#!/usr/bin/env python
# Copyright 2014-2021 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: Qiming Sun <osirpt.sun@gmail.com>
#
'''
Second order CASSCF
'''
from functools import reduce
from itertools import product
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf.mcscf import casci, mc1step, addons
from pyscf.mcscf.casci import get_fock, cas_natorb, canonicalize
from pyscf import scf
from pyscf.soscf import ciah
def _pack_ci_get_H (mc, mo, ci0):
# MRH 06/24/2020: get wrapped Hci and Hdiag functions for
# SA and SA-mix case. Put ci in a consistent format: list of raveled CI vecs
# so that list comprehension can do all the +-*/ and dot operations
orbsym = getattr (mo, 'orbsym', None)
if orbsym is None:
orbsym = getattr (mc.fcisolver, 'orbsym', None)
else:
orbsym = orbsym[mc.ncore:][:mc.ncas]
if mc.fcisolver.nroots == 1:
ci0 = [ci0.ravel ()]
def _pack_ci (x):
return x[0]
def _unpack_ci (x):
return [x.ravel ()]
else:
ci0 = [c.ravel () for c in ci0]
def _pack_ci (x):
return numpy.concatenate ([y.ravel () for y in x])
def _unpack_ci (x):
z = []
for i, c in enumerate (ci0):
y, x = x[:c.size], x[c.size:]
z.append (y)
return z
assert (len (ci0) == mc.fcisolver.nroots), '{} {}'.format (len (ci0), mc.fcisolver.nroots)
ncas = mc.ncas
nelecas = mc.nelecas
# State average mix
_state_arg = addons.StateAverageMixFCISolver_state_args
# _solver_arg = addons.StateAverageMixFCISolver_solver_args
if isinstance (mc.fcisolver, addons.StateAverageMixFCISolver):
linkstrl = []
linkstr = []
for solver, my_arg, my_kwargs in mc.fcisolver._loop_solver (_state_arg (ci0)):
nelec = mc.fcisolver._get_nelec (solver, nelecas)
if getattr (solver, 'gen_linkstr', None):
linkstrl.append (solver.gen_linkstr (ncas, nelec, True))
linkstr.append (solver.gen_linkstr (ncas, nelec, False))
else:
linkstrl.append (None)
linkstr.append (None)
solver.orbsym = orbsym
def _Hci (h1, h2, ci1):
hci = []
for ix, (solver, my_args, my_kwargs) in enumerate (mc.fcisolver._loop_solver (_state_arg (ci1))):
ci = my_args[0]
nelec = mc.fcisolver._get_nelec (solver, nelecas)
op = solver.absorb_h1e (h1, h2, ncas, nelec, 0.5) if h1 is not None else h2
if solver.nroots == 1: ci = [ci]
hci.extend ((solver.contract_2e (op, c, ncas, nelec, link_index=linkstrl[ix]).ravel () for c in ci))
return hci
def _Hdiag (h1, h2):
hdiag = []
for solver, my_args, my_kwargs in mc.fcisolver._loop_solver (_state_arg (ci0)):
nelec = mc.fcisolver._get_nelec (solver, nelecas)
my_hdiag = solver.make_hdiag (h1, h2, ncas, nelec)
for ix in range (solver.nroots): hdiag.append (my_hdiag)
return hdiag
# Not state average mix
else:
if getattr(mc.fcisolver, 'gen_linkstr', None):
linkstrl = mc.fcisolver.gen_linkstr(ncas, nelecas, True)
linkstr = mc.fcisolver.gen_linkstr(ncas, nelecas, False)
else:
linkstrl = linkstr = None
# Should work with either state average or normal
def _Hci (h1, h2, ket):
op = mc.fcisolver.absorb_h1e (h1, h2, ncas, nelecas, 0.5) if h1 is not None else h2
hci = [mc.fcisolver.contract_2e (op, k, ncas, nelecas, link_index=linkstrl).ravel () for k in ket]
return hci
def _Hdiag (h1, h2):
hdiag = mc.fcisolver.make_hdiag (h1, h2, ncas, nelecas)
return [hdiag for ix in range (len (ci0))]
return ci0, _Hci, _Hdiag, linkstrl, linkstr, _pack_ci, _unpack_ci
# gradients, hessian operator and hessian diagonal
[docs]
def gen_g_hop(casscf, mo, ci0, eris, verbose=None):
ncas = casscf.ncas
ncore = casscf.ncore
nocc = ncas + ncore
nelecas = casscf.nelecas
nmo = mo.shape[1]
ci0, _Hci, _Hdiag, linkstrl, linkstr, _pack_ci, _unpack_ci = _pack_ci_get_H (casscf, mo, ci0)
weights = getattr (casscf, 'weights', [1.0]) # MRH 06/24/2020 I'm proud of myself for thinking of this :)
nroots = len (weights)
