def type2_by_shell(mol, shls, ecpatm_id, ecpbas):
ish, jsh = shls
li = mol.bas_angular(ish)
npi = mol.bas_nprim(ish)
nci = mol.bas_nctr(ish)
ai = mol.bas_exp(ish)
ci = mol._libcint_ctr_coeff(ish)
icart = (li + 1) * (li + 2) // 2
lj = mol.bas_angular(jsh)
npj = mol.bas_nprim(jsh)
ncj = mol.bas_nctr(jsh)
aj = mol.bas_exp(jsh)
cj = mol._libcint_ctr_coeff(jsh)
jcart = (lj + 1) * (lj + 2) // 2
rc = mol.atom_coord(ecpatm_id)
rcb = rc - mol.bas_coord(jsh)
r_cb = numpy.linalg.norm(rcb)
rca = rc - mol.bas_coord(ish)
r_ca = numpy.linalg.norm(rca)
#rs, ws = radi.treutler(99)
rs, ws = radi.gauss_chebyshev(99)
i_fac_cache = cache_fac(li, rca)
j_fac_cache = cache_fac(lj, rcb)
g1 = numpy.zeros((nci, ncj, icart, jcart))
for lc in range(5): # up to g function
ecpbasi = ecpbas[ecpbas[:, ANG_OF] == lc]
if len(ecpbasi) == 0:
continue
ur = rad_part(mol, ecpbasi, rs) * ws
idx = abs(ur) > 1e-80
rur = numpy.array(
[ur[idx] * rs[idx]**lab for lab in range(li + lj + 1)])
fi = facs_rad(mol, ish, lc, r_ca, rs)[:, :, idx].copy()
fj = facs_rad(mol, jsh, lc, r_cb, rs)[:, :, idx].copy()
angi = facs_ang(type2_ang_part(li, lc, -rca), li, lc, i_fac_cache)
angj = facs_ang(type2_ang_part(lj, lc, -rcb), lj, lc, j_fac_cache)
for ic in range(nci):
for jc in range(ncj):
rad_all = numpy.einsum('pr,ir,jr->pij', rur, fi[ic], fj[jc])
for i1 in range(li + 1):
for j1 in range(lj + 1):
g1[ic, jc] += numpy.einsum('pq,imp,jmq->ij',
rad_all[i1 + j1], angi[i1],
angj[j1])
g1 *= (numpy.pi * 4)**2
gsph = numpy.empty((nci, ncj, li * 2 + 1, lj * 2 + 1))
for ic in range(nci):
for jc in range(ncj):
tmp = c2s_bra(lj, g1[ic, jc].T.copy())
gsph[ic, jc] = c2s_bra(li, tmp.T.copy())
return gsph.transpose(0, 2, 1, 3).reshape(nci * (li * 2 + 1), -1)
def test_prune(self):
grid = gen_grid.Grids(h2o)
grid.prune = gen_grid.sg1_prune
grid.atom_grid = {
"H": (10, 50),
"O": (10, 50),
}
grid.build(with_non0tab=False)
self.assertAlmostEqual(numpy.linalg.norm(grid.coords),
202.17732600266302, 9)
self.assertAlmostEqual(numpy.linalg.norm(grid.weights),
442.54536463517167, 9)
grid.prune = gen_grid.nwchem_prune
grid.build(with_non0tab=False)
self.assertAlmostEqual(numpy.linalg.norm(grid.coords),
149.55023044392638, 9)
self.assertAlmostEqual(numpy.linalg.norm(grid.weights),
586.36841824004455, 9)
z = 16
rad, dr = radi.gauss_chebyshev(50)
angs = gen_grid.sg1_prune(z, rad, 434, radii=radi.SG1RADII)
self.assertAlmostEqual(lib.fp(angs), -291.0794420982329, 9)
angs = gen_grid.nwchem_prune(z, rad, 434, radii=radi.BRAGG_RADII)
self.assertAlmostEqual(lib.fp(angs), -180.12023039394498, 9)
angs = gen_grid.nwchem_prune(z, rad, 26, radii=radi.BRAGG_RADII)
self.assertTrue(numpy.all(angs == 26))
def test_bessel(self):
rs = radi.gauss_chebyshev(99)[0]
bessel1 = numpy.empty(8)
for i, x in enumerate(rs):
bessel0 = scipy.special.sph_in(7, x)[0] * numpy.exp(-x)
libecp.ECPsph_ine(bessel1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(7), ctypes.c_double(x))
self.assertTrue(numpy.allclose(bessel0, bessel1))
