def get_phi1(pcmojb):
pcmobj.grids.build()
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
r_vdw = pcmobj.get_atomic_radii()
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = ddcosmo.make_fi(pcmobj, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
nexposed = numpy.count_nonzero(ui == 1)
nbury = numpy.count_nonzero(ui == 0)
on_shell = numpy.count_nonzero(ui > 0) - nexposed
nlm = (lmax + 1)**2
Lmat = ddcosmo.make_L(pcmobj, r_vdw, ylm_1sph, fi)
Lmat = Lmat.reshape(natm * nlm, -1)
cached_pol = ddcosmo.cache_fake_multipoles(pcmobj.grids, r_vdw,
lmax)
phi = ddcosmo.make_phi(pcmobj, dm, r_vdw, ui, ylm_1sph)
L_X = numpy.linalg.solve(Lmat, phi.ravel()).reshape(natm, -1)
psi, vmat, L_S = \
ddcosmo.make_psi_vmat(pcmobj, dm, r_vdw, ui, ylm_1sph,
cached_pol, L_X, Lmat)
phi1 = ddcosmo_grad.make_phi1(pcmobj, dm, r_vdw, ui, ylm_1sph)
phi1 = numpy.einsum('izjx,jx->iz', phi1, L_S)
return L_S, phi, phi1
def build(self):
if self.grids.coords is None:
self.grids.build(with_non0tab=True)
mol = self.mol
natm = mol.natm
lmax = self.lmax
r_vdw = self.get_atomic_radii()
coords_1sph, weights_1sph = make_grids_one_sphere(self.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = make_fi(self, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
nexposed = numpy.count_nonzero(ui == 1)
nbury = numpy.count_nonzero(ui == 0)
on_shell = numpy.count_nonzero(ui > 0) - nexposed
logger.debug(self, 'Num points exposed %d', nexposed)
logger.debug(self, 'Num points buried %d', nbury)
logger.debug(self, 'Num points on shell %d', on_shell)
nlm = (lmax + 1)**2
Lmat = make_L(self, r_vdw, ylm_1sph, fi)
Lmat = Lmat.reshape(natm * nlm, -1)
cached_pol = cache_fake_multipoles(self.grids, r_vdw, lmax)
self._intermediates = {
'r_vdw': r_vdw,
'ylm_1sph': ylm_1sph,
'ui': ui,
'Lmat': Lmat,
'cached_pol': cached_pol,
}
def test_psi_vmat(self):
pcm = ddcosmo.DDCOSMO(mol)
pcm.lmax = 2
r_vdw = ddcosmo.get_atomic_radii(pcm)
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui<0] = 0
grids = dft.gen_grid.Grids(mol).build()
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcm.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcm.lmax, True))
cached_pol = ddcosmo.cache_fake_multipoles(grids, r_vdw, pcm.lmax)
numpy.random.seed(1)
nao = mol.nao_nr()
dm = numpy.random.random((nao,nao))
dm = dm + dm.T
natm = mol.natm
nlm = (pcm.lmax+1)**2
LX = numpy.random.random((natm,nlm))
L = ddcosmo.make_L(pcm, r_vdw, ylm_1sph, fi)
psi, vmat = ddcosmo.make_psi_vmat(pcm, dm, r_vdw, ui, grids,
ylm_1sph, cached_pol, LX, L)[:2]
psi_ref = make_psi(pcm.mol, dm, r_vdw, pcm.lmax)
self.assertAlmostEqual(abs(psi_ref - psi).max(), 0, 12)
LS = numpy.linalg.solve(L.T.reshape(natm*nlm,-1),
psi_ref.ravel()).reshape(natm,nlm)
vmat_ref = make_vmat(pcm, r_vdw, pcm.lebedev_order, pcm.lmax, LX, LS)
self.assertAlmostEqual(abs(vmat_ref - vmat).max(), 0, 12)
def make_psi(mol, dm, r_vdw, lmax):
grids = dft.gen_grid.Grids(mol)
atom_grids_tab = grids.gen_atomic_grids(mol)
grids.build()
ao = dft.numint.eval_ao(mol, grids.coords)
den = dft.numint.eval_rho(mol, ao, dm)
den *= grids.weights
natm = mol.natm
nlm = (lmax+1)**2
psi = numpy.empty((natm,nlm))
i1 = 0
for ia in range(natm):
xnj, w = atom_grids_tab[mol.atom_symbol(ia)]
i0, i1 = i1, i1 + w.size
r = lib.norm(xnj, axis=1)
snj = xnj/r.reshape(-1,1)
Ys = sph.real_sph_vec(snj, lmax, True)
p1 = 0
for l in range(lmax+1):
fac = 4*numpy.pi/(l*2+1)
p0, p1 = p1, p1 + (l*2+1)
rr = numpy.zeros_like(r)
rr[r<=r_vdw[ia]] = r[r<=r_vdw[ia]]**l / r_vdw[ia]**(l+1)
rr[r> r_vdw[ia]] = r_vdw[ia]**l / r[r>r_vdw[ia]]**(l+1)
psi[ia,p0:p1] = -fac * numpy.einsum('n,n,mn->m', den[i0:i1], rr, Ys[l])
psi[ia,0] += numpy.sqrt(4*numpy.pi)/r_vdw[ia] * mol.atom_charge(ia)
return psi
def test_psi_vmat(self):
pcm = ddcosmo.DDCOSMO(mol)
pcm.lmax = 2
pcm.eps = 0
r_vdw = ddcosmo.get_atomic_radii(pcm)
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
grids = dft.gen_grid.Grids(mol).build()
pcm.grids = grids
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcm.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcm.lmax, True))
cached_pol = ddcosmo.cache_fake_multipoles(grids, r_vdw, pcm.lmax)
numpy.random.seed(1)
nao = mol.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
natm = mol.natm
nlm = (pcm.lmax + 1)**2
LX = numpy.random.random((natm, nlm))
L = ddcosmo.make_L(pcm, r_vdw, ylm_1sph, fi)
psi, vmat = ddcosmo.make_psi_vmat(pcm, dm, r_vdw, ui, ylm_1sph,
cached_pol, LX, L)[:2]
psi_ref = make_psi(pcm.mol, dm, r_vdw, pcm.lmax)
self.assertAlmostEqual(abs(psi_ref - psi).max(), 0, 12)
LS = numpy.linalg.solve(L.reshape(natm * nlm, -1).T,
psi_ref.ravel()).reshape(natm, nlm)
vmat_ref = make_vmat(pcm, r_vdw, pcm.lebedev_order, pcm.lmax, LX, LS)
self.assertAlmostEqual(abs(vmat_ref - vmat).max(), 0, 12)
def get_phi1(pcmojb):
pcmobj.grids.build()
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
r_vdw = pcmobj.get_atomic_radii()
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = ddcosmo.make_fi(pcmobj, r_vdw)
ui = 1 - fi
ui[ui<0] = 0
nexposed = numpy.count_nonzero(ui==1)
nbury = numpy.count_nonzero(ui==0)
on_shell = numpy.count_nonzero(ui>0) - nexposed
nlm = (lmax+1)**2
Lmat = ddcosmo.make_L(pcmobj, r_vdw, ylm_1sph, fi)
Lmat = Lmat.reshape(natm*nlm,-1)
cached_pol = ddcosmo.cache_fake_multipoles(pcmobj.grids, r_vdw, lmax)
phi = ddcosmo.make_phi(pcmobj, dm, r_vdw, ui)
L_X = numpy.linalg.solve(Lmat, phi.ravel()).reshape(natm,-1)
psi, vmat, L_S = \
ddcosmo.make_psi_vmat(pcmobj, dm, r_vdw, ui, pcmobj.grids, ylm_1sph,
cached_pol, L_X, Lmat)
phi1 = ddcosmo_grad.make_phi1(pcmobj, dm, r_vdw, ui)
phi1 = numpy.einsum('izjx,jx->iz', phi1, L_S)
return L_S, phi, phi1
def make_psi(mol, dm, r_vdw, lmax):
grids = dft.gen_grid.Grids(mol)
atom_grids_tab = grids.gen_atomic_grids(mol)
grids.build()
ao = dft.numint.eval_ao(mol, grids.coords)
den = dft.numint.eval_rho(mol, ao, dm)
den *= grids.weights
natm = mol.natm
nlm = (lmax + 1)**2
psi = numpy.empty((natm, nlm))
i1 = 0
for ia in range(natm):
xnj, w = atom_grids_tab[mol.atom_symbol(ia)]
i0, i1 = i1, i1 + w.size