# MRH 06/25/2020: Unfortunately, we need gpq for each root individually in H_op below.
# I want to minimize Python loops and I also want to call eris.ppaa as few times as possible
# because that is disk I/O for large molecules
# part5
jkcaa = numpy.empty((nroots,nocc,ncas))
# part2, part3
vhf_a = numpy.empty((nroots,nmo,nmo))
# part1 ~ (J + 2K)
try:
casdm1, casdm2 = casscf.fcisolver.states_make_rdm12 (ci0, ncas, nelecas, link_index=linkstr)
casdm1 = numpy.asarray (casdm1)
casdm2 = numpy.asarray (casdm2)
except AttributeError as e:
assert (not (isinstance (casscf.fcisolver, addons.StateAverageFCISolver))), e
casdm1, casdm2 = casscf.fcisolver.make_rdm12 (ci0, ncas, nelecas, link_index=linkstr)
casdm1 = numpy.asarray ([casdm1])
casdm2 = numpy.asarray ([casdm2])
dm2tmp = casdm2.transpose(0,2,3,1,4) + casdm2.transpose(0,1,3,2,4)
dm2tmp = dm2tmp.reshape(nroots,ncas**2,-1)
hdm2 = numpy.empty((nroots,nmo,ncas,nmo,ncas))
g_dm2 = numpy.empty((nroots,nmo,ncas))
eri_cas = numpy.empty((ncas,ncas,ncas,ncas))
jtmp = numpy.empty ((nroots,nmo,ncas,ncas))
ktmp = numpy.empty ((nroots,nmo,ncas,ncas))
for i in range(nmo):
jbuf = eris.ppaa[i]
kbuf = eris.papa[i]
if i < nocc:
jkcaa[:,i] = numpy.einsum('ik,rik->ri', 6*kbuf[:,i]-2*jbuf[i], casdm1)
vhf_a[:,i] = (numpy.einsum('quv,ruv->rq', jbuf, casdm1) -
numpy.einsum('uqv,ruv->rq', kbuf, casdm1) * .5)
for r, (dm2, dm2t) in enumerate (zip (casdm2, dm2tmp)):
jtmp[r] = lib.dot(jbuf.reshape(nmo,-1), dm2.reshape(ncas*ncas,-1)).reshape (nmo,ncas,ncas)
ktmp[r] = lib.dot(kbuf.transpose(1,0,2).reshape(nmo,-1), dm2t).reshape (nmo,ncas,ncas)
hdm2[:,i,:,:,:] = (ktmp+jtmp).transpose (0,2,1,3)
g_dm2[:,i,:] = numpy.einsum('ruuv->rv', jtmp[:,ncore:nocc])
if ncore <= i < nocc:
eri_cas[i-ncore] = jbuf[ncore:nocc]
jbuf = kbuf = jtmp = ktmp = dm2tmp = casdm2 = None
vhf_ca = eris.vhf_c + vhf_a
h1e_mo = reduce(numpy.dot, (mo.T, casscf.get_hcore(), mo))
################# gradient #################
gpq = numpy.zeros((nroots, nmo, nmo), dtype=h1e_mo.dtype)
gpq[:,:,:ncore] = (h1e_mo[None,:,:ncore] + vhf_ca[:,:,:ncore]) * 2
gpq[:,:,ncore:nocc] = numpy.dot(h1e_mo[:,ncore:nocc]+eris.vhf_c[:,ncore:nocc],casdm1).transpose (1,0,2)
gpq[:,:,ncore:nocc] += g_dm2
# Roll up intermediates that no longer need to be separated by root
vhf_ca = numpy.einsum ('r,rpq->pq', weights, vhf_ca)
casdm1 = numpy.einsum ('r,rpq->pq', weights, casdm1)
jkcaa = numpy.einsum ('r,rpq->pq', weights, jkcaa)
hdm2 = numpy.einsum ('r,rpqst->pqst', weights, hdm2)
h1cas_0 = h1e_mo[ncore:nocc,ncore:nocc] + eris.vhf_c[ncore:nocc,ncore:nocc]
hci0 = _Hci (h1cas_0, eri_cas, ci0)
eci0 = [c.dot(hc) for c, hc in zip (ci0, hci0)]
gci = [hc - c * e for hc, c, e in zip (hci0, ci0, eci0)]
def g_update(u, fcivec):
if not isinstance (casscf, addons.StateAverageMCSCFSolver): fcivec = [fcivec]
uc = u[:,:ncore].copy()
ua = u[:,ncore:nocc].copy()
rmat = u - numpy.eye(nmo)
ra = rmat[:,ncore:nocc].copy()
mo1 = numpy.dot(mo, u)
mo_c = numpy.dot(mo, uc)
mo_a = numpy.dot(mo, ua)
dm_c = numpy.dot(mo_c, mo_c.T) * 2
fcivec = [c / numpy.linalg.norm (c) for c in fcivec]
fciarg = fcivec if casscf.fcisolver.nroots > 1 else fcivec[0] # MRH 06/24/2020: this is inelegant...
