def test_eval_rho(self):
cell, grids = make_grids([61]*3)
numpy.random.seed(10)
nao = 10
ngrids = 500
dm = numpy.random.random((nao,nao))
dm = dm + dm.T
ao =(numpy.random.random((10,ngrids,nao)) +
numpy.random.random((10,ngrids,nao))*1j)
ao = ao.transpose(0,2,1).copy().transpose(0,2,1)
rho0 = numpy.zeros((6,ngrids), dtype=numpy.complex128)
rho0[0] = numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[0].conj())
rho0[1] = numpy.einsum('pi,ij,pj->p', ao[1], dm, ao[0].conj()) + numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[1].conj())
rho0[2] = numpy.einsum('pi,ij,pj->p', ao[2], dm, ao[0].conj()) + numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[2].conj())
rho0[3] = numpy.einsum('pi,ij,pj->p', ao[3], dm, ao[0].conj()) + numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[3].conj())
rho0[4]+= numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[4].conj()) + numpy.einsum('pi,ij,pj->p', ao[4], dm, ao[0].conj())
rho0[4]+= numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[7].conj()) + numpy.einsum('pi,ij,pj->p', ao[7], dm, ao[0].conj())
rho0[4]+= numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[9].conj()) + numpy.einsum('pi,ij,pj->p', ao[9], dm, ao[0].conj())
rho0[5]+= numpy.einsum('pi,ij,pj->p', ao[1], dm, ao[1].conj())
rho0[5]+= numpy.einsum('pi,ij,pj->p', ao[2], dm, ao[2].conj())
rho0[5]+= numpy.einsum('pi,ij,pj->p', ao[3], dm, ao[3].conj())
rho0[4]+= rho0[5]*2
rho0[5] *= .5
rho1 = numint.eval_rho(cell, ao, dm, xctype='MGGA')
self.assertTrue(numpy.allclose(rho0, rho1))
rho1 = numint.eval_rho(cell, ao, dm, xctype='GGA')
self.assertAlmostEqual(finger(rho1), -255.45150185669198, 7)
rho1 = numint.eval_rho(cell, ao[0], dm, xctype='LDA')
self.assertAlmostEqual(finger(rho1), -17.198879910245601, 7)
def test_eval_rho(self):
cell, grids = make_grids(30)
numpy.random.seed(10)
nao = 10
ngrids = 500
dm = numpy.random.random((nao,nao))
dm = dm + dm.T
ao =(numpy.random.random((10,ngrids,nao)) +
numpy.random.random((10,ngrids,nao))*1j)
rho0 = numpy.zeros((6,ngrids), dtype=numpy.complex128)
rho0[0] = numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[0].conj())
rho0[1] = numpy.einsum('pi,ij,pj->p', ao[1], dm, ao[0].conj()) + numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[1].conj())
rho0[2] = numpy.einsum('pi,ij,pj->p', ao[2], dm, ao[0].conj()) + numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[2].conj())
rho0[3] = numpy.einsum('pi,ij,pj->p', ao[3], dm, ao[0].conj()) + numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[3].conj())
rho0[4]+= numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[4].conj()) + numpy.einsum('pi,ij,pj->p', ao[4], dm, ao[0].conj())
rho0[4]+= numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[7].conj()) + numpy.einsum('pi,ij,pj->p', ao[7], dm, ao[0].conj())
rho0[4]+= numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[9].conj()) + numpy.einsum('pi,ij,pj->p', ao[9], dm, ao[0].conj())
rho0[5]+= numpy.einsum('pi,ij,pj->p', ao[1], dm, ao[1].conj())
rho0[5]+= numpy.einsum('pi,ij,pj->p', ao[2], dm, ao[2].conj())
rho0[5]+= numpy.einsum('pi,ij,pj->p', ao[3], dm, ao[3].conj())
rho0[4]+= rho0[5]*2
rho0[5] *= .5
rho1 = numint.eval_rho(cell, ao, dm, xctype='MGGA')
self.assertTrue(numpy.allclose(rho0, rho1))
def get_j_kpts(mydf, dm_kpts, hermi=1, kpts=np.zeros((1, 3)), kpts_band=None):
'''Get the Coulomb (J) AO matrix at sampled k-points.
