def dia(magobj, gauge_orig=None):
mol = magobj.mol
mf = magobj._scf
mo_energy = magobj._scf.mo_energy
mo_coeff = magobj._scf.mo_coeff
mo_occ = magobj._scf.mo_occ
orboa = mo_coeff[0][:,mo_occ[0] > 0]
orbob = mo_coeff[1][:,mo_occ[1] > 0]
dm0a = numpy.dot(orboa, orboa.T)
dm0b = numpy.dot(orbob, orbob.T)
dm0 = dm0a + dm0b
dme0a = numpy.dot(orboa * mo_energy[0][mo_occ[0] > 0], orboa.T)
dme0b = numpy.dot(orbob * mo_energy[1][mo_occ[1] > 0], orbob.T)
dme0 = dme0a + dme0b
e2 = rhf_mag._get_dia_1e(magobj, gauge_orig, dm0, dme0).ravel()
if gauge_orig is None:
vs = jk.get_jk(mol, [dm0, dm0a, dm0a, dm0b, dm0b],
['ijkl,ji->s2kl',
'ijkl,jk->s1il', 'ijkl,li->s1kj',
'ijkl,jk->s1il', 'ijkl,li->s1kj'],
'int2e_gg1', 's4', 9, hermi=1)
e2 += numpy.einsum('xpq,qp->x', vs[0], dm0)
e2 -= numpy.einsum('xpq,qp->x', vs[1], dm0a) * .5
e2 -= numpy.einsum('xpq,qp->x', vs[2], dm0a) * .5
e2 -= numpy.einsum('xpq,qp->x', vs[3], dm0b) * .5
e2 -= numpy.einsum('xpq,qp->x', vs[4], dm0b) * .5
vk = jk.get_jk(mol, [dm0a, dm0b], ['ijkl,jk->s1il', 'ijkl,jk->s1il'],
'int2e_g1g2', 'aa4', 9, hermi=0)
e2 -= numpy.einsum('xpq,qp->x', vk[0], dm0a)
e2 -= numpy.einsum('xpq,qp->x', vk[1], dm0b)
return -e2.reshape(3, 3)
def dia(magobj, gauge_orig=None):
mol = magobj.mol
mf = magobj._scf
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
orbo = mo_coeff[:, mo_occ > 0]
dm0 = numpy.dot(orbo, orbo.T) * 2
dm0 = lib.tag_array(dm0, mo_coeff=mo_coeff, mo_occ=mo_occ)
dme0 = numpy.dot(orbo * mo_energy[mo_occ > 0], orbo.T) * 2
e2 = rhf_mag._get_dia_1e(magobj, gauge_orig, dm0, dme0)
if gauge_orig is not None:
return -e2
# Computing the 2nd order Vxc integrals from GIAO
grids = mf.grids
ni = mf._numint
xc_code = mf.xc
xctype = ni._xc_type(xc_code)
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(xc_code, mol.spin)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dm0, hermi=1)
ngrids = len(grids.weights)
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory * .9 - mem_now)
BLKSIZE = numint.BLKSIZE
blksize = min(
int(max_memory / 12 * 1e6 / 8 / nao / BLKSIZE) * BLKSIZE, ngrids)
vmat = numpy.zeros((3, 3, nao, nao))
if xctype == 'LDA':
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize):
rho = make_rho(0, ao, mask, 'LDA')
vxc = ni.eval_xc(xc_code, rho, 0, deriv=1)[1]
vrho = vxc[0]
r_ao = numpy.einsum('pi,px->pxi', ao, coords)
aow = numpy.einsum('pxi,p,p->pxi', r_ao, weight, vrho)
vmat += lib.einsum('pxi,pyj->xyij', r_ao, aow)
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize):
rho = make_rho(0, ao, mask, 'GGA')
vxc = ni.eval_xc(xc_code, rho, 0, deriv=1)[1]
wv = numint._rks_gga_wv0(rho, vxc, weight)
# Computing \nabla (r * AO) = r * \nabla AO + [\nabla,r]_- * AO
r_ao = numpy.einsum('npi,px->npxi', ao, coords)
r_ao[1, :, 0] += ao[0]
r_ao[2, :, 1] += ao[0]
r_ao[3, :, 2] += ao[0]
aow = numpy.einsum('npxi,np->pxi', r_ao, wv)