r = lib.norm(xnj, axis=1)
snj = xnj / r.reshape(-1, 1)
Ys = sph.real_sph_vec(snj, lmax, True)
p1 = 0
for l in range(lmax + 1):
fac = 4 * numpy.pi / (l * 2 + 1)
p0, p1 = p1, p1 + (l * 2 + 1)
rr = numpy.zeros_like(r)
rr[r <= r_vdw[ia]] = r[r <= r_vdw[ia]]**l / r_vdw[ia]**(l + 1)
rr[r > r_vdw[ia]] = r_vdw[ia]**l / r[r > r_vdw[ia]]**(l + 1)
psi[ia, p0:p1] = -fac * numpy.einsum('n,n,mn->m', den[i0:i1], rr,
Ys[l])
psi[ia,
0] += numpy.sqrt(4 * numpy.pi) / r_vdw[ia] * mol.atom_charge(ia)
return psi
def gen_ddcosmo_solver(pcmobj, verbose=None):
'''Generate ddcosmo function to compute energy and potential matrix
'''
mol = pcmobj.mol
mm_mol = pcmobj.mm_mol
if pcmobj.grids.coords is None:
pcmobj.grids.build(with_non0tab=True)
natm = mol.natm
natm_mm = 0
if mm_mol is not None:
natm_mm = mm_mol.natm
natm_tot = natm + natm_mm
lmax = pcmobj.lmax
r_vdw = pcmobj.get_atomic_radii()
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = make_fi(pcmobj, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
nexposed = numpy.count_nonzero(ui == 1)
nbury = numpy.count_nonzero(ui == 0)
on_shell = numpy.count_nonzero(ui > 0) - nexposed
logger.debug(pcmobj, 'Num points exposed %d', nexposed)
logger.debug(pcmobj, 'Num points buried %d', nbury)
logger.debug(pcmobj, 'Num points on shell %d', on_shell)
nlm = (lmax + 1)**2
Lmat = make_L(pcmobj, r_vdw, ylm_1sph, fi)
Lmat = Lmat.reshape(natm * nlm, -1)
cached_pol = cache_fake_multipoles(pcmobj.grids, r_vdw, lmax)
def gen_vind(dm):
pcmobj._dm = dm
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
# spin-traced DM for UHF or ROHF
dm = dm[0] + dm[1]
phi = make_phi(pcmobj, dm, r_vdw, ui)[:natm]
# Lmax(natm*nlm,natm*nlm) * L_X(natm*nlm) = phi(natm*nlm)
L_X = numpy.linalg.solve(Lmat, phi.ravel()).reshape(natm, -1)
psi, vmat = make_psi_vmat(pcmobj, dm, r_vdw, ui, pcmobj.grids,
ylm_1sph, cached_pol, L_X, Lmat)[:2]
dielectric = pcmobj.eps
if dielectric > 0:
f_epsilon = (dielectric - 1.) / dielectric
else:
f_epsilon = 1
pcmobj.epcm = .5 * f_epsilon * numpy.einsum('jx,jx', psi, L_X)
pcmobj.vpcm = .5 * f_epsilon * vmat
return pcmobj.epcm, pcmobj.vpcm
return gen_vind
def test_solvent_nuc(self):
def get_nuc(mol):
pcm = ddcosmo.DDCOSMO(mol)
pcm.lmax = 2
pcm.eps = 0
natm = mol.natm
nao = mol.nao
nlm = (pcm.lmax + 1)**2
r_vdw = ddcosmo.get_atomic_radii(pcm)
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
pcm.grids = grids = dft.gen_grid.Grids(mol).run(level=0)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcm.lebedev_order)
ylm_1sph = numpy.vstack(
sph.real_sph_vec(coords_1sph, pcm.lmax, True))
cached_pol = ddcosmo.cache_fake_multipoles(grids, r_vdw, pcm.lmax)
L = ddcosmo.make_L(pcm, r_vdw, ylm_1sph, fi)
return nuc_part(pcm, r_vdw, ui, ylm_1sph, cached_pol, L)
pcm = ddcosmo.DDCOSMO(mol0)
pcm.lmax = 2
pcm.eps = 0
natm = mol0.natm
nao = mol0.nao
nlm = (pcm.lmax + 1)**2
r_vdw = ddcosmo.get_atomic_radii(pcm)
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
pcm.grids = grids = dft.gen_grid.Grids(mol0).run(level=0)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcm.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcm.lmax, True))
cached_pol = ddcosmo.cache_fake_multipoles(grids, r_vdw, pcm.lmax)
L = ddcosmo.make_L(pcm, r_vdw, ylm_1sph, fi)
dvmat = nuc_part1(pcm, r_vdw, ui, ylm_1sph, cached_pol, L)
vmat1 = get_nuc(mol1)
vmat2 = get_nuc(mol2)
self.assertAlmostEqual(
abs((vmat2 - vmat1) / dx - dvmat[0, 2]).max(), 0, 8)
nao = mol0.nao
numpy.random.seed(19)
dm = numpy.random.random((nao, nao))
vref = pcm._get_vind(dm)[1]
vmat = 0.5 * get_nuc(mol0)
vmat += pcm._B_dot_x(dm)
self.assertAlmostEqual(abs(vmat - vref).max(), 0, 14)
dm1 = numpy.random.random((2, nao, nao))
de = _ddcosmo_tdscf_grad._grad_ne(pcm, dm1, r_vdw, ui, ylm_1sph,
cached_pol, L)
ref = numpy.einsum('azij,nij->naz', dvmat, dm1)
self.assertAlmostEqual(abs(de - ref).max(), 0, 12)
def make_L(pcmobj, r_vdw, lebedev_order, lmax, eta=0.1):
mol = pcmobj.mol
natm = mol.natm
nlm = (lmax + 1)**2
leb_coords, leb_weights = ddcosmo.make_grids_one_sphere(lebedev_order)
nleb_grid = leb_weights.size
atom_coords = mol.atom_coords()
Ylm_sphere = numpy.vstack(sph.real_sph_vec(leb_coords, lmax, True))
fi = ddcosmo.make_fi(pcmobj, r_vdw)
L_diag = numpy.zeros((natm, nlm))
p1 = 0
for l in range(lmax + 1):
p0, p1 = p1, p1 + (l * 2 + 1)
L_diag[:, p0:p1] = 4 * numpy.pi / (l * 2 + 1)
L_diag /= r_vdw.reshape(-1, 1)
L = numpy.diag(L_diag.ravel()).reshape(natm, nlm, natm, nlm)
for ja in range(natm):
for ka in range(natm):
if ja == ka:
continue
vjk = r_vdw[ja] * leb_coords + atom_coords[ja] - atom_coords[ka]
v = lib.norm(vjk, axis=1)
tjk = v / r_vdw[ka]
sjk = vjk / v.reshape(-1, 1)
Ys = sph.real_sph_vec(sjk, lmax, True)
# scale the weight, see JCTC 9, 3637, Eq (16)
wjk = pcmobj.regularize_xt(tjk, eta, r_vdw[ka])
wjk[fi[ja] > 1] /= fi[ja, fi[ja] > 1]
tt = numpy.ones_like(wjk)
p1 = 0
for l in range(lmax + 1):
fac = 4 * numpy.pi / (l * 2 + 1) / r_vdw[ka]
p0, p1 = p1, p1 + (l * 2 + 1)
val = numpy.einsum('n,xn,n,mn->xm', leb_weights, Ylm_sphere,
wjk * tt, Ys[l])
L[ja, :, ka, p0:p1] += -fac * val
tt *= tjk
return L.reshape(natm * nlm, natm * nlm)
def make_vmat(pcm, r_vdw, lebedev_order, lmax, LX, LS):
mol = pcm.mol
grids = dft.gen_grid.Grids(mol)
atom_grids_tab = grids.gen_atomic_grids(mol)
grids.build()
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(lebedev_order)
ao = dft.numint.eval_ao(mol, grids.coords)
nao = ao.shape[1]
vmat = numpy.zeros((nao,nao))
i1 = 0
for ia in range(mol.natm):
xnj, w = atom_grids_tab[mol.atom_symbol(ia)]
i0, i1 = i1, i1 + w.size
r = lib.norm(xnj, axis=1)
Ys = sph.real_sph_vec(xnj/r.reshape(-1,1), lmax, True)
p1 = 0
for l in range(lmax+1):
fac = 4*numpy.pi/(l*2+1)
p0, p1 = p1, p1 + (l*2+1)
rr = numpy.zeros_like(r)
rr[r<=r_vdw[ia]] = r[r<=r_vdw[ia]]**l / r_vdw[ia]**(l+1)
rr[r> r_vdw[ia]] = r_vdw[ia]**l / r[r>r_vdw[ia]]**(l+1)
eta_nj = fac * numpy.einsum('n,mn,m->n', rr, Ys[l], LX[ia,p0:p1])
vmat -= numpy.einsum('n,np,nq->pq', grids.weights[i0:i1] * eta_nj,
ao[i0:i1], ao[i0:i1])
atom_coords = mol.atom_coords()