Args:
dm_kpts : (nkpts, nao, nao) ndarray or a list of (nkpts,nao,nao) ndarray
Density matrix at each k-point. If a list of k-point DMs, eg,
UHF alpha and beta DM, the alpha and beta DMs are contracted
separately.
kpts : (nkpts, 3) ndarray
Kwargs:
kpts_band : (3,) ndarray or (*,3) ndarray
A list of arbitrary "band" k-points at which to evalute the matrix.
Returns:
vj : (nkpts, nao, nao) ndarray
or list of vj if the input dm_kpts is a list of DMs
'''
cell = mydf.cell
mesh = mydf.mesh
low_dim_ft_type = mydf.low_dim_ft_type
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
coulG = tools.get_coulG(cell, mesh=mesh, low_dim_ft_type=low_dim_ft_type)
ngrids = len(coulG)
vR = rhoR = np.zeros((nset, ngrids))
for ao_ks_etc, p0, p1 in mydf.aoR_loop(mydf.grids, kpts):
ao_ks = ao_ks_etc[0]
for k, ao in enumerate(ao_ks):
for i in range(nset):
rhoR[i, p0:p1] += numint.eval_rho(cell, ao, dms[i, k])
ao = ao_ks = None
for i in range(nset):
rhoR[i] *= 1. / nkpts
rhoG = tools.fft(rhoR[i], mesh)
vG = coulG * rhoG
vR[i] = tools.ifft(vG, mesh).real
kpts_band, input_band = _format_kpts_band(kpts_band, kpts), kpts_band
nband = len(kpts_band)
weight = cell.vol / ngrids
vR *= weight
if gamma_point(kpts_band):
vj_kpts = np.zeros((nset, nband, nao, nao))
else:
vj_kpts = np.zeros((nset, nband, nao, nao), dtype=np.complex128)
for ao_ks_etc, p0, p1 in mydf.aoR_loop(mydf.grids, kpts_band):
ao_ks = ao_ks_etc[0]
for k, ao in enumerate(ao_ks):
for i in range(nset):
vj_kpts[i, k] += lib.dot(ao.T.conj() * vR[i, p0:p1], ao)
return _format_jks(vj_kpts, dm_kpts, input_band, kpts)
def get_vjR(cell, dm, aoR):
coulG = tools.get_coulG(cell)
rhoR = numint.eval_rho(cell, aoR, dm)
rhoG = tools.fft(rhoR, cell.gs)
vG = coulG * rhoG
vR = tools.ifft(vG, cell.gs)
if rhoR.dtype == np.double:
vR = vR.real
return vR
def get_j_kpts(mydf, dm_kpts, hermi=1, kpts=np.zeros((1,3)), kpt_band=None):
'''Get the Coulomb (J) AO matrix at sampled k-points.
Args:
dm_kpts : (nkpts, nao, nao) ndarray or a list of (nkpts,nao,nao) ndarray
Density matrix at each k-point. If a list of k-point DMs, eg,
UHF alpha and beta DM, the alpha and beta DMs are contracted
separately.
kpts : (nkpts, 3) ndarray
Kwargs:
kpt_band : (3,) ndarray
An arbitrary "band" k-point at which to evalute the matrix.
