def get_hcore(cell, kpts):
'''Part of the nuclear gradients of core Hamiltonian'''
h1 = np.asarray(cell.pbc_intor('int1e_ipkin', kpts=kpts))
dtype = h1.dtype
if cell._pseudo:
SI = cell.get_SI()
nao = cell.nao_nr()
Gv = cell.Gv
natom = cell.natm
coords = cell.get_uniform_grids()
ngrids, nkpts = len(coords), len(kpts)
vlocG = get_vlocG(cell)
vpplocG = -np.einsum('ij,ij->j', SI, vlocG)
vpplocG[0] = np.sum(get_alphas(cell))
vpplocR = tools.ifft(vpplocG, cell.mesh).real
fakemol = _make_fakemol()
ptr = mole.PTR_ENV_START
for kn, kpt in enumerate(kpts):
aos = eval_ao_kpts(cell, coords, kpt, deriv=1)[0]
vloc = np.einsum('agi,g,gj->aij', aos[1:].conj(), vpplocR, aos[0])
expir = np.exp(-1j * np.dot(coords, kpt))
aokG = np.asarray([
tools.fftk(np.asarray(ao.T, order='C'), cell.mesh, expir).T
for ao in aos
])
Gk = Gv + kpt
G_rad = lib.norm(Gk, axis=1)
vnl = np.zeros(vloc.shape, dtype=np.complex128)
for ia in range(natom):
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 = np.asarray(hl)
fakemol._bas[0, mole.ANG_OF] = l
fakemol._env[ptr + 3] = .5 * rl**2
fakemol._env[ptr + 4] = rl**(l + 1.5) * np.pi**1.25
pYlm_part = fakemol.eval_gto('GTOval', Gk)
pYlm = np.empty((nl, l * 2 + 1, ngrids))
for k in range(nl):
qkl = _qli(G_rad * rl, l, k)
pYlm[k] = pYlm_part.T * qkl
SPG_lmi = np.einsum('g,nmg->nmg', SI[ia].conj(), pYlm)
SPG_lm_aoG = np.einsum('nmg,agp->anmp', SPG_lmi, aokG)
tmp = np.einsum('ij,ajmp->aimp', hl, SPG_lm_aoG[1:])
vnl += np.einsum('aimp,imq->apq', tmp.conj(),
SPG_lm_aoG[0])
vnl *= (1. / ngrids**2)
if dtype == np.float64:
h1[kn, :] += vloc.real + vnl.real
else:
h1[kn, :] += vloc + vnl
else:
raise NotImplementedError
return h1
def hcore_deriv(atm_id):
shl0, shl1, p0, p1 = aoslices[atm_id]
symb = cell.atom_symbol(atm_id)
fakemol = _make_fakemol()
vloc_g = 1j * np.einsum('ga,g->ag', Gv, SI[atm_id] * vlocG[atm_id])
nkpts, nao = h1.shape[0], h1.shape[2]
hcore = np.zeros([3, nkpts, nao, nao], dtype=h1.dtype)
for kn, kpt in enumerate(kpts):
ao = eval_ao_kpts(cell, coords, kpt)[0]
rho = np.einsum('gi,gj->gij', ao.conj(), ao)
for ax in range(3):
vloc_R = tools.ifft(vloc_g[ax], mesh).real
vloc = np.einsum('gij,g->ij', rho, vloc_R)
hcore[ax, kn] += vloc
rho = None
aokG = tools.fftk(np.asarray(ao.T, order='C'), mesh,
np.exp(-1j * np.dot(coords, kpt))).T
ao = None
Gk = Gv + kpt
G_rad = lib.norm(Gk, axis=1)
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 = np.asarray(hl)
fakemol._bas[0, mole.ANG_OF] = l
fakemol._env[ptr + 3] = .5 * rl**2
fakemol._env[ptr + 4] = rl**(l + 1.5) * np.pi**1.25
pYlm_part = fakemol.eval_gto('GTOval', Gk)
pYlm = np.empty((nl, l * 2 + 1, ngrids))
for k in range(nl):
qkl = _qli(G_rad * rl, l, k)
pYlm[k] = pYlm_part.T * qkl
SPG_lmi = np.einsum('g,nmg->nmg', SI[atm_id].conj(), pYlm)
SPG_lm_aoG = np.einsum('nmg,gp->nmp', SPG_lmi, aokG)
SPG_lmi_G = 1j * np.einsum('nmg, ga->anmg', SPG_lmi, Gv)
SPG_lm_G_aoG = np.einsum('anmg, gp->anmp', SPG_lmi_G, aokG)
tmp_1 = np.einsum('ij,ajmp->aimp', hl, SPG_lm_G_aoG)
tmp_2 = np.einsum('ij,jmp->imp', hl, SPG_lm_aoG)
vppnl = np.einsum(
'imp,aimq->apq', SPG_lm_aoG.conj(), tmp_1) + np.einsum(
'aimp,imq->apq', SPG_lm_G_aoG.conj(), tmp_2)
vppnl *= (1. / ngrids**2)
if dtype == np.float64:
hcore[:, kn] += vppnl.real
else:
hcore[:, kn] += vppnl
hcore[:, kn, p0:p1] -= h1[kn, :, p0:p1]
hcore[:, kn, :, p0:p1] -= h1[kn, :, p0:p1].transpose(0, 2,
1).conj()
return hcore