Ylm_sphere = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui<0] = 0
xi_nj = numpy.einsum('n,jn,xn,jx->jn', weights_1sph, ui, Ylm_sphere, LS)
pmol = mol.copy()
for ia in range(mol.natm):
for i,c in enumerate(coords_1sph):
r = atom_coords[ia] + r_vdw[ia] * c
pmol.set_rinv_orig(r)
vmat += pmol.intor('int1e_rinv') * xi_nj[ia,i]
return vmat
def make_vmat(pcm, r_vdw, lebedev_order, lmax, LX, LS):
mol = pcm.mol
grids = dft.gen_grid.Grids(mol)
atom_grids_tab = grids.gen_atomic_grids(mol)
grids.build()
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(lebedev_order)
ao = dft.numint.eval_ao(mol, grids.coords)
nao = ao.shape[1]
vmat = numpy.zeros((nao, nao))
i1 = 0
for ia in range(mol.natm):
xnj, w = atom_grids_tab[mol.atom_symbol(ia)]
i0, i1 = i1, i1 + w.size
r = lib.norm(xnj, axis=1)
Ys = sph.real_sph_vec(xnj / r.reshape(-1, 1), lmax, True)
p1 = 0
for l in range(lmax + 1):
fac = 4 * numpy.pi / (l * 2 + 1)
p0, p1 = p1, p1 + (l * 2 + 1)
rr = numpy.zeros_like(r)
rr[r <= r_vdw[ia]] = r[r <= r_vdw[ia]]**l / r_vdw[ia]**(l + 1)
rr[r > r_vdw[ia]] = r_vdw[ia]**l / r[r > r_vdw[ia]]**(l + 1)
eta_nj = fac * numpy.einsum('n,mn,m->n', rr, Ys[l], LX[ia, p0:p1])
vmat -= numpy.einsum('n,np,nq->pq', grids.weights[i0:i1] * eta_nj,
ao[i0:i1], ao[i0:i1])
atom_coords = mol.atom_coords()
Ylm_sphere = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
xi_nj = numpy.einsum('n,jn,xn,jx->jn', weights_1sph, ui, Ylm_sphere, LS)
pmol = mol.copy()
for ia in range(mol.natm):
for i, c in enumerate(coords_1sph):
r = atom_coords[ia] + r_vdw[ia] * c
pmol.set_rinv_orig(r)
vmat += pmol.intor('int1e_rinv') * xi_nj[ia, i]
return vmat
def rsphar_vec(rvecs, lmax):
"""
Computes (all) real spherical harmonics up to the angular momentum lmax
Args:
rvecs : A list of Cartesian coordinates defining the theta and phi angles for spherical harmonic
lmax : Integer, maximal angular momentum
Result:
2-d numpy array of float64 elements with all spherical harmonics stored in order 0,0; 1,-1; 1,0; 1,+1 ... lmax,lmax, althogether 0 : (lmax+1)**2 elements.
"""
assert lmax>-1
ylm = sph.real_sph_vec(rvecs, lmax)
res = np.vstack(ylm).T.copy('C')
return res
def make_L(pcmobj, r_vdw, lebedev_order, lmax, eta=0.1):
mol = pcmobj.mol
natm = mol.natm
nlm = (lmax+1)**2
leb_coords, leb_weights = ddcosmo.make_grids_one_sphere(lebedev_order)
nleb_grid = leb_weights.size
atom_coords = mol.atom_coords()
Ylm_sphere = numpy.vstack(sph.real_sph_vec(leb_coords, lmax, True))
fi = ddcosmo.make_fi(pcmobj, r_vdw)
L_diag = numpy.zeros((natm,nlm))
p1 = 0
for l in range(lmax+1):
p0, p1 = p1, p1 + (l*2+1)
L_diag[:,p0:p1] = 4*numpy.pi/(l*2+1)
L_diag /= r_vdw.reshape(-1,1)
L = numpy.diag(L_diag.ravel()).reshape(natm,nlm,natm,nlm)
for ja in range(natm):
for ka in range(natm):
if ja == ka:
continue
vjk = r_vdw[ja] * leb_coords + atom_coords[ja] - atom_coords[ka]
v = lib.norm(vjk, axis=1)
tjk = v / r_vdw[ka]
sjk = vjk / v.reshape(-1,1)
Ys = sph.real_sph_vec(sjk, lmax, True)
# scale the weight, see JCTC 9, 3637, Eq (16)
wjk = pcmobj.regularize_xt(tjk, eta, r_vdw[ka])
wjk[fi[ja]>1] /= fi[ja,fi[ja]>1]
tt = numpy.ones_like(wjk)
p1 = 0
for l in range(lmax+1):
fac = 4*numpy.pi/(l*2+1) / r_vdw[ka]
p0, p1 = p1, p1 + (l*2+1)
val = numpy.einsum('n,xn,n,mn->xm', leb_weights, Ylm_sphere, wjk*tt, Ys[l])
L[ja,:,ka,p0:p1] += -fac * val
tt *= tjk
return L.reshape(natm*nlm,natm*nlm)
def test_L_x(self):
pcm = ddcosmo.DDCOSMO(mol)
r_vdw = ddcosmo.get_atomic_radii(pcm)
n = mol.natm * (pcm.lmax+1)**2
Lref = make_L(pcm, r_vdw, pcm.lebedev_order, pcm.lmax, pcm.eta).reshape(n,n)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcm.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcm.lmax, True))
fi = ddcosmo.make_fi(pcm, r_vdw)
L = ddcosmo.make_L(pcm, r_vdw, ylm_1sph, fi).reshape(n,n)
numpy.random.seed(1)
x = numpy.random.random(n)
self.assertTrue(abs(Lref.dot(n)-L.dot(n)).max() < 1e-12)
def gen_ddcosmo_solver(pcmobj, verbose=None):
'''Generate ddcosmo function to compute energy and potential matrix
'''
mol = pcmobj.mol
if pcmobj.grids.coords is None:
pcmobj.grids.build(with_non0tab=True)
natm = mol.natm
lmax = pcmobj.lmax
r_vdw = pcmobj.get_atomic_radii()
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = make_fi(pcmobj, r_vdw)
ui = 1 - fi
ui[ui<0] = 0
nexposed = numpy.count_nonzero(ui==1)
nbury = numpy.count_nonzero(ui==0)
on_shell = numpy.count_nonzero(ui>0) - nexposed
logger.debug(pcmobj, 'Num points exposed %d', nexposed)
logger.debug(pcmobj, 'Num points buried %d', nbury)
logger.debug(pcmobj, 'Num points on shell %d', on_shell)
nlm = (lmax+1)**2
Lmat = make_L(pcmobj, r_vdw, ylm_1sph, fi)
Lmat = Lmat.reshape(natm*nlm,-1)
cached_pol = cache_fake_multipoles(pcmobj.grids, r_vdw, lmax)
def gen_vind(dm):
pcmobj._dm = dm
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
# spin-traced DM for UHF or ROHF
dm = dm[0] + dm[1]
phi = make_phi(pcmobj, dm, r_vdw, ui)
L_X = numpy.linalg.solve(Lmat, phi.ravel()).reshape(natm,-1)
psi, vmat = make_psi_vmat(pcmobj, dm, r_vdw, ui, pcmobj.grids, ylm_1sph,
cached_pol, L_X, Lmat)[:2]
dielectric = pcmobj.eps
if dielectric > 0:
f_epsilon = (dielectric-1.)/dielectric
else:
f_epsilon = 1
pcmobj.epcm = .5 * f_epsilon * numpy.einsum('jx,jx', psi, L_X)
pcmobj.vpcm = .5 * f_epsilon * vmat
return pcmobj.epcm, pcmobj.vpcm
return gen_vind
def make_phi(pcmobj, dm, r_vdw, ui):
mol = pcmobj.mol
natm = mol.natm
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
ngrid_1sph = coords_1sph.shape[0]
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
dm = dm[0] + dm[1]
tril_dm = lib.pack_tril(dm + dm.T)
nao = dm.shape[0]
diagidx = numpy.arange(nao)
diagidx = diagidx * (diagidx + 1) // 2 + diagidx
tril_dm[diagidx] *= .5
atom_coords = mol.atom_coords()
atom_charges = mol.atom_charges()
extern_point_idx = ui > 0
cav_coords = (atom_coords.reshape(natm, 1, 3) +
numpy.einsum('r,gx->rgx', r_vdw, coords_1sph))
v_phi = numpy.empty((natm, ngrid_1sph))
for ia in range(natm):
# Note (-) sign is not applied to atom_charges, because (-) is explicitly
# included in rhs and L matrix
d_rs = atom_coords.reshape(-1, 1, 3) - cav_coords[ia]