def test_bessel(self):
rs = radi.gauss_chebyshev(99)[0]
bessel1 = numpy.empty(8)
for i,x in enumerate(rs):
bessel0 = scipy.special.sph_in(7, x)[0] * numpy.exp(-x)
libecp.ECPsph_ine(bessel1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(7), ctypes.c_double(x))
self.assertTrue(numpy.allclose(bessel0, bessel1))
def type2_by_shell(mol, shls, ecpatm_id, ecpbas):
ish, jsh = shls
li = mol.bas_angular(ish)
npi = mol.bas_nprim(ish)
nci = mol.bas_nctr(ish)
ai = mol.bas_exp(ish)
ci = mol.bas_ctr_coeff(ish)
icart = (li+1) * (li+2) // 2
lj = mol.bas_angular(jsh)
npj = mol.bas_nprim(jsh)
ncj = mol.bas_nctr(jsh)
aj = mol.bas_exp(jsh)
cj = mol.bas_ctr_coeff(jsh)
jcart = (lj+1) * (lj+2) // 2
rc = mol.atom_coord(ecpatm_id)
rcb = rc - mol.bas_coord(jsh)
r_cb = numpy.linalg.norm(rcb)
rca = rc - mol.bas_coord(ish)
r_ca = numpy.linalg.norm(rca)
#rs, ws = radi.treutler(99)
rs, ws = radi.gauss_chebyshev(99)
i_fac_cache = cache_fac(li, rca)
j_fac_cache = cache_fac(lj, rcb)
g1 = numpy.zeros((nci,ncj,icart,jcart))
for lc in range(5): # up to g function
ecpbasi = ecpbas[ecpbas[:,ANG_OF] == lc]
if len(ecpbasi) == 0:
continue
ur = rad_part(mol, ecpbasi, rs) * ws
idx = abs(ur) > 1e-40
rur = numpy.array([ur[idx] * rs[idx]**lab for lab in range(li+lj+1)])
fi = facs_rad(mol, ish, lc, r_ca, rs)[:,:,idx].copy()
fj = facs_rad(mol, jsh, lc, r_cb, rs)[:,:,idx].copy()
angi = facs_ang(type2_ang_part(li, lc, -rca), li, lc, i_fac_cache)
angj = facs_ang(type2_ang_part(lj, lc, -rcb), lj, lc, j_fac_cache)
for ic in range(nci):
for jc in range(ncj):
rad_all = numpy.einsum('pr,ir,jr->pij', rur, fi[ic], fj[jc])
for i1 in range(li+1):
for j1 in range(lj+1):
g1[ic,jc] += numpy.einsum('pq,imp,jmq->ij', rad_all[i1+j1],
angi[i1], angj[j1])
g1 *= (numpy.pi*4)**2
gsph = numpy.empty((nci,ncj,li*2+1,lj*2+1))
for ic in range(nci):
for jc in range(ncj):
tmp = c2s_bra(lj, g1[ic,jc].T.copy())
gsph[ic,jc] = c2s_bra(li, tmp.T.copy())
return gsph.transpose(0,2,1,3).reshape(nci*(li*2+1),-1)
def test_gauss_chebyshev(self):
rs0, ws0 = radi.gauss_chebyshev(99)
rs = numpy.empty_like(rs0)
ws = numpy.empty_like(ws0)
libecp.ECPgauss_chebyshev(rs.ctypes.data_as(ctypes.c_void_p),
ws.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(99))
self.assertTrue(numpy.allclose(rs0, rs))
self.assertTrue(numpy.allclose(ws0, ws))
def test_gauss_chebyshev(self):
rs0, ws0 = radi.gauss_chebyshev(99)
rs = numpy.empty_like(rs0)
ws = numpy.empty_like(ws0)
libecp.ECPgauss_chebyshev(rs.ctypes.data_as(ctypes.c_void_p),
ws.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(99))
self.assertTrue(numpy.allclose(rs0, rs))
self.assertTrue(numpy.allclose(ws0, ws))
def test_rad_part(self):
rs, ws = radi.gauss_chebyshev(99)
ur0 = rad_part(mol, mol._ecpbas, rs)
ecpshls = numpy.array(numpy.append(numpy.arange(len(mol._ecpbas)),-1), dtype=numpy.int32)
ur1 = numpy.empty_like(ur0)
libecp.ECPrad_part(ur1.ctypes.data_as(ctypes.c_void_p),
rs.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(rs)), ctypes.c_int(1),
