A, nocc_A:] = SAB.np
Sab.np[nocc_A:, :nocc_A] = SAB.np.T
Sab.np[np.diag_indices_from(Sab.np)] += 1
Sab.power(-1.0, 1.e-14)
Sab.np[np.diag_indices_from(Sab.np)] -= 1.0
Tmo_AA = core.Matrix.from_array(Sab.np[:nocc_A, :nocc_A])
Tmo_BB = core.Matrix.from_array(Sab.np[nocc_A:, nocc_A:])
Tmo_AB = core.Matrix.from_array(Sab.np[:nocc_A, nocc_A:])
T_A = np.dot(cache["Cocc_A"], Tmo_AA).dot(cache["Cocc_A"].np.T)
T_B = np.dot(cache["Cocc_B"], Tmo_BB).dot(cache["Cocc_B"].np.T)
T_AB = np.dot(cache["Cocc_A"], Tmo_AB).dot(cache["Cocc_B"].np.T)
S = cache["S"]
D_A = cache["D_A"]
P_A = cache["P_A"]
D_B = cache["D_B"]
P_B = cache["P_B"]
# Compute the J and K matrices
jk.C_clear()
jk.C_left_add(cache["Cocc_A"])
jk.C_right_add(core.doublet(cache["Cocc_A"], Tmo_AA, False, False))
jk.C_left_add(cache["Cocc_B"])
jk.C_right_add(core.doublet(cache["Cocc_A"], Tmo_AB, False, False))
jk.C_left_add(cache["Cocc_A"])
jk.C_right_add(core.Matrix.chain_dot(P_B, S, cache["Cocc_A"]))
jk.compute()
JT_A, JT_AB, Jij = jk.J()
KT_A, KT_AB, Kij = jk.K()
# Start S^2
Exch_s2 = 0.0
tmp = core.Matrix.chain_dot(D_A, S, D_B, S, P_A)
Exch_s2 -= 2.0 * w_B.vector_dot(tmp)
tmp = core.Matrix.chain_dot(D_B, S, D_A, S, P_B)
Exch_s2 -= 2.0 * w_A.vector_dot(tmp)
tmp = core.Matrix.chain_dot(P_A, S, D_B)
Exch_s2 -= 2.0 * Kij.vector_dot(tmp)
if do_print:
core.print_out(print_sapt_var("Exch10(S^2) ", Exch_s2, short=True))
core.print_out("\n")
# Start Sinf
Exch10 = 0.0
Exch10 -= 2.0 * np.vdot(cache["D_A"], cache["K_B"])
Exch10 += 2.0 * np.vdot(T_A, h_B.np)
Exch10 += 2.0 * np.vdot(T_B, h_A.np)
Exch10 += 2.0 * np.vdot(T_AB, h_A.np + h_B.np)
Exch10 += 4.0 * np.vdot(T_B, JT_AB.np - 0.5 * KT_AB.np)
Exch10 += 4.0 * np.vdot(T_A, JT_AB.np - 0.5 * KT_AB.np)
Exch10 += 4.0 * np.vdot(T_B, JT_A.np - 0.5 * KT_A.np)
Exch10 += 4.0 * np.vdot(T_AB, JT_AB.np - 0.5 * KT_AB.np.T)
if do_print:
core.set_variable("Exch10", Exch10)
core.print_out(print_sapt_var("Exch10", Exch10, short=True))
core.print_out("\n")
return {"Exch10(S^2)": Exch_s2, "Exch10": Exch10}
def _core_triplet(A, B, C, transA, transB, transC):
warnings.warn(
"Using `psi4.core.Matrix.triplet` instead of `psi4.core.triplet` is deprecated, and in 1.4 it will stop working\n",
category=FutureWarning,
stacklevel=2)
return core.triplet(A, B, C, transA, transB, transC)
def _so_to_mo(self, X):
"""Transform (C_occ)^T X C_vir"""
return [core.triplet(self.Co[i], X[i], self.Cv[i], True, False, False) for i in (0, 1)]
def cpscf_linear_response(wfn, *args, **kwargs):
"""
Compute the static properties from a reference wavefunction. The currently implemented properties are
- dipole polarizability
- quadrupole polarizability
Parameters
----------
wfn : psi4 wavefunction
The reference wavefunction.
args : list
The list of arguments. For each argument, such as ``dipole polarizability``, will return the corresponding
response. The user may also choose to pass a list or tuple of custom vectors.
kwargs : dict
Options that control how the response is computed. The following options are supported (with default values):
- ``conv_tol``: 1e-5
- ``max_iter``: 10
- ``print_lvl``: 2
Returns
-------
responses : list
The list of responses.
"""
mints = core.MintsHelper(wfn.basisset())
# list of dictionaries to control response calculations, count how many user-supplied vectors we have
complete_dict = []
n_user = 0
for arg in args:
# for each string keyword, append the appropriate dictionary (vide supra) to our list
if isinstance(arg, str):
ret = property_dicts.get(arg)
if ret:
complete_dict.append(ret)
else:
raise ValidationError('Do not understand {}. Abort.'.format(arg))
# the user passed a list of vectors. absorb them into a dictionary
elif isinstance(arg, tuple) or isinstance(arg, list):
complete_dict.append({
'name': 'User Vectors',
'length': len(arg),
'vectors': arg,
'vector names': ['User Vector {}_{}'.format(n_user, i) for i in range(len(arg))]
})
n_user += len(arg)
# single vector passed. stored in a dictionary as a list of length 1 (can be handled as the case above that way)
# note: the length is set to '0' to designate that it was not really passed as a list
else:
complete_dict.append({
'name': 'User Vector',
'length': 0,
'vectors': [arg],
'vector names': ['User Vector {}'.format(n_user)]
})
n_user += 1
# vectors will be passed to the cphf solver, vector_names stores the corresponding names
vectors = []
vector_names = []
# construct the list of vectors. for the keywords, fetch the appropriate tensors from MintsHelper
for prop in complete_dict:
if 'User' in prop['name']:
for name, vec in zip(prop['vector names'], prop['vectors']):
vectors.append(vec)
vector_names.append(name)
else:
tmp_vectors = prop['mints_function'](mints)
for tmp in tmp_vectors:
tmp.scale(-2.0) # RHF only
vectors.append(tmp)
vector_names.append(tmp.name)
# do we have any vectors to work with?
if len(vectors) == 0:
raise ValidationError('I have no vectors to work with. Aborting.')
# print information on module, vectors that will be used
_print_header(complete_dict, n_user)
# fetch wavefunction information
nbf = wfn.nmo()
ndocc = wfn.nalpha()
nvirt = nbf - ndocc
c_occ = wfn.Ca_subset("AO", "OCC")
c_vir = wfn.Ca_subset("AO", "VIR")
# the vectors need to be in the MO basis. if they have the shape nbf x nbf, transform.
for i in range(len(vectors)):
shape = vectors[i].shape
if shape == (nbf, nbf):
vectors[i] = core.triplet(c_occ, vectors[i], c_vir, True, False, False)
# verify that this vector already has the correct shape
elif shape != (ndocc, nvirt):
raise ValidationError('ERROR: "{}" has an unrecognized shape. Must be either ({}, {}) or ({}, {})'.format(
vector_names[i], nbf, nbf, ndocc, nvirt))
# compute response vectors for each input vector
params = [kwargs.pop("conv_tol", 1.e-5), kwargs.pop("max_iter", 10), kwargs.pop("print_lvl", 2)]
responses = wfn.cphf_solve(vectors, *params)
# zip vectors, responses for easy access
vectors = {k: v for k, v in zip(vector_names, vectors)}
responses = {k: v for k, v in zip(vector_names, responses)}
# compute response values, format output
output = []
for prop in complete_dict:
# try to replicate the data structure of the input
if 'User' in prop['name']:
if prop['length'] == 0:
output.append(responses[prop['vector names'][0]])
else:
buf = []
for name in prop['vector names']:
buf.append(responses[name])
output.append(buf)
else:
names = prop['vector names']
dim = len(names)
buf = np.zeros((dim, dim))
for i, i_name in enumerate(names):
for j, j_name in enumerate(names):
buf[i, j] = -1.0 * vectors[i_name].vector_dot(responses[j_name])
output.append(buf)
_print_output(complete_dict, output)
return output
def cpscf_linear_response(wfn, *args, **kwargs):
"""
Compute the static properties from a reference wavefunction. The currently implemented properties are
- dipole polarizability
- quadrupole polarizability
Parameters
----------
wfn : psi4 wavefunction
The reference wavefunction.
args : list
The list of arguments. For each argument, such as ``dipole polarizability``, will return the corresponding
response. The user may also choose to pass a list or tuple of custom vectors.
kwargs : dict
Options that control how the response is computed. The following options are supported (with default values):
- ``conv_tol``: 1e-5
- ``max_iter``: 10
- ``print_lvl``: 2
Returns
-------
responses : list
The list of responses.
"""
mints = core.MintsHelper(wfn.basisset())
# list of dictionaries to control response calculations, count how many user-supplied vectors we have
complete_dict = []
n_user = 0
for arg in args:
# for each string keyword, append the appropriate dictionary (vide supra) to our list
if isinstance(arg, str):
ret = property_dicts.get(arg)
if ret:
complete_dict.append(ret)
else:
raise ValidationError(
'Do not understand {}. Abort.'.format(arg))
# the user passed a list of vectors. absorb them into a dictionary
elif isinstance(arg, tuple) or isinstance(arg, list):
complete_dict.append({
'name':
'User Vectors',
'length':
len(arg),
'vectors':
arg,
'vector names': [
'User Vector {}_{}'.format(n_user, i)
for i in range(len(arg))
]
})
n_user += len(arg)
# single vector passed. stored in a dictionary as a list of length 1 (can be handled as the case above that way)
# note: the length is set to '0' to designate that it was not really passed as a list
else:
complete_dict.append({
'name':
'User Vector',
'length':
0,
'vectors': [arg],
'vector names': ['User Vector {}'.format(n_user)]
})
n_user += 1
# vectors will be passed to the cphf solver, vector_names stores the corresponding names
vectors = []
vector_names = []
# construct the list of vectors. for the keywords, fetch the appropriate tensors from MintsHelper
for prop in complete_dict:
if 'User' in prop['name']:
for name, vec in zip(prop['vector names'], prop['vectors']):
vectors.append(vec)
vector_names.append(name)
else:
tmp_vectors = prop['mints_function'](mints)
for tmp in tmp_vectors:
tmp.scale(-2.0) # RHF only
vectors.append(tmp)
vector_names.append(tmp.name)
# do we have any vectors to work with?
if len(vectors) == 0:
raise ValidationError('I have no vectors to work with. Aborting.')
