def get_pp(cell, kpt=np.zeros(3)):
'''Get the periodic pseudotential nuc-el AO matrix, with G=0 removed.
'''
coords = gen_grid.gen_uniform_grids(cell)
aoR = numint.eval_ao(cell, coords, kpt)
nao = cell.nao_nr()
SI = cell.get_SI()
vlocG = pseudo.get_vlocG(cell)
vlocG[:, 0] = 0
vpplocG = -np.sum(SI * vlocG, axis=0)
# vpploc evaluated in real-space
vpplocR = tools.ifft(vpplocG, cell.mesh)
vpploc = np.dot(aoR.T.conj(), vpplocR.reshape(-1, 1) * aoR)
# vppnonloc evaluated in reciprocal space
aokG = np.empty(aoR.shape, np.complex128)
expmikr = np.exp(-1j * np.dot(coords, kpt))
for i in range(nao):
aokG[:, i] = tools.fftk(aoR[:, i], cell.mesh, expmikr)
ngrids = len(aokG)
vppnl = np.zeros((nao, nao), dtype=np.complex128)
hs, projGs = pseudo.get_projG(cell, kpt)
for ia, [h_ia, projG_ia] in enumerate(zip(hs, projGs)):
for l, h in enumerate(h_ia):
nl = h.shape[0]
for m in range(-l, l + 1):
SPG_lm_aoG = np.zeros((nl, nao), dtype=np.complex128)
for i in range(nl):
SPG_lmi = SI[ia, :] * projG_ia[l][m][i]
SPG_lm_aoG[i, :] = np.einsum('g,gp->p', SPG_lmi.conj(),
aokG)
for i in range(nl):
for j in range(nl):
# Note: There is no (-1)^l here.
vppnl += h[i, j] * np.einsum('p,q->pq',
SPG_lm_aoG[i, :].conj(),
SPG_lm_aoG[j, :])
vppnl *= (1. / ngrids**2)
ovlp = cell.pbc_intor('int1e_ovlp_sph', hermi=1, kpts=kpt)
vpploc += 1. / cell.vol * np.sum(pseudo.get_alphas(cell)) * ovlp
return vpploc + vppnl
def get_pp(cell, kpt=np.zeros(3)):
'''Get the periodic pseudotential nuc-el AO matrix, with G=0 removed.
'''
coords = gen_grid.gen_uniform_grids(cell)
aoR = numint.eval_ao(cell, coords, kpt)
nao = cell.nao_nr()
SI = cell.get_SI()
vlocG = pseudo.get_vlocG(cell)
vlocG[:,0] = 0
vpplocG = -np.sum(SI * vlocG, axis=0)
# vpploc evaluated in real-space
vpplocR = tools.ifft(vpplocG, cell.mesh)
vpploc = np.dot(aoR.T.conj(), vpplocR.reshape(-1,1)*aoR)
# vppnonloc evaluated in reciprocal space
aokG = np.empty(aoR.shape, np.complex128)
expmikr = np.exp(-1j*np.dot(coords,kpt))
for i in range(nao):
aokG[:,i] = tools.fftk(aoR[:,i], cell.mesh, expmikr)
ngrids = len(aokG)
vppnl = np.zeros((nao,nao), dtype=np.complex128)
hs, projGs = pseudo.get_projG(cell, kpt)
for ia, [h_ia,projG_ia] in enumerate(zip(hs,projGs)):
for l, h in enumerate(h_ia):
nl = h.shape[0]
for m in range(-l,l+1):
SPG_lm_aoG = np.zeros((nl,nao), dtype=np.complex128)
for i in range(nl):
SPG_lmi = SI[ia,:] * projG_ia[l][m][i]
SPG_lm_aoG[i,:] = np.einsum('g,gp->p', SPG_lmi.conj(), aokG)
for i in range(nl):
for j in range(nl):
# Note: There is no (-1)^l here.
vppnl += h[i,j]*np.einsum('p,q->pq',
SPG_lm_aoG[i,:].conj(),
SPG_lm_aoG[j,:])
vppnl *= (1./ngrids**2)
ovlp = cell.pbc_intor('int1e_ovlp_sph', hermi=1, kpts=kpt)
vpploc += 1./cell.vol * np.sum(pseudo.get_alphas(cell)) * ovlp
return vpploc + vppnl