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 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 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 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 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 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_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_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 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_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 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 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 = ddcosmo.get_atomic_radii(self)
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
self.lebedev_order)
ylm_1sph = numpy.vstack(sph.real_sph_vec(coords_1sph, lmax, True))
fi = ddcosmo.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 = ddcosmo.make_L(self, r_vdw, ylm_1sph, fi)
Lmat = Lmat.reshape(natm * nlm, -1)
Amat = make_A(self, r_vdw, ylm_1sph, ui).reshape(natm * nlm, -1)
fac = 2 * numpy.pi * (self.eps + 1) / (self.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(self.grids, r_vdw, lmax)
self._intermediates = {
'r_vdw': r_vdw,
'ylm_1sph': ylm_1sph,
'ui': ui,
'Lmat': Lmat,
'A_diele': A_diele,
'A_inf': A_inf,
'cached_pol': cached_pol,
}
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 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 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
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)