# print information on module, vectors that will be used
_print_header(complete_dict, n_user)
# fetch wavefunction information
nbf = wfn.nmo()
ndocc = wfn.nalpha()
nvirt = nbf - ndocc
c_occ = wfn.Ca_subset("AO", "OCC")
c_vir = wfn.Ca_subset("AO", "VIR")
# the vectors need to be in the MO basis. if they have the shape nbf x nbf, transform.
for i in range(len(vectors)):
shape = vectors[i].shape
if shape == (nbf, nbf):
vectors[i] = core.triplet(c_occ, vectors[i], c_vir, True, False,
False)
# verify that this vector already has the correct shape
elif shape != (ndocc, nvirt):
raise ValidationError(
'ERROR: "{}" has an unrecognized shape. Must be either ({}, {}) or ({}, {})'
.format(vector_names[i], nbf, nbf, ndocc, nvirt))
# compute response vectors for each input vector
params = [
kwargs.pop("conv_tol", 1.e-5),
kwargs.pop("max_iter", 10),
kwargs.pop("print_lvl", 2)
]
responses = wfn.cphf_solve(vectors, *params)
# zip vectors, responses for easy access
vectors = {k: v for k, v in zip(vector_names, vectors)}
responses = {k: v for k, v in zip(vector_names, responses)}
# compute response values, format output
output = []
for prop in complete_dict:
# try to replicate the data structure of the input
if 'User' in prop['name']:
if prop['length'] == 0:
output.append(responses[prop['vector names'][0]])
else:
buf = []
for name in prop['vector names']:
buf.append(responses[name])
output.append(buf)
else:
names = prop['vector names']
dim = len(names)
buf = np.zeros((dim, dim))
for i, i_name in enumerate(names):
for j, j_name in enumerate(names):
buf[i, j] = -1.0 * vectors[i_name].vector_dot(
responses[j_name])
output.append(buf)
_print_output(complete_dict, output)
return output
def build_sapt_jk_cache(wfn_A, wfn_B, jk, do_print=True):
"""
Constructs the DCBS cache data required to compute ELST/EXCH/IND
"""
core.print_out("\n ==> Preparing SAPT Data Cache <== \n\n")
jk.print_header()
cache = {}
cache["wfn_A"] = wfn_A
cache["wfn_B"] = wfn_B
# First grab the orbitals
cache["Cocc_A"] = wfn_A.Ca_subset("AO", "OCC")
cache["Cvir_A"] = wfn_A.Ca_subset("AO", "VIR")
cache["Cocc_B"] = wfn_B.Ca_subset("AO", "OCC")
cache["Cvir_B"] = wfn_B.Ca_subset("AO", "VIR")
cache["eps_occ_A"] = wfn_A.epsilon_a_subset("AO", "OCC")
cache["eps_vir_A"] = wfn_A.epsilon_a_subset("AO", "VIR")
cache["eps_occ_B"] = wfn_B.epsilon_a_subset("AO", "OCC")
cache["eps_vir_B"] = wfn_B.epsilon_a_subset("AO", "VIR")
# Build the densities as HF takes an extra "step"
cache["D_A"] = core.doublet(
cache["Cocc_A"], cache["Cocc_A"], False, True)
cache["D_B"] = core.doublet(
cache["Cocc_B"], cache["Cocc_B"], False, True)
cache["P_A"] = core.doublet(
cache["Cvir_A"], cache["Cvir_A"], False, True)
cache["P_B"] = core.doublet(
cache["Cvir_B"], cache["Cvir_B"], False, True)
# Potential ints
mints = core.MintsHelper(wfn_A.basisset())
cache["V_A"] = mints.ao_potential()
# cache["V_A"].axpy(1.0, wfn_A.Va())
mints = core.MintsHelper(wfn_B.basisset())
cache["V_B"] = mints.ao_potential()
# cache["V_B"].axpy(1.0, wfn_B.Va())
# Anything else we might need
cache["S"] = wfn_A.S().clone()
# J and K matrices
jk.C_clear()
# Normal J/K for Monomer A
jk.C_left_add(wfn_A.Ca_subset("SO", "OCC"))
jk.C_right_add(wfn_A.Ca_subset("SO", "OCC"))
# Normal J/K for Monomer B
jk.C_left_add(wfn_B.Ca_subset("SO", "OCC"))
jk.C_right_add(wfn_B.Ca_subset("SO", "OCC"))
# K_O J/K
C_O_A = core.triplet(
cache["D_B"], cache["S"], cache["Cocc_A"], False, False, False)
jk.C_left_add(C_O_A)
jk.C_right_add(cache["Cocc_A"])
jk.compute()
# Clone them as the JK object will overwrite.
cache["J_A"] = jk.J()[0].clone()
cache["K_A"] = jk.K()[0].clone()
cache["J_B"] = jk.J()[1].clone()
cache["K_B"] = jk.K()[1].clone()
cache["J_O"] = jk.J()[2].clone()
cache["K_O"] = jk.K()[2].clone()
cache["K_O"].transpose_this()
monA_nr = wfn_A.molecule().nuclear_repulsion_energy()
monB_nr = wfn_B.molecule().nuclear_repulsion_energy()
dimer_nr = wfn_A.molecule().extract_subsets(
[1, 2]).nuclear_repulsion_energy()
cache["nuclear_repulsion_energy"] = dimer_nr - monA_nr - monB_nr
return cache
def induction(cache, jk, do_print=True, maxiter=12, conv=1.e-8, do_response=True, Sinf=False, sapt_jk_B=None):
"""
Compute Ind20 and Exch-Ind20 quantities from a SAPT cache and JK object.
"""
if do_print:
core.print_out("\n ==> E20 Induction <== \n\n")
# Build Induction and Exchange-Induction potentials
S = cache["S"]
D_A = cache["D_A"]
V_A = cache["V_A"]
J_A = cache["J_A"]
K_A = cache["K_A"]
D_B = cache["D_B"]
V_B = cache["V_B"]
J_B = cache["J_B"]
K_B = cache["K_B"]
K_O = cache["K_O"]
J_O = cache["J_O"]
jk.C_clear()
jk.C_left_add(core.Matrix.chain_dot(D_B, S, cache["Cocc_A"]))
jk.C_right_add(cache["Cocc_A"])
jk.C_left_add(core.Matrix.chain_dot(D_B, S, D_A, S, cache["Cocc_B"]))
jk.C_right_add(cache["Cocc_B"])
jk.C_left_add(core.Matrix.chain_dot(D_A, S, D_B, S, cache["Cocc_A"]))
jk.C_right_add(cache["Cocc_A"])
jk.compute()
J_Ot, J_P_B, J_P_A = jk.J()
K_Ot, K_P_B, K_P_A = jk.K()
# Exch-Ind Potential A
EX_A = K_B.clone()
EX_A.scale(-1.0)
EX_A.axpy(-2.0, core.Matrix.chain_dot(S, D_B, J_A))
EX_A.axpy(1.0, K_O)
EX_A.axpy(-2.0, J_O)
EX_A.axpy(1.0, core.Matrix.chain_dot(S, D_B, K_A))
EX_A.axpy(-2.0, core.Matrix.chain_dot(J_B, D_B, S))
EX_A.axpy(1.0, core.Matrix.chain_dot(K_B, D_B, S))
EX_A.axpy(2.0, core.Matrix.chain_dot(S, D_B, J_A, D_B, S))
EX_A.axpy(2.0, core.Matrix.chain_dot(J_B, D_A, S, D_B, S))
EX_A.axpy(-1.0, core.Matrix.chain_dot(K_O, D_B, S))
EX_A.axpy(2.0, J_P_B)
EX_A.axpy(2.0, core.Matrix.chain_dot(S, D_B, S, D_A, J_B))
EX_A.axpy(-1.0, core.Matrix.chain_dot(S, D_B,
K_O, trans=[False, False, True]))
EX_A.axpy(-1.0, core.Matrix.chain_dot(S, D_B, V_A))
EX_A.axpy(-1.0, core.Matrix.chain_dot(V_B, D_B, S))
EX_A.axpy(1.0, core.Matrix.chain_dot(S, D_B, V_A, D_B, S))
EX_A.axpy(1.0, core.Matrix.chain_dot(V_B, D_A, S, D_B, S))
EX_A.axpy(1.0, core.Matrix.chain_dot(S, D_B, S, D_A, V_B))
EX_A = core.Matrix.chain_dot(
cache["Cocc_A"], EX_A, cache["Cvir_A"], trans=[True, False, False])
# Exch-Ind Potential B
EX_B = K_A.clone()
EX_B.scale(-1.0)
EX_B.axpy(-2.0, core.Matrix.chain_dot(S, D_A, J_B))
EX_B.axpy(1.0, K_O.transpose())
EX_B.axpy(-2.0, J_O)
EX_B.axpy(1.0, core.Matrix.chain_dot(S, D_A, K_B))
EX_B.axpy(-2.0, core.Matrix.chain_dot(J_A, D_A, S))
EX_B.axpy(1.0, core.Matrix.chain_dot(K_A, D_A, S))
EX_B.axpy(2.0, core.Matrix.chain_dot(S, D_A, J_B, D_A, S))
EX_B.axpy(2.0, core.Matrix.chain_dot(J_A, D_B, S, D_A, S))
EX_B.axpy(-1.0, core.Matrix.chain_dot(K_O,
D_A, S, trans=[True, False, False]))
EX_B.axpy(2.0, J_P_A)
EX_B.axpy(2.0, core.Matrix.chain_dot(S, D_A, S, D_B, J_A))
EX_B.axpy(-1.0, core.Matrix.chain_dot(S, D_A, K_O))
EX_B.axpy(-1.0, core.Matrix.chain_dot(S, D_A, V_B))
EX_B.axpy(-1.0, core.Matrix.chain_dot(V_A, D_A, S))
EX_B.axpy(1.0, core.Matrix.chain_dot(S, D_A, V_B, D_A, S))
EX_B.axpy(1.0, core.Matrix.chain_dot(V_A, D_B, S, D_A, S))
EX_B.axpy(1.0, core.Matrix.chain_dot(S, D_A, S, D_B, V_A))
EX_B = core.Matrix.chain_dot(
cache["Cocc_B"], EX_B, cache["Cvir_B"], trans=[True, False, False])
# Build electrostatic potenital
w_A = cache["V_A"].clone()
w_A.axpy(2.0, cache["J_A"])
w_B = cache["V_B"].clone()
w_B.axpy(2.0, cache["J_B"])
w_B_MOA = core.triplet(
cache["Cocc_A"], w_B, cache["Cvir_A"], True, False, False)
w_A_MOB = core.triplet(
cache["Cocc_B"], w_A, cache["Cvir_B"], True, False, False)
# Do uncoupled
core.print_out(" => Uncoupled Induction <= \n\n")
unc_x_B_MOA = w_B_MOA.clone()
unc_x_B_MOA.np[
:] /= (cache["eps_occ_A"].np.reshape(-1, 1) - cache["eps_vir_A"].np)
unc_x_A_MOB = w_A_MOB.clone()
unc_x_A_MOB.np[
:] /= (cache["eps_occ_B"].np.reshape(-1, 1) - cache["eps_vir_B"].np)
unc_ind_ab = 2.0 * unc_x_B_MOA.vector_dot(w_B_MOA)
unc_ind_ba = 2.0 * unc_x_A_MOB.vector_dot(w_A_MOB)
unc_indexch_ab = 2.0 * unc_x_B_MOA.vector_dot(EX_A)
unc_indexch_ba = 2.0 * unc_x_A_MOB.vector_dot(EX_B)
ret = {}
ret["Ind20,u (A<-B)"] = unc_ind_ab
ret["Ind20,u (A->B)"] = unc_ind_ba
ret["Ind20,u"] = unc_ind_ab + unc_ind_ba
ret["Exch-Ind20,u (A<-B)"] = unc_indexch_ab
ret["Exch-Ind20,u (A->B)"] = unc_indexch_ba
ret["Exch-Ind20,u"] = unc_indexch_ba + unc_indexch_ab
plist = ["Ind20,u (A<-B)", "Ind20,u (A->B)", "Ind20,u", "Exch-Ind20,u (A<-B)",
"Exch-Ind20,u (A->B)", "Exch-Ind20,u"]