v_phi[ia] = numpy.einsum('z,zp->p', atom_charges,
1. / lib.norm(d_rs, axis=2))
max_memory = pcmobj.max_memory - lib.current_memory()[0]
blksize = int(max(max_memory * 1e6 / 8 / nao**2, 400))
cav_coords = cav_coords[extern_point_idx]
v_phi_e = numpy.empty(cav_coords.shape[0])
int3c2e = mol._add_suffix('int3c2e')
cintopt = gto.moleintor.make_cintopt(mol._atm, mol._bas, mol._env, int3c2e)
for i0, i1 in lib.prange(0, cav_coords.shape[0], blksize):
fakemol = gto.fakemol_for_charges(cav_coords[i0:i1])
v_nj = df.incore.aux_e2(mol,
fakemol,
intor=int3c2e,
aosym='s2ij',
cintopt=cintopt)
v_phi_e[i0:i1] = numpy.einsum('x,xk->k', tril_dm, v_nj)
v_phi[extern_point_idx] -= v_phi_e
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
phi = -numpy.einsum('n,xn,jn,jn->jx', weights_1sph, ylm_1sph, ui, v_phi)
return phi
def test_B_dot_x(self):
pcm = ddcosmo.DDCOSMO(mol)
pcm.lmax = 2
pcm.eps = 0
natm = mol.natm
nao = mol.nao
nlm = (pcm.lmax + 1)**2
r_vdw = ddcosmo.get_atomic_radii(pcm)
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
grids = dft.gen_grid.Grids(mol).run(level=0)
pcm.grids = grids
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcm.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcm.lmax, True))
cached_pol = ddcosmo.cache_fake_multipoles(grids, r_vdw, pcm.lmax)
L = ddcosmo.make_L(pcm, r_vdw, ylm_1sph, fi)
B = make_B(pcm, r_vdw, ui, ylm_1sph, cached_pol, L)
numpy.random.seed(19)
dm = numpy.random.random((2, nao, nao))
Bx = numpy.einsum('ijkl,xkl->xij', B, dm)
phi = ddcosmo.make_phi(pcm, dm, r_vdw, ui, ylm_1sph, with_nuc=False)
Xvec = numpy.linalg.solve(L.reshape(natm * nlm, -1),
phi.reshape(-1, natm * nlm).T)
Xvec = Xvec.reshape(natm, nlm, -1).transpose(2, 0, 1)
psi, vref, LS = ddcosmo.make_psi_vmat(pcm,
dm,
r_vdw,
ui,
ylm_1sph,
cached_pol,
Xvec,
L,
with_nuc=False)
self.assertAlmostEqual(abs(Bx - vref).max(), 0, 12)
e1 = numpy.einsum('nij,nij->n', psi, Xvec)
e2 = numpy.einsum('nij,nij->n', phi, LS)
e3 = numpy.einsum('nij,nij->n', dm, vref) * .5
self.assertAlmostEqual(abs(e1 - e2).max(), 0, 12)
self.assertAlmostEqual(abs(e1 - e3).max(), 0, 12)
vmat = pcm._B_dot_x(dm)
self.assertEqual(vmat.shape, (2, nao, nao))
self.assertAlmostEqual(abs(vmat - vref * .5).max(), 0, 12)
self.assertAlmostEqual(lib.fp(vmat), -17.383712106418606, 12)
def gen_ddpcm_solver(pcmobj, verbose=None):
mol = pcmobj.mol
if pcmobj.grids.coords is None:
pcmobj.grids.build(with_non0tab=True)
natm = mol.natm
lmax = pcmobj.lmax
r_vdw = ddcosmo.get_atomic_radii(pcmobj)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = ddcosmo.make_fi(pcmobj, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
nexposed = numpy.count_nonzero(ui == 1)
nbury = numpy.count_nonzero(ui == 0)
on_shell = numpy.count_nonzero(ui > 0) - nexposed
logger.debug(pcmobj, 'Num points exposed %d', nexposed)
logger.debug(pcmobj, 'Num points buried %d', nbury)
logger.debug(pcmobj, 'Num points on shell %d', on_shell)
nlm = (lmax + 1)**2
Lmat = ddcosmo.make_L(pcmobj, r_vdw, ylm_1sph, fi)
Lmat = Lmat.reshape(natm * nlm, -1)
Amat = make_A(pcmobj, r_vdw, ylm_1sph, ui).reshape(natm * nlm, -1)
fac = 2 * numpy.pi * (pcmobj.eps + 1) / (pcmobj.eps - 1)
A_diele = Amat + fac * numpy.eye(natm * nlm)
A_inf = Amat + 2 * numpy.pi * numpy.eye(natm * nlm)
cached_pol = ddcosmo.cache_fake_multipoles(pcmobj.grids, r_vdw, lmax)
def gen_vind(dm):
phi = ddcosmo.make_phi(pcmobj, dm, r_vdw, ui)
phi = numpy.linalg.solve(A_diele, A_inf.dot(phi.ravel()))
Xvec = numpy.linalg.solve(Lmat, phi.ravel()).reshape(natm, -1)
psi, vmat = ddcosmo.make_psi_vmat(pcmobj, dm, r_vdw, ui, pcmobj.grids,
ylm_1sph, cached_pol, Xvec, Lmat)[:2]
dielectric = pcmobj.eps
f_epsilon = (dielectric - 1.) / dielectric
epcm = .5 * f_epsilon * numpy.einsum('jx,jx', psi, Xvec)
vpcm = .5 * f_epsilon * vmat
return epcm, vpcm
return gen_vind
def test_L_x(self):
pcm = ddcosmo.DDCOSMO(mol)
r_vdw = ddcosmo.get_atomic_radii(pcm)
n = mol.natm * (pcm.lmax + 1)**2
Lref = make_L(pcm, r_vdw, pcm.lebedev_order, pcm.lmax,
pcm.eta).reshape(n, n)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcm.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcm.lmax, True))
fi = ddcosmo.make_fi(pcm, r_vdw)
L = ddcosmo.make_L(pcm, r_vdw, ylm_1sph, fi).reshape(n, n)
numpy.random.seed(1)
x = numpy.random.random(n)
self.assertTrue(abs(Lref.dot(n) - L.dot(n)).max() < 1e-12)
def test_L1(self):
pcmobj = ddcosmo.DDCOSMO(mol0)
r_vdw = pcmobj.get_atomic_radii()
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
fi = ddcosmo.make_fi(pcmobj, r_vdw)
L1 = ddcosmo_grad.make_L1(pcmobj, r_vdw, ylm_1sph, fi)
pcmobj = ddcosmo.DDCOSMO(mol1)
fi = ddcosmo.make_fi(pcmobj, r_vdw)
L_1 = ddcosmo.make_L(pcmobj, r_vdw, ylm_1sph, fi)
pcmobj = ddcosmo.DDCOSMO(mol2)
fi = ddcosmo.make_fi(pcmobj, r_vdw)
L_2 = ddcosmo.make_L(pcmobj, r_vdw, ylm_1sph, fi)
self.assertAlmostEqual(abs((L_2-L_1)/dx - L1[0,2]).max(), 0, 7)
def test_L1(self):
pcmobj = ddcosmo.DDCOSMO(mol0)
r_vdw = pcmobj.get_atomic_radii()
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
fi = ddcosmo.make_fi(pcmobj, r_vdw)
L1 = ddcosmo_grad.make_L1(pcmobj, r_vdw, ylm_1sph, fi)
pcmobj = ddcosmo.DDCOSMO(mol1)
fi = ddcosmo.make_fi(pcmobj, r_vdw)
L_1 = ddcosmo.make_L(pcmobj, r_vdw, ylm_1sph, fi)
pcmobj = ddcosmo.DDCOSMO(mol2)
fi = ddcosmo.make_fi(pcmobj, r_vdw)
L_2 = ddcosmo.make_L(pcmobj, r_vdw, ylm_1sph, fi)
self.assertAlmostEqual(abs((L_2-L_1)/dx - L1[0,2]).max(), 0, 7)
def gen_ddpcm_solver(pcmobj, verbose=None):
mol = pcmobj.mol
if pcmobj.grids.coords is None:
pcmobj.grids.build(with_non0tab=True)
natm = mol.natm
lmax = pcmobj.lmax
r_vdw = ddcosmo.get_atomic_radii(pcmobj)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = ddcosmo.make_fi(pcmobj, r_vdw)
ui = 1 - fi
ui[ui<0] = 0
nexposed = numpy.count_nonzero(ui==1)
nbury = numpy.count_nonzero(ui==0)
on_shell = numpy.count_nonzero(ui>0) - nexposed
logger.debug(pcmobj, 'Num points exposed %d', nexposed)
logger.debug(pcmobj, 'Num points buried %d', nbury)
logger.debug(pcmobj, 'Num points on shell %d', on_shell)