casdm1, casdm2 = casscf.fcisolver.make_rdm12(fciarg, ncas, nelecas, link_index=linkstr)
#casscf.with_dep4 = False
#casscf.ci_response_space = 3
#casscf.ci_grad_trust_region = 3
#casdm1, casdm2, gci, fcivec = casscf.update_casdm(mo, u, fcivec, 0, eris, locals())
dm_a = reduce(numpy.dot, (mo_a, casdm1, mo_a.T))
vj, vk = casscf.get_jk(casscf.mol, (dm_c, dm_a))
vhf_c = reduce(numpy.dot, (mo1.T, vj[0]-vk[0]*.5, mo1[:,:nocc]))
vhf_a = reduce(numpy.dot, (mo1.T, vj[1]-vk[1]*.5, mo1[:,:nocc]))
h1e_mo1 = reduce(numpy.dot, (u.T, h1e_mo, u[:,:nocc]))
p1aa = numpy.empty((nmo,ncas,ncas*ncas))
paa1 = numpy.empty((nmo,ncas*ncas,ncas))
aaaa = numpy.empty([ncas]*4)
for i in range(nmo):
jbuf = eris.ppaa[i]
kbuf = eris.papa[i]
p1aa[i] = lib.dot(ua.T, jbuf.reshape(nmo,-1))
paa1[i] = lib.dot(kbuf.transpose(0,2,1).reshape(-1,nmo), ra)
if ncore <= i < nocc:
aaaa[i-ncore] = jbuf[ncore:nocc]
# active space Hamiltonian up to 2nd order
aa11 = lib.dot(ua.T, p1aa.reshape(nmo,-1)).reshape([ncas]*4)
aa11 = aa11 + aa11.transpose(2,3,0,1) - aaaa
a11a = lib.dot(ra.T, paa1.reshape(nmo,-1)).reshape((ncas,)*4)
a11a = a11a + a11a.transpose(1,0,2,3)
a11a = a11a + a11a.transpose(0,1,3,2)
eri_cas_2 = aa11 + a11a
h1cas_2 = h1e_mo1[ncore:nocc,ncore:nocc] + vhf_c[ncore:nocc,ncore:nocc]
hci0 = _Hci (h1cas_2, eri_cas_2, fcivec)
gci = [hc - c * c.dot(hc) for c, hc in zip (fcivec, hci0)]
gci = [g * w for g, w in zip (gci, weights)]
g = numpy.zeros_like(h1e_mo)
g[:,:ncore] = (h1e_mo1[:,:ncore] + vhf_c[:,:ncore] + vhf_a[:,:ncore]) * 2
g[:,ncore:nocc] = numpy.dot(h1e_mo1[:,ncore:nocc]+vhf_c[:,ncore:nocc], casdm1)
# 0000 + 1000 + 0100 + 0010 + 0001 + 1100 + 1010 + 1001 (missing 0110 + 0101 + 0011)
p1aa = lib.dot(u.T, p1aa.reshape(nmo,-1)).reshape(nmo,ncas,ncas,ncas)
paa1 = lib.dot(u.T, paa1.reshape(nmo,-1)).reshape(nmo,ncas,ncas,ncas)
p1aa += paa1
p1aa += paa1.transpose(0,1,3,2)
g[:,ncore:nocc] += numpy.einsum('puwx,wxuv->pv', p1aa, casdm2)
g_orb = casscf.pack_uniq_var(g-g.T)
gci = _pack_ci (gci)
return numpy.hstack((g_orb*2, gci*2))
############## hessian, diagonal ###########
# part7
dm1 = numpy.zeros((nmo,nmo))
idx = numpy.arange(ncore)
dm1[idx,idx] = 2
dm1[ncore:nocc,ncore:nocc] = casdm1
h_diag = numpy.einsum('ii,jj->ij', h1e_mo, dm1) - h1e_mo * dm1
h_diag = h_diag + h_diag.T
# part8
g_diag = numpy.einsum ('r,rpp->p', weights, gpq)
h_diag -= g_diag + g_diag.reshape(-1,1)
idx = numpy.arange(nmo)
h_diag[idx,idx] += g_diag * 2
# part2, part3
v_diag = vhf_ca.diagonal() # (pr|kl) * E(sq,lk)
h_diag[:,:ncore] += v_diag.reshape(-1,1) * 2
h_diag[:ncore] += v_diag * 2
idx = numpy.arange(ncore)
h_diag[idx,idx] -= v_diag[:ncore] * 4
# V_{pr} E_{sq}
tmp = numpy.einsum('ii,jj->ij', eris.vhf_c, casdm1)
h_diag[:,ncore:nocc] += tmp
h_diag[ncore:nocc,:] += tmp.T
tmp = -eris.vhf_c[ncore:nocc,ncore:nocc] * casdm1
h_diag[ncore:nocc,ncore:nocc] += tmp + tmp.T
# part4
# -2(pr|sq) + 4(pq|sr) + 4(pq|rs) - 2(ps|rq)
tmp = 6 * eris.k_pc - 2 * eris.j_pc
h_diag[ncore:,:ncore] += tmp[ncore:]
h_diag[:ncore,ncore:] += tmp[ncore:].T
# part5 and part6 diag
# -(qr|kp) E_s^k p in core, sk in active
h_diag[:nocc,ncore:nocc] -= jkcaa
h_diag[ncore:nocc,:nocc] -= jkcaa.T
v_diag = numpy.einsum('ijij->ij', hdm2)