if do_print:
for name in plist:
# core.set_variable(name, ret[name])
core.print_out(print_sapt_var(name, ret[name], short=True))
core.print_out("\n")
# Exch-Ind without S^2
if Sinf:
nocc_A = cache["Cocc_A"].shape[1]
nocc_B = cache["Cocc_B"].shape[1]
SAB = core.triplet(
cache["Cocc_A"], cache["S"], cache["Cocc_B"], True, False, False)
num_occ = nocc_A + nocc_B
Sab = core.Matrix(num_occ, num_occ)
Sab.np[:nocc_A, nocc_A:] = SAB.np
Sab.np[nocc_A:, :nocc_A] = SAB.np.T
Sab.np[np.diag_indices_from(Sab.np)] += 1
Sab.power(-1.0, 1.e-14)
Tmo_AA = core.Matrix.from_array(Sab.np[:nocc_A, :nocc_A])
Tmo_BB = core.Matrix.from_array(Sab.np[nocc_A:, nocc_A:])
Tmo_AB = core.Matrix.from_array(Sab.np[:nocc_A, nocc_A:])
T_A = core.triplet(cache["Cocc_A"], Tmo_AA, cache["Cocc_A"], False, False, True)
T_B = core.triplet(cache["Cocc_B"], Tmo_BB, cache["Cocc_B"], False, False, True)
T_AB = core.triplet(cache["Cocc_A"], Tmo_AB, cache["Cocc_B"], False, False, True)
sT_A = core.Matrix.chain_dot(cache["Cvir_A"], unc_x_B_MOA, Tmo_AA, cache["Cocc_A"],
trans=[False, True, False, True])
sT_B = core.Matrix.chain_dot(cache["Cvir_B"], unc_x_A_MOB, Tmo_BB, cache["Cocc_B"],
trans=[False, True, False, True])
sT_AB = core.Matrix.chain_dot(cache["Cvir_A"], unc_x_B_MOA, Tmo_AB, cache["Cocc_B"],
trans=[False, True, False, True])
sT_BA = core.Matrix.chain_dot(cache["Cvir_B"], unc_x_A_MOB, Tmo_AB, cache["Cocc_A"],
trans=[False, True, True, True])
jk.C_clear()
jk.C_left_add(core.Matrix.chain_dot(cache["Cocc_A"], Tmo_AA))
jk.C_right_add(cache["Cocc_A"])
jk.C_left_add(core.Matrix.chain_dot(cache["Cocc_B"], Tmo_BB))
jk.C_right_add(cache["Cocc_B"])
jk.C_left_add(core.Matrix.chain_dot(cache["Cocc_A"], Tmo_AB))
jk.C_right_add(cache["Cocc_B"])
jk.compute()
J_AA_inf, J_BB_inf, J_AB_inf = jk.J()
K_AA_inf, K_BB_inf, K_AB_inf = jk.K()
# A <- B
EX_AA_inf = V_B.clone()
EX_AA_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_AB, V_B, trans=[False, True, False]))
EX_AA_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_B, V_B))
EX_AA_inf.axpy(2.00, J_AB_inf)
EX_AA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_AB_inf, trans=[False, True, False]))
EX_AA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_B, J_AB_inf))
EX_AA_inf.axpy(2.00, J_BB_inf)
EX_AA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_BB_inf, trans=[False, True, False]))
EX_AA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_B, J_BB_inf))
EX_AA_inf.axpy(-1.00, K_AB_inf.transpose())
EX_AA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_AB_inf, trans=[False, True, True]))
EX_AA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_B, K_AB_inf, trans=[False, False, True]))
EX_AA_inf.axpy(-1.00, K_BB_inf)
EX_AA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_BB_inf, trans=[False, True, False]))
EX_AA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_B, K_BB_inf))
EX_AB_inf = V_A.clone()
EX_AB_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_AB, V_A, trans=[False, True, False]))
EX_AB_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_B, V_A))
EX_AB_inf.axpy(2.00, J_AA_inf)
EX_AB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_AA_inf, trans=[False, True, False]))
EX_AB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_B, J_AA_inf))
EX_AB_inf.axpy(2.00, J_AB_inf)
EX_AB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_AB_inf, trans=[False, True, False]))
EX_AB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_B, J_AB_inf))
EX_AB_inf.axpy(-1.00, K_AA_inf)
EX_AB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_AA_inf, trans=[False, True, False]))
EX_AB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_B, K_AA_inf))
EX_AB_inf.axpy(-1.00, K_AB_inf)
EX_AB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_AB_inf, trans=[False, True, False]))
EX_AB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_B, K_AB_inf))
# B <- A
EX_BB_inf = V_A.clone()
EX_BB_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_AB, V_A))
EX_BB_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_A, V_A))
EX_BB_inf.axpy(2.00, J_AB_inf)
EX_BB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_AB_inf))
EX_BB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_A, J_AB_inf))
EX_BB_inf.axpy(2.00, J_AA_inf)
EX_BB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_AA_inf))
EX_BB_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_A, J_AA_inf))
EX_BB_inf.axpy(-1.00, K_AB_inf)
EX_BB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_AB_inf))
EX_BB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_A, K_AB_inf))
EX_BB_inf.axpy(-1.00, K_AA_inf)
EX_BB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_AA_inf))
EX_BB_inf.axpy(1.00, core.Matrix.chain_dot(S, T_A, K_AA_inf))
EX_BA_inf = V_B.clone()
EX_BA_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_AB, V_B))
EX_BA_inf.axpy(-1.00, core.Matrix.chain_dot(S, T_A, V_B))
EX_BA_inf.axpy(2.00, J_BB_inf)
EX_BA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_BB_inf))
EX_BA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_A, J_BB_inf))
EX_BA_inf.axpy(2.00, J_AB_inf)
EX_BA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_AB, J_AB_inf))
EX_BA_inf.axpy(-2.00, core.Matrix.chain_dot(S, T_A, J_AB_inf))
EX_BA_inf.axpy(-1.00, K_BB_inf)
EX_BA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_BB_inf))
EX_BA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_A, K_BB_inf))
EX_BA_inf.axpy(-1.00, K_AB_inf.transpose())
EX_BA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_AB, K_AB_inf, trans=[False, False, True]))
EX_BA_inf.axpy(1.00, core.Matrix.chain_dot(S, T_A, K_AB_inf, trans=[False, False, True]))
unc_ind_ab_total = 2.0 * (sT_A.vector_dot(EX_AA_inf) + sT_AB.vector_dot(EX_AB_inf))
unc_ind_ba_total = 2.0 * (sT_B.vector_dot(EX_BB_inf) + sT_BA.vector_dot(EX_BA_inf))
unc_indexch_ab_inf = unc_ind_ab_total - unc_ind_ab
unc_indexch_ba_inf = unc_ind_ba_total - unc_ind_ba
ret["Exch-Ind20,u (A<-B) (S^inf)"] = unc_indexch_ab_inf
ret["Exch-Ind20,u (A->B) (S^inf)"] = unc_indexch_ba_inf
ret["Exch-Ind20,u (S^inf)"] = unc_indexch_ba_inf + unc_indexch_ab_inf
if do_print:
for name in plist[3:]:
name = name + ' (S^inf)'
core.print_out(print_sapt_var(name, ret[name], short=True))
core.print_out("\n")
# Do coupled
if do_response:
core.print_out("\n => Coupled Induction <= \n\n")
x_B_MOA, x_A_MOB = _sapt_cpscf_solve(
cache, jk, w_B_MOA, w_A_MOB, 20, 1.e-6, sapt_jk_B=sapt_jk_B)
ind_ab = 2.0 * x_B_MOA.vector_dot(w_B_MOA)
ind_ba = 2.0 * x_A_MOB.vector_dot(w_A_MOB)
indexch_ab = 2.0 * x_B_MOA.vector_dot(EX_A)
indexch_ba = 2.0 * x_A_MOB.vector_dot(EX_B)
ret["Ind20,r (A<-B)"] = ind_ab
ret["Ind20,r (A->B)"] = ind_ba
ret["Ind20,r"] = ind_ab + ind_ba
ret["Exch-Ind20,r (A<-B)"] = indexch_ab
ret["Exch-Ind20,r (A->B)"] = indexch_ba
ret["Exch-Ind20,r"] = indexch_ba + indexch_ab
if do_print:
core.print_out("\n")
for name in plist:
name = name.replace(",u", ",r")
# core.set_variable(name, ret[name])
core.print_out(print_sapt_var(name, ret[name], short=True))
core.print_out("\n")
# Exch-Ind without S^2
if Sinf:
cT_A = core.Matrix.chain_dot(cache["Cvir_A"], x_B_MOA, Tmo_AA, cache["Cocc_A"],
trans=[False, True, False, True])
cT_B = core.Matrix.chain_dot(cache["Cvir_B"], x_A_MOB, Tmo_BB, cache["Cocc_B"],
trans=[False, True, False, True])
cT_AB = core.Matrix.chain_dot(cache["Cvir_A"], x_B_MOA, Tmo_AB, cache["Cocc_B"],
trans=[False, True, False, True])
cT_BA = core.Matrix.chain_dot(cache["Cvir_B"], x_A_MOB, Tmo_AB, cache["Cocc_A"],
trans=[False, True, True, True])
ind_ab_total = 2.0 * (cT_A.vector_dot(EX_AA_inf) + cT_AB.vector_dot(EX_AB_inf))
ind_ba_total = 2.0 * (cT_B.vector_dot(EX_BB_inf) + cT_BA.vector_dot(EX_BA_inf))
indexch_ab_inf = ind_ab_total - ind_ab
indexch_ba_inf = ind_ba_total - ind_ba
ret["Exch-Ind20,r (A<-B) (S^inf)"] = indexch_ab_inf
ret["Exch-Ind20,r (A->B) (S^inf)"] = indexch_ba_inf
ret["Exch-Ind20,r (S^inf)"] = indexch_ba_inf + indexch_ab_inf
if do_print:
for name in plist[3:]:
name = name.replace(",u", ",r") + ' (S^inf)'
core.print_out(print_sapt_var(name, ret[name], short=True))
core.print_out("\n")
return ret
def exchange(cache, jk, do_print=True):
"""
Computes the E10 exchange (S^2 and S^inf) from a build_sapt_jk_cache datacache.
