#!/usr/bin/env python
# Copyright 2014-2018 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Author: Zhi-Hao Cui <zhcui0408@gmail.com>
#
"""
Brueckner coupled-cluster doubles (BCCD).
"""
from functools import reduce
import numpy as np
from scipy import linalg as la
from pyscf import lib
[docs]
def get_umat_from_t1(t1):
"""
Get rotation matrix from t1.
"""
if isinstance(t1, np.ndarray) and t1.ndim == 2:
nocc, nvir = t1.shape
amat = np.zeros((nocc+nvir, nocc+nvir), dtype=t1.dtype)
amat[:nocc, -nvir:] = -t1
amat[-nvir:, :nocc] = t1.conj().T
umat = la.expm(amat)
else: # UHF
spin = len(t1)
nmo = np.sum(t1[0].shape)
umat = np.zeros((spin, nmo, nmo), dtype=np.result_type(*t1))
for s in range(spin):
nocc, nvir = t1[s].shape
amat = np.zeros((nmo, nmo), dtype=t1[s].dtype)
amat[:nocc, -nvir:] = -t1[s]
amat[-nvir:, :nocc] = t1[s].conj().T
umat[s] = la.expm(amat)
return umat
transform_l1_to_bo = transform_t1_to_bo
transform_l2_to_bo = transform_t2_to_bo
[docs]
def get_mo_ovlp(mo1, mo2, ovlp):
"""
Get MO overlap, C_1.conj().T ovlp C_2.
"""
ovlp = np.asarray(ovlp)
mo1 = np.asarray(mo1)
mo2 = np.asarray(mo2)
if mo1.ndim == 2:
res = reduce(np.dot, (mo1.conj().T, ovlp, mo2))
else:
assert mo1.shape[0] == mo2.shape[0]
spin, nao, nmo1 = mo1.shape
nmo2 = mo2.shape[-1]
res = np.zeros((spin, nmo1, nmo2), dtype=np.result_type(mo1, mo2))
for s in range(spin):
res[s] = reduce(np.dot, (mo1[s].conj().T, ovlp, mo2[s]))
return res
[docs]
def logm(mrot):
if np.iscomplexobj(mrot):
return la.logm(mrot)
else:
rs = mrot + mrot.T
rl, rv = la.eigh(rs)
rd = rv.T @ mrot @ rv
ra, rdet = 1, rd[0, 0]
for i in range(1, len(rd)):
ra, rdet = rdet, rd[i, i] * rdet - \
rd[i - 1, i] * rd[i, i - 1] * ra
assert rdet > 0
ld = np.zeros_like(rd)
for i in range(0, len(rd) // 2 * 2, 2):
xcos = (rd[i, i] + rd[i + 1, i + 1]) * 0.5
xsin = (rd[i, i + 1] - rd[i + 1, i]) * 0.5
theta = np.arctan2(xsin, xcos)
ld[i, i + 1] = theta
ld[i + 1, i] = -theta
return rv @ ld @ rv.T
[docs]
def bccd_kernel_(mycc, u=None, conv_tol_normu=1e-5, max_cycle=20, diis=True,
canonicalization=True, verbose=4):
"""
Brueckner coupled-cluster wrapper, using an outer-loop algorithm.
Args:
mycc: a converged CCSD object.
u: initial transformation matrix.
conv_tol_normu: convergence tolerance for u matrix.
max_cycle: Maximum number of BCC cycles.
diis: whether perform DIIS.
canonicalization: whether to semi-canonicalize the Brueckner orbitals.
verbose: verbose for CCSD inner iterations.
Returns:
mycc: a modified CC object with t1 vanished.
mycc._scf and mycc will be modified.
"""
log = lib.logger.new_logger(mycc, verbose)
log.info("BCCD loop starts.")