nlm = (lmax+1)**2
Lmat = ddcosmo.make_L(pcmobj, r_vdw, ylm_1sph, fi)
Lmat = Lmat.reshape(natm*nlm,-1)
Amat = make_A(pcmobj, r_vdw, ylm_1sph, ui).reshape(natm*nlm,-1)
fac = 2*numpy.pi * (pcmobj.eps+1) / (pcmobj.eps-1)
A_diele = Amat + fac * numpy.eye(natm*nlm)
A_inf = Amat + 2*numpy.pi * numpy.eye(natm*nlm)
cached_pol = ddcosmo.cache_fake_multipoles(pcmobj.grids, r_vdw, lmax)
def gen_vind(dm):
phi = ddcosmo.make_phi(pcmobj, dm, r_vdw, ui)
phi = numpy.linalg.solve(A_diele, A_inf.dot(phi.ravel()))
L_X = numpy.linalg.solve(Lmat, phi.ravel()).reshape(natm,-1)
psi, vmat = ddcosmo.make_psi_vmat(pcmobj, dm, r_vdw, ui, pcmobj.grids,
ylm_1sph, cached_pol, L_X, Lmat)[:2]
dielectric = pcmobj.eps
f_epsilon = (dielectric-1.)/dielectric
epcm = .5 * f_epsilon * numpy.einsum('jx,jx', psi, L_X)
return epcm, .5 * f_epsilon * vmat
return gen_vind
def test_phi(self):
pcm = ddcosmo.DDCOSMO(mol)
r_vdw = ddcosmo.get_atomic_radii(pcm)
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui<0] = 0
numpy.random.seed(1)
nao = mol.nao_nr()
dm = numpy.random.random((nao,nao))
dm = dm + dm.T
v_phi = make_v_phi(mol, dm, r_vdw, pcm.lebedev_order)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcm.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcm.lmax, True))
phi = -numpy.einsum('n,xn,jn,jn->jx', weights_1sph, ylm_1sph, ui, v_phi)
phi1 = ddcosmo.make_phi(pcm, dm, r_vdw, ui)
self.assertTrue(abs(phi - phi1).max() < 1e-12)
def kernel(pcmobj, dm, verbose=None):
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
if pcmobj.grids.coords is None:
pcmobj.grids.build(with_non0tab=True)
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
# UHF density matrix
dm = dm[0] + dm[1]
r_vdw = ddcosmo.get_atomic_radii(pcmobj)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = ddcosmo.make_fi(pcmobj, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
cached_pol = ddcosmo.cache_fake_multipoles(pcmobj.grids, r_vdw, lmax)
nlm = (lmax + 1)**2
L0 = ddcosmo.make_L(pcmobj, r_vdw, ylm_1sph, fi)
L0 = L0.reshape(natm * nlm, -1)
L1 = make_L1(pcmobj, r_vdw, ylm_1sph, fi)
phi0 = ddcosmo.make_phi(pcmobj, dm, r_vdw, ui)
phi1 = make_phi1(pcmobj, dm, r_vdw, ui)
L0_X = numpy.linalg.solve(L0, phi0.ravel()).reshape(natm, -1)
psi0, vmat, L0_S = \
ddcosmo.make_psi_vmat(pcmobj, dm, r_vdw, ui, pcmobj.grids, ylm_1sph,
cached_pol, L0_X, L0)
e_psi1 = make_e_psi1(pcmobj, dm, r_vdw, ui, pcmobj.grids, ylm_1sph,
cached_pol, L0_X, L0)
dielectric = pcmobj.eps
if dielectric > 0:
f_epsilon = (dielectric - 1.) / dielectric
else:
f_epsilon = 1
de = .5 * f_epsilon * e_psi1
de += .5 * f_epsilon * numpy.einsum('jx,azjx->az', L0_S, phi1)
de -= .5 * f_epsilon * numpy.einsum('aziljm,il,jm->az', L1, L0_S, L0_X)
return de
def make_phi(pcmobj, dm, r_vdw, ui):
mol = pcmobj.mol
natm = mol.natm
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
ngrid_1sph = coords_1sph.shape[0]
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
dm = dm[0] + dm[1]
tril_dm = lib.pack_tril(dm+dm.T)
nao = dm.shape[0]
diagidx = numpy.arange(nao)
diagidx = diagidx*(diagidx+1)//2 + diagidx
tril_dm[diagidx] *= .5
atom_coords = mol.atom_coords()
atom_charges = mol.atom_charges()
extern_point_idx = ui > 0
cav_coords = (atom_coords.reshape(natm,1,3)
+ numpy.einsum('r,gx->rgx', r_vdw, coords_1sph))
v_phi = numpy.empty((natm,ngrid_1sph))
for ia in range(natm):
# Note (-) sign is not applied to atom_charges, because (-) is explicitly
# included in rhs and L matrix
d_rs = atom_coords.reshape(-1,1,3) - cav_coords[ia]
v_phi[ia] = numpy.einsum('z,zp->p', atom_charges, 1./lib.norm(d_rs,axis=2))
max_memory = pcmobj.max_memory - lib.current_memory()[0]
blksize = int(max(max_memory*1e6/8/nao**2, 400))
cav_coords = cav_coords[extern_point_idx]
v_phi_e = numpy.empty(cav_coords.shape[0])
int3c2e = mol._add_suffix('int3c2e')
for i0, i1 in lib.prange(0, cav_coords.shape[0], blksize):
fakemol = gto.fakemol_for_charges(cav_coords[i0:i1])
v_nj = df.incore.aux_e2(mol, fakemol, intor=int3c2e, aosym='s2ij')
v_phi_e[i0:i1] = numpy.einsum('x,xk->k', tril_dm, v_nj)
v_phi[extern_point_idx] -= v_phi_e
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
phi = -numpy.einsum('n,xn,jn,jn->jx', weights_1sph, ylm_1sph, ui, v_phi)
return phi
def kernel(pcmobj, dm, verbose=None):
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
if pcmobj.grids.coords is None:
pcmobj.grids.build(with_non0tab=True)
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
# UHF density matrix
dm = dm[0] + dm[1]
r_vdw = ddcosmo.get_atomic_radii(pcmobj)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = ddcosmo.make_fi(pcmobj, r_vdw)
ui = 1 - fi
ui[ui<0] = 0
cached_pol = ddcosmo.cache_fake_multipoles(pcmobj.grids, r_vdw, lmax)
nlm = (lmax+1)**2
L0 = ddcosmo.make_L(pcmobj, r_vdw, ylm_1sph, fi)
L0 = L0.reshape(natm*nlm,-1)
L1 = make_L1(pcmobj, r_vdw, ylm_1sph, fi)
phi0 = ddcosmo.make_phi(pcmobj, dm, r_vdw, ui)
phi1 = make_phi1(pcmobj, dm, r_vdw, ui)
L0_X = numpy.linalg.solve(L0, phi0.ravel()).reshape(natm,-1)
psi0, vmat, L0_S = \
ddcosmo.make_psi_vmat(pcmobj, dm, r_vdw, ui, pcmobj.grids, ylm_1sph,
cached_pol, L0_X, L0)
e_psi1 = make_e_psi1(pcmobj, dm, r_vdw, ui, pcmobj.grids, ylm_1sph,
cached_pol, L0_X, L0)
dielectric = pcmobj.eps
if dielectric > 0:
f_epsilon = (dielectric-1.)/dielectric
else:
f_epsilon = 1
de = .5 * f_epsilon * e_psi1
de+= .5 * f_epsilon * numpy.einsum('jx,azjx->az', L0_S, phi1)
de-= .5 * f_epsilon * numpy.einsum('aziljm,il,jm->az', L1, L0_S, L0_X)
return de
def getB(mol):
pcm = ddcosmo.DDCOSMO(mol)
pcm.lmax = 2
pcm.eps = 0
natm = mol.natm
nao = mol.nao
nlm = (pcm.lmax + 1)**2
r_vdw = ddcosmo.get_atomic_radii(pcm)
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
pcm.grids = grids = dft.gen_grid.Grids(mol).run(level=0)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcm.lebedev_order)
ylm_1sph = numpy.vstack(
sph.real_sph_vec(coords_1sph, pcm.lmax, True))
cached_pol = ddcosmo.cache_fake_multipoles(grids, r_vdw, pcm.lmax)
L = ddcosmo.make_L(pcm, r_vdw, ylm_1sph, fi)
return make_B(pcm, r_vdw, ui, ylm_1sph, cached_pol, L)