"""
if do_print:
core.print_out("\n ==> E10 Exchange <== \n\n")
# Build potenitals
h_A = cache["V_A"].clone()
h_A.axpy(2.0, cache["J_A"])
h_A.axpy(-1.0, cache["K_A"])
h_B = cache["V_B"].clone()
h_B.axpy(2.0, cache["J_B"])
h_B.axpy(-1.0, cache["K_B"])
w_A = cache["V_A"].clone()
w_A.axpy(2.0, cache["J_A"])
w_B = cache["V_B"].clone()
w_B.axpy(2.0, cache["J_B"])
# Build inverse exchange metric
nocc_A = cache["Cocc_A"].shape[1]
nocc_B = cache["Cocc_B"].shape[1]
SAB = core.triplet(
cache["Cocc_A"], cache["S"], cache["Cocc_B"], True, False, False)
num_occ = nocc_A + nocc_B
Sab = core.Matrix(num_occ, num_occ)
Sab.np[:nocc_A, nocc_A:] = SAB.np
Sab.np[nocc_A:, :nocc_A] = SAB.np.T
Sab.np[np.diag_indices_from(Sab.np)] += 1
Sab.power(-1.0, 1.e-14)
Sab.np[np.diag_indices_from(Sab.np)] -= 1.0
Tmo_AA = core.Matrix.from_array(Sab.np[:nocc_A, :nocc_A])
Tmo_BB = core.Matrix.from_array(Sab.np[nocc_A:, nocc_A:])
Tmo_AB = core.Matrix.from_array(Sab.np[:nocc_A, nocc_A:])
T_A = np.dot(cache["Cocc_A"], Tmo_AA).dot(cache["Cocc_A"].np.T)
T_B = np.dot(cache["Cocc_B"], Tmo_BB).dot(cache["Cocc_B"].np.T)
T_AB = np.dot(cache["Cocc_A"], Tmo_AB).dot(cache["Cocc_B"].np.T)
S = cache["S"]
D_A = cache["D_A"]
P_A = cache["P_A"]
D_B = cache["D_B"]
P_B = cache["P_B"]
# Compute the J and K matrices
jk.C_clear()
jk.C_left_add(cache["Cocc_A"])
jk.C_right_add(core.doublet(cache["Cocc_A"], Tmo_AA, False, False))
jk.C_left_add(cache["Cocc_B"])
jk.C_right_add(core.doublet(cache["Cocc_A"], Tmo_AB, False, False))
jk.C_left_add(cache["Cocc_A"])
jk.C_right_add(core.Matrix.chain_dot(P_B, S, cache["Cocc_A"]))
jk.compute()
JT_A, JT_AB, Jij = jk.J()
KT_A, KT_AB, Kij = jk.K()
# Start S^2
Exch_s2 = 0.0
tmp = core.Matrix.chain_dot(D_A, S, D_B, S, P_A)
Exch_s2 -= 2.0 * w_B.vector_dot(tmp)
tmp = core.Matrix.chain_dot(D_B, S, D_A, S, P_B)
Exch_s2 -= 2.0 * w_A.vector_dot(tmp)
tmp = core.Matrix.chain_dot(P_A, S, D_B)
Exch_s2 -= 2.0 * Kij.vector_dot(tmp)
if do_print:
core.print_out(print_sapt_var("Exch10(S^2) ", Exch_s2, short=True))
core.print_out("\n")
# Start Sinf
Exch10 = 0.0
Exch10 -= 2.0 * np.vdot(cache["D_A"], cache["K_B"])
Exch10 += 2.0 * np.vdot(T_A, h_B.np)
Exch10 += 2.0 * np.vdot(T_B, h_A.np)
Exch10 += 2.0 * np.vdot(T_AB, h_A.np + h_B.np)
Exch10 += 4.0 * np.vdot(T_B, JT_AB.np - 0.5 * KT_AB.np)
Exch10 += 4.0 * np.vdot(T_A, JT_AB.np - 0.5 * KT_AB.np)
Exch10 += 4.0 * np.vdot(T_B, JT_A.np - 0.5 * KT_A.np)
Exch10 += 4.0 * np.vdot(T_AB, JT_AB.np - 0.5 * KT_AB.np.T)
if do_print:
core.set_variable("Exch10", Exch10)
core.print_out(print_sapt_var("Exch10", Exch10, short=True))
core.print_out("\n")
return {"Exch10(S^2)": Exch_s2, "Exch10": Exch10}
def df_fdds_dispersion(primary,
auxiliary,
cache,
leg_points=10,
leg_lambda=0.3,
do_print=True):
rho_thresh = core.get_option("SAPT", "SAPT_FDDS_V2_RHO_CUTOFF")
if do_print:
core.print_out("\n ==> E20 Dispersion (CHF FDDS) <== \n\n")
core.print_out(" Legendre Points: % 10d\n" % leg_points)
core.print_out(" Lambda Shift: % 10.3f\n" % leg_lambda)
core.print_out(" Fxc Kernal: % 10s\n" % "ALDA")
core.print_out(" (P|Fxc|Q) Thresh: % 8.3e\n" % rho_thresh)
# Build object
df_matrix_keys = ["Cocc_A", "Cvir_A", "Cocc_B", "Cvir_B"]
fdds_matrix_cache = {key: cache[key] for key in df_matrix_keys}
df_vector_keys = ["eps_occ_A", "eps_vir_A", "eps_occ_B", "eps_vir_B"]
fdds_vector_cache = {key: cache[key] for key in df_vector_keys}
fdds_obj = core.FDDS_Dispersion(primary, auxiliary, fdds_matrix_cache,
fdds_vector_cache)
# Aux Densities
D = fdds_obj.project_densities([cache["D_A"], cache["D_B"]])
# Temps
half_Saux = fdds_obj.aux_overlap().clone()
half_Saux.power(-0.5, 1.e-12)
halfp_Saux = fdds_obj.aux_overlap().clone()
halfp_Saux.power(0.5, 1.e-12)
# Builds potentials
W_A = fdds_obj.metric().clone()
W_A.axpy(1.0,
_compute_fxc(D[0], half_Saux, halfp_Saux, rho_thresh=rho_thresh))
W_B = fdds_obj.metric().clone()
W_B.axpy(1.0,
_compute_fxc(D[1], half_Saux, halfp_Saux, rho_thresh=rho_thresh))
# Nuke the densities
del D
metric = fdds_obj.metric()
metric_inv = fdds_obj.metric_inv()
# Integrate
core.print_out("\n => Time Integration <= \n\n")
val_pack = ("Omega", "Weight", "Disp20,u", "Disp20", "time [s]")
core.print_out("% 12s % 12s % 14s % 14s % 10s\n" % val_pack)
# print("% 12s % 12s % 14s % 14s % 10s" % val_pack)
start_time = time.time()
total_uc = 0
total_c = 0
for point, weight in zip(*np.polynomial.legendre.leggauss(leg_points)):
omega = leg_lambda * (1.0 - point) / (1.0 + point)
lambda_scale = ((2.0 * leg_lambda) / (point + 1.0)**2)
# Monomer A
X_A = fdds_obj.form_unc_amplitude("A", omega)
# Coupled A
X_A_coupled = X_A.clone()
XSW_A = core.triplet(X_A, metric_inv, W_A, False, False, False)
amplitude_inv = metric.clone()
amplitude_inv.axpy(1.0, XSW_A)
nremoved = 0
amplitude = amplitude_inv.pseudoinverse(1.e-13, nremoved)
amplitude.transpose_this() # Why is this coming out transposed?