ecpshls.ctypes.data_as(ctypes.c_void_p),
mol._ecpbas.ctypes.data_as(ctypes.c_void_p),
mol._atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(mol.natm),
mol._bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(mol.nbas),
mol._env.ctypes.data_as(ctypes.c_void_p))
self.assertTrue(numpy.allclose(ur0, ur1))
def test_rad_part(self):
rs, ws = radi.gauss_chebyshev(99)
ur0 = rad_part(mol, mol._ecpbas, rs)
ur1 = numpy.empty_like(ur0)
libecp.ECPrad_part(ur1.ctypes.data_as(ctypes.c_void_p),
rs.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(0), ctypes.c_int(len(rs)), ctypes.c_int(1),
(ctypes.c_int*2)(0, len(mol._ecpbas)),
mol._ecpbas.ctypes.data_as(ctypes.c_void_p),
mol._atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(mol.natm),
mol._bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(mol.nbas),
mol._env.ctypes.data_as(ctypes.c_void_p),
lib.c_null_ptr())
self.assertTrue(numpy.allclose(ur0, ur1))
def test_rad_part(self):
rs, ws = radi.gauss_chebyshev(99)
ur0 = rad_part(mol, mol._ecpbas, rs)
ur1 = numpy.empty_like(ur0)
libecp.ECPrad_part(ur1.ctypes.data_as(ctypes.c_void_p),
rs.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(0),
ctypes.c_int(len(rs)), ctypes.c_int(1),
(ctypes.c_int * 2)(0, len(mol._ecpbas)),
mol._ecpbas.ctypes.data_as(ctypes.c_void_p),
mol._atm.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(mol.natm),
mol._bas.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(mol.nbas),
mol._env.ctypes.data_as(ctypes.c_void_p),
lib.c_null_ptr())
self.assertTrue(numpy.allclose(ur0, ur1))
def test_type1_rad(self):
k = 1.621
aij = .792
rs, ws = radi.gauss_chebyshev(99)
ur = rad_part(mol, mol._ecpbas, rs) * ws
def gen_type1_rad(li):
rad_all0 = type1_rad_part(li, k, aij, ur, rs)
rad_all1 = numpy.zeros_like(rad_all0)
libecp.type1_rad_part(rad_all1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(li),
ctypes.c_double(k), ctypes.c_double(aij),
ur.ctypes.data_as(ctypes.c_void_p),
rs.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(rs)), ctypes.c_int(1))
self.assertTrue(numpy.allclose(rad_all0, rad_all1))
for l in range(13):
gen_type1_rad(l)
def test_rad_part(self):
rs, ws = radi.gauss_chebyshev(99)
ur0 = rad_part(mol, mol._ecpbas, rs)
ecpshls = numpy.array(numpy.append(numpy.arange(len(mol._ecpbas)), -1),
dtype=numpy.int32)
ur1 = numpy.empty_like(ur0)
libecp.ECPrad_part(ur1.ctypes.data_as(ctypes.c_void_p),
rs.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(rs)), ctypes.c_int(1),
ecpshls.ctypes.data_as(ctypes.c_void_p),
mol._ecpbas.ctypes.data_as(ctypes.c_void_p),
mol._atm.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(mol.natm),
mol._bas.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(mol.nbas),
mol._env.ctypes.data_as(ctypes.c_void_p))
self.assertTrue(numpy.allclose(ur0, ur1))
def test_type2_rad_part(self):
rc = .8712
rs, ws = radi.gauss_chebyshev(99)
def type2_facs_rad(ish, lc):
facs0 = facs_rad(mol, ish, lc, rc, rs).transpose(0,2,1).copy()