def test_phi(self):
pcm = ddcosmo.DDCOSMO(mol)
r_vdw = ddcosmo.get_atomic_radii(pcm)
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
numpy.random.seed(1)
nao = mol.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
v_phi = make_v_phi(mol, dm, r_vdw, pcm.lebedev_order)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcm.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcm.lmax, True))
phi = -numpy.einsum('n,xn,jn,jn->jx', weights_1sph, ylm_1sph, ui,
v_phi)
phi1 = ddcosmo.make_phi(pcm, dm, r_vdw, ui, ylm_1sph)
self.assertTrue(abs(phi - phi1).max() < 1e-12)
def test_make_ylm(self):
numpy.random.seed(1)
lmax = 6
r = numpy.random.random((100,3)) - numpy.ones(3)*.5
r = r / lib.norm(r,axis=1).reshape(-1,1)
ngrid = r.shape[0]
cosphi = r[:,2]
sinphi = (1-cosphi**2)**.5
costheta = numpy.ones(ngrid)
sintheta = numpy.zeros(ngrid)
costheta[sinphi!=0] = r[sinphi!=0,0] / sinphi[sinphi!=0]
sintheta[sinphi!=0] = r[sinphi!=0,1] / sinphi[sinphi!=0]
costheta[costheta> 1] = 1
costheta[costheta<-1] =-1
sintheta[sintheta> 1] = 1
sintheta[sintheta<-1] =-1
varphi = numpy.arccos(cosphi)
theta = numpy.arccos(costheta)
theta[sintheta<0] = 2*numpy.pi - theta[sintheta<0]
ylmref = []
for l in range(lmax+1):
ylm = numpy.empty((l*2+1,ngrid))
ylm[l] = scipy.special.sph_harm(0, l, theta, varphi).real
for m in range(1, l+1):
f1 = scipy.special.sph_harm(-m, l, theta, varphi)
f2 = scipy.special.sph_harm( m, l, theta, varphi)
# complex to real spherical functions
if m % 2 == 1:
ylm[l-m] = (-f1.imag - f2.imag) / numpy.sqrt(2)
ylm[l+m] = ( f1.real - f2.real) / numpy.sqrt(2)
else:
ylm[l-m] = (-f1.imag + f2.imag) / numpy.sqrt(2)
ylm[l+m] = ( f1.real + f2.real) / numpy.sqrt(2)
if l == 1:
ylm = ylm[[2,0,1]]
ylmref.append(ylm)
ylmref = numpy.vstack(ylmref)
ylm = numpy.vstack(sph.real_sph_vec(r, lmax, True))
self.assertTrue(abs(ylmref - ylm).max() < 1e-14)
def test_make_ylm(self):
numpy.random.seed(1)
lmax = 6
r = numpy.random.random((100, 3)) - numpy.ones(3) * .5
r = r / lib.norm(r, axis=1).reshape(-1, 1)
ngrid = r.shape[0]
cosphi = r[:, 2]
sinphi = (1 - cosphi**2)**.5
costheta = numpy.ones(ngrid)
sintheta = numpy.zeros(ngrid)
costheta[sinphi != 0] = r[sinphi != 0, 0] / sinphi[sinphi != 0]
sintheta[sinphi != 0] = r[sinphi != 0, 1] / sinphi[sinphi != 0]
costheta[costheta > 1] = 1
costheta[costheta < -1] = -1
sintheta[sintheta > 1] = 1
sintheta[sintheta < -1] = -1
varphi = numpy.arccos(cosphi)
theta = numpy.arccos(costheta)
theta[sintheta < 0] = 2 * numpy.pi - theta[sintheta < 0]
ylmref = []
for l in range(lmax + 1):
ylm = numpy.empty((l * 2 + 1, ngrid))
ylm[l] = scipy.special.sph_harm(0, l, theta, varphi).real
for m in range(1, l + 1):
f1 = scipy.special.sph_harm(-m, l, theta, varphi)
f2 = scipy.special.sph_harm(m, l, theta, varphi)
# complex to real spherical functions
if m % 2 == 1:
ylm[l - m] = (-f1.imag - f2.imag) / numpy.sqrt(2)
ylm[l + m] = (f1.real - f2.real) / numpy.sqrt(2)
else:
ylm[l - m] = (-f1.imag + f2.imag) / numpy.sqrt(2)
ylm[l + m] = (f1.real + f2.real) / numpy.sqrt(2)
if l == 1:
ylm = ylm[[2, 0, 1]]
ylmref.append(ylm)
ylmref = numpy.vstack(ylmref)
ylm = numpy.vstack(sph.real_sph_vec(r, lmax, True))
self.assertTrue(abs(ylmref - ylm).max() < 1e-14)
def test_real_sph_vec(self):
r = numpy.random.random((5,3))
ref = real_sph_ref(r, 5)
ylm = sph.real_sph_vec(r, 5)
self.assertAlmostEqual(abs(ref - numpy.vstack(ylm).T).max(), 0, 14)
def test_B1(self):
def getB(mol):
pcm = ddcosmo.DDCOSMO(mol)
pcm.lmax = 2
pcm.eps = 0
natm = mol.natm
nao = mol.nao
nlm = (pcm.lmax + 1)**2
r_vdw = ddcosmo.get_atomic_radii(pcm)
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
pcm.grids = grids = dft.gen_grid.Grids(mol).run(level=0)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcm.lebedev_order)
ylm_1sph = numpy.vstack(
sph.real_sph_vec(coords_1sph, pcm.lmax, True))
cached_pol = ddcosmo.cache_fake_multipoles(grids, r_vdw, pcm.lmax)
L = ddcosmo.make_L(pcm, r_vdw, ylm_1sph, fi)
return make_B(pcm, r_vdw, ui, ylm_1sph, cached_pol, L)
pcm = ddcosmo.DDCOSMO(mol0)
pcm.lmax = 2
pcm.eps = 0
natm = mol0.natm
nao = mol0.nao
nlm = (pcm.lmax + 1)**2
r_vdw = ddcosmo.get_atomic_radii(pcm)
fi = ddcosmo.make_fi(pcm, r_vdw)
ui = 1 - fi
ui[ui < 0] = 0
pcm.grids = grids = dft.gen_grid.Grids(mol0).run(level=0)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcm.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcm.lmax, True))
cached_pol = ddcosmo.cache_fake_multipoles(grids, r_vdw, pcm.lmax)
L = ddcosmo.make_L(pcm, r_vdw, ylm_1sph, fi)
dB = make_B1(pcm, r_vdw, ui, ylm_1sph, cached_pol, L)
B1 = getB(mol1)
B2 = getB(mol2)
self.assertAlmostEqual(abs((B2 - B1) / dx - dB[0, 2]).max(), 0, 8)
nao = mol0.nao
numpy.random.seed(1)
dm1 = numpy.random.random((2, nao, nao))
dm2 = numpy.random.random((2, nao, nao))
dm = dm1[0]
ref = numpy.einsum('azpqrs,npq->nazrs', dB, dm1)
v = B1_dot_x(pcm, dm, r_vdw, ui, ylm_1sph, cached_pol, L)
self.assertAlmostEqual(abs(v - ref[0]).max(), 0, 12)
de = _ddcosmo_tdscf_grad._grad_ee(pcm, dm1, dm2, r_vdw, ui, ylm_1sph,
cached_pol, L)
ref = numpy.einsum('nazij,nij->naz', ref, dm2)
self.assertAlmostEqual(abs(de - ref).max(), 0, 12)
numpy.random.seed(1)
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
ref = ddcosmo_grad.kernel(pcm, dm)
dielectric = pcm.eps
if dielectric > 0:
f_epsilon = (dielectric - 1.) / dielectric
else:
f_epsilon = 1
de = _ddcosmo_tdscf_grad._grad_nn(pcm, r_vdw, ui, ylm_1sph, cached_pol,
L)
de += _ddcosmo_tdscf_grad._grad_ne(pcm, dm, r_vdw, ui, ylm_1sph,
cached_pol, L)
de += .5 * _ddcosmo_tdscf_grad._grad_ee(pcm, dm, dm, r_vdw, ui,
ylm_1sph, cached_pol, L)
de *= .5 * f_epsilon
self.assertAlmostEqual(abs(de - ref).max(), 0, 12)
def make_phi1(pcmobj, dm, r_vdw, ui):
mol = pcmobj.mol
natm = mol.natm
nlm = (pcmobj.lmax+1)**2
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
dm = dm[0] + dm[1]
tril_dm = lib.pack_tril(dm+dm.T)
nao = dm.shape[0]
diagidx = numpy.arange(nao)
diagidx = diagidx*(diagidx+1)//2 + diagidx
tril_dm[diagidx] *= .5
atom_coords = mol.atom_coords()