X_A_coupled.axpy(
-1.0, core.triplet(XSW_A, amplitude, X_A, False, False, False))
del XSW_A, amplitude
X_B = fdds_obj.form_unc_amplitude("B", omega)
# print(np.linalg.norm(X_B))
# Coupled B
X_B_coupled = X_B.clone()
XSW_B = core.triplet(X_B, metric_inv, W_B, False, False, False)
amplitude_inv = metric.clone()
amplitude_inv.axpy(1.0, XSW_B)
amplitude = amplitude_inv.pseudoinverse(1.e-13, nremoved)
amplitude.transpose_this() # Why is this coming out transposed?
X_B_coupled.axpy(
-1.0, core.triplet(XSW_B, amplitude, X_B, False, False, False))
del XSW_B, amplitude
# Make sure the results are symmetrized
for tensor in [X_A, X_B, X_A_coupled, X_B_coupled]:
tensor.add(tensor.transpose())
tensor.scale(0.5)
# Combine
tmp_uc = core.triplet(metric_inv, X_A, metric_inv, False, False, False)
value_uc = tmp_uc.vector_dot(X_B)
del tmp_uc
tmp_c = core.triplet(metric_inv, X_A_coupled, metric_inv, False, False,
False)
value_c = tmp_c.vector_dot(X_B_coupled)
del tmp_c
# Tally
total_uc += value_uc * weight * lambda_scale
total_c += value_c * weight * lambda_scale
if do_print:
tmp_disp_unc = value_uc * weight * lambda_scale
tmp_disp = value_c * weight * lambda_scale
fdds_time = time.time() - start_time
val_pack = (omega, weight, tmp_disp_unc, tmp_disp, fdds_time)
core.print_out("% 12.3e % 12.3e % 14.3e % 14.3e %10d\n" % val_pack)
# print("% 12.3e % 12.3e % 14.3e % 14.3e %10d" % val_pack)
Disp20_uc = -1.0 / (2.0 * np.pi) * total_uc
Disp20_c = -1.0 / (2.0 * np.pi) * total_c
core.print_out("\n")
core.print_out(print_sapt_var("Disp20,u", Disp20_uc, short=True) + "\n")
core.print_out(print_sapt_var("Disp20", Disp20_c, short=True) + "\n")
return {"Disp20,FDDS (unc)": Disp20_uc, "Disp20": Disp20_c}
def _so_to_mo(self, X):
"""Transform (C_occ)^T X C_vir"""
return core.triplet(self.Co, X, self.Cv, True, False, False)
def _core_triplet(A, B, C, transA, transB, transC):
warnings.warn(
"Using `psi4.core.Matrix.triplet` instead of `psi4.core.triplet` is deprecated, and in 1.4 it will stop working\n",
category=FutureWarning,
stacklevel=2)
return core.triplet(A, B, C, transA, transB, transC)
def _so_to_mo(self, X):
"""Transform (C_occ)^T X C_vir"""
return core.triplet(self.Co, X, self.Cv, True, False, False)
def mcscf_solver(ref_wfn):
# Build CIWavefunction
core.prepare_options_for_module("DETCI")
ciwfn = core.CIWavefunction(ref_wfn)
# Hush a lot of CI output
ciwfn.set_print(0)
# Begin with a normal two-step
step_type = 'Initial CI'
total_step = core.Matrix("Total step", ciwfn.get_dimension('OA'), ciwfn.get_dimension('AV'))
start_orbs = ciwfn.get_orbitals("ROT").clone()
ciwfn.set_orbitals("ROT", start_orbs)
# Grab da options
mcscf_orb_grad_conv = core.get_option("DETCI", "MCSCF_R_CONVERGENCE")
mcscf_e_conv = core.get_option("DETCI", "MCSCF_E_CONVERGENCE")
mcscf_max_macroiteration = core.get_option("DETCI", "MCSCF_MAXITER")
mcscf_type = core.get_option("DETCI", "MCSCF_TYPE")
mcscf_d_file = core.get_option("DETCI", "CI_FILE_START") + 3
mcscf_nroots = core.get_option("DETCI", "NUM_ROOTS")
mcscf_wavefunction_type = core.get_option("DETCI", "WFN")
mcscf_ndet = ciwfn.ndet()
mcscf_nuclear_energy = ciwfn.molecule().nuclear_repulsion_energy()
mcscf_steplimit = core.get_option("DETCI", "MCSCF_MAX_ROT")
mcscf_rotate = core.get_option("DETCI", "MCSCF_ROTATE")
# DIIS info
mcscf_diis_start = core.get_option("DETCI", "MCSCF_DIIS_START")
mcscf_diis_freq = core.get_option("DETCI", "MCSCF_DIIS_FREQ")
mcscf_diis_error_type = core.get_option("DETCI", "MCSCF_DIIS_ERROR_TYPE")
mcscf_diis_max_vecs = core.get_option("DETCI", "MCSCF_DIIS_MAX_VECS")
# One-step info
mcscf_target_conv_type = core.get_option("DETCI", "MCSCF_ALGORITHM")
mcscf_so_start_grad = core.get_option("DETCI", "MCSCF_SO_START_GRAD")
mcscf_so_start_e = core.get_option("DETCI", "MCSCF_SO_START_E")
mcscf_current_step_type = 'Initial CI'
# Start with SCF energy and other params
scf_energy = ciwfn.variable("HF TOTAL ENERGY")
eold = scf_energy
norb_iter = 1
converged = False
ah_step = False
qc_step = False
approx_integrals_only = True
# Fake info to start with the initial diagonalization
ediff = 1.e-4
orb_grad_rms = 1.e-3
# Grab needed objects
diis_obj = solvers.DIIS(mcscf_diis_max_vecs)
mcscf_obj = ciwfn.mcscf_object()
# Execute the rotate command
for rot in mcscf_rotate:
if len(rot) != 4:
raise p4util.PsiException("Each element of the MCSCF rotate command requires 4 arguements (irrep, orb1, orb2, theta).")
irrep, orb1, orb2, theta = rot
if irrep > ciwfn.Ca().nirrep():
raise p4util.PsiException("MCSCF_ROTATE: Expression %s irrep number is larger than the number of irreps" %
(str(rot)))
if max(orb1, orb2) > ciwfn.Ca().coldim()[irrep]:
raise p4util.PsiException("MCSCF_ROTATE: Expression %s orbital number exceeds number of orbitals in irrep" %
(str(rot)))
theta = np.deg2rad(theta)
x = ciwfn.Ca().nph[irrep][:, orb1].copy()
y = ciwfn.Ca().nph[irrep][:, orb2].copy()
xp = np.cos(theta) * x - np.sin(theta) * y
yp = np.sin(theta) * x + np.cos(theta) * y
ciwfn.Ca().nph[irrep][:, orb1] = xp
ciwfn.Ca().nph[irrep][:, orb2] = yp
# Limited RAS functionality
if core.get_local_option("DETCI", "WFN") == "RASSCF" and mcscf_target_conv_type != "TS":
core.print_out("\n Warning! Only the TS algorithm for RASSCF wavefunction is currently supported.\n")
core.print_out(" Switching to the TS algorithm.\n\n")
mcscf_target_conv_type = "TS"
# Print out headers
if mcscf_type == "CONV":
mtype = " @MCSCF"
core.print_out("\n ==> Starting MCSCF iterations <==\n\n")
core.print_out(" Iter Total Energy Delta E Orb RMS CI RMS NCI NORB\n")
elif mcscf_type == "DF":
mtype = " @DF-MCSCF"
core.print_out("\n ==> Starting DF-MCSCF iterations <==\n\n")
core.print_out(" Iter Total Energy Delta E Orb RMS CI RMS NCI NORB\n")
else:
mtype = " @AO-MCSCF"
core.print_out("\n ==> Starting AO-MCSCF iterations <==\n\n")
core.print_out(" Iter Total Energy Delta E Orb RMS CI RMS NCI NORB\n")
# Iterate !
for mcscf_iter in range(1, mcscf_max_macroiteration + 1):
# Transform integrals, diagonalize H
ciwfn.transform_mcscf_integrals(approx_integrals_only)
nci_iter = ciwfn.diag_h(abs(ediff) * 1.e-2, orb_grad_rms * 1.e-3)
# After the first diag we need to switch to READ
ciwfn.set_ci_guess("DFILE")
ciwfn.form_opdm()
ciwfn.form_tpdm()
ci_grad_rms = ciwfn.variable("DETCI AVG DVEC NORM")
# Update MCSCF object
Cocc = ciwfn.get_orbitals("DOCC")
Cact = ciwfn.get_orbitals("ACT")
Cvir = ciwfn.get_orbitals("VIR")
opdm = ciwfn.get_opdm(-1, -1, "SUM", False)
tpdm = ciwfn.get_tpdm("SUM", True)
mcscf_obj.update(Cocc, Cact, Cvir, opdm, tpdm)
current_energy = ciwfn.variable("MCSCF TOTAL ENERGY")
orb_grad_rms = mcscf_obj.gradient_rms()
ediff = current_energy - eold
# Print iterations
print_iteration(mtype, mcscf_iter, current_energy, ediff, orb_grad_rms, ci_grad_rms,
nci_iter, norb_iter, mcscf_current_step_type)
eold = current_energy
if mcscf_current_step_type == 'Initial CI':
mcscf_current_step_type = 'TS'
# Check convergence
if (orb_grad_rms < mcscf_orb_grad_conv) and (abs(ediff) < abs(mcscf_e_conv)) and\
(mcscf_iter > 3) and not qc_step:
core.print_out("\n %s has converged!\n\n" % mtype);