facs1 = numpy.empty_like(facs0)
libecp.type2_facs_rad(facs1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(ish), ctypes.c_int(lc),
ctypes.c_double(rc),
rs.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(rs)), ctypes.c_int(1),
mol._atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(mol.natm),
mol._bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(mol.nbas),
mol._env.ctypes.data_as(ctypes.c_void_p))
self.assertTrue(numpy.allclose(facs0, facs1))
for ish in range(mol.nbas):
for lc in range(5):
type2_facs_rad(ish, lc)
def test_type1_rad(self):
k = 1.621
aij = .792
rs, ws = radi.gauss_chebyshev(99)
ur = rad_part(mol, mol._ecpbas, rs) * ws
def gen_type1_rad(li):
rad_all0 = type1_rad_part(li, k, aij, ur, rs)
rad_all1 = numpy.zeros_like(rad_all0)
libecp.type1_rad_part(rad_all1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(li), ctypes.c_double(k),
ctypes.c_double(aij),
ur.ctypes.data_as(ctypes.c_void_p),
rs.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(rs)), ctypes.c_int(1))
self.assertTrue(numpy.allclose(rad_all0, rad_all1))
for l in range(13):
gen_type1_rad(l)
def test_type2_rad_part(self):
rc = .8712
rs, ws = radi.gauss_chebyshev(99)
def type2_facs_rad(ish, lc):
facs0 = facs_rad(mol, ish, lc, rc, rs).transpose(0, 2, 1).copy()
facs1 = numpy.empty_like(facs0)
libecp.type2_facs_rad(facs1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(ish), ctypes.c_int(lc),
ctypes.c_double(rc),
rs.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(rs)), ctypes.c_int(1),
mol._atm.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(mol.natm),
mol._bas.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(mol.nbas),
mol._env.ctypes.data_as(ctypes.c_void_p))
self.assertTrue(numpy.allclose(facs0, facs1))
for ish in range(mol.nbas):
for lc in range(5):
type2_facs_rad(ish, lc)
def test_prune(self):
grid = gen_grid.Grids(h2o)
grid.prune = gen_grid.sg1_prune
grid.atom_grid = {"H": (10, 50), "O": (10, 50),}
grid.build(with_non0tab=False)
self.assertAlmostEqual(numpy.linalg.norm(grid.coords), 202.17732600266302, 9)
self.assertAlmostEqual(numpy.linalg.norm(grid.weights), 442.54536463517167, 9)
grid.prune = gen_grid.nwchem_prune
grid.build(with_non0tab=False)
self.assertAlmostEqual(numpy.linalg.norm(grid.coords), 149.55023044392638, 9)
self.assertAlmostEqual(numpy.linalg.norm(grid.weights), 586.36841824004455, 9)
z = 16
rad, dr = radi.gauss_chebyshev(50)
angs = gen_grid.sg1_prune(z, rad, 434, radii=radi.SG1RADII)
self.assertAlmostEqual(lib.finger(angs), -291.0794420982329, 9)
angs = gen_grid.nwchem_prune(z, rad, 434, radii=radi.BRAGG_RADII)
self.assertAlmostEqual(lib.finger(angs), -180.12023039394498, 9)
angs = gen_grid.nwchem_prune(z, rad, 26, radii=radi.BRAGG_RADII)
self.assertTrue(numpy.all(angs==26))
def so_by_shell(mol, shls, ecpatm_id, ecpbas):
'''SO-ECP
i/2 <Pauli_matrix dot l U(r)>
'''
ish, jsh = shls
li = mol.bas_angular(ish)
npi = mol.bas_nprim(ish)
nci = mol.bas_nctr(ish)
ai = mol.bas_exp(ish)