atom_charges = mol.atom_charges()
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
extern_point_idx = ui > 0
fi1 = make_fi1(pcmobj, pcmobj.get_atomic_radii())
fi1[:,:,ui==0] = 0
ui1 = -fi1
ngrid_1sph = weights_1sph.size
v_phi0 = numpy.empty((natm,ngrid_1sph))
for ia in range(natm):
cav_coords = atom_coords[ia] + r_vdw[ia] * coords_1sph
d_rs = atom_coords.reshape(-1,1,3) - cav_coords
v_phi0[ia] = numpy.einsum('z,zp->p', atom_charges, 1./lib.norm(d_rs,axis=2))
phi1 = -numpy.einsum('n,ln,azjn,jn->azjl', weights_1sph, ylm_1sph, ui1, v_phi0)
for ia in range(natm):
cav_coords = atom_coords[ia] + r_vdw[ia] * coords_1sph
for ja in range(natm):
rs = atom_coords[ja] - cav_coords
d_rs = lib.norm(rs, axis=1)
v_phi = atom_charges[ja] * numpy.einsum('px,p->px', rs, 1./d_rs**3)
tmp = numpy.einsum('n,ln,n,nx->xl', weights_1sph, ylm_1sph, ui[ia], v_phi)
phi1[ja,:,ia] += tmp # response of the other atoms
phi1[ia,:,ia] -= tmp # response of cavity grids
int3c2e = mol._add_suffix('int3c2e')
int3c2e_ip1 = mol._add_suffix('int3c2e_ip1')
aoslices = mol.aoslice_by_atom()
for ia in range(natm):
cav_coords = atom_coords[ia] + r_vdw[ia] * coords_1sph
#fakemol = gto.fakemol_for_charges(cav_coords[ui[ia]>0])
fakemol = gto.fakemol_for_charges(cav_coords)
v_nj = df.incore.aux_e2(mol, fakemol, intor=int3c2e, aosym='s1')
v_phi = numpy.einsum('ij,ijk->k', dm, v_nj)
phi1[:,:,ia] += numpy.einsum('n,ln,azn,n->azl', weights_1sph, ylm_1sph, ui1[:,:,ia], v_phi)
v_e1_nj = df.incore.aux_e2(mol, fakemol, intor=int3c2e_ip1, comp=3, aosym='s1')
v_e2_nj = v_e1_nj + v_e1_nj.transpose(0,2,1,3)
phi1_e2_nj = numpy.einsum('ji,xijr->xr', dm, v_e2_nj)
phi1[ia,:,ia] += numpy.einsum('n,ln,n,xn->xl', weights_1sph, ylm_1sph, ui[ia], phi1_e2_nj)
for ja in range(natm):
shl0, shl1, p0, p1 = aoslices[ja]
phi1_nj = numpy.einsum('ij,xijr->xr', dm[p0:p1 ], v_e1_nj[:,p0:p1])
phi1_nj += numpy.einsum('ji,xijr->xr', dm[:,p0:p1], v_e1_nj[:,p0:p1])
phi1[ja,:,ia] -= numpy.einsum('n,ln,n,xn->xl', weights_1sph, ylm_1sph, ui[ia], phi1_nj)
return phi1
def make_phi(pcmobj, dm, r_vdw, ui):
'''
Eq. (13) g_j
'''
mol = pcmobj.mol
natm = mol.natm
natm_tot = natm
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
ngrid_1sph = coords_1sph.shape[0]
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
dm = dm[0] + dm[1]
tril_dm = lib.pack_tril(dm + dm.T)
nao = dm.shape[0]
diagidx = numpy.arange(nao)
diagidx = diagidx * (diagidx + 1) // 2 + diagidx
tril_dm[diagidx] *= .5
atom_coords = mol.atom_coords()
atom_charges = list(mol.atom_charges()) # list
# An apparent surface charge (ASC) on Gamma: the surface area of the whole system (QM + MM)
# \sigma_j (s) = \sum_lm X_j^{lm} Y_lm (s)
#
if pcmobj.mm_mol is not None:
atom_coords = numpy.vstack((atom_coords, pcmobj.mm_mol.atom_coords()))
atom_charges += list(pcmobj.mm_mol.atom_charges()) # list
natm_tot += pcmobj.mm_mol.natm
cav_coords = (atom_coords.reshape(natm_tot, 1, 3) +
numpy.einsum('r,gx->rgx', r_vdw, coords_1sph))
v_phi = numpy.empty((natm_tot, ngrid_1sph))
for ia in range(natm_tot):
# Note (-) sign is not applied to atom_charges, because (-) is explicitly
# included in rhs and L matrix
d_rs = atom_coords.reshape(-1, 1, 3) - cav_coords[ia]
v_phi[ia] = numpy.einsum('z,zp->p', atom_charges,
1. / lib.norm(d_rs, axis=2))
max_memory = pcmobj.max_memory - lib.current_memory()[0]
blksize = int(max(max_memory * 1e6 / 8 / nao**2, 400))
# from the electronic density of QM
extern_point_idx = ui > 0
cav_coords = cav_coords[extern_point_idx]
v_phi_e = numpy.empty(cav_coords.shape[0])
int3c2e = mol._add_suffix('int3c2e')
cintopt = gto.moleintor.make_cintopt(mol._atm, mol._bas, mol._env, int3c2e)
for i0, i1 in lib.prange(0, cav_coords.shape[0], blksize):
fakemol = gto.fakemol_for_charges(cav_coords[i0:i1])
v_nj = df.incore.aux_e2(mol,
fakemol,
intor=int3c2e,
aosym='s2ij',
cintopt=cintopt)
v_phi_e[i0:i1] = numpy.einsum('x,xk->k', tril_dm, v_nj)
v_phi[extern_point_idx] -= v_phi_e
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
# Eq(13)
phi = -numpy.einsum('n,xn,jn,jn->jx', weights_1sph, ylm_1sph, ui, v_phi)
return phi
from pyscf import mcscf
from pyscf import cc
mol = gto.M(atom='H 0 0 0; H 0 1 1.2; H 1. .1 0; H .5 .5 1')
natm = mol.natm
r_vdw = [radii.VDW[gto.charge(mol.atom_symbol(i))]
for i in range(natm)]
r_vdw = numpy.asarray(r_vdw)
pcmobj = DDCOSMO(mol)
pcmobj.regularize_xt = lambda t, eta, scale: regularize_xt(t, eta)
pcmobj.lebedev_order = 7
pcmobj.lmax = 6
pcmobj.eta = 0.1
nlm = (pcmobj.lmax+1)**2
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
fi = make_fi(pcmobj, r_vdw)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
L = make_L(pcmobj, r_vdw, ylm_1sph, fi)
print(lib.finger(L) - 6.2823493771037473)
mol = gto.Mole()
mol.atom = ''' O 0.00000000 0.00000000 -0.11081188
H -0.00000000 -0.84695236 0.59109389
H -0.00000000 0.89830571 0.52404783 '''
mol.basis = '3-21g' #cc-pvdz'
mol.build()
cm = DDCOSMO(mol)
cm.verbose = 4
mf = ddcosmo_for_scf(scf.RHF(mol), cm)#.newton()
mf.verbose = 4
print(mf.kernel() - -75.570364368059)
cm.verbose = 3
def make_phi1(pcmobj, dm, r_vdw, ui):
mol = pcmobj.mol
natm = mol.natm
nlm = (pcmobj.lmax+1)**2
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
dm = dm[0] + dm[1]
tril_dm = lib.pack_tril(dm+dm.T)
nao = dm.shape[0]
diagidx = numpy.arange(nao)
diagidx = diagidx*(diagidx+1)//2 + diagidx
tril_dm[diagidx] *= .5
atom_coords = mol.atom_coords()
atom_charges = mol.atom_charges()
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
extern_point_idx = ui > 0
fi1 = make_fi1(pcmobj, pcmobj.get_atomic_radii())
fi1[:,:,ui==0] = 0
ui1 = -fi1
ngrid_1sph = weights_1sph.size
v_phi0 = numpy.empty((natm,ngrid_1sph))
for ia in range(natm):
cav_coords = atom_coords[ia] + r_vdw[ia] * coords_1sph
d_rs = atom_coords.reshape(-1,1,3) - cav_coords
v_phi0[ia] = numpy.einsum('z,zp->p', atom_charges, 1./lib.norm(d_rs,axis=2))
phi1 = -numpy.einsum('n,ln,azjn,jn->azjl', weights_1sph, ylm_1sph, ui1, v_phi0)
for ia in range(natm):
cav_coords = atom_coords[ia] + r_vdw[ia] * coords_1sph
for ja in range(natm):