converged = True
break
# Which orbital convergence are we doing?
if ah_step:
converged, norb_iter, step = ah_iteration(mcscf_obj, print_micro=False)
norb_iter += 1
if converged:
mcscf_current_step_type = 'AH'
else:
core.print_out(" !Warning. Augmented Hessian did not converge. Taking an approx step.\n")
step = mcscf_obj.approx_solve()
mcscf_current_step_type = 'TS, AH failure'
else:
step = mcscf_obj.approx_solve()
step_type = 'TS'
maxstep = step.absmax()
if maxstep > mcscf_steplimit:
core.print_out(' Warning! Maxstep = %4.2f, scaling to %4.2f\n' % (maxstep, mcscf_steplimit))
step.scale(mcscf_steplimit / maxstep)
xstep = total_step.clone()
total_step.add(step)
# Do or add DIIS
if (mcscf_iter >= mcscf_diis_start) and ("TS" in mcscf_current_step_type):
# Figure out DIIS error vector
if mcscf_diis_error_type == "GRAD":
error = core.triplet(ciwfn.get_orbitals("OA"),
mcscf_obj.gradient(),
ciwfn.get_orbitals("AV"),
False, False, True)
else:
error = step
diis_obj.add(total_step, error)
if not (mcscf_iter % mcscf_diis_freq):
total_step = diis_obj.extrapolate()
mcscf_current_step_type = 'TS, DIIS'
# Build the rotation by continuous updates
if mcscf_iter == 1:
totalU = mcscf_obj.form_rotation_matrix(total_step)
else:
xstep.axpy(-1.0, total_step)
xstep.scale(-1.0)
Ustep = mcscf_obj.form_rotation_matrix(xstep)
totalU = core.doublet(totalU, Ustep, False, False)
# Build the rotation directly (not recommended)
# orbs_mat = mcscf_obj.Ck(start_orbs, total_step)
# Finally rotate and set orbitals
orbs_mat = core.doublet(start_orbs, totalU, False, False)
ciwfn.set_orbitals("ROT", orbs_mat)
# Figure out what the next step should be
if (orb_grad_rms < mcscf_so_start_grad) and (abs(ediff) < abs(mcscf_so_start_e)) and\
(mcscf_iter >= 2):
if mcscf_target_conv_type == 'AH':
approx_integrals_only = False
ah_step = True
elif mcscf_target_conv_type == 'OS':
approx_integrals_only = False
mcscf_current_step_type = 'OS, Prep'
break
else:
continue
#raise p4util.PsiException("")
# If we converged do not do onestep
if converged or (mcscf_target_conv_type != 'OS'):
one_step_iters = []
# If we are not converged load in Dvec and build iters array
else:
one_step_iters = range(mcscf_iter + 1, mcscf_max_macroiteration + 1)
dvec = ciwfn.D_vector()
dvec.init_io_files(True)
dvec.read(0, 0)
dvec.symnormalize(1.0, 0)
ci_grad = ciwfn.new_civector(1, mcscf_d_file + 1, True, True)
ci_grad.set_nvec(1)
ci_grad.init_io_files(True)
# Loop for onestep
for mcscf_iter in one_step_iters:
# Transform integrals and update the MCSCF object
ciwfn.transform_mcscf_integrals(ciwfn.H(), False)
ciwfn.form_opdm()
ciwfn.form_tpdm()
# Update MCSCF object
Cocc = ciwfn.get_orbitals("DOCC")
Cact = ciwfn.get_orbitals("ACT")
Cvir = ciwfn.get_orbitals("VIR")
opdm = ciwfn.get_opdm(-1, -1, "SUM", False)
tpdm = ciwfn.get_tpdm("SUM", True)
mcscf_obj.update(Cocc, Cact, Cvir, opdm, tpdm)
orb_grad_rms = mcscf_obj.gradient_rms()
# Warning! Does not work for SA-MCSCF
current_energy = mcscf_obj.current_total_energy()
current_energy += mcscf_nuclear_energy
ciwfn.set_variable("CI ROOT %d TOTAL ENERGY" % 1, current_energy)
ciwfn.set_variable("CURRENT ENERGY", current_energy)
ciwfn.set_energy(current_energy)
docc_energy = mcscf_obj.current_docc_energy()
ci_energy = mcscf_obj.current_ci_energy()
# Compute CI gradient
ciwfn.sigma(dvec, ci_grad, 0, 0)
ci_grad.scale(2.0, 0)
ci_grad.axpy(-2.0 * ci_energy, dvec, 0, 0)
ci_grad_rms = ci_grad.norm(0)
orb_grad_rms = mcscf_obj.gradient().rms()
ediff = current_energy - eold
print_iteration(mtype, mcscf_iter, current_energy, ediff, orb_grad_rms, ci_grad_rms,
nci_iter, norb_iter, mcscf_current_step_type)
mcscf_current_step_type = 'OS'
eold = current_energy
if (orb_grad_rms < mcscf_orb_grad_conv) and (abs(ediff) < abs(mcscf_e_conv)):
core.print_out("\n %s has converged!\n\n" % mtype);
converged = True
break
# Take a step
converged, norb_iter, nci_iter, step = qc_iteration(dvec, ci_grad, ciwfn, mcscf_obj)
# Rotate integrals to new frame
total_step.add(step)
orbs_mat = mcscf_obj.Ck(ciwfn.get_orbitals("ROT"), step)
ciwfn.set_orbitals("ROT", orbs_mat)
core.print_out(mtype + " Final Energy: %20.15f\n" % current_energy)
# Die if we did not converge
if (not converged):
if core.get_global_option("DIE_IF_NOT_CONVERGED"):
raise p4util.PsiException("MCSCF: Iterations did not converge!")
else:
core.print_out("\nWarning! MCSCF iterations did not converge!\n\n")
# Print out CI vector information
if mcscf_target_conv_type == 'OS':
dvec.close_io_files()
ci_grad.close_io_files()
# For orbital invariant methods we transform the orbitals to the natural or
# semicanonical basis. Frozen doubly occupied and virtual orbitals are not
# modified.
if core.get_option("DETCI", "WFN") == "CASSCF":
# Do we diagonalize the opdm?
if core.get_option("DETCI", "NAT_ORBS"):
ciwfn.ci_nat_orbs()
else:
ciwfn.semicanonical_orbs()
# Retransform intragrals and update CI coeffs., OPDM, and TPDM
ciwfn.transform_mcscf_integrals(approx_integrals_only)
nci_iter = ciwfn.diag_h(abs(ediff) * 1.e-2, orb_grad_rms * 1.e-3)
ciwfn.set_ci_guess("DFILE")
ciwfn.form_opdm()
ciwfn.form_tpdm()
proc_util.print_ci_results(ciwfn, "MCSCF", scf_energy, current_energy, print_opdm_no=True)
# Set final energy
ciwfn.set_variable("CURRENT ENERGY", ciwfn.variable("MCSCF TOTAL ENERGY"))
ciwfn.set_energy(ciwfn.variable("MCSCF TOTAL ENERGY"))
# What do we need to cleanup?
if core.get_option("DETCI", "MCSCF_CI_CLEANUP"):
ciwfn.cleanup_ci()
if core.get_option("DETCI", "MCSCF_DPD_CLEANUP"):
ciwfn.cleanup_dpd()
del diis_obj
del mcscf_obj
return ciwfn
def _so_to_mo(self, X):
"""Transform (C_occ)^T X C_vir"""
return [
core.triplet(self.Co[i], X[i], self.Cv[i], True, False, False)
for i in (0, 1)
]
def cpscf_linear_response(wfn, *args, **kwargs):
"""
Compute the static properties from a reference wavefunction. The currently implemented properties are
- dipole polarizability
- quadrupole polarizability
Parameters
----------
wfn : psi4 wavefunction
The reference wavefunction.
args : list
The list of arguments. For each argument, such as ``dipole polarizability``, will return the corresponding
response.
kwargs : dict
Options that control how the response is computed. The following options are supported (with default values):
- ``conv_tol``: 1e-5
- ``max_iter``: 10
- ``print_lvl``: 2
Returns
-------
responses : list
The list of response tensors.
"""
mints = core.MintsHelper(wfn.basisset())
# list of dictionaries to control response calculations
complete_dict = []
for arg in args:
# for each string keyword, append the appropriate dictionary (vide supra) to our list
if not isinstance(arg, str):
# TODO: better to raise TypeError?
raise ValidationError("Property name must be of type string.")
ret = property_dicts.get(arg)
if ret:
complete_dict.append(ret)
else:
raise ValidationError(f"Do not understand '{arg}'.")
# vectors will be passed to the cphf solver, vector_names stores the corresponding names
vectors = []
vector_names = []
restricted = wfn.same_a_b_orbs()
# construct the list of vectors. for the keywords, fetch the appropriate tensors from MintsHelper
for prop in complete_dict:
tmp_vectors = prop['mints_function'](mints)
for tmp in tmp_vectors:
tmp.scale(-1.0)
vectors.append(tmp)
vector_names.append(tmp.name)
# do we have any vectors to work with?
if len(vectors) == 0:
raise ValidationError('No vectors to work with. Aborting.')