ci = mol._libcint_ctr_coeff(ish)
icart = (li + 1) * (li + 2) // 2
lj = mol.bas_angular(jsh)
npj = mol.bas_nprim(jsh)
ncj = mol.bas_nctr(jsh)
aj = mol.bas_exp(jsh)
cj = mol._libcint_ctr_coeff(jsh)
jcart = (lj + 1) * (lj + 2) // 2
rc = mol.atom_coord(ecpatm_id)
rcb = rc - mol.bas_coord(jsh)
r_cb = numpy.linalg.norm(rcb)
rca = rc - mol.bas_coord(ish)
r_ca = numpy.linalg.norm(rca)
#rs, ws = radi.treutler(99)
rs, ws = radi.gauss_chebyshev(99)
i_fac_cache = cache_fac(li, rca)
j_fac_cache = cache_fac(lj, rcb)
g1 = numpy.zeros((nci, ncj, 3, icart, jcart), dtype=numpy.complex128)
for lc in range(5): # up to g function
ecpbasi = ecpbas[ecpbas[:, ANG_OF] == lc]
if len(ecpbasi) == 0:
continue
ur = rad_part(mol, ecpbasi, rs) * ws
idx = abs(ur) > 1e-80
rur = numpy.array(
[ur[idx] * rs[idx]**lab for lab in range(li + lj + 1)])
fi = facs_rad(mol, ish, lc, r_ca, rs)[:, :, idx].copy()
fj = facs_rad(mol, jsh, lc, r_cb, rs)[:, :, idx].copy()
angi = facs_ang(type2_ang_part(li, lc, -rca), li, lc, i_fac_cache)
angj = facs_ang(type2_ang_part(lj, lc, -rcb), lj, lc, j_fac_cache)
# Note the factor 2/(2l+1) in JCP 82 2664 is not multiplied here
# because the ECP parameter has been scaled by 2/(2l+1) in CRENBL
jmm = angular_moment_matrix(lc)
for ic in range(nci):
for jc in range(ncj):
rad_all = numpy.einsum('pr,ir,jr->pij', rur, fi[ic], fj[jc])
for i1 in range(li + 1):
for j1 in range(lj + 1):
g1[ic, jc] += numpy.einsum('pq,imp,jnq,lmn->lij',
rad_all[i1 + j1], angi[i1],
angj[j1], jmm)
g1 *= (numpy.pi * 4)**2
gspinor = numpy.empty((nci, ncj, li * 4 + 2, lj * 4 + 2),
dtype=numpy.complex128)
for ic in range(nci):
for jc in range(ncj):
ui = numpy.asarray(gto.cart2spinor_l(li))
uj = numpy.asarray(gto.cart2spinor_l(lj))
s = lib.PauliMatrices * .5j
gspinor[ic, jc] = numpy.einsum('sxy,spq,xpi,yqj->ij', s, g1[ic,
jc],
ui.conj(), uj)
return gspinor.transpose(0, 2, 1, 3).reshape(nci * (li * 4 + 2), -1)
def type1_by_shell(mol, shls, ecpatm_id, ecpbas):
ish, jsh = shls
li = mol.bas_angular(ish)
npi = mol.bas_nprim(ish)
nci = mol.bas_nctr(ish)
ai = mol.bas_exp(ish)
ci = mol._libcint_ctr_coeff(ish)
icart = (li + 1) * (li + 2) // 2
lj = mol.bas_angular(jsh)
npj = mol.bas_nprim(jsh)
ncj = mol.bas_nctr(jsh)
aj = mol.bas_exp(jsh)
cj = mol._libcint_ctr_coeff(jsh)
jcart = (lj + 1) * (lj + 2) // 2
rc = mol.atom_coord(ecpatm_id)
rca = rc - mol.bas_coord(ish)
r2ca = numpy.dot(rca, rca)
rcb = rc - mol.bas_coord(jsh)
r2cb = numpy.dot(rcb, rcb)
# Note the Mole._libcint_ctr_coeff are normalized to radial part
cei = numpy.einsum('ij,i->ij', ci, numpy.exp(-ai * r2ca))
cej = numpy.einsum('ij,i->ij', cj, numpy.exp(-aj * r2cb))
#rs, ws = radi.treutler(99)
rs, ws = radi.gauss_chebyshev(99)
ur = rad_part(mol, ecpbas, rs) * ws
rad_ang_all = numpy.zeros(
(nci, ncj, li + lj + 1, li + lj + 1, li + lj + 1))
for ip in range(npi):
for jp in range(npj):
rij = ai[ip] * rca + aj[jp] * rcb
aij = ai[ip] + aj[jp]
k = 2 * numpy.linalg.norm(rij)
rad_all = type1_rad_part(li + lj, k, aij, ur, rs)
