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
def get_pp(mydf, kpts=None):
'''Get the periodic pseudotential nuc-el AO matrix, with G=0 removed.
'''
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1, 3))
else:
kpts_lst = numpy.reshape(kpts, (-1, 3))
gs = mydf.gs
SI = cell.get_SI()
Gv = cell.get_Gv(gs)
vpplocG = pseudo.get_vlocG(cell, Gv)
vpplocG = -numpy.einsum('ij,ij->j', SI, vpplocG)
vpplocG[0] = numpy.sum(
pseudo.get_alphas(cell)) # from get_jvloc_G0 function
ngs = len(vpplocG)
# vpploc evaluated in real-space
vpplocR = tools.ifft(vpplocG, cell.gs).real
vpp = [
lib.dot(aoR.T.conj() * vpplocR, aoR)
for k, aoR in mydf.aoR_loop(gs, kpts_lst)
]
# vppnonloc evaluated in reciprocal space
fakemol = gto.Mole()
fakemol._atm = numpy.zeros((1, gto.ATM_SLOTS), dtype=numpy.int32)
fakemol._bas = numpy.zeros((1, gto.BAS_SLOTS), dtype=numpy.int32)
ptr = gto.PTR_ENV_START
fakemol._env = numpy.zeros(ptr + 10)
fakemol._bas[0, gto.NPRIM_OF] = 1
fakemol._bas[0, gto.NCTR_OF] = 1
fakemol._bas[0, gto.PTR_EXP] = ptr + 3
fakemol._bas[0, gto.PTR_COEFF] = ptr + 4
# buf for SPG_lmi upto l=0..3 and nl=3
buf = numpy.empty((48, ngs), dtype=numpy.complex128)
def vppnl_by_k(kpt):
Gk = Gv + kpt
G_rad = lib.norm(Gk, axis=1)
aokG = ft_ao.ft_ao(cell, Gv, kpt=kpt) * (ngs / cell.vol)
vppnl = 0
for ia in range(cell.natm):
symb = cell.atom_symbol(ia)
if symb not in cell._pseudo:
continue
pp = cell._pseudo[symb]
p1 = 0
for l, proj in enumerate(pp[5:]):
rl, nl, hl = proj
if nl > 0:
fakemol._bas[0, gto.ANG_OF] = l
fakemol._env[ptr + 3] = .5 * rl**2
fakemol._env[ptr + 4] = rl**(l + 1.5) * numpy.pi**1.25
pYlm_part = dft.numint.eval_ao(fakemol, Gk, deriv=0)
p0, p1 = p1, p1 + nl * (l * 2 + 1)
# pYlm is real, SI[ia] is complex
pYlm = numpy.ndarray((nl, l * 2 + 1, ngs),
dtype=numpy.complex128,
buffer=buf[p0:p1])
for k in range(nl):
qkl = pseudo.pp._qli(G_rad * rl, l, k)
pYlm[k] = pYlm_part.T * qkl
#:SPG_lmi = numpy.einsum('g,nmg->nmg', SI[ia].conj(), pYlm)
#:SPG_lm_aoG = numpy.einsum('nmg,gp->nmp', SPG_lmi, aokG)
#:tmp = numpy.einsum('ij,jmp->imp', hl, SPG_lm_aoG)
#:vppnl += numpy.einsum('imp,imq->pq', SPG_lm_aoG.conj(), tmp)
if p1 > 0:
SPG_lmi = buf[:p1]
SPG_lmi *= SI[ia].conj()
SPG_lm_aoGs = lib.zdot(SPG_lmi, aokG)
p1 = 0
for l, proj in enumerate(pp[5:]):
rl, nl, hl = proj
if nl > 0:
p0, p1 = p1, p1 + nl * (l * 2 + 1)
hl = numpy.asarray(hl)
SPG_lm_aoG = SPG_lm_aoGs[p0:p1].reshape(
nl, l * 2 + 1, -1)
tmp = numpy.einsum('ij,jmp->imp', hl, SPG_lm_aoG)
vppnl += numpy.einsum('imp,imq->pq', SPG_lm_aoG.conj(),
tmp)
return vppnl * (1. / ngs**2)
for k, kpt in enumerate(kpts_lst):
vppnl = vppnl_by_k(kpt)
if gamma_point(kpt):
vpp[k] = vpp[k].real + vppnl.real
else:
vpp[k] += vppnl
if kpts is None or numpy.shape(kpts) == (3, ):
vpp = vpp[0]
return numpy.asarray(vpp)
def get_pp(mydf, kpts=None):
"""Get the periodic pseudotential nuc-el AO matrix, with G=0 removed.