vmat += lib.einsum('pxi,pyj->xyij', r_ao[0], aow)
rho = vxc = vrho = vsigma = wv = aow = None
vmat = vmat + vmat.transpose(0, 1, 3, 2)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
vmat = _add_giao_phase(mol, vmat)
e2 += numpy.einsum('qp,xypq->xy', dm0, vmat)
vmat = None
e2 = e2.ravel()
# Handle the hybrid functional and the range-separated functional
if abs(hyb) > 1e-10:
vs = jk.get_jk(mol, [dm0] * 3,
['ijkl,ji->s2kl', 'ijkl,jk->s1il', 'ijkl,li->s1kj'],
'int2e_gg1',
's4',
9,
hermi=1)
e2 += numpy.einsum('xpq,qp->x', vs[0], dm0)
e2 -= numpy.einsum('xpq,qp->x', vs[1], dm0) * .25 * hyb
e2 -= numpy.einsum('xpq,qp->x', vs[2], dm0) * .25 * hyb
vk = jk.get_jk(mol,
dm0,
'ijkl,jk->s1il',
'int2e_g1g2',
'aa4',
9,
hermi=0)
e2 -= numpy.einsum('xpq,qp->x', vk, dm0) * .5 * hyb
if abs(omega) > 1e-10:
with mol.with_range_coulomb(omega):
vs = jk.get_jk(mol, [dm0] * 2,
['ijkl,jk->s1il', 'ijkl,li->s1kj'],
'int2e_gg1',
's4',
9,
hermi=1)
e2 -= numpy.einsum('xpq,qp->x', vs[0],
dm0) * .25 * (alpha - hyb)
e2 -= numpy.einsum('xpq,qp->x', vs[1],
dm0) * .25 * (alpha - hyb)
vk = jk.get_jk(mol,
dm0,
'ijkl,jk->s1il',
'int2e_g1g2',
'aa4',
9,
hermi=0)
e2 -= numpy.einsum('xpq,qp->x', vk, dm0) * .5 * (alpha - hyb)
else:
vj = jk.get_jk(mol,
dm0,
'ijkl,ji->s2kl',
'int2e_gg1',
's4',
9,
hermi=1)
e2 += numpy.einsum('xpq,qp->x', vj, dm0)
return -e2.reshape(3, 3)
def dia(magobj, gauge_orig=None):
mol = magobj.mol
mf = magobj._scf
mo_energy = magobj._scf.mo_energy
mo_coeff = magobj._scf.mo_coeff
mo_occ = magobj._scf.mo_occ
orboa = mo_coeff[0][:,mo_occ[0] > 0]
orbob = mo_coeff[1][:,mo_occ[1] > 0]
dm0a = lib.tag_array(orboa.dot(orboa.T), mo_coeff=mo_coeff[0], mo_occ=mo_occ[0])
dm0b = lib.tag_array(orbob.dot(orbob.T), mo_coeff=mo_coeff[1], mo_occ=mo_occ[1])
dm0 = dm0a + dm0b
dme0a = numpy.dot(orboa * mo_energy[0][mo_occ[0] > 0], orboa.T)
dme0b = numpy.dot(orbob * mo_energy[1][mo_occ[1] > 0], orbob.T)
dme0 = dme0a + dme0b
e2 = rhf_mag._get_dia_1e(magobj, gauge_orig, dm0, dme0)
if gauge_orig is not None:
return -e2
# Computing the 2nd order Vxc integrals from GIAO
grids = mf.grids
ni = mf._numint
xc_code = mf.xc
xctype = ni._xc_type(xc_code)
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(xc_code, mol.spin)
make_rhoa, nset, nao = ni._gen_rho_evaluator(mol, dm0a, hermi=1)
make_rhob = ni._gen_rho_evaluator(mol, dm0b, hermi=1)[0]
ngrids = len(grids.weights)
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.9-mem_now)
BLKSIZE = numint.BLKSIZE
blksize = min(int(max_memory/12*1e6/8/nao/BLKSIZE)*BLKSIZE, ngrids)
vmata = numpy.zeros((3,3,nao,nao))
vmatb = numpy.zeros((3,3,nao,nao))
if xctype == 'LDA':
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize):
rho = (make_rhoa(0, ao, mask, 'LDA'),
make_rhob(0, ao, mask, 'LDA'))
vxc = ni.eval_xc(xc_code, rho, spin=1, deriv=1)[1]
vrho = vxc[0]