# print information on module, vectors that will be used
_print_header(complete_dict)
nbf = wfn.basisset().nbf()
Co = [wfn.Ca_subset("AO", "OCC"), wfn.Cb_subset("AO", "OCC")]
Cv = [wfn.Ca_subset("AO", "VIR"), wfn.Cb_subset("AO", "VIR")]
vectors_transformed = []
for vector in vectors:
if vector.shape != (nbf, nbf):
raise ValidationError(
f"Vector must be of shape ({nbf}, {nbf}) for transformation"
" to the SO basis.")
v_a = core.triplet(Co[0], vector, Cv[0], True, False, False)
vectors_transformed.append(v_a)
if not restricted:
v_b = core.triplet(Co[1], vector, Cv[1], True, False, False)
vectors_transformed.append(v_b)
# compute response vectors for each input vector
params = [
kwargs.pop("conv_tol", 1.e-5),
kwargs.pop("max_iter", 10),
kwargs.pop("print_lvl", 2)
]
responses_list = wfn.cphf_solve(vectors_transformed, *params)
# zip vectors, responses for easy access
if restricted:
vectors = {
f"{k}_a": v
for k, v in zip(vector_names, vectors_transformed)
}
responses = {f"{k}_a": v for k, v in zip(vector_names, responses_list)}
else:
vectors = {
f"{k}_a": v
for k, v in zip(vector_names, vectors_transformed[::2])
}
vectors.update({
f"{k}_b": v
for k, v in zip(vector_names, vectors_transformed[1::2])
})
responses = {
f"{k}_a": v
for k, v in zip(vector_names, responses_list[::2])
}
responses.update(
{f"{k}_b": v
for k, v in zip(vector_names, responses_list[1::2])})
# compute response values, format output
output = []
pref = -4.0 if restricted else -2.0
for prop in complete_dict:
names = prop['vector names']
dim = len(names)
buf = np.zeros((dim, dim))
for i, i_name in enumerate(names):
for j, j_name in enumerate(names):
buf[i, j] = pref * vectors[f"{i_name}_a"].vector_dot(
responses[f"{j_name}_a"])
if not restricted:
buf[i, j] += pref * vectors[f"{i_name}_b"].vector_dot(
responses[f"{j_name}_b"])
output.append(buf)
_print_output(complete_dict, output)
return output
def df_fdds_dispersion(primary, auxiliary, cache, leg_points=10, leg_lambda=0.3, do_print=True):
rho_thresh = core.get_option("SAPT", "SAPT_FDDS_V2_RHO_CUTOFF")
if do_print:
core.print_out("\n ==> E20 Dispersion (CHF FDDS) <== \n\n")
core.print_out(" Legendre Points: % 10d\n" % leg_points)
core.print_out(" Lambda Shift: % 10.3f\n" % leg_lambda)
core.print_out(" Fxc Kernal: % 10s\n" % "ALDA")
core.print_out(" (P|Fxc|Q) Thresh: % 8.3e\n" % rho_thresh)
# Build object
df_matrix_keys = ["Cocc_A", "Cvir_A", "Cocc_B", "Cvir_B"]
fdds_matrix_cache = {key: cache[key] for key in df_matrix_keys}
df_vector_keys = ["eps_occ_A", "eps_vir_A", "eps_occ_B", "eps_vir_B"]
fdds_vector_cache = {key: cache[key] for key in df_vector_keys}
fdds_obj = core.FDDS_Dispersion(primary, auxiliary, fdds_matrix_cache, fdds_vector_cache)
# Aux Densities
D = fdds_obj.project_densities([cache["D_A"], cache["D_B"]])
# Temps
half_Saux = fdds_obj.aux_overlap().clone()
half_Saux.power(-0.5, 1.e-12)
halfp_Saux = fdds_obj.aux_overlap().clone()
halfp_Saux.power(0.5, 1.e-12)
# Builds potentials
W_A = fdds_obj.metric().clone()
W_A.axpy(1.0, _compute_fxc(D[0], half_Saux, halfp_Saux, rho_thresh=rho_thresh))
W_B = fdds_obj.metric().clone()
W_B.axpy(1.0, _compute_fxc(D[1], half_Saux, halfp_Saux, rho_thresh=rho_thresh))
# Nuke the densities
del D
metric = fdds_obj.metric()
metric_inv = fdds_obj.metric_inv()
# Integrate
core.print_out("\n => Time Integration <= \n\n")
val_pack = ("Omega", "Weight", "Disp20,u", "Disp20", "time [s]")
core.print_out("% 12s % 12s % 14s % 14s % 10s\n" % val_pack)
# print("% 12s % 12s % 14s % 14s % 10s" % val_pack)
start_time = time.time()
total_uc = 0
total_c = 0
for point, weight in zip(*np.polynomial.legendre.leggauss(leg_points)):
omega = leg_lambda * (1.0 - point) / (1.0 + point)
lambda_scale = ((2.0 * leg_lambda) / (point + 1.0)**2)
# Monomer A
X_A = fdds_obj.form_unc_amplitude("A", omega)
# Coupled A
X_A_coupled = X_A.clone()
XSW_A = core.triplet(X_A, metric_inv, W_A, False, False, False)
amplitude_inv = metric.clone()
amplitude_inv.axpy(1.0, XSW_A)
nremoved = 0
amplitude = amplitude_inv.pseudoinverse(1.e-13, nremoved)
amplitude.transpose_this() # Why is this coming out transposed?
X_A_coupled.axpy(-1.0, core.triplet(XSW_A, amplitude, X_A, False, False, False))
del XSW_A, amplitude
X_B = fdds_obj.form_unc_amplitude("B", omega)
# print(np.linalg.norm(X_B))
# Coupled B
X_B_coupled = X_B.clone()
XSW_B = core.triplet(X_B, metric_inv, W_B, False, False, False)
amplitude_inv = metric.clone()
amplitude_inv.axpy(1.0, XSW_B)
amplitude = amplitude_inv.pseudoinverse(1.e-13, nremoved)
amplitude.transpose_this() # Why is this coming out transposed?
X_B_coupled.axpy(-1.0, core.triplet(XSW_B, amplitude, X_B, False, False, False))
del XSW_B, amplitude
# Make sure the results are symmetrized
for tensor in [X_A, X_B, X_A_coupled, X_B_coupled]:
tensor.add(tensor.transpose())
tensor.scale(0.5)
# Combine
tmp_uc = core.triplet(metric_inv, X_A, metric_inv, False, False, False)
value_uc = tmp_uc.vector_dot(X_B)
del tmp_uc
tmp_c = core.triplet(metric_inv, X_A_coupled, metric_inv, False, False, False)
value_c = tmp_c.vector_dot(X_B_coupled)
del tmp_c
# Tally
total_uc += value_uc * weight * lambda_scale
total_c += value_c * weight * lambda_scale
if do_print:
tmp_disp_unc = value_uc * weight * lambda_scale
tmp_disp = value_c * weight * lambda_scale
fdds_time = time.time() - start_time
val_pack = (omega, weight, tmp_disp_unc, tmp_disp, fdds_time)
core.print_out("% 12.3e % 12.3e % 14.3e % 14.3e %10d\n" % val_pack)
# print("% 12.3e % 12.3e % 14.3e % 14.3e %10d" % val_pack)
Disp20_uc = -1.0 / (2.0 * np.pi) * total_uc
Disp20_c = -1.0 / (2.0 * np.pi) * total_c
core.print_out("\n")
core.print_out(print_sapt_var("Disp20,u", Disp20_uc, short=True) + "\n")
core.print_out(print_sapt_var("Disp20", Disp20_c, short=True) + "\n")
return {"Disp20,FDDS (unc)": Disp20_uc, "Disp20": Disp20_c}
def mcscf_solver(ref_wfn):
# Build CIWavefunction
core.prepare_options_for_module("DETCI")
ciwfn = core.CIWavefunction(ref_wfn)
ciwfn.set_module("detci")
# Hush a lot of CI output
ciwfn.set_print(0)
# Begin with a normal two-step
step_type = 'Initial CI'
total_step = core.Matrix("Total step", ciwfn.get_dimension('OA'),
ciwfn.get_dimension('AV'))
start_orbs = ciwfn.get_orbitals("ROT").clone()
ciwfn.set_orbitals("ROT", start_orbs)
# Grab da options
mcscf_orb_grad_conv = core.get_option("DETCI", "MCSCF_R_CONVERGENCE")
mcscf_e_conv = core.get_option("DETCI", "MCSCF_E_CONVERGENCE")
mcscf_max_macroiteration = core.get_option("DETCI", "MCSCF_MAXITER")
mcscf_type = core.get_option("DETCI", "MCSCF_TYPE")
mcscf_d_file = core.get_option("DETCI", "CI_FILE_START") + 3
mcscf_nroots = core.get_option("DETCI", "NUM_ROOTS")
mcscf_wavefunction_type = core.get_option("DETCI", "WFN")
mcscf_ndet = ciwfn.ndet()
mcscf_nuclear_energy = ciwfn.molecule().nuclear_repulsion_energy()
mcscf_steplimit = core.get_option("DETCI", "MCSCF_MAX_ROT")
mcscf_rotate = core.get_option("DETCI", "MCSCF_ROTATE")
# DIIS info
mcscf_diis_start = core.get_option("DETCI", "MCSCF_DIIS_START")
mcscf_diis_freq = core.get_option("DETCI", "MCSCF_DIIS_FREQ")
mcscf_diis_error_type = core.get_option("DETCI", "MCSCF_DIIS_ERROR_TYPE")
mcscf_diis_max_vecs = core.get_option("DETCI", "MCSCF_DIIS_MAX_VECS")
# One-step info
mcscf_target_conv_type = core.get_option("DETCI", "MCSCF_ALGORITHM")
mcscf_so_start_grad = core.get_option("DETCI", "MCSCF_SO_START_GRAD")
mcscf_so_start_e = core.get_option("DETCI", "MCSCF_SO_START_E")
mcscf_current_step_type = 'Initial CI'
# Start with SCF energy and other params
scf_energy = ciwfn.variable("HF TOTAL ENERGY")
eold = scf_energy
norb_iter = 1
converged = False
ah_step = False
qc_step = False
approx_integrals_only = True
# Fake info to start with the initial diagonalization
ediff = 1.e-4
orb_grad_rms = 1.e-3
# Grab needed objects
diis_obj = solvers.DIIS(mcscf_diis_max_vecs)
mcscf_obj = ciwfn.mcscf_object()
# Execute the rotate command
for rot in mcscf_rotate:
if len(rot) != 4:
raise p4util.PsiException(
"Each element of the MCSCF rotate command requires 4 arguements (irrep, orb1, orb2, theta)."
