def _get_vxc_deriv1(hessobj, mo_coeff, mo_occ, max_memory): mol = hessobj.mol mf = hessobj.base if hessobj.grids is not None: grids = hessobj.grids else: grids = mf.grids if grids.coords is None: grids.build(with_non0tab=True) nao, nmo = mo_coeff[0].shape ni = mf._numint xctype = ni._xc_type(mf.xc) aoslices = mol.aoslice_by_atom() shls_slice = (0, mol.nbas) ao_loc = mol.ao_loc_nr() dm0a, dm0b = mf.make_rdm1(mo_coeff, mo_occ) vmata = numpy.zeros((mol.natm,3,nao,nao)) vmatb = numpy.zeros((mol.natm,3,nao,nao)) max_memory = max(2000, max_memory-(vmata.size+vmatb.size)*8/1e6) if xctype == 'LDA': ao_deriv = 1 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rhoa = ni.eval_rho2(mol, ao[0], mo_coeff[0], mo_occ[0], mask, xctype) rhob = ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask, xctype) vxc, fxc = ni.eval_xc(mf.xc, (rhoa,rhob), 1, deriv=2)[1:3] vrho = vxc[0] u_u, u_d, d_d = fxc[0].T ao_dm0a = numint._dot_ao_dm(mol, ao[0], dm0a, mask, shls_slice, ao_loc) ao_dm0b = numint._dot_ao_dm(mol, ao[0], dm0b, mask, shls_slice, ao_loc) aow1a = numpy.einsum('xpi,p->xpi', ao[1:], weight*vrho[:,0]) aow1b = numpy.einsum('xpi,p->xpi', ao[1:], weight*vrho[:,1]) for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] # First order density = rho1 * 2. *2 is not applied because + c.c. in the end rho1a = numpy.einsum('xpi,pi->xp', ao[1:,:,p0:p1], ao_dm0a[:,p0:p1]) rho1b = numpy.einsum('xpi,pi->xp', ao[1:,:,p0:p1], ao_dm0b[:,p0:p1]) wv = u_u * rho1a + u_d * rho1b wv *= weight aow = numpy.einsum('pi,xp->xpi', ao[0], wv) aow[:,:,p0:p1] += aow1a[:,:,p0:p1] rks_grad._d1_dot_(vmata[ia], mol, aow, ao[0], mask, ao_loc, True) wv = u_d * rho1a + d_d * rho1b wv *= weight aow = numpy.einsum('pi,xp->xpi', ao[0], wv) aow[:,:,p0:p1] += aow1b[:,:,p0:p1] rks_grad._d1_dot_(vmatb[ia], mol, aow, ao[0], mask, ao_loc, True) ao_dm0a = ao_dm0b = aow = aow1a = aow1b = None for ia in range(mol.natm): vmata[ia] = -vmata[ia] - vmata[ia].transpose(0,2,1) vmatb[ia] = -vmatb[ia] - vmatb[ia].transpose(0,2,1) elif xctype == 'GGA': ao_deriv = 2 vipa = numpy.zeros((3,nao,nao)) vipb = numpy.zeros((3,nao,nao)) for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rhoa = ni.eval_rho2(mol, ao[:4], mo_coeff[0], mo_occ[0], mask, xctype) rhob = ni.eval_rho2(mol, ao[:4], mo_coeff[1], mo_occ[1], mask, xctype) vxc, fxc = ni.eval_xc(mf.xc, (rhoa,rhob), 1, deriv=2)[1:3] wva, wvb = numint._uks_gga_wv0((rhoa,rhob), vxc, weight) rks_grad._gga_grad_sum_(vipa, mol, ao, wva, mask, ao_loc) rks_grad._gga_grad_sum_(vipb, mol, ao, wvb, mask, ao_loc) ao_dm0a = [numint._dot_ao_dm(mol, ao[i], dm0a, mask, shls_slice, ao_loc) for i in range(4)] ao_dm0b = [numint._dot_ao_dm(mol, ao[i], dm0b, mask, shls_slice, ao_loc) for i in range(4)] for ia in