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 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
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 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 _B_dot_x(self, dm):
'''
Compute the matrix-vector product B * x. The B matrix, as defined in
the paper R. Cammi, JPCA, 104, 5631 (2000), is the second order
derivatives of E_solvation wrt density matrices.
Note: In ddCOSMO, strictly, B is not symmetric. To make it compatible
with the CIS framework, it is symmetrized in current implementation.
'''
if not self._intermediates or self.grids.coords is None:
self.build()
mol = self.mol
r_vdw = self._intermediates['r_vdw']
ylm_1sph = self._intermediates['ylm_1sph']
ui = self._intermediates['ui']
Lmat = self._intermediates['Lmat']
A_diele = self._intermediates['A_diele']
A_inf = self._intermediates['A_inf']
cached_pol = self._intermediates['cached_pol']
natm = mol.natm
nlm = (self.lmax + 1)**2
phi = ddcosmo.make_phi(self, dm, r_vdw, ui, ylm_1sph, with_nuc=False)
phi = numpy.linalg.solve(A_diele,
A_inf.dot(phi.reshape(-1, natm * nlm).T))
Xvec = numpy.linalg.solve(Lmat, phi)
Xvec = Xvec.reshape(natm, nlm, -1).transpose(2, 0, 1)
vmat = ddcosmo.make_psi_vmat(self,
dm,
r_vdw,
ui,
ylm_1sph,
cached_pol,
Xvec,
Lmat,
with_nuc=False)[1]
dielectric = self.eps
f_epsilon = (dielectric - 1.) / dielectric
return .5 * f_epsilon * vmat
