def _get_vxc(ni, mol, grids, x_id, c_id, dms, relativity=0, hermi=1,
max_memory=2000, verbose=None):
natocc = []
natorb = []
if isinstance(dms, numpy.ndarray) and dms.ndim == 2:
e, c = scipy.linalg.eigh(dms)
natocc.append(e)
natorb.append(c)
nao = dms.shape[0]
else:
for dm in dms:
e, c = scipy.linalg.eigh(dm)
natocc.append(e)
natorb.append(c)
nao = dms[0].shape[0]
xctype = numint._xc_type(x_id, c_id)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
blksize = min(int(max_memory/6*1e6/8/nao/BLKSIZE)*BLKSIZE, ngrids)
nset = len(natocc)
nelec = numpy.zeros(nset)
excsum = numpy.zeros(nset)
vmat = numpy.zeros((nset,3,nao,nao))
if xctype == 'LDA':
buf = numpy.empty((4,blksize,nao))
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=1, non0tab=non0tab, out=buf)
for idm in range(nset):
rho = ni.eval_rho2(mol, ao[0], natorb[idm], natocc[idm], non0tab, xctype)
exc, vxc = ni.eval_xc(x_id, c_id, rho, 0, relativity, 1, verbose)[:2]
vrho = vxc[0]
den = rho * weight
nelec[idm] += den.sum()
excsum[idm] += (den * exc).sum()
aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho)
vmat[idm,0] += numint._dot_ao_ao(mol, ao[1], aow, nao, ip1-ip0, non0tab)
vmat[idm,1] += numint._dot_ao_ao(mol, ao[2], aow, nao, ip1-ip0, non0tab)
vmat[idm,2] += numint._dot_ao_ao(mol, ao[3], aow, nao, ip1-ip0, non0tab)
rho = exc = vxc = vrho = aow = None
elif xctype == 'GGA':
buf = numpy.empty((10,blksize,nao))
XX, XY, XZ = 4, 5, 6
YX, YY, YZ = 5, 7, 8
ZX, ZY, ZZ = 6, 8, 9
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=2, non0tab=non0tab, out=buf)
for idm in range(nset):
rho = ni.eval_rho2(mol, ao, natorb[idm], natocc[idm], non0tab, xctype)
exc, vxc = ni.eval_xc(x_id, c_id, rho, 0, relativity, 1, verbose)[:2]
vrho, vsigma = vxc[:2]
den = rho[0] * weight
nelec[idm] += den.sum()
excsum[idm] += (den * exc).sum()
wv = numpy.empty_like(rho)
# *.5 because vmat + vmat.T implicitly
wv[0] = weight * vrho * .5
wv[1:] = rho[1:] * (weight * vsigma * 2)
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
vmat[idm,0] += numint._dot_ao_ao(mol, ao[1], aow, nao, ip1-ip0, non0tab)
vmat[idm,1] += numint._dot_ao_ao(mol, ao[2], aow, nao, ip1-ip0, non0tab)
vmat[idm,2] += numint._dot_ao_ao(mol, ao[3], aow, nao, ip1-ip0, non0tab)
aow = numpy.einsum('pi,p->pi', ao[1] , wv[0])
aow+= numpy.einsum('pi,p->pi', ao[XX], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[XY], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[XZ], wv[3])
vmat[idm,0] += numint._dot_ao_ao(mol, aow, ao[0], nao, ip1-ip0, non0tab)
aow = numpy.einsum('pi,p->pi', ao[2] , wv[0])
aow+= numpy.einsum('pi,p->pi', ao[YX], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[YY], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[YZ], wv[3])
vmat[idm,1] += numint._dot_ao_ao(mol, aow, ao[0], nao, ip1-ip0, non0tab)
aow = numpy.einsum('pi,p->pi', ao[3] , wv[0])
aow+= numpy.einsum('pi,p->pi', ao[ZX], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[ZY], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[ZZ], wv[3])
vmat[idm,2] += numint._dot_ao_ao(mol, aow, ao[0], nao, ip1-ip0, non0tab)
rho = exc = vxc = vrho = vsigma = wv = aow = None
else:
raise NotImplementedError('meta-GGA')
if nset == 1:
vmat = vmat.reshape(3,nao,nao)
return vmat
def _contract_xc_kernel(td, x_id, c_id, dmvo, singlet=True, max_memory=2000):
mf = td._scf
mol = td.mol
ni = mf._numint
grids = mf.grids
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
ndm = len(dmvo)
dmvo = numpy.asarray(dmvo)
dmvo = (dmvo + dmvo.transpose(0,2,1)) * .5
xctype = numint._xc_type(x_id, c_id)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
blksize = min(int(max_memory*1e6/8/nao/BLKSIZE)*BLKSIZE, ngrids)
v1ao = numpy.zeros((ndm,nao,nao))
if xctype == 'LDA':
buf = numpy.empty((blksize,nao))
if singlet:
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=0, non0tab=non0tab, out=buf)
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, non0tab, 'LDA')
rho *= .5 # alpha density
fxc = ni.eval_xc(x_id, c_id, (rho,rho), 1, deriv=2)[2]
u_u, u_d, d_d = v2rho2 = fxc[0].T
frho = u_u + u_d
for i, dm in enumerate(dmvo):
rho1 = ni.eval_rho(mol, ao, dm, non0tab, xctype)
aow = numpy.einsum('pi,p->pi', ao, weight*frho*rho1)
v1ao[i] += numint._dot_ao_ao(mol, aow, ao, nao, ip1-ip0, non0tab)
rho1 = aow = None
for i in range(ndm):
v1ao[i] = (v1ao[i] + v1ao[i].T) * .5
else:
# because frho = u_u - u_d = 0
pass
elif xctype == 'GGA':
buf = numpy.empty((4,blksize,nao))
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=1, non0tab=non0tab, out=buf)
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, non0tab, 'GGA')
rho *= .5 # alpha density
vxc, fxc = ni.eval_xc(x_id, c_id, (rho,rho), 1, deriv=2)[1:3]
vsigma = vxc[1].T
u_u, u_d, d_d = fxc[0].T # v2rho2
u_uu, u_ud, u_dd, d_uu, d_ud, d_dd = fxc[1].T # v2rhosigma
uu_uu, uu_ud, uu_dd, ud_ud, ud_dd, dd_dd = fxc[2].T # v2sigma2
if singlet:
fgamma = 2*vsigma[0] + vsigma[1]
frho = u_u + u_d
fgg = uu_uu + .5*ud_ud + 2*uu_ud + uu_dd
frhogamma = u_uu + u_dd + u_ud
else:
fgamma = 2*vsigma[0] - vsigma[1]
frho = u_u - u_d
fgg = uu_uu - uu_dd
frhogamma = u_uu - u_dd
for i, dm in enumerate(dmvo):
# rho1[0 ] = |b><j| z_{bj}
# rho1[1:] = \nabla(|b><j|) z_{bj}
rho1 = ni.eval_rho(mol, ao, dm, non0tab, 'GGA')
# sigma1 = \nabla(\rho_\alpha+\rho_\beta) dot \nabla(|b><j|) z_{bj}
# *2 for alpha + beta
sigma1 = numpy.einsum('xi,xi->i', rho[1:], rho1[1:]) * 2
wv = frho * rho1[0]
wv += frhogamma * sigma1
wv *= weight
if c_id == 131 or x_id in (402, 404, 411, 416, 419):
# second derivative of LYP functional in libxc library diverge
wv[rho[0] < 4.57e-11] = 0
aow = numpy.einsum('pi,p->pi', ao[0], wv)
v1ao[i] += numint._dot_ao_ao(mol, aow, ao[0], nao, ip1-ip0, non0tab)
for k in range(3):
wv = fgg * sigma1 * rho[1+k]
wv += frhogamma * rho1[0] * rho[1+k]
wv *= 2 # *2 because \nabla\rho = \nabla(\rho_\alpha+\rho_\beta)
wv += fgamma * rho1[1+k]
wv *= weight
if c_id == 131 or x_id in (402, 404, 411, 416, 419):
# second derivative of LYP functional in libxc library diverge
wv[rho[0] < 4.57e-11] = 0
aow = numpy.einsum('ip,i->ip', ao[0], wv)
#v1ao += numint._dot_ao_ao(mol, aow, ao[1+k], nao, ip1-ip0, non0tab)
#v1ao += numint._dot_ao_ao(mol, ao[1+k], aow, nao, ip1-ip0, non0tab)
# v1ao+v1ao.T at the end
v1ao[i] += 2*numint._dot_ao_ao(mol, aow, ao[1+k], nao, ip1-ip0, non0tab)
aow = None
for i in range(ndm):
v1ao[i] = (v1ao[i] + v1ao[i].T) * .5
else:
raise NotImplementedError('meta-GGA')
return v1ao
def _contract_xc_kernel(td_grad, x_id, c_id, xai, oovv=None, with_vxc=True,
with_kxc=True, singlet=True, max_memory=4000):
mol = td_grad.mol
mf = td_grad._scf
ni = mf._numint
grids = mf.grids
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()
orbv = mo_coeff[:,nocc:]
orbo = mo_coeff[:,:nocc]
# dmvo ~ reduce(numpy.dot, (orbv, Xai, orbo.T))
dmvo = (xai + xai.T) * .5 # because K_{ai,bj} == K_{ai,bj}
f1vo = numpy.zeros((4,nao,nao))
deriv = 2
if oovv is not None:
f1oo = numpy.zeros((4,nao,nao))
else:
f1oo = None
if with_vxc:
v1ao = numpy.zeros((4,nao,nao))
else:
v1ao = None
if with_kxc:
k1ao = numpy.zeros((4,nao,nao))
deriv = 3
else:
k1ao = None
xctype = numint._xc_type(x_id, c_id)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
max_memory = max_memory - 4*nao**2*8/1e6
blksize = min(int(max_memory/6*1e6/8/nao/BLKSIZE)*BLKSIZE, ngrids)
if xctype == 'LDA':
buf = numpy.empty((4,blksize,nao))
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=1, non0tab=non0tab, out=buf)
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, non0tab, 'LDA')
vxc, fxc, kxc = ni.eval_xc(x_id, c_id, rho, 0, deriv=deriv)[1:]
wfxc = fxc[0] * weight * 2 # *2 for alpha+beta