"""
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1, 3))
else:
kpts_lst = numpy.reshape(kpts, (-1, 3))
gs = mydf.gs
SI = cell.get_SI()
Gv = cell.get_Gv(gs)
vpplocG = pseudo.get_vlocG(cell, Gv)
vpplocG = -numpy.einsum("ij,ij->j", SI, vpplocG)
vpplocG[0] = numpy.sum(pseudo.get_alphas(cell)) # from get_jvloc_G0 function
ngs = len(vpplocG)
nao = cell.nao_nr()
# vpploc evaluated in real-space
vpplocR = tools.ifft(vpplocG, cell.gs).real
vpp = [lib.dot(aoR.T.conj() * vpplocR, aoR) for k, aoR in mydf.aoR_loop(gs, kpts_lst)]
# vppnonloc evaluated in reciprocal space
fakemol = gto.Mole()
fakemol._atm = numpy.zeros((1, gto.ATM_SLOTS), dtype=numpy.int32)
fakemol._bas = numpy.zeros((1, gto.BAS_SLOTS), dtype=numpy.int32)
ptr = gto.PTR_ENV_START
fakemol._env = numpy.zeros(ptr + 10)
fakemol._bas[0, gto.NPRIM_OF] = 1
fakemol._bas[0, gto.NCTR_OF] = 1
fakemol._bas[0, gto.PTR_EXP] = ptr + 3
fakemol._bas[0, gto.PTR_COEFF] = ptr + 4
def vppnl_by_k(kpt):
Gk = Gv + kpt
G_rad = lib.norm(Gk, axis=1)
aokG = ft_ao.ft_ao(cell, Gv, kpt=kpt) * (ngs / cell.vol)
vppnl = 0
for ia in range(cell.natm):
symb = cell.atom_symbol(ia)
if symb not in cell._pseudo:
continue
pp = cell._pseudo[symb]
for l, proj in enumerate(pp[5:]):
rl, nl, hl = proj
if nl > 0:
hl = numpy.asarray(hl)
fakemol._bas[0, gto.ANG_OF] = l
fakemol._env[ptr + 3] = 0.5 * rl ** 2
fakemol._env[ptr + 4] = rl ** (l + 1.5) * numpy.pi ** 1.25
pYlm_part = dft.numint.eval_ao(fakemol, Gk, deriv=0)
pYlm = numpy.empty((nl, l * 2 + 1, ngs))
for k in range(nl):
qkl = pseudo.pp._qli(G_rad * rl, l, k)
pYlm[k] = pYlm_part.T * qkl
# pYlm is real
SPG_lmi = numpy.einsum("g,nmg->nmg", SI[ia].conj(), pYlm)
SPG_lm_aoG = numpy.einsum("nmg,gp->nmp", SPG_lmi, aokG)
tmp = numpy.einsum("ij,jmp->imp", hl, SPG_lm_aoG)
vppnl += numpy.einsum("imp,imq->pq", SPG_lm_aoG.conj(), tmp)
return vppnl * (1.0 / ngs ** 2)
for k, kpt in enumerate(kpts_lst):
vppnl = vppnl_by_k(kpt)
if abs(kpt).sum() < 1e-9: # gamma_point
vpp[k] = vpp[k].real + vppnl.real
else:
vpp[k] += vppnl
if kpts is None or numpy.shape(kpts) == (3,):
vpp = vpp[0]
return vpp
def get_jvloc_G0(cell, kpt=None):
'''Get the (separately) divergent Hartree + Vloc G=0 contribution.'''
return 1./cell.vol * np.sum(pseudo.get_alphas(cell)) * get_ovlp(cell, kpt)