r_ao = numpy.einsum('pi,px->pxi', ao, coords)
aow = numpy.einsum('pxi,p,p->pxi', r_ao, weight, vrho[:,0])
vmata += lib.einsum('pxi,pyj->xyij', r_ao, aow)
aow = numpy.einsum('pxi,p,p->pxi', r_ao, weight, vrho[:,1])
vmatb += lib.einsum('pxi,pyj->xyij', r_ao, aow)
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize):
rho = (make_rhoa(0, ao, mask, 'GGA'),
make_rhob(0, ao, mask, 'GGA'))
vxc = ni.eval_xc(xc_code, rho, spin=1, deriv=1)[1]
wva, wvb = numint._uks_gga_wv0(rho, vxc, weight)
# Computing \nabla (r * AO) = r * \nabla AO + [\nabla,r]_- * AO
r_ao = numpy.einsum('npi,px->npxi', ao, coords)
r_ao[1,:,0] += ao[0]
r_ao[2,:,1] += ao[0]
r_ao[3,:,2] += ao[0]
aow = numpy.einsum('npxi,np->pxi', r_ao, wva)
vmata += lib.einsum('pxi,pyj->xyij', r_ao[0], aow)
aow = numpy.einsum('npxi,np->pxi', r_ao, wvb)
vmata += lib.einsum('pxi,pyj->xyij', r_ao[0], aow)
rho = vxc = vrho = vsigma = wv = aow = None
vmata = vmata + vmata.transpose(0,1,3,2)
vmatb = vmatb + vmatb.transpose(0,1,3,2)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
vmata = rks_mag._add_giao_phase(mol, vmata)
vmatb = rks_mag._add_giao_phase(mol, vmatb)
e2 += numpy.einsum('qp,xypq->xy', dm0a, vmata)
e2 += numpy.einsum('qp,xypq->xy', dm0b, vmatb)
vmata = vmatb = None
e2 = e2.ravel()
# Handle the hybrid functional and the range-separated functional
if abs(hyb) > 1e-10:
vs = jk.get_jk(mol, [dm0, dm0a, dm0a, dm0b, dm0b],
['ijkl,ji->s2kl',
'ijkl,jk->s1il', 'ijkl,li->s1kj',
'ijkl,jk->s1il', 'ijkl,li->s1kj'],
'int2e_gg1', 's4', 9, hermi=1)
e2 += numpy.einsum('xpq,qp->x', vs[0], dm0)
e2 -= numpy.einsum('xpq,qp->x', vs[1], dm0a) * .5 * hyb
e2 -= numpy.einsum('xpq,qp->x', vs[2], dm0a) * .5 * hyb
e2 -= numpy.einsum('xpq,qp->x', vs[3], dm0b) * .5 * hyb
e2 -= numpy.einsum('xpq,qp->x', vs[4], dm0b) * .5 * hyb
vk = jk.get_jk(mol, [dm0a, dm0b], ['ijkl,jk->s1il', 'ijkl,jk->s1il'],
'int2e_g1g2', 'aa4', 9, hermi=0)
e2 -= numpy.einsum('xpq,qp->x', vk[0], dm0a) * hyb
e2 -= numpy.einsum('xpq,qp->x', vk[1], dm0b) * hyb
if abs(omega) > 1e-10:
with mol.with_range_coulomb(omega):
vs = jk.get_jk(mol, [dm0a, dm0a, dm0b, dm0b],
['ijkl,jk->s1il', 'ijkl,li->s1kj',
'ijkl,jk->s1il', 'ijkl,li->s1kj'],
'int2e_gg1', 's4', 9, hermi=1)
e2 -= numpy.einsum('xpq,qp->x', vs[0], dm0a) * .5 * (alpha-hyb)
e2 -= numpy.einsum('xpq,qp->x', vs[1], dm0a) * .5 * (alpha-hyb)
e2 -= numpy.einsum('xpq,qp->x', vs[2], dm0b) * .5 * (alpha-hyb)
e2 -= numpy.einsum('xpq,qp->x', vs[3], dm0b) * .5 * (alpha-hyb)
vk = jk.get_jk(mol, [dm0a, dm0b], ['ijkl,jk->s1il', 'ijkl,jk->s1il'],
'int2e_g1g2', 'aa4', 9, hermi=0)
e2 -= numpy.einsum('xpq,qp->x', vk[0], dm0a) * (alpha-hyb)
e2 -= numpy.einsum('xpq,qp->x', vk[1], dm0b) * (alpha-hyb)
else:
vj = jk.get_jk(mol, dm0, 'ijkl,ji->s2kl',
'int2e_gg1', 's4', 9, hermi=1)
e2 += numpy.einsum('xpq,qp->x', vj, dm0)
return -e2.reshape(3, 3)