if singlet:
rho1 = ni.eval_rho(mol, ao[0], dmvo, non0tab, 'LDA')
aow = numpy.einsum('pi,p->pi', ao[0], wfxc*rho1)
for k in range(4):
f1vo[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, ip1-ip0, non0tab)
if oovv is not None:
rho2 = ni.eval_rho(mol, ao[0], oovv, non0tab, 'LDA')
aow = numpy.einsum('pi,p->pi', ao[0], wfxc*rho2)
for k in range(4):
f1oo[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, ip1-ip0, non0tab)
if with_vxc:
aow = numpy.einsum('pi,p->pi', ao[0], vxc[0]*weight)
for k in range(4):
v1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, ip1-ip0, non0tab)
if singlet and with_kxc:
aow = numpy.einsum('pi,p->pi', ao[0], kxc[0]*weight*rho1**2)
for k in range(4):
k1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, ip1-ip0, non0tab)
vxc = fxc = kxc = aow = rho = rho1 = rho2 = None
if singlet and with_kxc:
k1ao *= 4
elif xctype == 'GGA':
raise NotImplementedError('GGA')
else:
raise NotImplementedError('meta-GGA')
f1vo[1:] *= -1
if f1oo is not None: f1oo[1:] *= -1
if v1ao is not None: v1ao[1:] *= -1
if k1ao is not None: k1ao[1:] *= -1
return f1vo, f1oo, v1ao, k1ao
def _get_vxc_giao(ni, mol, grids, x_id, c_id, dm,
max_memory=2000, verbose=None):
natocc, natorb = scipy.linalg.eigh(dm)
nao = dm.shape[0]
xctype = numint._xc_type(x_id, c_id)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
blksize = min(int(max_memory/6*1e6/12/nao/BLKSIZE)*BLKSIZE, ngrids)
vmat = numpy.zeros((3,nao,nao))
if xctype == 'LDA':
buf = numpy.empty((4,blksize,nao))
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=0, non0tab=non0tab, out=buf)
rho = ni.eval_rho2(mol, ao, natorb, natocc, non0tab, xctype)
vxc = ni.eval_xc(x_id, c_id, rho, 0, deriv=1)[1]
vrho = vxc[0]
aow = numpy.einsum('pi,p->pi', ao, weight*vrho)
giao = mol.eval_gto('GTOval_ig_sph', coords, comp=3,
non0tab=non0tab, out=buf[1:])
vmat[0] += numint._dot_ao_ao(mol, aow, giao[0], nao, ip1-ip0, non0tab)
vmat[1] += numint._dot_ao_ao(mol, aow, giao[1], nao, ip1-ip0, non0tab)
vmat[2] += numint._dot_ao_ao(mol, aow, giao[2], nao, ip1-ip0, non0tab)
rho = vxc = vrho = aow = giao = None
elif xctype == 'GGA':
buf = numpy.empty((10,blksize,nao))
XX, XY, XZ = 0, 1, 2
YX, YY, YZ = 3, 4, 5
ZX, ZY, ZZ = 6, 7, 8
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=1, non0tab=non0tab, out=buf)
rho = ni.eval_rho2(mol, ao, natorb, natocc, non0tab, xctype)
vxc = ni.eval_xc(x_id, c_id, rho, 0, deriv=1)[1]
vrho, vsigma = vxc[:2]
wv = numpy.empty_like(rho)
wv[0] = weight * vrho
wv[1:] = rho[1:] * (weight * vsigma * 2)
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
giao = mol.eval_gto('GTOval_ig_sph', coords, 3,
non0tab=non0tab, out=buf[4:])
vmat[0] += numint._dot_ao_ao(mol, aow, giao[0], nao, ip1-ip0, non0tab)
vmat[1] += numint._dot_ao_ao(mol, aow, giao[1], nao, ip1-ip0, non0tab)
vmat[2] += numint._dot_ao_ao(mol, aow, giao[2], nao, ip1-ip0, non0tab)
giao = mol.eval_gto('GTOval_ipig_sph', coords, 9,
non0tab=non0tab, out=buf[1:])
aow = numpy.einsum('pi,p->pi', giao[XX], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YX], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZX], wv[3])
vmat[0] += numint._dot_ao_ao(mol, ao[0], aow, nao, ip1-ip0, non0tab)
aow = numpy.einsum('pi,p->pi', giao[XY], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YY], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZY], wv[3])
vmat[1] += numint._dot_ao_ao(mol, ao[0], aow, nao, ip1-ip0, non0tab)
aow = numpy.einsum('pi,p->pi', giao[XZ], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YZ], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZZ], wv[3])
vmat[2] += numint._dot_ao_ao(mol, ao[0], aow, nao, ip1-ip0, non0tab)
rho = vxc = vrho = vsigma = wv = aow = giao = None
else:
raise NotImplementedError('meta-GGA')
return vmat - vmat.transpose(0,2,1)