rs = atom_coords[ja] - cav_coords
d_rs = lib.norm(rs, axis=1)
v_phi = atom_charges[ja] * numpy.einsum('px,p->px', rs, 1./d_rs**3)
tmp = numpy.einsum('n,ln,n,nx->xl', weights_1sph, ylm_1sph, ui[ia], v_phi)
phi1[ja,:,ia] += tmp # response of the other atoms
phi1[ia,:,ia] -= tmp # response of cavity grids
int3c2e = mol._add_suffix('int3c2e')
int3c2e_ip1 = mol._add_suffix('int3c2e_ip1')
aoslices = mol.aoslice_by_atom()
for ia in range(natm):
cav_coords = atom_coords[ia] + r_vdw[ia] * coords_1sph
#fakemol = gto.fakemol_for_charges(cav_coords[ui[ia]>0])
fakemol = gto.fakemol_for_charges(cav_coords)
v_nj = df.incore.aux_e2(mol, fakemol, intor=int3c2e, aosym='s1')
v_phi = numpy.einsum('ij,ijk->k', dm, v_nj)
phi1[:,:,ia] += numpy.einsum('n,ln,azn,n->azl', weights_1sph, ylm_1sph, ui1[:,:,ia], v_phi)
v_e1_nj = df.incore.aux_e2(mol, fakemol, intor=int3c2e_ip1, comp=3, aosym='s1')
v_e2_nj = v_e1_nj + v_e1_nj.transpose(0,2,1,3)
phi1_e2_nj = numpy.einsum('ji,xijr->xr', dm, v_e2_nj)
phi1[ia,:,ia] += numpy.einsum('n,ln,n,xn->xl', weights_1sph, ylm_1sph, ui[ia], phi1_e2_nj)
for ja in range(natm):
shl0, shl1, p0, p1 = aoslices[ja]
phi1_nj = numpy.einsum('ij,xijr->xr', dm[p0:p1 ], v_e1_nj[:,p0:p1])
phi1_nj += numpy.einsum('ji,xijr->xr', dm[:,p0:p1], v_e1_nj[:,p0:p1])
phi1[ja,:,ia] -= numpy.einsum('n,ln,n,xn->xl', weights_1sph, ylm_1sph, ui[ia], phi1_nj)
return phi1
from pyscf import mcscf
from pyscf import cc
mol = gto.M(atom='H 0 0 0; H 0 1 1.2; H 1. .1 0; H .5 .5 1')
natm = mol.natm
r_vdw = [radii.VDW[gto.charge(mol.atom_symbol(i))]
for i in range(natm)]
r_vdw = numpy.asarray(r_vdw)
pcmobj = DDCOSMO(mol)
pcmobj.regularize_xt = lambda t, eta, scale: regularize_xt(t, eta)
pcmobj.lebedev_order = 7
pcmobj.lmax = 6
pcmobj.eta = 0.1
nlm = (pcmobj.lmax+1)**2
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
fi = make_fi(pcmobj, r_vdw)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, pcmobj.lmax, True))
L = make_L(pcmobj, r_vdw, ylm_1sph, fi)
print(lib.finger(L) - 6.2823493771037473)
mol = gto.Mole()
mol.atom = ''' O 0.00000000 0.00000000 -0.11081188
H -0.00000000 -0.84695236 0.59109389
H -0.00000000 0.89830571 0.52404783 '''
mol.basis = '3-21g' #cc-pvdz'
mol.build()
cm = DDCOSMO(mol)
cm.verbose = 4
mf = ddcosmo_for_scf(scf.RHF(mol), cm)#.newton()
mf.verbose = 4
print(mf.kernel() - -75.570364368059)
cm.verbose = 3
def tda_grad(td, z):
'''ddcosmo TDA gradients'''
mol = td.mol
mf = td._scf
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
nocc = (mo_occ > 0).sum()
nvir = nmo - nocc
z = z[0].reshape(nocc, nvir).T * numpy.sqrt(2)
orbv = mo_coeff[:, nocc:]
orbo = mo_coeff[:, :nocc]
r_vdw = ddcosmo.get_atomic_radii(td.with_solvent)
fi = ddcosmo.make_fi(td.with_solvent, r_vdw)
ui = 1 - fi
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
td.with_solvent.lebedev_order)
ylm_1sph = numpy.vstack(
sph.real_sph_vec(coords_1sph, td.with_solvent.lmax, True))
grids = td.with_solvent.grids
cached_pol = ddcosmo.cache_fake_multipoles(grids, r_vdw,
td.with_solvent.lmax)
L = ddcosmo.make_L(td.with_solvent, r_vdw, ylm_1sph, fi)
def fvind(x):
v_mo = numpy.einsum('iabj,xai->xbj', g[:nocc, nocc:, nocc:, :nocc], x)
v_mo += numpy.einsum('aibj,xai->xbj', g[nocc:, :nocc, nocc:, :nocc], x)
return v_mo
h1 = rhf_grad.get_hcore(mol)
s1 = rhf_grad.get_ovlp(mol)
eri1 = -mol.intor('int2e_ip1', aosym='s1', comp=3)
eri1 = eri1.reshape(3, nao, nao, nao, nao)
eri0 = ao2mo.kernel(mol, mo_coeff)
eri0 = ao2mo.restore(1, eri0, nmo).reshape(nmo, nmo, nmo, nmo)
g = eri0 * 2 - eri0.transpose(0, 3, 2, 1)
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:, :nocc] = mo_energy[:nocc]
zeta[:nocc, nocc:] = mo_energy[nocc:]
dielectric = td.with_solvent.eps
if dielectric > 0:
f_epsilon = (dielectric - 1.) / dielectric
else:
f_epsilon = 1
pcm_nuc = .5 * f_epsilon * nuc_part1(td.with_solvent, r_vdw, ui, ylm_1sph,
cached_pol, L)
B0 = .5 * f_epsilon * make_B(td.with_solvent, r_vdw, ui, ylm_1sph,
cached_pol, L)
B0 = lib.einsum('pqrs,pi,qj,rk,sl->ijkl', B0, mo_coeff, mo_coeff, mo_coeff,
mo_coeff)
g += B0 * 2
B1 = .5 * f_epsilon * make_B1(td.with_solvent, r_vdw, ui, ylm_1sph,
cached_pol, L)
offsetdic = mol.offset_nr_by_atom()
de = numpy.zeros((mol.natm, 3))
for ia in range(mol.natm):
shl0, shl1, p0, p1 = offsetdic[ia]
mol.set_rinv_origin(mol.atom_coord(ia))
h1ao = -mol.atom_charge(ia) * mol.intor('int1e_iprinv', comp=3)
h1ao[:, p0:p1] += h1[:, p0:p1]
h1ao = h1ao + h1ao.transpose(0, 2, 1)
h1ao += pcm_nuc[ia]
h1mo = numpy.einsum('pi,xpq,qj->xij', mo_coeff, h1ao, mo_coeff)
s1mo = numpy.einsum('pi,xpq,qj->xij', mo_coeff[p0:p1], s1[:, p0:p1],
mo_coeff)
s1mo = s1mo + s1mo.transpose(0, 2, 1)
f1 = h1mo - numpy.einsum('xpq,pq->xpq', s1mo, zeta)
f1 -= numpy.einsum('klpq,xlk->xpq', g[:nocc, :nocc],
s1mo[:, :nocc, :nocc])
eri1a = eri1.copy()
eri1a[:, :p0] = 0
eri1a[:, p1:] = 0
eri1a = eri1a + eri1a.transpose(0, 2, 1, 3, 4)
eri1a = eri1a + eri1a.transpose(0, 3, 4, 1, 2)
g1 = lib.einsum('xpqrs,pi,qj,rk,sl->xijkl', eri1a, mo_coeff, mo_coeff,
mo_coeff, mo_coeff)
tmp1 = lib.einsum('xpqrs,pi,qj,rk,sl->xijkl', B1[ia], mo_coeff,
mo_coeff, mo_coeff, mo_coeff)
g1 = g1 * 2 - g1.transpose(0, 1, 4, 3, 2)
g1 += tmp1 * 2
f1 += numpy.einsum('xkkpq->xpq', g1[:, :nocc, :nocc])
f1ai = f1[:, nocc:, :nocc].copy()
c1 = s1mo * -.5
c1vo = cphf.solve(fvind, mo_energy, mo_occ, f1ai, max_cycle=50)[0]
c1[:, nocc:, :nocc] = c1vo
c1[:, :nocc,
nocc:] = -(s1mo[:, nocc:, :nocc] + c1vo).transpose(0, 2, 1)
f1 += numpy.einsum('kapq,xak->xpq', g[:nocc, nocc:], c1vo)
f1 += numpy.einsum('akpq,xak->xpq', g[nocc:, :nocc], c1vo)
e1 = numpy.einsum('xaijb,ai,bj->x', g1[:, nocc:, :nocc, :nocc, nocc:],
z, z)
e1 += numpy.einsum('xab,ai,bi->x', f1[:, nocc:, nocc:], z, z)
e1 -= numpy.einsum('xij,ai,aj->x', f1[:, :nocc, :nocc], z, z)
g1 = numpy.einsum('pjkl,xpi->xijkl', g, c1)
g1 += numpy.einsum('ipkl,xpj->xijkl', g, c1)
g1 += numpy.einsum('ijpl,xpk->xijkl', g, c1)
g1 += numpy.einsum('ijkp,xpl->xijkl', g, c1)
e1 += numpy.einsum('xaijb,ai,bj->x', g1[:, nocc:, :nocc, :nocc, nocc:],
z, z)
de[ia] = e1
return de