range(mol.natm): wva = dR_rho1a = rks_hess._make_dR_rho1(ao, ao_dm0a, ia, aoslices) wvb = dR_rho1b = rks_hess._make_dR_rho1(ao, ao_dm0b, ia, aoslices) wva[0], wvb[0] = numint._uks_gga_wv1((rhoa,rhob), (dR_rho1a[0],dR_rho1b[0]), vxc, fxc, weight) wva[1], wvb[1] = numint._uks_gga_wv1((rhoa,rhob), (dR_rho1a[1],dR_rho1b[1]), vxc, fxc, weight) wva[2], wvb[2] = numint._uks_gga_wv1((rhoa,rhob), (dR_rho1a[2],dR_rho1b[2]), vxc, fxc, weight) aow = numpy.einsum('npi,Xnp->Xpi', ao[:4], wva) rks_grad._d1_dot_(vmata[ia], mol, aow, ao[0], mask, ao_loc, True) aow = numpy.einsum('npi,Xnp->Xpi', ao[:4], wvb) rks_grad._d1_dot_(vmatb[ia], mol, aow, ao[0], mask, ao_loc, True) ao_dm0a = ao_dm0b = aow = None for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] vmata[ia,:,p0:p1] += vipa[:,p0:p1] vmata[ia] = -vmata[ia] - vmata[ia].transpose(0,2,1) vmatb[ia,:,p0:p1] += vipb[:,p0:p1] vmatb[ia] = -vmatb[ia] - vmatb[ia].transpose(0,2,1) elif xctype == 'MGGA': raise NotImplementedError('meta-GGA') return vmata, vmatb
def _get_vxc_deriv2(hessobj, mo_coeff, mo_occ, max_memory): mol = hessobj.mol mf = hessobj.base if hessobj.grids is not None: grids = hessobj.grids else: grids = mf.grids if grids.coords is None: grids.build(with_non0tab=True) nao, nmo = mo_coeff[0].shape ni = mf._numint xctype = ni._xc_type(mf.xc) aoslices = mol.aoslice_by_atom() shls_slice = (0, mol.nbas) ao_loc = mol.ao_loc_nr() dm0a, dm0b = mf.make_rdm1(mo_coeff, mo_occ) vmata = numpy.zeros((mol.natm,3,3,nao,nao)) vmatb = numpy.zeros((mol.natm,3,3,nao,nao)) ipipa = numpy.zeros((3,3,nao,nao)) ipipb = numpy.zeros((3,3,nao,nao)) if xctype == 'LDA': ao_deriv = 1 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rhoa = ni.eval_rho2(mol, ao[0], mo_coeff[0], mo_occ[0], mask, xctype) rhob = ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask, xctype) vxc, fxc = ni.eval_xc(mf.xc, (rhoa,rhob), 1, deriv=2)[1:3] vrho = vxc[0] u_u, u_d, d_d = fxc[0].T aow = numpy.einsum('xpi,p->xpi', ao[1:4], weight*vrho[:,0]) rks_hess._d1d2_dot_(ipipa, mol, aow, ao[1:4], mask, ao_loc, False) aow = numpy.einsum('xpi,p->xpi', ao[1:4], weight*vrho[:,1]) rks_hess._d1d2_dot_(ipipb, mol, aow, ao[1:4], mask, ao_loc, False) ao_dm0a = numint._dot_ao_dm(mol, ao[0], dm0a, mask, shls_slice, ao_loc) ao_dm0b = numint._dot_ao_dm(mol, ao[0], dm0b, mask, shls_slice, ao_loc) for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] # *2 for \nabla|ket> in rho1 rho1a = numpy.einsum('xpi,pi->xp', ao[1:,:,p0:p1], ao_dm0a[:,p0:p1]) * 2 rho1b = numpy.einsum('xpi,pi->xp', ao[1:,:,p0:p1], ao_dm0b[:,p0:p1]) * 2 wv = u_u * rho1a + u_d * rho1b wv *= weight # aow ~ rho1 ~ d/dR1 aow = numpy.einsum('pi,xp->xpi', ao[0], wv) rks_hess._d1d2_dot_(vmata[ia], mol, ao[1:4], aow, mask, ao_loc, False) wv = u_d * rho1a + d_d * rho1b wv *= weight aow = numpy.einsum('pi,xp->xpi', ao[0], wv) rks_hess._d1d2_dot_(vmatb[ia], mol, ao[1:4], aow, mask, ao_loc, False) ao_dm0a = ao_dm0b = aow = None for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] vmata[ia,:,:,:,p0:p1] += ipipa[:,:,:,p0:p1] vmatb[ia,:,:,:,p0:p1] += ipipb[:,:,:,p0:p1] elif xctype == 'GGA': ao_deriv = 2 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rhoa = ni.eval_rho2(mol, ao[:4], mo_coeff[0], mo_occ[0], mask, xctype) rhob = ni.eval_rho2(mol, ao[:4], mo_coeff[1], mo_occ[1], mask, xctype) vxc, fxc = ni.eval_xc(mf.xc, (rhoa,rhob), 1, deriv=2)[1:3] wva, wvb = numint._uks_gga_wv0((rhoa,rhob), vxc, weight) aow = rks_grad._make_dR_dao_w(ao, wva) rks_hess._d1d2_dot_(ipipa, mol, aow, ao[1:4], mask, ao_loc, False) aow = rks_grad._make_dR_dao_w(ao, wvb) rks_hess._d1d2_dot_(ipipb, mol, aow, ao[1:4], mask, ao_loc, False) ao_dm0a = [numint._dot_ao_dm(mol, ao[i], dm0a, mask, shls_slice, ao_loc) for i in range(4)] ao_dm0b = [numint._dot_ao_dm(mol, ao[i], dm0b, mask, shls_slice, ao_loc) for i in range(4)] for ia in range(mol.natm): wva = dR_rho1a = rks_hess._make_dR_rho1(ao, ao_dm0a, ia, aoslices) wvb = dR_rho1b = rks_hess._make_dR_rho1(ao, ao_dm0b, ia, aoslices) wva[0], wvb[0] = numint._uks_gga_wv1((rhoa,rhob), (dR_rho1a[0],dR_rho1b[0]), vxc, fxc, weight) wva[1], wvb[1] = numint._uks_gga_wv1((rhoa,rhob), (dR_rho1a[1],dR_rho1b[1]), vxc, fxc, weight) wva[2], wvb[2] = numint._uks_gga_wv1((rhoa,rhob), (dR_rho1a[2],dR_rho1b[2]), vxc, fxc, weight) aow = rks_grad._make_dR_dao_w(ao, wva[0]) rks_grad._d1_dot_(vmata[ia,0], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wva[1]) rks_grad._d1_dot_(vmata[ia,1], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wva[2]) rks_grad._d1_dot_(vmata[ia,2], mol, aow, ao[0], mask, ao_loc, True) aow = numpy.einsum('npi,Xnp->Xpi', ao[:4], wva) rks_hess._d1d2_dot_(vmata[ia], mol, ao[1:4], aow, mask, ao_loc, False) aow = rks_grad._make_dR_dao_w(ao, wvb[0]) rks_grad._d1_dot_(vmatb[ia,0], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wvb[1]) rks_grad._d1_dot_(vmatb[ia,1], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wvb[2]) rks_grad._d1_dot_(vmatb[ia,2], mol, aow, ao[0], mask, ao_loc, True) aow = numpy.einsum('npi,Xnp->Xpi', ao[:4], wvb) rks_hess._d1d2_dot_(vmatb[ia], mol, ao[1:4], aow, mask, ao_loc, False) ao_dm0a = ao_dm0b = aow = None for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] vmata[ia,:,:,:,p0:p1] += ipipa[:,:,:,p0:p1] vmata[ia,:,:,:,p0:p1] += ipipa[:,:,p0:p1].transpose(1,0,3,2) vmatb[ia,:,:,:,p0:p1] += ipipb[:,:,:,p0:p1] vmatb[ia,:,:,:,p0:p1] += ipipb[:,:,p0:p1].transpose(1,0,3,2) elif xctype == 'MGGA': raise NotImplementedError('meta-GGA') return vmata, vmatb