)
irrep, orb1, orb2, theta = rot
if irrep > ciwfn.Ca().nirrep():
raise p4util.PsiException(
"MCSCF_ROTATE: Expression %s irrep number is larger than the number of irreps"
% (str(rot)))
if max(orb1, orb2) > ciwfn.Ca().coldim()[irrep]:
raise p4util.PsiException(
"MCSCF_ROTATE: Expression %s orbital number exceeds number of orbitals in irrep"
% (str(rot)))
theta = np.deg2rad(theta)
x = ciwfn.Ca().nph[irrep][:, orb1].copy()
y = ciwfn.Ca().nph[irrep][:, orb2].copy()
xp = np.cos(theta) * x - np.sin(theta) * y
yp = np.sin(theta) * x + np.cos(theta) * y
ciwfn.Ca().nph[irrep][:, orb1] = xp
ciwfn.Ca().nph[irrep][:, orb2] = yp
# Limited RAS functionality
if core.get_local_option(
"DETCI", "WFN") == "RASSCF" and mcscf_target_conv_type != "TS":
core.print_out(
"\n Warning! Only the TS algorithm for RASSCF wavefunction is currently supported.\n"
)
core.print_out(" Switching to the TS algorithm.\n\n")
mcscf_target_conv_type = "TS"
# Print out headers
if mcscf_type == "CONV":
mtype = " @MCSCF"
core.print_out("\n ==> Starting MCSCF iterations <==\n\n")
core.print_out(
" Iter Total Energy Delta E Orb RMS CI RMS NCI NORB\n"
)
elif mcscf_type == "DF":
mtype = " @DF-MCSCF"
core.print_out("\n ==> Starting DF-MCSCF iterations <==\n\n")
core.print_out(
" Iter Total Energy Delta E Orb RMS CI RMS NCI NORB\n"
)
else:
mtype = " @AO-MCSCF"
core.print_out("\n ==> Starting AO-MCSCF iterations <==\n\n")
core.print_out(
" Iter Total Energy Delta E Orb RMS CI RMS NCI NORB\n"
)
# Iterate !
for mcscf_iter in range(1, mcscf_max_macroiteration + 1):
# Transform integrals, diagonalize H
ciwfn.transform_mcscf_integrals(approx_integrals_only)
nci_iter = ciwfn.diag_h(abs(ediff) * 1.e-2, orb_grad_rms * 1.e-3)
# After the first diag we need to switch to READ
ciwfn.set_ci_guess("DFILE")
ciwfn.form_opdm()
ciwfn.form_tpdm()
ci_grad_rms = ciwfn.variable("DETCI AVG DVEC NORM")
# Update MCSCF object
Cocc = ciwfn.get_orbitals("DOCC")
Cact = ciwfn.get_orbitals("ACT")
Cvir = ciwfn.get_orbitals("VIR")
opdm = ciwfn.get_opdm(-1, -1, "SUM", False)
tpdm = ciwfn.get_tpdm("SUM", True)
mcscf_obj.update(Cocc, Cact, Cvir, opdm, tpdm)
current_energy = ciwfn.variable("MCSCF TOTAL ENERGY")
ciwfn.reset_ci_H0block()
orb_grad_rms = mcscf_obj.gradient_rms()
ediff = current_energy - eold
# Print iterations
print_iteration(mtype, mcscf_iter, current_energy, ediff, orb_grad_rms,
ci_grad_rms, nci_iter, norb_iter,
mcscf_current_step_type)
eold = current_energy
if mcscf_current_step_type == 'Initial CI':
mcscf_current_step_type = 'TS'
# Check convergence
if (orb_grad_rms < mcscf_orb_grad_conv) and (abs(ediff) < abs(mcscf_e_conv)) and\
(mcscf_iter > 3) and not qc_step:
core.print_out("\n %s has converged!\n\n" % mtype)
converged = True
break
# Which orbital convergence are we doing?
if ah_step:
converged, norb_iter, step = ah_iteration(mcscf_obj,
print_micro=False)
norb_iter += 1
if converged:
mcscf_current_step_type = 'AH'
else:
core.print_out(
" !Warning. Augmented Hessian did not converge. Taking an approx step.\n"
)
step = mcscf_obj.approx_solve()
mcscf_current_step_type = 'TS, AH failure'
else:
step = mcscf_obj.approx_solve()
step_type = 'TS'
maxstep = step.absmax()
if maxstep > mcscf_steplimit:
core.print_out(
' Warning! Maxstep = %4.2f, scaling to %4.2f\n' %
(maxstep, mcscf_steplimit))
step.scale(mcscf_steplimit / maxstep)
xstep = total_step.clone()
total_step.add(step)
# Do or add DIIS
if (mcscf_iter >= mcscf_diis_start) and ("TS"
in mcscf_current_step_type):
# Figure out DIIS error vector
if mcscf_diis_error_type == "GRAD":
error = core.triplet(ciwfn.get_orbitals("OA"),
mcscf_obj.gradient(),
ciwfn.get_orbitals("AV"), False, False,
True)
else:
error = step
diis_obj.add(total_step, error)
if not (mcscf_iter % mcscf_diis_freq):
total_step = diis_obj.extrapolate()
mcscf_current_step_type = 'TS, DIIS'
# Build the rotation by continuous updates
if mcscf_iter == 1:
totalU = mcscf_obj.form_rotation_matrix(total_step)
else:
xstep.axpy(-1.0, total_step)
xstep.scale(-1.0)
Ustep = mcscf_obj.form_rotation_matrix(xstep)
totalU = core.doublet(totalU, Ustep, False, False)
# Build the rotation directly (not recommended)
# orbs_mat = mcscf_obj.Ck(start_orbs, total_step)
# Finally rotate and set orbitals
orbs_mat = core.doublet(start_orbs, totalU, False, False)
ciwfn.set_orbitals("ROT", orbs_mat)
# Figure out what the next step should be
if (orb_grad_rms < mcscf_so_start_grad) and (abs(ediff) < abs(mcscf_so_start_e)) and\
(mcscf_iter >= 2):
if mcscf_target_conv_type == 'AH':
approx_integrals_only = False
ah_step = True
elif mcscf_target_conv_type == 'OS':
approx_integrals_only = False
mcscf_current_step_type = 'OS, Prep'
break
else:
continue
#raise p4util.PsiException("")
# If we converged do not do onestep
if converged or (mcscf_target_conv_type != 'OS'):
one_step_iters = []
# If we are not converged load in Dvec and build iters array
else:
one_step_iters = range(mcscf_iter + 1, mcscf_max_macroiteration + 1)
dvec = ciwfn.D_vector()
dvec.init_io_files(True)
dvec.read(0, 0)
dvec.symnormalize(1.0, 0)
ci_grad = ciwfn.new_civector(1, mcscf_d_file + 1, True, True)
ci_grad.set_nvec(1)
ci_grad.init_io_files(True)
# Loop for onestep
for mcscf_iter in one_step_iters:
# Transform integrals and update the MCSCF object
ciwfn.transform_mcscf_integrals(ciwfn.H(), False)
ciwfn.form_opdm()
ciwfn.form_tpdm()
# Update MCSCF object
Cocc = ciwfn.get_orbitals("DOCC")
Cact = ciwfn.get_orbitals("ACT")
Cvir = ciwfn.get_orbitals("VIR")
opdm = ciwfn.get_opdm(-1, -1, "SUM", False)
tpdm = ciwfn.get_tpdm("SUM", True)
mcscf_obj.update(Cocc, Cact, Cvir, opdm, tpdm)
orb_grad_rms = mcscf_obj.gradient_rms()
# Warning! Does not work for SA-MCSCF
current_energy = mcscf_obj.current_total_energy()
current_energy += mcscf_nuclear_energy
ciwfn.set_variable("CI ROOT %d TOTAL ENERGY" % 1, current_energy)
ciwfn.set_variable("CURRENT ENERGY", current_energy)
ciwfn.set_energy(current_energy)
docc_energy = mcscf_obj.current_docc_energy()
ci_energy = mcscf_obj.current_ci_energy()
# Compute CI gradient
ciwfn.sigma(dvec, ci_grad, 0, 0)
ci_grad.scale(2.0, 0)
ci_grad.axpy(-2.0 * ci_energy, dvec, 0, 0)
ci_grad_rms = ci_grad.norm(0)
orb_grad_rms = mcscf_obj.gradient().rms()
ediff = current_energy - eold
print_iteration(mtype, mcscf_iter, current_energy, ediff, orb_grad_rms,
ci_grad_rms, nci_iter, norb_iter,
mcscf_current_step_type)
mcscf_current_step_type = 'OS'
eold = current_energy
if (orb_grad_rms < mcscf_orb_grad_conv) and (abs(ediff) <
abs(mcscf_e_conv)):
core.print_out("\n %s has converged!\n\n" % mtype)
converged = True
break
# Take a step
converged, norb_iter, nci_iter, step = qc_iteration(
dvec, ci_grad, ciwfn, mcscf_obj)
# Rotate integrals to new frame
total_step.add(step)
orbs_mat = mcscf_obj.Ck(ciwfn.get_orbitals("ROT"), step)
ciwfn.set_orbitals("ROT", orbs_mat)
core.print_out(mtype + " Final Energy: %20.15f\n" % current_energy)
# Die if we did not converge
if (not converged):
if core.get_global_option("DIE_IF_NOT_CONVERGED"):
raise p4util.PsiException("MCSCF: Iterations did not converge!")
else:
core.print_out("\nWarning! MCSCF iterations did not converge!\n\n")
# Print out CI vector information
if mcscf_target_conv_type == 'OS':
dvec.close_io_files()
ci_grad.close_io_files()
# For orbital invariant methods we transform the orbitals to the natural or
# semicanonical basis. Frozen doubly occupied and virtual orbitals are not
# modified.
if core.get_option("DETCI", "WFN") == "CASSCF":
# Do we diagonalize the opdm?
if core.get_option("DETCI", "NAT_ORBS"):
ciwfn.ci_nat_orbs()
else:
ciwfn.semicanonical_orbs()
# Retransform intragrals and update CI coeffs., OPDM, and TPDM
ciwfn.transform_mcscf_integrals(approx_integrals_only)
ciwfn.set_print(1)
ciwfn.set_ci_guess("H0_BLOCK")
nci_iter = ciwfn.diag_h(mcscf_e_conv, mcscf_e_conv**0.5)
ciwfn.form_opdm()
ciwfn.form_tpdm()
proc_util.print_ci_results(ciwfn,
"MCSCF",
scf_energy,
current_energy,
print_opdm_no=True)
# Set final energy
ciwfn.set_variable("CURRENT ENERGY", ciwfn.variable("MCSCF TOTAL ENERGY"))
ciwfn.set_energy(ciwfn.variable("MCSCF TOTAL ENERGY"))
# What do we need to cleanup?
if core.get_option("DETCI", "MCSCF_CI_CLEANUP"):
ciwfn.cleanup_ci()
if core.get_option("DETCI", "MCSCF_DPD_CLEANUP"):
ciwfn.cleanup_dpd()
del diis_obj
del mcscf_obj
return ciwfn