def trans_mo(mo_coeff, u):
mo_coeff = np.asarray(mo_coeff)
if mo_coeff.ndim == 2:
res = np.dot(mo_coeff, u)
else:
spin, nao, nmo = mo_coeff.shape
res = np.zeros((spin, nao, nmo), dtype=mo_coeff.dtype)
for s in range(spin):
res[s] = np.dot(mo_coeff[s], u[s])
return res
def u2A(u):
if u.ndim == 2:
if la.det(u) < 0:
u[:, 0] *= -1
A = logm(u)
else:
if la.det(u[0]) < 0:
u[0][:, 0] *= -1
A_a = logm(u[0])
if la.det(u[1]) < 0:
u[1][:, 0] *= -1
A_b = logm(u[1])
A = np.asarray((A_a, A_b))
return A
def A2u(A):
if A.ndim == 2:
u = la.expm(A)
else:
u_a = la.expm(A[0])
u_b = la.expm(A[1])
u = np.asarray((u_a, u_b))
return u
mf = mycc._scf
ovlp = mf.get_ovlp()
adiis = lib.diis.DIIS()
frozen = mycc.frozen
level_shift = mycc.level_shift
frozen_mask = mycc.get_frozen_mask()
if u is None:
u = get_umat_from_t1(mycc.t1)
mo_coeff_new = np.array(mycc.mo_coeff, copy=True)
if u.ndim == 2:
mo_coeff_ref = np.array(mycc.mo_coeff[:, frozen_mask], copy=True)
u_tot = np.eye(u.shape[-1], dtype=mo_coeff_ref.dtype)
else:
mo_coeff_ref = np.array((mycc.mo_coeff[0][:, frozen_mask[0]],
mycc.mo_coeff[1][:, frozen_mask[1]]),
copy=True)
u_tot = np.asarray((np.eye(u.shape[-1]), np.eye(u.shape[-1])),
dtype=mo_coeff_ref.dtype)
with lib.temporary_env(mf, verbose=verbose):
e_tot_last = mycc.e_tot
for i in range(max_cycle):
u_tot = trans_mo(u_tot, u)
if diis:
A = u2A(u_tot)
if u_tot.ndim == 2:
A = adiis.update(A, xerr=mycc.t1)
u_tot = A2u(A)
mo_xcore = trans_mo(mo_coeff_ref, u_tot)
u = get_mo_ovlp(mf.mo_coeff[:, frozen_mask], mo_xcore, ovlp)
mo_coeff_new[:, frozen_mask] = mo_xcore
else:
t1_ravel = np.hstack((mycc.t1[0].ravel(), mycc.t1[1].ravel()))
A = adiis.update(A, xerr=t1_ravel)
u_tot = A2u(A)
u = []
for s in range(2):
mo_xcore = trans_mo(mo_coeff_ref[s], u_tot[s])
u.append(get_mo_ovlp(mf.mo_coeff[s][:, frozen_mask[s]], mo_xcore, ovlp))
mo_coeff_new[s][:, frozen_mask[s]] = mo_xcore
u = np.asarray(u)
else:
mo_coeff_new = trans_mo(mo_coeff_ref, u_tot)
mf.mo_coeff = mo_coeff_new
mf.e_tot = mf.energy_tot()
t1 = transform_t1_to_bo(mycc.t1, u)
t2 = transform_t2_to_bo(mycc.t2, u)
mycc.__init__(mf)
mycc.frozen = frozen
mycc.level_shift = level_shift
mycc.verbose = verbose
mycc.kernel(t1=t1, t2=t2)
dE = mycc.e_tot - e_tot_last
e_tot_last = mycc.e_tot
if not mycc.converged:
log.warn("CC not converged")
if u_tot.ndim == 2:
t1_norm = la.norm(mycc.t1)
else:
t1_ravel = np.hstack((mycc.t1[0].ravel(), mycc.t1[1].ravel()))
t1_norm = la.norm(t1_ravel)
log.info("BCC iter: %4d E: %20.12f dE: %12.3e |t1|: %12.3e",
i, mycc.e_tot, dE, t1_norm)
if t1_norm < conv_tol_normu:
break
u = get_umat_from_t1(mycc.t1)
else:
log.warn("BCC: not converged, max_cycle reached.")
# semi-canonicalization
if canonicalization:
dm = mf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
vhf = mf.get_veff(mycc.mol, dm)
fockao = mf.get_fock(vhf=vhf, dm=dm)
e_corr = mycc.e_corr
if u.ndim == 2:
fock = mycc.mo_coeff.conj().T @ fockao @ mycc.mo_coeff
fock_xcore = fock[np.ix_(frozen_mask, frozen_mask)]
foo = fock_xcore[:mycc.nocc, :mycc.nocc]
fvv = fock_xcore[mycc.nocc:, mycc.nocc:]
ew_o, ev_o = la.eigh(foo)
ew_v, ev_v = la.eigh(fvv)
umat_xcore = la.block_diag(ev_o, ev_v)
umat = np.eye(mycc.mo_coeff.shape[-1])
umat[np.ix_(frozen_mask, frozen_mask)] = umat_xcore
mf.mo_coeff = mf.mo_coeff @ umat
mycc.mo_coeff = mf.mo_coeff
else:
umat = []
umat_xcore = []
for s in range(2):
fock = mycc.mo_coeff[s].conj().T @ fockao[s] @ mycc.mo_coeff[s]
fock_xcore = fock[np.ix_(frozen_mask[s], frozen_mask[s])]
foo = fock_xcore[:mycc.nocc[s], :mycc.nocc[s]]
fvv = fock_xcore[mycc.nocc[s]:, mycc.nocc[s]:]
ew_o, ev_o = la.eigh(foo)
ew_v, ev_v = la.eigh(fvv)
umat_xcore.append(la.block_diag(ev_o, ev_v))
umat_s = np.eye(mycc.mo_coeff[s].shape[-1])
umat_s[np.ix_(frozen_mask[s], frozen_mask[s])] = umat_xcore[-1]
umat.append(umat_s)
umat = np.asarray(umat)
mf.mo_coeff = np.einsum('spm, smn -> spn', mf.mo_coeff, umat)
mycc.mo_coeff = mf.mo_coeff
t1 = transform_t1_to_bo(mycc.t1, umat_xcore)
t2 = transform_t2_to_bo(mycc.t2, umat_xcore)
mf.e_tot = mf.energy_tot()
mycc.__init__(mf)
mycc.e_hf = mycc.get_e_hf()
mycc.e_corr = e_corr
mycc.frozen = frozen
mycc.level_shift = level_shift
mycc.verbose = verbose
mycc.t1 = t1
mycc.t2 = t2
return mycc