def _get_vxc_deriv1(hessobj, mo_coeff, mo_occ, max_memory): """" This functions is slightly different from hessian.rks._get_vxc_deriv1 in that <\nabla u|Vxc|v> is removed""" mol = hessobj.mol mf = hessobj.base if hessobj.grids is not None: grids = hessobj.grids else: grids = mf.grids if grids.coords is None: grids.build(with_non0tab=True) nao, nmo = mo_coeff.shape ni = mf._numint xctype = ni._xc_type(mf.xc) aoslices = mol.aoslice_by_atom() shls_slice = (0, mol.nbas) ao_loc = mol.ao_loc_nr() dm0 = mf.make_rdm1(mo_coeff, mo_occ) vmat = np.zeros((mol.natm, 3, nao, nao)) max_memory = max(2000, max_memory - vmat.size * 8 / 1e6) if xctype == 'LDA': ao_deriv = 1 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA') vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3] vrho = vxc[0] frr = fxc[0] ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice, ao_loc) for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] rho1 = np.einsum('xpi,pi->xp', ao[1:, :, p0:p1], ao_dm0[:, p0:p1]) aow = np.einsum('pi,xp->xpi', ao[0], weight * frr * rho1) rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True) ao_dm0 = aow = None for ia in range(mol.natm): vmat[ia] = -vmat[ia] - vmat[ia].transpose(0, 2, 1) elif xctype == 'GGA': ao_deriv = 2 v_ip = np.zeros((3, nao, nao)) for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[:4], mo_coeff, mo_occ, mask, 'GGA') vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3] wv = numint._rks_gga_wv0(rho, vxc, weight) #rks_grad._gga_grad_sum_(v_ip, mol, ao, wv, mask, ao_loc) ao_dm0 = [ numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc) for i in range(4) ] for ia in range(mol.natm): wv = dR_rho1 = rks_hess._make_dR_rho1(ao, ao_dm0, ia, aoslices) wv[0] = numint._rks_gga_wv1(rho, dR_rho1[0], vxc, fxc, weight) wv[1] = numint._rks_gga_wv1(rho, dR_rho1[1], vxc, fxc, weight) wv[2] = numint._rks_gga_wv1(rho, dR_rho1[2], vxc, fxc, weight) aow = np.einsum('npi,Xnp->Xpi', ao[:4], wv) rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True) ao_dm0 = aow = None for ia in range(mol.natm): vmat[ia] = -vmat[ia] - vmat[ia].transpose(0, 2, 1) elif xctype == 'MGGA': raise NotImplementedError('meta-GGA') return vmat
def _get_vxc_deriv2(hessobj, mo_coeff, mo_occ, max_memory): mol = hessobj.mol mf = hessobj.base if hessobj.grids is not None: grids = hessobj.grids else: grids = mf.grids if grids.coords is None: grids.build(with_non0tab=True) nao, nmo = mo_coeff[0].shape ni = mf._numint xctype = ni._xc_type(mf.xc) aoslices = mol.aoslice_by_atom() shls_slice = (0, mol.nbas) ao_loc = mol.ao_loc_nr() dm0a, dm0b = mf.make_rdm1(mo_coeff, mo_occ) vmata = numpy.zeros((mol.natm, 3, 3, nao, nao)) vmatb = numpy.zeros((mol.natm, 3, 3, nao, nao)) ipipa = numpy.zeros((3, 3, nao, nao)) ipipb = numpy.zeros((3, 3, nao, nao)) if xctype == 'LDA': ao_deriv = 1 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rhoa = ni.eval_rho2(mol, ao[0], mo_coeff[0], mo_occ[0], mask, xctype) rhob = ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask, xctype) vxc, fxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=2)[1:3] vrho = vxc[0] u_u, u_d, d_d = fxc[0].T aow = numpy.einsum('xpi,p->xpi', ao[1:4], weight * vrho[:, 0]) rks_hess._d1d2_dot_(ipipa, mol, aow, ao[1:4], mask, ao_loc, False) aow = numpy.einsum('xpi,p->xpi', ao[1:4], weight * vrho[:, 1]) rks_hess._d1d2_dot_(ipipb, mol, aow, ao[1:4], mask, ao_loc, False) ao_dm0a = numint._dot_ao_dm(mol, ao[0], dm0a, mask, shls_slice, ao_loc) ao_dm0b = numint._dot_ao_dm(mol, ao[0], dm0b, mask, shls_slice, ao_loc) for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] # *2 for \nabla|ket> in rho1 rho1a = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1], ao_dm0a[:, p0:p1]) * 2 rho1b = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1], ao_dm0b[:, p0:p1]) * 2 wv = u_u * rho1a + u_d * rho1b wv *= weight # aow ~ rho1 ~ d/dR1 aow = numpy.einsum('pi,xp->xpi', ao[0], wv) rks_hess._d1d2_dot_(vmata[ia], mol, ao[1:4], aow, mask, ao_loc, False) wv = u_d * rho1a + d_d * rho1b wv *= weight aow = numpy.einsum('pi,xp->xpi', ao[0], wv) rks_hess._d1d2_dot_(vmatb[ia], mol, ao[1:4], aow, mask, ao_loc, False) ao_dm0a = ao_dm0b = aow = None for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] vmata[ia, :, :, :, p0:p1] += ipipa[:, :, :, p0:p1] vmatb[ia, :, :, :, p0:p1] += ipipb[:, :, :, p0:p1] elif xctype == 'GGA': ao_deriv = 2 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rhoa = ni.eval_rho2(mol, ao[:4], mo_coeff[0], mo_occ[0], mask, xctype) rhob = ni.eval_rho2(mol, ao[:4], mo_coeff[1], mo_occ[1], mask, xctype) vxc, fxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=2)[1:3] wva, wvb = numint._uks_gga_wv0((rhoa, rhob), vxc, weight) aow = rks_grad._make_dR_dao_w(ao, wva) rks_hess._d1d2_dot_(ipipa, mol, aow, ao[1:4], mask, ao_loc, False) aow = rks_grad._make_dR_dao_w(ao, wvb) rks_hess._d1d2_dot_(ipipb, mol, aow, ao[1:4], mask, ao_loc, False) ao_dm0a = [ numint._dot_ao_dm(mol, ao[i], dm0a, mask, shls_slice, ao_loc) for i in range(4) ] ao_dm0b = [ numint._dot_ao_dm(mol, ao[i], dm0b, mask, shls_slice, ao_loc) for i in range(4) ] for ia in range(mol.natm): wva = dR_rho1a = rks_hess._make_dR_rho1( ao, ao_dm0a, ia, aoslices) wvb = dR_rho1b = rks_hess._make_dR_rho1( ao, ao_dm0b, ia, aoslices) wva[0], wvb[0] = numint._uks_gga_wv1( (rhoa, rhob), (dR_rho1a[0], dR_rho1b[0]), vxc, fxc, weight) wva[1], wvb[1] = numint._uks_gga_wv1( (rhoa, rhob), (dR_rho1a[1], dR_rho1b[1]), vxc, fxc, weight) wva[2], wvb[2] = numint._uks_gga_wv1( (rhoa, rhob), (dR_rho1a[2], dR_rho1b[2]), vxc, fxc, weight) aow = rks_grad._make_dR_dao_w(ao, wva[0]) rks_grad._d1_dot_(vmata[ia, 0], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wva[1]) rks_grad._d1_dot_(vmata[ia, 1], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wva[2]) rks_grad._d1_dot_(vmata[ia, 2], mol, aow, ao[0], mask, ao_loc, True) aow = [numint._scale_ao(ao[:4], wva[i, :4]) for i in range(3)] rks_hess._d1d2_dot_(vmata[ia], mol, ao[1:4], aow, mask, ao_loc, False) aow = rks_grad._make_dR_dao_w(ao, wvb[0]) rks_grad._d1_dot_(vmatb[ia, 0], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wvb[1]) rks_grad._d1_dot_(vmatb[ia, 1], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wvb[2]) rks_grad._d1_dot_(vmatb[ia, 2], mol, aow, ao[0], mask, ao_loc, True) aow = [numint._scale_ao(ao[:4], wvb[i, :4]) for i in range(3)] rks_hess._d1d2_dot_(vmatb[ia], mol, ao[1:4], aow, mask, ao_loc, False) ao_dm0a = ao_dm0b = aow = None for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] vmata[ia, :, :, :, p0:p1] += ipipa[:, :, :, p0:p1] vmata[ia, :, :, :, p0:p1] += ipipa[:, :, p0:p1].transpose(1, 0, 3, 2) vmatb[ia, :, :, :, p0:p1] += ipipb[:, :, :, p0:p1] vmatb[ia, :, :, :, p0:p1] += ipipb[:, :, p0:p1].transpose(1, 0, 3, 2) elif xctype == 'MGGA': XX, XY, XZ = 4, 5, 6 YX, YY, YZ = 5, 7, 8 ZX, ZY, ZZ = 6, 8, 9 ao_deriv = 2 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rhoa = ni.eval_rho2(mol, ao[:10], mo_coeff[0], mo_occ[0], mask, xctype) rhob = ni.eval_rho2(mol, ao[:10], mo_coeff[1], mo_occ[1], mask, xctype) vxc, fxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=2)[1:3] wva, wvb = numint._uks_mgga_wv0((rhoa, rhob), vxc, weight) aow = rks_grad._make_dR_dao_w(ao, wva) rks_hess._d1d2_dot_(ipipa, mol, aow, ao[1:4], mask, ao_loc, False) aow = rks_grad._make_dR_dao_w(ao, wvb) rks_hess._d1d2_dot_(ipipb, mol, aow, ao[1:4], mask, ao_loc, False) aow = [numint._scale_ao(ao[i], wva[5]) for i in range(4, 10)] rks_hess._d1d2_dot_(ipipa, mol, [aow[0], aow[1], aow[2]], [ao[XX], ao[XY], ao[XZ]], mask, ao_loc, False) rks_hess._d1d2_dot_(ipipa, mol, [aow[1], aow[3], aow[4]], [ao[YX], ao[YY], ao[YZ]], mask, ao_loc, False) rks_hess._d1d2_dot_(ipipa, mol, [aow[2], aow[4], aow[5]], [ao[ZX], ao[ZY], ao[ZZ]], mask, ao_loc, False) aow = [numint._scale_ao(ao[i], wvb[5]) for i in range(4, 10)] rks_hess._d1d2_dot_(ipipb, mol, [aow[0], aow[1], aow[2]], [ao[XX], ao[XY], ao[XZ]], mask, ao_loc, False) rks_hess._d1d2_dot_(ipipb, mol, [aow[1], aow[3], aow[4]], [ao[YX], ao[YY], ao[YZ]], mask, ao_loc, False) rks_hess._d1d2_dot_(ipipb, mol, [aow[2], aow[4], aow[5]], [ao[ZX], ao[ZY], ao[ZZ]], mask, ao_loc, False) ao_dm0a = [ numint._dot_ao_dm(mol, ao[i], dm0a, mask, shls_slice, ao_loc) for i in