def kernel(mycc, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None, mf_grad=None, verbose=logger.INFO): if t1 is None: t1 = mycc.t1 if t2 is None: t2 = mycc.t2 if l1 is None: l1 = mycc.l1 if l2 is None: l2 = mycc.l2 if eris is None: eris = ccsd._ERIS(mycc) if mf_grad is None: mf_grad = rhf_grad.Gradients(mycc._scf) log = logger.Logger(mycc.stdout, mycc.verbose) time0 = time.clock(), time.time() mol = mycc.mol if mycc.frozen is not 0: raise NotImplementedError('frozen orbital ccsd_grad') moidx = ccsd.get_moidx(mycc) mo_coeff = mycc.mo_coeff[:, moidx] #FIXME: ensure mycc.mo_coeff is canonical orbital mo_energy = eris.fock.diagonal() nocc, nvir = t1.shape nao, nmo = mo_coeff.shape nao_pair = nao * (nao + 1) // 2 log.debug('Build ccsd rdm1 intermediates') d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2) doo, dov, dvo, dvv = d1 time1 = log.timer('rdm1 intermediates', *time0) log.debug('Build ccsd rdm2 intermediates') d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2) time1 = log.timer('rdm2 intermediates', *time1) log.debug('Build ccsd response_rdm1') Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris, d1, d2) time1 = log.timer('response_rdm1 intermediates', *time1) dm1mo = response_dm1(mycc, t1, t2, l1, l2, eris, (Ioo, Ivv, Ivo, Xvo)) dm1mo[:nocc, :nocc] = doo * 2 dm1mo[nocc:, nocc:] = dvv * 2 dm1ao = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T)) im1 = numpy.zeros_like(dm1mo) im1[:nocc, :nocc] = Ioo im1[nocc:, nocc:] = Ivv im1[nocc:, :nocc] = Ivo im1[:nocc, nocc:] = Ivo.T im1 = reduce(numpy.dot, (mo_coeff, im1, mo_coeff.T)) time1 = log.timer('response_rdm1', *time1) log.debug('symmetrized rdm2 and MO->AO transformation') dm1_with_hf = dm1mo.copy() for i in range(nocc): dm1_with_hf[i, i] += 1 dm2ao = _rdm2_mo2ao(mycc, d2, dm1_with_hf, mo_coeff) time1 = log.timer('MO->AO transformation', *time1) log.debug('h1 and JK1') h1 = mf_grad.get_hcore(mol) s1 = mf_grad.get_ovlp(mol) zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5 zeta[nocc:, :nocc] = mo_energy[:nocc] zeta[:nocc, nocc:] = mo_energy[:nocc].reshape(-1, 1) zeta = reduce(numpy.dot, (mo_coeff, zeta * dm1mo, mo_coeff.T)) p1 = numpy.dot(mo_coeff[:, :nocc], mo_coeff[:, :nocc].T) vhf4sij = reduce(numpy.dot, (p1, mycc._scf.get_veff(mol, dm1ao + dm1ao.T), p1)) time1 = log.timer('h1 and JK1', *time1) # Hartree-Fock part contribution hf_dm1 = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ) dm1ao += hf_dm1 zeta += mf_grad.make_rdm1e(mycc.mo_energy, mycc.mo_coeff, mycc.mo_occ) if atmlst is None: atmlst = range(mol.natm) offsetdic = mol.offset_nr_by_atom() de = numpy.zeros((len(atmlst), 3)) for k, ia in enumerate(atmlst): shl0, shl1, p0, p1 = offsetdic[ia] # s[1] dot I, note matrix im1 is not hermitian de[k] = (numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1]) + numpy.einsum('xji,ij->x', s1[:, p0:p1], im1[:, p0:p1])) # h[1] \dot DM, *2 for +c.c., contribute to f1 h1ao = mf_grad._grad_rinv(mol, ia) h1ao[:, p0:p1] += h1[:, p0:p1] de[k] += (numpy.einsum('xij,ij->x', h1ao, dm1ao) + numpy.einsum('xji,ij->x', h1ao, dm1ao)) # -s[1]*e \dot DM, contribute to f1 de[k] -= (numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1]) + numpy.einsum('xji,ij->x', s1[:, p0:p1], zeta[:, p0:p1])) # -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf4sij[p0:p1]) * 2 # 2e AO integrals dot 2pdm