h_diag[ncore:nocc,:] += v_diag.T
h_diag[:,ncore:nocc] += v_diag
# Does this term contribute to internal rotation?
# h_diag[ncore:nocc,ncore:nocc] -= v_diag[:,ncore:nocc]*2
h_diag = casscf.pack_uniq_var(h_diag)
# Fix intermediate normalization? - MRH 2023/09/15
hci_diag = [hd - ec - gc*c*2 for hd, ec, gc, c in zip (_Hdiag (h1cas_0, eri_cas), eci0, gci, ci0)]
hci_diag = [h * w for h, w in zip (hci_diag, weights)]
hdiag_all = numpy.hstack((h_diag*2, _pack_ci (hci_diag)*2))
g_orb = numpy.einsum ('r,rpq->pq', weights, gpq)
g_orb = casscf.pack_uniq_var(g_orb-g_orb.T)
gci = [g * w for g, w in zip (gci, weights)]
g_all = numpy.hstack((g_orb*2, _pack_ci (gci)*2))
ngorb = g_orb.size
def h_op(x):
x1 = casscf.unpack_uniq_var(x[:ngorb])
ci1 = _unpack_ci (x[ngorb:])
# H_cc
# Fix intermediate normalization? - MRH 2023/09/15
hci1 = [hc1 - c1 * ec0 for hc1, c1, ec0 in zip (_Hci (h1cas_0, eri_cas, ci1), ci1, eci0)]
hci1 = [hc1 - (hc0 - c0*ec0)*c0.dot(c1) for hc1, hc0, c0, ec0, c1 in zip (hci1, hci0, ci0, eci0, ci1)]
hci1 = [hc1 - c0*(hc0 - c0*ec0).dot(c1) for hc1, hc0, c0, ec0, c1 in zip (hci1, hci0, ci0, eci0, ci1)]
# H_co
rc = x1[:,:ncore]
ra = x1[:,ncore:nocc]
ddm_c = numpy.zeros((nmo,nmo))
ddm_c[:,:ncore] = rc[:,:ncore] * 2
ddm_c[:ncore,:]+= rc[:,:ncore].T * 2
tdm1, tdm2 = casscf.fcisolver.trans_rdm12(ci1, ci0, ncas, nelecas, link_index=linkstr)
tdm1 = tdm1 + tdm1.T
tdm2 = tdm2 + tdm2.transpose(1,0,3,2)
tdm2 =(tdm2 + tdm2.transpose(2,3,0,1)) * .5
vhf_a = numpy.empty((nmo,ncore))
paaa = numpy.empty((nmo,ncas,ncas,ncas))
jk = 0
for i in range(nmo):
jbuf = eris.ppaa[i]
kbuf = eris.papa[i]
paaa[i] = jbuf[ncore:nocc]
vhf_a[i] = numpy.einsum('quv,uv->q', jbuf[:ncore], tdm1)
vhf_a[i]-= numpy.einsum('uqv,uv->q', kbuf[:,:ncore], tdm1) * .5
jk += numpy.einsum('quv,q->uv', jbuf, ddm_c[i])
jk -= numpy.einsum('uqv,q->uv', kbuf, ddm_c[i]) * .5
g_dm2 = numpy.einsum('puwx,wxuv->pv', paaa, tdm2)
aaaa = numpy.dot(ra.T, paaa.reshape(nmo,-1)).reshape([ncas]*4)
aaaa = aaaa + aaaa.transpose(1,0,2,3)
aaaa = aaaa + aaaa.transpose(2,3,0,1)
h1aa = numpy.dot(h1e_mo[ncore:nocc]+eris.vhf_c[ncore:nocc], ra)
h1aa = h1aa + h1aa.T + jk
kci0 = _Hci (h1aa, aaaa, ci0)
kci0 = [kc0 - kc0.dot(c0) * c0 for kc0, c0 in zip (kci0, ci0)]
hci1 = [hc1 + kc0 for hc1, kc0 in zip (hci1, kci0)]
hci1 = [h * w for h, w in zip (hci1, weights)]
# H_oo
# part7
# (-h_{sp} R_{rs} gamma_{rq} - h_{rq} R_{pq} gamma_{sp})/2 + (pr<->qs)
x2 = reduce(lib.dot, (h1e_mo, x1, dm1))
# part8
# (g_{ps}\delta_{qr}R_rs + g_{qr}\delta_{ps}) * R_pq)/2 + (pr<->qs)
g_orb = numpy.einsum ('r,rpq->pq', weights, gpq)
x2 -= numpy.dot((g_orb + g_orb.T), x1) * .5
# part2
# (-2Vhf_{sp}\delta_{qr}R_pq - 2Vhf_{qr}\delta_{sp}R_rs)/2 + (pr<->qs)
x2[:ncore] += reduce(numpy.dot, (x1[:ncore,ncore:], vhf_ca[ncore:])) * 2
# part3
# (-Vhf_{sp}gamma_{qr}R_{pq} - Vhf_{qr}gamma_{sp}R_{rs})/2 + (pr<->qs)
x2[ncore:nocc] += reduce(numpy.dot, (casdm1, x1[ncore:nocc], eris.vhf_c))
# part1
x2[:,ncore:nocc] += numpy.einsum('purv,rv->pu', hdm2, x1[:,ncore:nocc])
if ncore > 0:
# part4, part5, part6
# Due to x1_rs [4(pq|sr) + 4(pq|rs) - 2(pr|sq) - 2(ps|rq)] for r>s p>q,
# == -x1_sr [4(pq|sr) + 4(pq|rs) - 2(pr|sq) - 2(ps|rq)] for r>s p>q,
# x2[:,:ncore] += H * x1[:,:ncore] => (becuase x1=-x1.T) =>
# x2[:,:ncore] += -H' * x1[:ncore] => (becuase x2-x2.T) =>
# x2[:ncore] += H' * x1[:ncore]
va, vc = casscf.update_jk_in_ah(mo, x1, casdm1, eris)
x2[ncore:nocc] += va
x2[:ncore,ncore:] += vc
# H_oc
s10 = [c1.dot(c0) * 2 * w for c1, c0, w in zip (ci1, ci0, weights)]
x2[:,:ncore] += ((h1e_mo[:,:ncore]+eris.vhf_c[:,:ncore]) * sum (s10) + vhf_a) * 2
x2[:,ncore:nocc] += numpy.dot(h1e_mo[:,ncore:nocc]+eris.vhf_c[:,ncore:nocc], tdm1)
x2[:,ncore:nocc] += g_dm2
x2 -= numpy.einsum ('r,rpq->pq', s10, gpq)
# (pr<->qs)
x2 = x2 - x2.T
return numpy.hstack((casscf.pack_uniq_var(x2)*2, _pack_ci (hci1)*2))
return g_all, g_update, h_op, hdiag_all
# MRH, 04/08/2019: enable multiple roots
# MRH, 06/29/2020: enable state-average mix
[docs]
def update_orb_ci(casscf, mo, ci0, eris, x0_guess=None,
conv_tol_grad=1e-4, max_stepsize=None, verbose=None):
log = logger.new_logger(casscf, verbose)
if max_stepsize is None:
max_stepsize = casscf.max_stepsize
nmo = mo.shape[1]
# MRH, 04/08/2019: enable multiple roots
if casscf.fcisolver.nroots == 1:
ci0 = ci0.ravel ()
else:
ci0 = [c.ravel () for c in ci0]
g_all, g_update, h_op, h_diag = gen_g_hop(casscf, mo, ci0, eris)
ngorb = numpy.count_nonzero (casscf.uniq_var_indices (nmo, casscf.ncore, casscf.ncas, casscf.frozen))
norm_gkf = norm_gall = numpy.linalg.norm(g_all)
log.debug(' |g|=%5.3g (%4.3g %4.3g) (keyframe)', norm_gall,
numpy.linalg.norm(g_all[:ngorb]),
numpy.linalg.norm(g_all[ngorb:]))
def precond(x, e):
if callable(h_diag):
x = h_diag(x, e-casscf.ah_level_shift)
else:
hdiagd = h_diag-(e-casscf.ah_level_shift)
hdiagd[abs(hdiagd)<1e-8] = 1e-8
x = x/hdiagd
x *= 1/numpy.linalg.norm(x)
return x
def scale_down_step(dxi, hdxi):
dxmax = abs(dxi).max()
if dxmax > casscf.max_stepsize:
scale = casscf.max_stepsize / dxmax
log.debug1('Scale rotation by %g', scale)
dxi *= scale
hdxi *= scale
return dxi, hdxi
class Statistic:
def __init__(self):
self.imic = 0
self.tot_hop = 0
self.tot_kf = 1 # The call to gen_g_hop
if x0_guess is None:
x0_guess = g_all
g_op = lambda: g_all
stat = Statistic()
dr = 0
ikf = 0
u = numpy.eye(nmo)
ci_kf = ci0
if norm_gall < conv_tol_grad*.3:
return u, ci_kf, norm_gall, stat, x0_guess
for ah_conv, ihop, w, dxi, hdxi, residual, seig \
in ciah.davidson_cc(h_op, g_op, precond, x0_guess,
tol=casscf.ah_conv_tol, max_cycle=casscf.ah_max_cycle,
lindep=casscf.ah_lindep, verbose=log):
stat.tot_hop = ihop
norm_residual = numpy.linalg.norm(residual)
if (ah_conv or ihop == casscf.ah_max_cycle or # make sure to use the last step
((norm_residual < casscf.ah_start_tol) and (ihop >= casscf.ah_start_cycle)) or
(seig < casscf.ah_lindep)):
stat.imic += 1
dxmax = abs(dxi).max()
dxi, hdxi = scale_down_step(dxi, hdxi)
dr += dxi
g_all = g_all + hdxi
norm_dr = numpy.linalg.norm(dr)
norm_gall = numpy.linalg.norm(g_all)
norm_gorb = numpy.linalg.norm(g_all[:ngorb])
norm_gci = numpy.linalg.norm(g_all[ngorb:])
log.debug(' imic %d(%d) |g|=%3.2e (%2.1e %2.1e) |dxi|=%3.2e '
'max(x)=%3.2e |dr|=%3.2e eig=%2.1e seig=%2.1e',
stat.imic, ihop, norm_gall, norm_gorb, norm_gci, numpy.linalg.norm(dxi),
dxmax, norm_dr, w, seig)
max_cycle = max(casscf.max_cycle_micro,
casscf.max_cycle_micro-int(numpy.log(norm_gkf+1e-7)*2))
log.debug1('Set max_cycle %d', max_cycle)
ikf += 1
if stat.imic > 3 and norm_gall > norm_gkf*casscf.ah_grad_trust_region:
g_all = g_all - hdxi
dr -= dxi
norm_gall = numpy.linalg.norm(g_all)
log.debug('|g| >> keyframe, Restore previouse step')
break
elif (stat.imic >= max_cycle or norm_gall < conv_tol_grad*.3):
break
elif ((ikf >= max(casscf.kf_interval, casscf.kf_interval-numpy.log(norm_dr+1e-7)) or
# Insert keyframe if the keyframe and the esitimated grad are too different
norm_gall < norm_gkf/casscf.kf_trust_region)):
ikf = 0
u, ci_kf = extract_rotation(casscf, dr, u, ci_kf)
dr[:] = 0
g_kf1 = g_update(u, ci_kf)
stat.tot_kf += 1
norm_gkf1 = numpy.linalg.norm(g_kf1)
norm_gorb = numpy.linalg.norm(g_kf1[:ngorb])
norm_gci = numpy.linalg.norm(g_kf1[ngorb:])
norm_dg = numpy.linalg.norm(g_kf1-g_all)
log.debug('Adjust keyframe to |g|= %4.3g (%4.3g %4.3g) '
'|g-correction|= %4.3g',
norm_gkf1, norm_gorb, norm_gci, norm_dg)
if (norm_dg < norm_gall*casscf.ah_grad_trust_region # kf not too diff
#or norm_gkf1 < norm_gkf # grad is decaying
# close to solution
or norm_gkf1 < conv_tol_grad*casscf.ah_grad_trust_region):
g_all = g_kf1
g_kf1 = None
norm_gall = norm_gkf = norm_gkf1
else:
g_all = g_all - hdxi
dr -= dxi
norm_gall = norm_gkf = numpy.linalg.norm(g_all)
log.debug('Out of trust region. Restore previouse step')
break
u, ci_kf = extract_rotation(casscf, dr, u, ci_kf)
if casscf.fcisolver.nroots == 1:
dci_kf = ci_kf - ci0
else:
dci_kf = numpy.concatenate ([(x-y).ravel () for x, y in zip (ci_kf, ci0)])
log.debug(' tot inner=%d |g|= %4.3g (%4.3g %4.3g) |u-1|= %4.3g |dci|= %4.3g',
stat.imic, norm_gall, norm_gorb, norm_gci,
numpy.linalg.norm(u-numpy.eye(nmo)),
numpy.linalg.norm(dci_kf))
return u, ci_kf, norm_gkf, stat, dxi
[docs]
def kernel(casscf, mo_coeff, tol=1e-7, conv_tol_grad=None,
ci0=None, callback=None, verbose=logger.NOTE, dump_chk=True):
'''Second order CASSCF driver
'''
log = logger.new_logger(casscf, verbose)
log.warn('SO-CASSCF (Second order CASSCF) is an experimental feature. '
'Its performance is bad for large systems.')