range(4) ] ao_dm0b = [ numint._dot_ao_dm(mol, ao[i], dm0b, mask, shls_slice, ao_loc) for i in range(4) ] for ia in range(mol.natm): wva = dR_rho1a = rks_hess._make_dR_rho1( ao, ao_dm0a, ia, aoslices, xctype) wvb = dR_rho1b = rks_hess._make_dR_rho1( ao, ao_dm0b, ia, aoslices, xctype) wva[0], wvb[0] = numint._uks_mgga_wv1( (rhoa, rhob), (dR_rho1a[0], dR_rho1b[0]), vxc, fxc, weight) wva[1], wvb[1] = numint._uks_mgga_wv1( (rhoa, rhob), (dR_rho1a[1], dR_rho1b[1]), vxc, fxc, weight) wva[2], wvb[2] = numint._uks_mgga_wv1( (rhoa, rhob), (dR_rho1a[2], dR_rho1b[2]), vxc, fxc, weight) aow = rks_grad._make_dR_dao_w(ao, wva[0]) rks_grad._d1_dot_(vmata[ia, 0], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wva[1]) rks_grad._d1_dot_(vmata[ia, 1], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wva[2]) rks_grad._d1_dot_(vmata[ia, 2], mol, aow, ao[0], mask, ao_loc, True) aow = [numint._scale_ao(ao[:4], wva[i, :4]) for i in range(3)] rks_hess._d1d2_dot_(vmata[ia], mol, ao[1:4], aow, mask, ao_loc, False) aow = rks_grad._make_dR_dao_w(ao, wvb[0]) rks_grad._d1_dot_(vmatb[ia, 0], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wvb[1]) rks_grad._d1_dot_(vmatb[ia, 1], mol, aow, ao[0], mask, ao_loc, True) aow = rks_grad._make_dR_dao_w(ao, wvb[2]) rks_grad._d1_dot_(vmatb[ia, 2], mol, aow, ao[0], mask, ao_loc, True) aow = [numint._scale_ao(ao[:4], wvb[i, :4]) for i in range(3)] rks_hess._d1d2_dot_(vmatb[ia], mol, ao[1:4], aow, mask, ao_loc, False) # *2 because wv[5] is scaled by 0.5 in _rks_mgga_wv1 wv = wva[:, 5] * 2 aow = [numint._scale_ao(ao[1], wv[i]) for i in range(3)] rks_hess._d1d2_dot_(vmata[ia], mol, [ao[XX], ao[XY], ao[XZ]], aow, mask, ao_loc, False) aow = [numint._scale_ao(ao[2], wv[i]) for i in range(3)] rks_hess._d1d2_dot_(vmata[ia], mol, [ao[YX], ao[YY], ao[YZ]], aow, mask, ao_loc, False) aow = [numint._scale_ao(ao[3], wv[i]) for i in range(3)] rks_hess._d1d2_dot_(vmata[ia], mol, [ao[ZX], ao[ZY], ao[ZZ]], aow, mask, ao_loc, False) wv = wvb[:, 5] * 2 aow = [numint._scale_ao(ao[1], wv[i]) for i in range(3)] rks_hess._d1d2_dot_(vmatb[ia], mol, [ao[XX], ao[XY], ao[XZ]], aow, mask, ao_loc, False) aow = [numint._scale_ao(ao[2], wv[i]) for i in range(3)] rks_hess._d1d2_dot_(vmatb[ia], mol, [ao[YX], ao[YY], ao[YZ]], aow, mask, ao_loc, False) aow = [numint._scale_ao(ao[3], wv[i]) for i in range(3)] rks_hess._d1d2_dot_(vmatb[ia], mol, [ao[ZX], ao[ZY], ao[ZZ]], aow, mask, ao_loc, False) for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] vmata[ia, :, :, :, p0:p1] += ipipa[:, :, :, p0:p1] vmata[ia, :, :, :, p0:p1] += ipipa[:, :, p0:p1].transpose(1, 0, 3, 2) vmatb[ia, :, :, :, p0:p1] += ipipb[:, :, :, p0:p1] vmatb[ia, :, :, :, p0:p1] += ipipb[:, :, p0:p1].transpose(1, 0, 3, 2) return vmata, vmatb