Source code for pyscf.mcscf.newton_casscf

#!/usr/bin/env python
# Copyright 2014-2019 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
'''

import time
import copy
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) hci_diag = [hd - ec - gc*c*4 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 hci1 = [hc1 - c1 * ec0 for hc1, c1, ec0 in zip (_Hci (h1cas_0, eri_cas, ci1), ci1, eci0)] hci1 = [hc1 - 2*(hc0 - c0*ec0)*c0.dot(c1) for hc1, hc0, c0, ec0, c1 in zip (hci1, hci0, ci0, eci0, ci1)] hci1 = [hc1 - 2*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 extract_rotation(casscf, dr, u, ci0): nroots = casscf.fcisolver.nroots nmo = casscf.mo_coeff.shape[1] ngorb = numpy.count_nonzero (casscf.uniq_var_indices (nmo, casscf.ncore, casscf.ncas, casscf.frozen)) u = numpy.dot(u, casscf.update_rotate_matrix(dr[:ngorb])) if nroots == 1: ci0 = [ci0] p0 = ngorb ci1 = [] for c in ci0: p1 = p0 + c.size d = c.ravel () + dr[p0:p1] d *= 1./numpy.linalg.norm (d) ci1.append (d) p0 = p1 if nroots == 1: ci1 = ci1[0] return u, ci1
[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)) g_kf = g_all 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_kf = 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 = (time.clock(), time.time()) 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.CASCI.__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.CASCI.__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.callback = None 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 self._keys = set(self.__dict__.keys())
[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) assert(nvir > 0 and ncore > 0 and self.ncas > 0) 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 = %d', 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 CASCI 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) if eris is None: fcasci = copy.copy(self) fcasci.ao2mo = self.get_h2cas else: fcasci = mc1step._fake_h_for_fast_casci(self, mo_coeff, eris) e_tot, e_cas, fcivec = casci.kernel(fcasci, mo_coeff, ci0, log) 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): ss = self.fcisolver.spin_square(fcivec, self.ncas, self.nelecas) 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')
# Don't remove the two functions. They are used in df/approx_hessian code
[docs] def get_h2eff(self, mo_coeff=None): return self.get_h2cas(mo_coeff)
[docs] def get_h2cas(self, mo_coeff=None): return casci.CASCI.ao2mo(self, mo_coeff)
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)