cput0 = (logger.process_clock(), logger.perf_counter())
log.debug('Start SO-CASSCF (newton CASSCF)')
if callback is None:
callback = casscf.callback
mo = mo_coeff
nmo = mo_coeff.shape[1]
#TODO: lazy evaluate eris, to leave enough memory for FCI solver
eris = casscf.ao2mo(mo)
e_tot, e_cas, fcivec = casscf.casci(mo, ci0, eris, log, locals())
if casscf.ncas == nmo and not casscf.internal_rotation:
if casscf.canonicalization:
log.debug('CASSCF canonicalization')
mo, fcivec, mo_energy = casscf.canonicalize(mo, fcivec, eris,
casscf.sorting_mo_energy,
casscf.natorb, verbose=log)
return True, e_tot, e_cas, fcivec, mo, mo_energy
casdm1 = casscf.fcisolver.make_rdm1(fcivec, casscf.ncas, casscf.nelecas)
if conv_tol_grad is None:
conv_tol_grad = numpy.sqrt(tol)
logger.info(casscf, 'Set conv_tol_grad to %g', conv_tol_grad)
conv_tol_ddm = conv_tol_grad * 3
conv = False
totmicro = totinner = 0
norm_gorb = norm_gci = -1
de, elast = e_tot, e_tot
dr0 = None
t2m = t1m = log.timer('Initializing newton CASSCF', *cput0)
imacro = 0
tot_hop = 0
tot_kf = 0
while not conv and imacro < casscf.max_cycle_macro:
imacro += 1
u, fcivec, norm_gall, stat, dr0 = \
update_orb_ci(casscf, mo, fcivec, eris, dr0, conv_tol_grad*.3, verbose=log)
tot_hop += stat.tot_hop
tot_kf += stat.tot_kf
t2m = log.timer('update_orb_ci', *t2m)
eris = None
mo = casscf.rotate_mo(mo, u, log)
eris = casscf.ao2mo(mo)
t2m = log.timer('update eri', *t2m)
e_tot, e_cas, fcivec = casscf.casci(mo, fcivec, eris, log, locals())
log.timer('CASCI solver', *t2m)
t2m = t1m = log.timer('macro iter %d'%imacro, *t1m)
de, elast = e_tot - elast, e_tot
if (abs(de) < tol and norm_gall < conv_tol_grad):
conv = True
if dump_chk:
casscf.dump_chk(locals())
if callable(callback):
callback(locals())
if conv:
log.info('newton CASSCF converged in %d macro (%d KF %d Hx) steps',
imacro, tot_kf, tot_hop)
else:
log.info('newton CASSCF not converged, %d macro (%d KF %d Hx) steps',
imacro, tot_kf, tot_hop)
casdm1 = casscf.fcisolver.make_rdm1(fcivec, casscf.ncas, casscf.nelecas)
if casscf.canonicalization:
log.info('CASSCF canonicalization')
mo, fcivec, mo_energy = \
casscf.canonicalize(mo, fcivec, eris, casscf.sorting_mo_energy,
casscf.natorb, casdm1, log)
if casscf.natorb: # dump_chk may save casdm1
ncas = casscf.ncas
ncore = casscf.ncore
nocc = ncas + ncore
occ, ucas = casscf._eig(-casdm1, ncore, nocc)
casdm1 = -occ
else:
if casscf.natorb:
# FIXME (pyscf-2.0): Whether to transform natural orbitals in
# active space when this flag is enabled?
log.warn('The attribute natorb of mcscf object affects only the '
'orbital canonicalization.\n'
'If you would like to get natural orbitals in active space '
'without touching core and external orbitals, an explicit '
'call to mc.cas_natorb_() is required')
mo_energy = None
if dump_chk:
casscf.dump_chk(locals())
log.timer('newton CASSCF', *cput0)
return conv, e_tot, e_cas, fcivec, mo, mo_energy
[docs]
class CASSCF(mc1step.CASSCF):
__doc__ = casci.CASBase.__doc__ + '''CASSCF
Extra attributes for CASSCF:
conv_tol : float
Converge threshold. Default is 1e-7
conv_tol_grad : float
Converge threshold for CI gradients and orbital rotation gradients.
Default is 1e-4
max_stepsize : float
The step size for orbital rotation. Small step (0.005 - 0.05) is prefered.
(see notes in max_cycle_micro_inner attribute)
Default is 0.03.
max_cycle_macro : int
Max number of macro iterations. Default is 50.
max_cycle_micro : int
Max number of micro (CIAH) iterations in each macro iteration.
ah_level_shift : float, for AH solver.