#ang_all = type1_ang_part(li+lj, -rij)
#rad_ang = numpy.einsum('pl,lijk->pijk', rad_all, ang_all)
rad_ang = type1_rad_ang(li + lj, rij, rad_all)
for ic in range(nci):
for jc in range(ncj):
rad_ang_all[ic,
jc] += rad_ang * cei[ip, ic] * cej[jp, jc] * (
4 * numpy.pi)**2
ifac = type1_cache_fac(li, rca)
jfac = type1_cache_fac(lj, rcb)
g1 = numpy.zeros((nci, ncj, icart, jcart))
for ic in range(nci):
for jc in range(ncj):
for mi, (ix, iy, iz) in enumerate(loop_cart(li)):
for mj, (jx, jy, jz) in enumerate(loop_cart(lj)):
tmp = 0
for i1, i2, i3 in loop_xyz(ix, iy, iz):
for j1, j2, j3 in loop_xyz(jx, jy, jz):
fac = ifac[mi, i1, i2, i3] * jfac[mj, j1, j2, j3]
tmp += fac * rad_ang_all[ic, jc, i1 + j1, i2 + j2,
i3 + j3]
g1[ic, jc, mi, mj] = tmp
gsph = numpy.empty((nci, ncj, li * 2 + 1, lj * 2 + 1))
for ic in range(nci):
for jc in range(ncj):
tmp = c2s_bra(lj, g1[ic, jc].T.copy())
gsph[ic, jc] = c2s_bra(li, tmp.T.copy())
return gsph.transpose(0, 2, 1, 3).reshape(nci * (li * 2 + 1), -1)
def type1_by_shell(mol, shls, ecpatm_id, ecpbas):
ish, jsh = shls
li = mol.bas_angular(ish)
npi = mol.bas_nprim(ish)
nci = mol.bas_nctr(ish)
ai = mol.bas_exp(ish)
ci = mol.bas_ctr_coeff(ish)
icart = (li+1) * (li+2) // 2
lj = mol.bas_angular(jsh)
npj = mol.bas_nprim(jsh)
ncj = mol.bas_nctr(jsh)
aj = mol.bas_exp(jsh)
cj = mol.bas_ctr_coeff(jsh)
jcart = (lj+1) * (lj+2) // 2
rc = mol.atom_coord(ecpatm_id)
rca = rc - mol.bas_coord(ish)
r2ca = numpy.dot(rca, rca)
rcb = rc - mol.bas_coord(jsh)
r2cb = numpy.dot(rcb, rcb)
# Note the Mole.bas_ctr_coeff are normalized to radial part
cei = numpy.einsum('ij,i->ij', ci, numpy.exp(-ai * r2ca))
cej = numpy.einsum('ij,i->ij', cj, numpy.exp(-aj * r2cb))
#rs, ws = radi.treutler(99)
rs, ws = radi.gauss_chebyshev(99)
ur = rad_part(mol, ecpbas, rs) * ws
rad_ang_all = numpy.zeros((nci,ncj,li+lj+1,li+lj+1,li+lj+1))
for ip in range(npi):
for jp in range(npj):
rij = ai[ip] * rca + aj[jp] * rcb
aij = ai[ip] + aj[jp]
k = 2*numpy.linalg.norm(rij)
rad_all = type1_rad_part(li+lj, k, aij, ur, rs)
#ang_all = type1_ang_part(li+lj, -rij)
#rad_ang = numpy.einsum('pl,lijk->pijk', rad_all, ang_all)
rad_ang = type1_rad_ang(li+lj, rij, rad_all)
for ic in range(nci):
for jc in range(ncj):
rad_ang_all[ic,jc] += rad_ang * cei[ip,ic]*cej[jp,jc] * (4*numpy.pi)**2
ifac = type1_cache_fac(li, rca)
jfac = type1_cache_fac(lj, rcb)
g1 = numpy.zeros((nci,ncj,icart,jcart))
for ic in range(nci):
for jc in range(ncj):
for mi,(ix,iy,iz) in enumerate(loop_cart(li)):
for mj,(jx,jy,jz) in enumerate(loop_cart(lj)):
tmp = 0
for i1, i2, i3 in loop_xyz(ix, iy, iz):
for j1, j2, j3 in loop_xyz(jx, jy, jz):
fac = ifac[mi,i1,i2,i3] * jfac[mj,j1,j2,j3]
tmp += fac * rad_ang_all[ic,jc,i1+j1,i2+j2,i3+j3]
g1[ic,jc,mi,mj] = tmp
gsph = numpy.empty((nci,ncj,li*2+1,lj*2+1))
for ic in range(nci):
for jc in range(ncj):
tmp = c2s_bra(lj, g1[ic,jc].T.copy())
gsph[ic,jc] = c2s_bra(li, tmp.T.copy())
return gsph.transpose(0,2,1,3).reshape(nci*(li*2+1),-1)