eri1 = mol.intor('int2e_ip1', comp=3, aosym='s2kl', shls_slice=(shl0, shl1, 0, mol.nbas, 0, mol.nbas, 0, mol.nbas)) eri1 = eri1.reshape(3, p1 - p0, nao, -1) dm2buf = _load_block_tril(dm2ao, p0, p1) de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2buf) * 2 eri1 = dm2buf = None log.debug('grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k]) time1 = log.timer('grad of atom %d' % ia, *time1) de += rhf_grad.grad_nuc(mol) log.note('CCSD gradinets') log.note('==============') log.note(' x y z') for k, ia in enumerate(atmlst): log.note('%d %s %15.9f %15.9f %15.9f', ia, mol.atom_symbol(ia), *de[k]) log.timer('CCSD gradients', *time0) return de
def IX_intermediates(mycc, t1, t2, l1, l2, eris=None, d1=None, d2=None): if eris is None: # Note eris are in Chemist's notation eris = ccsd._ERIS(mycc) if d1 is None: d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2) if d2 is None: d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2) doo, dov, dvo, dvv = d1 dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2 log = logger.Logger(mycc.stdout, mycc.verbose) nocc, nvir = t1.shape nov = nocc * nvir # Note Ioo, Ivv are not hermitian Ioo = numpy.zeros((nocc, nocc)) Ivv = numpy.zeros((nvir, nvir)) Ivo = numpy.zeros((nvir, nocc)) Xvo = numpy.zeros((nvir, nocc)) eris_oooo = _cp(eris.oooo) eris_ooov = _cp(eris.ooov) d_oooo = _cp(doooo) d_oooo = _cp(d_oooo + d_oooo.transpose(1, 0, 2, 3)) #:Ioo += numpy.einsum('jmlk,imlk->ij', d_oooo, eris_oooo) * 2 Ioo += lib.dot(eris_oooo.reshape(nocc, -1), d_oooo.reshape(nocc, -1).T, 2) d_oooo = _cp(d_oooo.transpose(0, 2, 3, 1)) #:Xvo += numpy.einsum('iljk,ljka->ai', d_oooo, eris_ooov) * 2 Xvo += lib.dot( eris_ooov.reshape(-1, nvir).T, d_oooo.reshape(nocc, -1).T, 2) Xvo += (numpy.einsum('kj,kjia->ai', doo, eris_ooov) * 4 - numpy.einsum('kj,ikja->ai', doo + doo.T, eris_ooov)) eris_oooo = eris_ooov = d_oooo = None d_ooov = _cp(dooov) eris_oooo = _cp(eris.oooo) eris_ooov = _cp(eris.ooov) #:Ivv += numpy.einsum('ijkb,ijka->ab', d_ooov, eris_ooov) #:Ivo += numpy.einsum('jlka,jlki->ai', d_ooov, eris_oooo) Ivv += lib.dot(eris_ooov.reshape(-1, nvir).T, d_ooov.reshape(-1, nvir)) Ivo += lib.dot(d_ooov.reshape(-1, nvir).T, eris_oooo.reshape(-1, nocc)) #:Ioo += numpy.einsum('klja,klia->ij', d_ooov, eris_ooov) #:Xvo += numpy.einsum('kjib,kjba->ai', d_ooov, eris.oovv) eris_oovv = _cp(eris.oovv) tmp = _cp(d_ooov.transpose(0, 1, 3, 2).reshape(-1, nocc)) tmpooov = _cp(eris_ooov.transpose(0, 1, 3, 2)) Ioo += lib.dot(tmpooov.reshape(-1, nocc).T, tmp) Xvo += lib.dot(eris_oovv.reshape(-1, nvir).T, tmp) eris_oooo = tmp = None d_ooov = d_ooov + d_ooov.transpose(1, 0, 2, 3) eris_ovov = _cp(eris.ovov) #:Ioo += numpy.einsum('jlka,ilka->ij', d_ooov, eris_ooov) #:Xvo += numpy.einsum('ijkb,kbja->ai', d_ooov, eris.ovov) Ioo += lib.dot(eris_ooov.reshape(nocc, -1), d_ooov.reshape(nocc, -1).T) Xvo += lib.dot( eris_ovov.reshape(-1, nvir).T, _cp(d_ooov.transpose(0, 2, 3, 1).reshape(nocc, -1)).T) d_ooov = None #:Ioo += numpy.einsum('kjba,kiba->ij', d_oovv, eris.oovv) #:Ivv += numpy.einsum('ijcb,ijca->ab', d_oovv, eris.oovv) #:Ivo += numpy.einsum('kjba,kjib->ai', d_oovv, eris.ooov) d_oovv = _cp(doovv + doovv.transpose(1, 0, 3, 2)) for i in range(nocc): Ioo += lib.dot(eris_oovv[i].reshape(nocc, -1), d_oovv[i].reshape(nocc, -1).T) Ivv += lib.dot(eris_oovv.reshape(-1, nvir).T, d_oovv.reshape(-1, nvir)) Ivo += lib.dot(d_oovv.reshape(-1, nvir).T, tmpooov.reshape(-1, nocc)) d_oovv = _ccsd.precontract(d_oovv.reshape(-1, nvir, nvir)).reshape(nocc, nocc, -1) eris_ooov = tmpooov = None blksize = 4 d_ovov = numpy.empty((nocc, nvir, nocc, nvir)) for p0, p1 in prange(0, nocc, blksize): d_ovov[p0:p1] = _cp(dovov[p0:p1]) d_ovvo = _cp(dovvo[p0:p1]) for i in range(p0, p1): d_ovov[i] += d_ovvo[i - p0].transpose(0, 2, 1) d_ovvo = None #:d_ovov = d_ovov + d_ovov.transpose(2,3,0,1) lib.transpose_sum(d_ovov.reshape(nov, nov), inplace=True) #:Ivo += numpy.einsum('jbka,jbki->ai', d_ovov, eris.ovoo) Ivo += lib.dot( d_ovov.reshape(-1, nvir).T, _cp(eris.ovoo).reshape(-1, nocc)) #:Ioo += numpy.einsum('jakb,iakb->ij', d_ovov, eris.ovov) #:Ivv += numpy.einsum('jcib,jcia->ab', d_ovov, eris.ovov) Ioo += lib.dot(eris_ovov.reshape(nocc, -1), d_ovov.reshape(nocc, -1).T) Ivv += lib.dot(eris_ovov.reshape(-1, nvir).T, d_ovov.reshape(-1, nvir)) nvir_pair = nvir * (nvir + 1) // 2 bufe_ovvv = numpy.empty((blksize, nvir, nvir, nvir)) bufc_ovvv = numpy.empty((blksize, nvir, nvir_pair)) bufc_ovvv.data = bufe_ovvv.data c_vvvo = numpy.empty((nvir_pair, nvir, nocc)) for p0, p1 in prange(0, nocc, blksize): d_ovvv = numpy.empty((p1 - p0, nvir, nvir, nvir)) #:Ivo += numpy.einsum('jadc,jidc->ai', d_ovvv, eris_oovv) for i in range(p1 - p0): lib.dot(dovvv[p0 + i].reshape(nvir, -1), eris_oovv[p0 + i].reshape(nocc, -1).T, 1, Ivo, 1) c_ovvv = bufc_ovvv[:p1 - p0] # tril part of (d_ovvv + d_ovvv.transpose(0,1,3,2)) _ccsd.precontract(dovvv[p0:p1].reshape(-1, nvir, nvir), out=c_ovvv) for i0, i1, in prange(0, nvir_pair, BLKSIZE): for j0, j1 in prange(0, nvir, BLKSIZE // (p1 - p0) + 1): c_vvvo[i0:i1, j0:j1, p0:p1] = c_ovvv[:, j0:j1, i0:i1].transpose(2, 1, 0) eris_ovx = _cp(eris.ovvv[p0:p1]) #:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv) #:Ivv += numpy.einsum('ibdc,iadc->ab', d_ovvv, eris_ovvv) for i in range(p1 - p0): lib.dot(eris_ovx[i].reshape(nvir, -1), d_oovv[p0 + i].reshape(nocc, -1).T, 1, Xvo, 1) lib.dot(eris_ovx[i].reshape(nvir, -1), c_ovvv[i].reshape(nvir, -1).T, 1, Ivv, 1) eris_ovvv = bufe_ovvv[:p1 - p0] lib.unpack_tril(eris_ovx.reshape(-1, nvir_pair), out=eris_ovvv.reshape(-1, nvir**2)) eris_ovx = None #:Xvo += numpy.einsum('icjb,acjb->ai', d_ovov, eris_vvov) d_ovvo = _cp(d_ovov[p0:p1].transpose(0, 1, 3, 2)) lib.dot( eris_ovvv.reshape(-1, nvir).T, d_ovvo.reshape(-1, nocc), 1, Xvo, 1) e_ovvo, d_ovvo = d_ovvo, None for i in range(p1 - p0): d_ovvv[i] = _ccsd.sum021(dovvv[p0 + i]) e_ovvo[i] = eris_ovov[p0 + i].transpose(0, 2, 1) #:Ivo += numpy.einsum('jcab,jcib->ai', d_ovvv, eris_ovov) #:Ivv += numpy.einsum('icdb,icda->ab', d_ovvv, eris_ovvv) lib.dot( d_ovvv.reshape(-1, nvir).T, e_ovvo[:p1 - p0].reshape(-1, nocc), 1, Ivo, 1) lib.dot( eris_ovvv.reshape(-1, nvir).T, d_ovvv.reshape(-1, nvir), 1, Ivv, 1) Xvo[:, p0:p1] += (numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 4 - numpy.einsum('cb,icba->ai', dvv + dvv.T, eris_ovvv)) d_oovv = d_ovvv = bufc_ovvv = bufe_ovvv = None eris_ovov = eris_ovvv = eris_oovv = e_ovvo = None eris_ovvv = _cp(eris.ovvv) bufe_vvvo = numpy.empty((blksize * nvir, nvir, nocc)) bufe_vvvv = numpy.empty((blksize * nvir, nvir, nvir)) bufd_vvvv = numpy.empty((blksize * nvir, nvir, nvir)) for p0, p1 in prange(0, nvir, blksize): off0 = p0 * (p0 + 1) // 2 off1 = p1 * (p1 + 1) // 2 d_vvvv = _cp(dvvvv[off0:off1]) * 4 for i in range(p0, p1): d_vvvv[i * (i + 1) // 2 + i - off0] *= .5 d_vvvv = lib.unpack_tril(d_vvvv, out=bufd_vvvv[:off1 - off0]) eris_vvvv = lib.unpack_tril(eris.vvvv[off0:off1], out=bufe_vvvv[:off1 - off0]) #:Ivv += numpy.einsum('decb,deca->ab', d_vvvv, eris_vvvv) * 2 #:Xvo += numpy.einsum('icdb,acdb->ai', d_ovvv, eris_vvvv) lib.dot( eris_vvvv.reshape(-1, nvir).T, d_vvvv.reshape(-1, nvir), 2, Ivv, 1) d_vvvo = _cp(c_vvvo[off0:off1]) lib.dot( eris_vvvv.reshape(-1, nvir).T, d_vvvo.reshape(-1, nocc), 1, Xvo, 1) #:Ioo += numpy.einsum('abjc,abci->ij', d_vvov, eris_vvvo) #:Ivo += numpy.einsum('dbca,dbci->ai', d_vvvv, eris_vvvo) * 2 eris_vvvo = bufe_vvvo[:off1 - off0] for i0, i1 in prange(off0, off1, BLKSIZE): for j0, j1, in prange(0, nvir, BLKSIZE // nocc + 1): eris_vvvo[i0 - off0:i1 - off0, j0:j1, :] = eris_ovvv[:, j0:j1, i0:i1].transpose(2, 1, 0) lib.dot( eris_vvvo.reshape(-1, nocc).T, d_vvvo.reshape(-1, nocc), 1, Ioo, 1) lib.dot( d_vvvv.reshape(-1, nvir).T, eris_vvvo.reshape(-1, nocc), 2, Ivo, 1) Ioo *= -1 Ivv *= -1 Ivo *= -1 Xvo += Ivo return Ioo, Ivv, Ivo, Xvo
def IX_intermediates(mycc, t1, t2, l1, l2, eris=None, d1=None, d2=None): if eris is None: # Note eris are in Chemist's notation eris = ccsd._ERIS(mycc) if d1 is None: doo, dvv = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2) else: doo, dvv = d1 if d2 is None: d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2) dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2 log = logger.Logger(mycc.stdout, mycc.verbose) nocc, nvir = t1.shape nov = nocc * nvir # Note Ioo, Ivv are not hermitian Ioo = numpy.zeros((nocc,nocc)) Ivv = numpy.zeros((nvir,nvir)) Ivo = numpy.zeros((nvir,nocc)) Xvo = numpy.zeros((nvir,nocc)) eris_oooo = _cp(eris.oooo) eris_ooov = _cp(eris.ooov) d_oooo = _cp(doooo) d_oooo = _cp(d_oooo + d_oooo.transpose(1,0,2,3)) #:Ioo += numpy.einsum('jmlk,imlk->ij', d_oooo, eris_oooo) * 2 Ioo += lib.dot(eris_oooo.reshape(nocc,-1), d_oooo.reshape(nocc,-1).T, 2) d_oooo = _cp(d_oooo.transpose(0,2,3,1)) #:Xvo += numpy.einsum('iljk,ljka->ai', d_oooo, eris_ooov) * 2 Xvo += lib.dot(eris_ooov.reshape(-1,nvir).T, d_oooo.reshape(nocc,-1).T, 2) Xvo +=(numpy.einsum('kj,kjia->ai', doo, eris_ooov) * 4 - numpy.einsum('kj,ikja->ai', doo+doo.T, eris_ooov)) eris_oooo = eris_ooov = d_oooo = None d_ooov = _cp(dooov) eris_oooo = _cp(eris.oooo) eris_ooov = _cp(eris.ooov) #:Ivv += numpy.einsum('ijkb,ijka->ab', d_ooov, eris_ooov) #:Ivo += numpy.einsum('jlka,jlki->ai', d_ooov, eris_oooo) Ivv += lib.dot(eris_ooov.reshape(-1,nvir).T, d_ooov.reshape(-1,nvir)) Ivo += lib.dot(d_ooov.reshape(-1,nvir).T, eris_oooo.reshape(-1,nocc)) #:Ioo += numpy.einsum('klja,klia->ij', d_ooov, eris_ooov) #:Xvo += numpy.einsum('kjib,kjba->ai', d_ooov, eris.oovv) eris_oovv = _cp(eris.oovv) tmp = _cp(d_ooov.transpose(0,1,3,2).reshape(-1,nocc)) tmpooov = _cp(eris_ooov.transpose(0,1,3,2)) Ioo += lib.dot(tmpooov.reshape(-1,nocc).T, tmp) Xvo += lib.dot(eris_oovv.reshape(-1,nvir).T, tmp) eris_oooo = tmp = None d_ooov = d_ooov + d_ooov.transpose(1,0,2,3) eris_ovov = _cp(eris.ovov) #:Ioo += numpy.einsum('jlka,ilka->ij', d_ooov, eris_ooov) #:Xvo += numpy.einsum('ijkb,kbja->ai', d_ooov, eris.ovov) Ioo += lib.dot(eris_ooov.reshape(nocc,-1), d_ooov.reshape(nocc,-1).T) Xvo += lib.dot(eris_ovov.reshape(-1,nvir).T, _cp(d_ooov.transpose(0,2,3,1).reshape(nocc,-1)).T) d_ooov = None #:Ioo += numpy.einsum('kjba,kiba->ij', d_oovv, eris.oovv) #:Ivv += numpy.einsum('ijcb,ijca->ab', d_oovv, eris.oovv) #:Ivo += numpy.einsum('kjba,kjib->ai', d_oovv, eris.ooov) d_oovv = _cp(doovv + doovv.transpose(1,0,3,2)) for i in range(nocc): Ioo += lib.dot(eris_oovv[i].reshape(nocc, -1), d_oovv[i].reshape(nocc,-1).T) Ivv += lib.dot(eris_oovv.reshape(-1,nvir).T, d_oovv.reshape(-1,nvir)) Ivo += lib.dot(d_oovv.reshape(-1,nvir).T, tmpooov.reshape(-1,nocc)) d_oovv = _ccsd.precontract(d_oovv.reshape(-1,nvir,nvir)).reshape(nocc,nocc,-1) eris_ooov = tmpooov = None blksize = 4 d_ovov = numpy.empty((nocc,nvir,nocc,nvir)) for p0, p1 in prange(0, nocc, blksize): d_ovov[p0:p1] = _cp(dovov[p0:p1]) d_ovvo = _cp(dovvo[p0:p1]) for i in range(p0,p1): d_ovov[i] += d_ovvo[i-p0].transpose(0,2,1) d_ovvo = None #:d_ovov = d_ovov + d_ovov.transpose(2,3,0,1) lib.transpose_sum(d_ovov.reshape(nov,nov), inplace=True) #:Ivo += numpy.einsum('jbka,jbki->ai', d_ovov, eris.ovoo) Ivo += lib.dot(d_ovov.reshape(-1,nvir).T, _cp(eris.ovoo).reshape(-1,nocc)) #:Ioo += numpy.einsum('jakb,iakb->ij', d_ovov, eris.ovov) #:Ivv += numpy.einsum('jcib,jcia->ab', d_ovov, eris.ovov) Ioo += lib.dot(eris_ovov.reshape(nocc,-1), d_ovov.reshape(nocc,-1).T) Ivv += lib.dot(eris_ovov.reshape(-1,nvir).T, d_ovov.reshape(-1,nvir)) nvir_pair = nvir * (nvir+1) // 2 bufe_ovvv = numpy.empty((blksize,nvir,nvir,nvir)) bufc_ovvv = numpy.empty((blksize,nvir,nvir_pair)) bufc_ovvv.data = bufe_ovvv.data c_vvvo = numpy.empty((nvir_pair,nvir,nocc)) for p0, p1 in prange(0, nocc, blksize): d_ovvv = numpy.empty((p1-p0,nvir,nvir,nvir)) #:Ivo += numpy.einsum('jadc,jidc->ai', d_ovvv, eris_oovv) for i in range(p1-p0): lib.dot(dovvv[p0+i].reshape(nvir,-1), eris_oovv[p0+i].reshape(nocc,-1).T, 1, Ivo, 1) c_ovvv = bufc_ovvv[:p1-p0] # tril part of (d_ovvv + d_ovvv.transpose(0,1,3,2)) _ccsd.precontract(dovvv[p0:p1].reshape(-1,nvir,nvir), out=c_ovvv) for i0, i1, in prange(0, nvir_pair, BLKSIZE): for j0, j1 in prange(0, nvir, BLKSIZE//(p1-p0)+1): c_vvvo[i0:i1,j0:j1,p0:p1] = c_ovvv[:,j0:j1,i0:i1].transpose(2,1,0) eris_ovx = _cp(eris.ovvv[p0:p1]) #:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv) #:Ivv += numpy.einsum('ibdc,iadc->ab', d_ovvv, eris_ovvv) for i in range(p1-p0): lib.dot(eris_ovx[i].reshape(nvir,-1), d_oovv[p0+i].reshape(nocc,-1).T, 1, Xvo, 1) lib.dot(eris_ovx[i].reshape(nvir,-1), c_ovvv[i].reshape(nvir,-1).T, 1, Ivv, 1) eris_ovvv = bufe_ovvv[:p1-p0] _ccsd.unpack_tril(eris_ovx.reshape(-1,nvir_pair), out=eris_ovvv.reshape(-1,nvir**2)) eris_ovx = None #:Xvo += numpy.einsum('icjb,acjb->ai', d_ovov, eris_vvov) d_ovvo = _cp(d_ovov[p0:p1].transpose(0,1,3,2)) lib.dot(eris_ovvv.reshape(-1,nvir).T, d_ovvo.reshape(-1,nocc), 1, Xvo, 1) e_ovvo, d_ovvo = d_ovvo, None for i in range(p1-p0): d_ovvv[i] = _ccsd.sum021(dovvv[p0+i]) e_ovvo[i] = eris_ovov[p0+i].transpose(0,2,1) #:Ivo += numpy.einsum('jcab,jcib->ai', d_ovvv, eris_ovov) #:Ivv += numpy.einsum('icdb,icda->ab', d_ovvv, eris_ovvv) lib.dot(d_ovvv.reshape(-1,nvir).T, e_ovvo[:p1-p0].reshape(-1,nocc), 1, Ivo, 1) lib.dot(eris_ovvv.reshape(-1,nvir).T, d_ovvv.reshape(-1,nvir), 1, Ivv, 1) Xvo[:,p0:p1] +=(numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 4 - numpy.einsum('cb,icba->ai', dvv+dvv.T, eris_ovvv)) d_oovv = d_ovvv = bufc_ovvv = bufe_ovvv = None eris_ovov = eris_ovvv = eris_oovv = e_ovvo = None eris_ovvv = _cp(eris.ovvv) bufe_vvvo = numpy.empty((blksize*nvir,nvir,nocc)) bufe_vvvv = numpy.empty((blksize*nvir,nvir,nvir)) bufd_vvvv = numpy.empty((blksize*nvir,nvir,nvir)) for p0, p1 in prange(0, nvir, blksize): off0 = p0*(p0+1)//2 off1 = p1*(p1+1)//2 d_vvvv = _cp(dvvvv[off0:off1]) * 4 for i in range(p0, p1): d_vvvv[i*(i+1)//2+i-off0] *= .5 d_vvvv = _ccsd.unpack_tril(d_vvvv, out=bufd_vvvv[:off1-off0]) eris_vvvv = _ccsd.unpack_tril(eris.vvvv[off0:off1], out=bufe_vvvv[:off1-off0]) #:Ivv += numpy.einsum('decb,deca->ab', d_vvvv, eris_vvvv) * 2 #:Xvo += numpy.einsum('icdb,acdb->ai', d_ovvv, eris_vvvv) lib.dot(eris_vvvv.reshape(-1,nvir).T, d_vvvv.reshape(-1,nvir), 2, Ivv, 1) d_vvvo = _cp(c_vvvo[off0:off1]) lib.dot(eris_vvvv.reshape(-1,nvir).T, d_vvvo.reshape(-1,nocc), 1, Xvo, 1) #:Ioo += numpy.einsum('abjc,abci->ij', d_vvov, eris_vvvo) #:Ivo += numpy.einsum('dbca,dbci->ai', d_vvvv, eris_vvvo) * 2 eris_vvvo = bufe_vvvo[:off1-off0] for i0, i1 in prange(off0, off1, BLKSIZE): for j0, j1, in prange(0, nvir, BLKSIZE//nocc+1): eris_vvvo[i0-off0:i1-off0,j0:j1,:] = eris_ovvv[:,j0:j1,i0:i1].transpose(2,1,0) lib.dot(eris_vvvo.reshape(-1,nocc).T, d_vvvo.reshape(-1,nocc), 1, Ioo, 1) lib.dot(d_vvvv.reshape(-1,nvir).T, eris_vvvo.reshape(-1,nocc), 2, Ivo, 1) Ioo *= -1 Ivv *= -1 Ivo *= -1 Xvo += Ivo return Ioo, Ivv, Ivo, Xvo
def kernel(mycc, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None, grad_hf=None, verbose=logger.INFO): if t1 is None: t1 = mycc.t1 if t2 is None: t2 = mycc.t2 if l1 is None: l1 = mycc.l1 if l2 is None: l2 = mycc.l2 if eris is None: eris = ccsd._ERIS(mycc) if grad_hf is None: grad_hf = rhf_grad.Gradients(mycc._scf) log = logger.Logger(mycc.stdout, mycc.verbose) time0 = time.clock(), time.time() mol = mycc.mol moidx = numpy.ones(mycc.mo_energy.size, dtype=numpy.bool) if isinstance(mycc.frozen, (int, numpy.integer)): raise NotImplementedError('frozen orbital ccsd_grad') moidx[:mycc.frozen] = False else: moidx[mycc.frozen] = False mo_coeff = mycc.mo_coeff[:,moidx] #FIXME: ensure mycc.mo_coeff is canonical orbital mo_energy = mycc.mo_energy[moidx] nocc, nvir = t1.shape nao, nmo = mo_coeff.shape nao_pair = nao * (nao+1) // 2 log.debug('Build ccsd rdm1 intermediates') doo, dvv = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2) time1 = log.timer('rdm1 intermediates', *time0) log.debug('Build ccsd rdm2 intermediates') d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2) time1 = log.timer('rdm2 intermediates', *time1) log.debug('Build ccsd response_rdm1') Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris, (doo,dvv), d2) time1 = log.timer('response_rdm1 intermediates', *time1) dm1mo = response_dm1(mycc, t1, t2, l1, l2, eris, (Ioo, Ivv, Ivo, Xvo)) dm1mo[:nocc,:nocc] = doo * 2 dm1mo[nocc:,nocc:] = dvv * 2 dm1ao = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T)) im1 = numpy.zeros_like(dm1mo) im1[:nocc,:nocc] = Ioo im1[nocc:,nocc:] = Ivv im1[nocc:,:nocc] = Ivo im1[:nocc,nocc:] = Ivo.T im1 = reduce(numpy.dot, (mo_coeff, im1, mo_coeff.T)) time1 = log.timer('response_rdm1', *time1) log.debug('symmetrized rdm2 and MO->AO transformation') dm2ao = _rdm2_mo2ao(mycc, d2, dm1mo, mo_coeff) time1 = log.timer('MO->AO transformation', *time1) #TODO: pass hf_grad object to compute h1 and s1 log.debug('h1 