Level shift for the Davidson diagonalization in AH solver. Default is 1e-8.
ah_conv_tol : float, for AH solver.
converge threshold for AH solver. Default is 1e-12.
ah_max_cycle : float, for AH solver.
Max number of iterations allowd in AH solver. Default is 30.
ah_lindep : float, for AH solver.
Linear dependence threshold for AH solver. Default is 1e-14.
ah_start_tol : flat, for AH solver.
In AH solver, the orbital rotation is started without completely solving the AH problem.
This value is to control the start point. Default is 0.2.
ah_start_cycle : int, for AH solver.
In AH solver, the orbital rotation is started without completely solving the AH problem.
This value is to control the start point. Default is 2.
``ah_conv_tol``, ``ah_max_cycle``, ``ah_lindep``, ``ah_start_tol`` and ``ah_start_cycle``
can affect the accuracy and performance of CASSCF solver. Lower
``ah_conv_tol`` and ``ah_lindep`` might improve the accuracy of CASSCF
optimization, but decrease the performance.
>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.conv_tol = 1e-10
>>> mc.ah_conv_tol = 1e-5
>>> mc.kernel()
-109.044401898486001
>>> mc.ah_conv_tol = 1e-10
>>> mc.kernel()
-109.044401887945668
chkfile : str
Checkpoint file to save the intermediate orbitals during the CASSCF optimization.
Default is the checkpoint file of mean field object.
callback : function(envs_dict) => None
callback function takes one dict as the argument which is
generated by the builtin function :func:`locals`, so that the
callback function can access all local variables in the current
envrionment.
Saved results
e_tot : float
Total MCSCF energy (electronic energy plus nuclear repulsion)
ci : ndarray
CAS space FCI coefficients
converged : bool
It indicates CASSCF optimization converged or not.
mo_coeff : ndarray
Optimized CASSCF orbitals coefficients
Examples:
>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.kernel()[0]
-109.044401882238134
'''
def __init__(self, mf_or_mol, ncas, nelecas, ncore=None, frozen=None):
casci.CASBase.__init__(self, mf_or_mol, ncas, nelecas, ncore)
self.frozen = frozen
# the max orbital rotation and CI increment, prefer small step size
self.max_stepsize = .03
self.max_cycle_macro = 50
self.max_cycle_micro = 10
self.conv_tol = 1e-7
self.conv_tol_grad = None
# for augmented hessian
self.ah_level_shift = 1e-8
self.ah_conv_tol = 1e-12
self.ah_max_cycle = 30
self.ah_lindep = 1e-14
self.ah_start_tol = 5e2
self.ah_start_cycle = 3
self.ah_grad_trust_region = 3.
self.kf_trust_region = 3.
self.kf_interval = 5
self.internal_rotation = False
self.chkfile = self._scf.chkfile
self.chk_ci = False
self.fcisolver.max_cycle = 25
#self.fcisolver.max_space = 25
##################################################
# don't modify the following attributes, they are not input options
self.e_tot = None
self.e_cas = None
self.ci = None
self.mo_coeff = self._scf.mo_coeff
self.mo_energy = self._scf.mo_energy
self.converged = False
self._max_stepsize = None
[docs]
def dump_flags(self, verbose=None):
log = logger.new_logger(self, verbose)
log.info('')
log.info('******** %s ********', self.__class__)
ncore = self.ncore
ncas = self.ncas
nvir = self.mo_coeff.shape[1] - ncore - ncas
log.info('CAS (%de+%de, %do), ncore = %d, nvir = %d',
self.nelecas[0], self.nelecas[1], self.ncas, ncore, nvir)
if self.frozen is not None:
log.info('frozen orbitals %s', str(self.frozen))
log.info('max_cycle_macro = %d', self.max_cycle_macro)
log.info('max_cycle_micro = %d', self.max_cycle_micro)
log.info('conv_tol = %g', self.conv_tol)
log.info('conv_tol_grad = %s', self.conv_tol_grad)
log.info('orbital rotation max_stepsize = %g', self.max_stepsize)
log.info('augmented hessian ah_max_cycle = %d', self.ah_max_cycle)
log.info('augmented hessian ah_conv_tol = %g', self.ah_conv_tol)
log.info('augmented hessian ah_linear dependence = %g', self.ah_lindep)
log.info('augmented hessian ah_level shift = %g', self.ah_level_shift)
log.info('augmented hessian ah_start_tol = %g', self.ah_start_tol)
log.info('augmented hessian ah_start_cycle = %d', self.ah_start_cycle)
log.info('augmented hessian ah_grad_trust_region = %g', self.ah_grad_trust_region)
log.info('kf_trust_region = %g', self.kf_trust_region)
log.info('kf_interval = %d', self.kf_interval)
log.info('natorb = %s', self.natorb)
log.info('canonicalization = %s', self.canonicalization)
log.info('chkfile = %s', self.chkfile)
log.info('max_memory %d MB (current use %d MB)',
self.max_memory, lib.current_memory()[0])
log.info('internal_rotation = %s', self.internal_rotation)
try:
self.fcisolver.dump_flags(self.verbose)
except AttributeError:
pass
if self.mo_coeff is None:
log.warn('Orbital for CASSCF is not specified. You probably need '
'call SCF.kernel() to initialize orbitals.')
return self
[docs]
def kernel(self, mo_coeff=None, ci0=None, callback=None):
return mc1step.CASSCF.kernel(self, mo_coeff, ci0, callback, kernel)
[docs]
def casci(self, mo_coeff, ci0=None, eris=None, verbose=None, envs=None):
log = logger.new_logger(self, verbose)
fcasci = mc1step._fake_h_for_fast_casci(self, mo_coeff, eris)
e_tot, e_cas, fcivec = casci.kernel(fcasci, mo_coeff, ci0, log,
envs=envs)
if not isinstance(e_cas, (float, numpy.number)):
raise RuntimeError('Multiple roots are detected in fcisolver. '
'CASSCF does not know which state to optimize.\n'
'See also mcscf.state_average or mcscf.state_specific for excited states.')
if envs is not None and log.verbose >= logger.INFO:
log.debug('CAS space CI energy = %.15g', e_cas)
if getattr(self.fcisolver, 'spin_square', None):
try:
ss = self.fcisolver.spin_square(fcivec, self.ncas, self.nelecas)
except NotImplementedError:
ss = None
else:
ss = None
if 'imacro' in envs: # Within CASSCF iteration
stat = envs['stat']
if ss is None:
log.info('macro %d (%d JK %d micro), '
'CASSCF E = %.15g dE = %.4g |grad|=%5.3g',
envs['imacro'], stat.tot_hop+stat.tot_kf, stat.imic,
e_tot, e_tot-envs['elast'], envs['norm_gall'])
else:
log.info('macro %d (%d JK %d micro), '
'CASSCF E = %.15g dE = %.4g |grad|=%5.3g S^2 = %.7f',
envs['imacro'], stat.tot_hop+stat.tot_kf, stat.imic,
e_tot, e_tot-envs['elast'], envs['norm_gall'], ss[0])
else: # Initialization step
elast = envs.get('elast', 0)
if ss is None:
log.info('CASCI E = %.15g', e_tot)
else:
log.info('CASCI E = %.15g dE = %.8g S^2 = %.7f',
e_tot, e_tot-elast, ss[0])
return e_tot, e_cas, fcivec
[docs]
def update_ao2mo(self, mo):
raise DeprecationWarning('update_ao2mo was obseleted since pyscf v1.0. '
'Use .ao2mo method instead')
if __name__ == '__main__':
from pyscf import gto
import pyscf.fci
mol = gto.Mole()
mol.verbose = 0
mol.output = None#"out_h2o"
mol.atom = [
['H', ( 1.,-1. , 0. )],
['H', ( 0.,-1. ,-1. )],
['H', ( 1.,-0.5 ,-1. )],
['H', ( 0.,-0.5 ,-1. )],
['H', ( 0.,-0.5 ,-0. )],
['H', ( 0.,-0. ,-1. )],
['H', ( 1.,-0.5 , 0. )],
['H', ( 0., 1. , 1. )],
]
mol.basis = {'H': 'sto-3g',
'O': '6-31g',}
mol.build()
m = scf.RHF(mol)
ehf = m.scf()
emc = kernel(CASSCF(m, 4, 4), m.mo_coeff, verbose=4)[1]
print(ehf, emc, emc-ehf)
print(emc - -3.22013929407)
mc = CASSCF(m, 4, (3,1))
mc.verbose = 4
#mc.fcisolver = pyscf.fci.direct_spin1
mc.fcisolver = pyscf.fci.solver(mol, False)
emc = kernel(mc, m.mo_coeff, verbose=4)[1]
print(emc - -15.950852049859-mol.energy_nuc())
mol.atom = [
['H', ( 5.,-1. , 1. )],
['H', ( 0.,-5. ,-2. )],
['H', ( 4.,-0.5 ,-3. )],
['H', ( 0.,-4.5 ,-1. )],
['H', ( 3.,-0.5 ,-0. )],
['H', ( 0.,-3. ,-1. )],
['H', ( 2.,-2.5 , 0. )],
['H', ( 1., 1. , 3. )],
]
mol.basis = {'H': 'sto-3g',
'O': '6-31g',}
mol.build()
m = scf.RHF(mol)
ehf = m.scf()
emc = kernel(CASSCF(m, 4, 4), m.mo_coeff, verbose=4)[1]
print(ehf, emc, emc-ehf)
print(emc - -3.62638367550087, emc - -3.6268060528596635)
mc = CASSCF(m, 4, (3,1))
mc.verbose = 4
#mc.fcisolver = pyscf.fci.direct_spin1
mc.fcisolver = pyscf.fci.solver(mol, False)
emc = kernel(mc, m.mo_coeff, verbose=4)[1]
print(emc - -3.62638367550087)
mol.atom = [
['O', ( 0., 0. , 0. )],
['H', ( 0., -0.757, 0.587)],
['H', ( 0., 0.757 , 0.587)],]
mol.basis = {'H': 'cc-pvdz',
'O': 'cc-pvdz',}
mol.build()
m = scf.RHF(mol)
ehf = m.scf()
mc = CASSCF(m, 6, 4)
mc.fcisolver = pyscf.fci.solver(mol)
mc.verbose = 4
mo = addons.sort_mo(mc, m.mo_coeff, (3,4,6,7,8,9), 1)
emc = mc.mc1step(mo)[0]
print(ehf, emc, emc-ehf)
#-76.0267656731 -76.0873922924 -0.0606266193028
print(emc - -76.0873923174, emc - -76.0926176464)
mc = CASSCF(m, 6, (3,1))
mo = addons.sort_mo(mc, m.mo_coeff, (3,4,6,7,8,9), 1)
#mc.fcisolver = pyscf.fci.direct_spin1
mc.fcisolver = pyscf.fci.solver(mol, False)
mc.verbose = 4
emc = mc.mc1step(mo)[0]
#mc.analyze()
print(emc - -75.7155632535814)
mc.internal_rotation = True
emc = mc.mc1step(mo)[0]
print(emc - -75.7155632535814)