and JK1') h1 = grad_hf.get_hcore(mol) s1 = grad_hf.get_ovlp(mol) zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5 zeta[nocc:,:nocc] = mo_energy[:nocc] zeta[:nocc,nocc:] = mo_energy[:nocc].reshape(-1,1) zeta = reduce(numpy.dot, (mo_coeff, zeta*dm1mo, mo_coeff.T)) p1 = numpy.dot(mo_coeff[:,:nocc], mo_coeff[:,:nocc].T) vhf4sij = reduce(numpy.dot, (p1, mycc._scf.get_veff(mol, dm1ao+dm1ao.T), p1)) time1 = log.timer('h1 and JK1', *time1) # Hartree-Fock part contribution hf_dm1 = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ) dm1ao += hf_dm1 zeta += grad_hf.make_rdm1e(mycc.mo_energy, mycc.mo_coeff, mycc.mo_occ) if atmlst is None: atmlst = range(mol.natm) offsetdic = grad_hf.aorange_by_atom() de = numpy.zeros((len(atmlst),3)) for k, ia in enumerate(atmlst): shl0, shl1, p0, p1 = offsetdic[ia] # s[1] dot I, note matrix im1 is not hermitian de[k] =(numpy.einsum('xij,ij->x', s1[:,p0:p1], im1[p0:p1]) + numpy.einsum('xji,ij->x', s1[:,p0:p1], im1[:,p0:p1])) # h[1] \dot DM, *2 for +c.c., contribute to f1 vrinv = grad_hf._grad_rinv(mol, ia) de[k] +=(numpy.einsum('xij,ij->x', h1[:,p0:p1], dm1ao[p0:p1] ) + numpy.einsum('xji,ij->x', h1[:,p0:p1], dm1ao[:,p0:p1])) de[k] +=(numpy.einsum('xij,ij->x', vrinv, dm1ao) + numpy.einsum('xji,ij->x', vrinv, dm1ao)) # -s[1]*e \dot DM, contribute to f1 de[k] -=(numpy.einsum('xij,ij->x', s1[:,p0:p1], zeta[p0:p1] ) + numpy.einsum('xji,ij->x', s1[:,p0:p1], zeta[:,p0:p1])) # -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T de[k] -= numpy.einsum('xij,ij->x', s1[:,p0:p1], vhf4sij[p0:p1]) * 2 # 2e AO integrals dot 2pdm eri1 = gto.moleintor.getints('cint2e_ip1_sph', mol._atm, mol._bas, mol._env, numpy.arange(shl0,shl1), comp=3, aosym='s2kl').reshape(3,p1-p0,nao,-1) dm2buf = _load_block_tril(dm2ao, p0, p1) de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2buf) * 2 for i in range(3): #:tmp = _ccsd.unpack_tril(eri1[i].reshape(-1,nao_pair)) #:vj = numpy.einsum('ijkl,kl->ij', tmp, hf_dm1) #:vk = numpy.einsum('ijkl,jk->il', tmp, hf_dm1) vj, vk = hf_get_jk_incore(eri1[i], hf_dm1) de[k,i] -=(numpy.einsum('ij,ij->', vj, hf_dm1[p0:p1]) - numpy.einsum('ij,ij->', vk, hf_dm1[p0:p1])*.5) * 2 eri1 = dm2buf = None log.debug('grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k]) time1 = log.timer('grad of atom %d'%ia, *time1) log.note('CCSD gradinets') log.note('==============') log.note(' x y z') for k, ia in enumerate(atmlst): log.note('%d %s %15.9f %15.9f %15.9f', ia, mol.atom_symbol(ia), de[k,0], de[k,1], de[k,2]) log.timer('CCSD gradients', *time0) return de
def kernel(mycc, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None, mf_grad=None, verbose=logger.INFO): if t1 is None: t1 = mycc.t1 if t2 is None: t2 = mycc.t2 if l1 is None: l1 = mycc.l1 if l2 is None: l2 = mycc.l2 if eris is None: eris = ccsd._ERIS(mycc) if mf_grad is None: mf_grad = rhf_grad.Gradients(mycc._scf) log = logger.Logger(mycc.stdout, mycc.verbose) time0 = time.clock(), time.time() mol = mycc.mol moidx = numpy.ones(mycc.mo_energy.size, dtype=numpy.bool) if isinstance(mycc.frozen, (int, numpy.integer)): raise NotImplementedError("frozen orbital ccsd_grad") moidx[: mycc.frozen] = False else: moidx[mycc.frozen] = False mo_coeff = mycc.mo_coeff[:, moidx] # FIXME: ensure mycc.mo_coeff is canonical orbital mo_energy = mycc.mo_energy[moidx] nocc, nvir = t1.shape nao, nmo = mo_coeff.shape nao_pair = nao * (nao + 1) // 2 log.debug("Build ccsd rdm1 intermediates") d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2) doo, dov, dvo, dvv = d1 time1 = log.timer("rdm1 intermediates", *time0) log.debug("Build ccsd rdm2 intermediates") d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2) time1 = log.timer("rdm2 intermediates", *time1) log.debug("Build ccsd response_rdm1") Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris, d1, d2) time1 = log.timer("response_rdm1 intermediates", *time1) dm1mo = response_dm1(mycc, t1, t2, l1, l2, eris, (Ioo, Ivv, Ivo, Xvo)) dm1mo[:nocc, :nocc] = doo * 2 dm1mo[nocc:, nocc:] = dvv * 2 dm1ao = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T)) im1 = numpy.zeros_like(dm1mo) im1[:nocc, :nocc] = Ioo im1[nocc:, nocc:] = Ivv im1[nocc:, :nocc] = Ivo im1[:nocc, nocc:] = Ivo.T im1 = reduce(numpy.dot, (mo_coeff, im1, mo_coeff.T)) time1 = log.timer("response_rdm1", *time1) log.debug("symmetrized rdm2 and MO->AO transformation") dm1_with_hf = dm1mo.copy() for i in range(nocc): dm1_with_hf[i, i] += 1 dm2ao = _rdm2_mo2ao(mycc, d2, dm1_with_hf, mo_coeff) time1 = log.timer("MO->AO transformation", *time1) log.debug("h1 and JK1") h1 = mf_grad.get_hcore(mol) s1 = mf_grad.get_ovlp(mol) zeta = lib.direct_sum("i+j->ij", mo_energy, mo_energy) * 0.5 zeta[nocc:, :nocc] = mo_energy[:nocc] zeta[:nocc, nocc:] = mo_energy[:nocc].reshape(-1, 1) zeta = reduce(numpy.dot, (mo_coeff, zeta * dm1mo, mo_coeff.T)) p1 = numpy.dot(mo_coeff[:, :nocc], mo_coeff[:, :nocc].T) vhf4sij = reduce(numpy.dot, (p1, mycc._scf.get_veff(mol, dm1ao + dm1ao.T), p1)) time1 = log.timer("h1 and JK1", *time1) # Hartree-Fock part contribution hf_dm1 = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ) dm1ao += hf_dm1 zeta += mf_grad.make_rdm1e(mycc.mo_energy, mycc.mo_coeff, mycc.mo_occ) if atmlst is None: atmlst = range(mol.natm) offsetdic = mol.offset_nr_by_atom() de = numpy.zeros((len(atmlst), 3)) for k, ia in enumerate(atmlst): shl0, shl1, p0, p1 = offsetdic[ia] # s[1] dot I, note matrix im1 is not hermitian de[k] = numpy.einsum("xij,ij->x", s1[:, p0:p1], im1[p0:p1]) + numpy.einsum( "xji,ij->x", s1[:, p0:p1], im1[:, p0:p1] ) # h[1] \dot DM, *2 for +c.c., contribute to f1 h1ao = mf_grad._grad_rinv(mol, ia) h1ao[:, p0:p1] += h1[:, p0:p1] de[k] += numpy.einsum("xij,ij->x", h1ao, dm1ao) + numpy.einsum("xji,ij->x", h1ao, dm1ao) # -s[1]*e \dot DM, contribute to f1 de[k] -= numpy.einsum("xij,ij->x", s1[:, p0:p1], zeta[p0:p1]) + numpy.einsum( "xji,ij->x", s1[:, p0:p1], zeta[:, p0:p1] ) # -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T de[k] -= numpy.einsum("xij,ij->x", s1[:, p0:p1], vhf4sij[p0:p1]) * 2 # 2e AO integrals dot 2pdm eri1 = gto.moleintor.getints( "cint2e_ip1_sph", mol._atm, mol._bas, mol._env, numpy.arange(shl0, shl1), comp=3, aosym="s2kl" ).reshape(3, p1 - p0, nao, -1) dm2buf = _load_block_tril(dm2ao, p0, p1) de[k] -= numpy.einsum("xijk,ijk->x", eri1, dm2buf) * 2 eri1 = dm2buf = None log.debug("grad of atom %d %s = %s", ia, mol.atom_symbol(ia), de[k]) time1 = log.timer("grad of atom %d" % ia, *time1) log.note("CCSD gradinets") log.note("==============") log.note(" x y z") for k, ia in enumerate(atmlst): log.note("%d %s %15.9f %15.9f %15.9f", ia, mol.atom_symbol(ia), de[k, 0], de[k, 1], de[k, 2]) log.timer("CCSD gradients", *time0) return de