Returns:
vj : (nkpts, nao, nao) ndarray
or list of vj if the input dm_kpts is a list of DMs
'''
cell = mydf.cell
gs = mydf.gs
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
coulG = tools.get_coulG(cell, gs=gs)
ngs = len(coulG)
vR = rhoR = np.zeros((nset,ngs))
for k, aoR in mydf.aoR_loop(gs, kpts):
for i in range(nset):
rhoR[i] += numint.eval_rho(cell, aoR, dms[i,k])
for i in range(nset):
rhoR[i] *= 1./nkpts
rhoG = tools.fft(rhoR[i], gs)
vG = coulG * rhoG
vR[i] = tools.ifft(vG, gs).real
if kpt_band is not None:
for k, aoR_kband in mydf.aoR_loop(gs, kpts, kpt_band):
pass
vj_kpts = [cell.vol/ngs * lib.dot(aoR_kband.T.conj()*vR[i], aoR_kband)
for i in range(nset)]
if dm_kpts.ndim == 3: # One set of dm_kpts for KRHF
vj_kpts = vj_kpts[0]
return lib.asarray(vj_kpts)
else:
vj_kpts = []
weight = cell.vol / ngs
for k, aoR in mydf.aoR_loop(gs, kpts):
for i in range(nset):
vj_kpts.append(weight * lib.dot(aoR.T.conj()*vR[i], aoR))
vj_kpts = lib.asarray(vj_kpts).reshape(nkpts,nset,nao,nao)
return vj_kpts.transpose(1,0,2,3).reshape(dm_kpts.shape)
def get_vjR(cell, dm, aoR):
coulG = tools.get_coulG(cell)
rhoR = numint.eval_rho(cell, aoR, dm)
rhoG = tools.fft(rhoR, cell.gs)
vG = coulG*rhoG
vR = tools.ifft(vG, cell.gs)
if rhoR.dtype == np.double:
vR = vR.real
return vR
def get_j_kpts(mydf, dm_kpts, hermi=1, kpts=np.zeros((1, 3)), kpt_band=None):
"""Get the Coulomb (J) AO matrix at sampled k-points.
Args:
dm_kpts : (nkpts, nao, nao) ndarray or a list of (nkpts,nao,nao) ndarray
Density matrix at each k-point. If a list of k-point DMs, eg,
UHF alpha and beta DM, the alpha and beta DMs are contracted
separately.
kpts : (nkpts, 3) ndarray
Kwargs:
kpt_band : (3,) ndarray
An arbitrary "band" k-point at which to evalute the matrix.
Returns:
vj : (nkpts, nao, nao) ndarray
or list of vj if the input dm_kpts is a list of DMs
"""
cell = mydf.cell
gs = mydf.gs
dm_kpts = lib.asarray(dm_kpts, order="C")
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
coulG = tools.get_coulG(cell, gs=gs)
ngs = len(coulG)
vR = rhoR = np.zeros((nset, ngs))
for k, aoR in mydf.aoR_loop(gs, kpts):
for i in range(nset):
rhoR[i] += numint.eval_rho(cell, aoR, dms[i, k])
for i in range(nset):
rhoR[i] *= 1.0 / nkpts
rhoG = tools.fft(rhoR[i], gs)
vG = coulG * rhoG
vR[i] = tools.ifft(vG, gs).real
if kpt_band is not None:
for k, aoR_kband in mydf.aoR_loop(gs, kpts, kpt_band):
pass
vj_kpts = [cell.vol / ngs * lib.dot(aoR_kband.T.conj() * vR[i], aoR_kband) for i in range(nset)]
if dm_kpts.ndim == 3: # One set of dm_kpts for KRHF
vj_kpts = vj_kpts[0]
return lib.asarray(vj_kpts)
else:
vj_kpts = []
weight = cell.vol / ngs
for k, aoR in mydf.aoR_loop(gs, kpts):
for i in range(nset):
vj_kpts.append(weight * lib.dot(aoR.T.conj() * vR[i], aoR))
vj_kpts = lib.asarray(vj_kpts).reshape(nkpts, nset, nao, nao)
return vj_kpts.transpose(1, 0, 2, 3).reshape(dm_kpts.shape)
def density(cell, outfile, dm, nx=60, ny=60, nz=60, moN=-1, fileFormat="cube"):
'''Calculates electron density and write out in CHGCAR format.
Args:
cell : Cell
pbc Cell
outfile : str
Name of Cube file to be written.
dm : ndarray
Density matrix of molecule.
Kwargs:
nx : int
Number of grid point divisions in x direction.
Note this is function of the molecule's size; a larger molecule
will have a coarser representation than a smaller one for the
same value.
ny : int
Number of grid point divisions in y direction.
nz : int
Number of grid point divisions in z direction.
Returns:
No return value. This function outputs a VASP chgcarlike file
(with phase if desired)...it can be opened in VESTA or VMD or
many other softwares
Examples:
>>> # generates the first MO from the list of mo_coefficents
>>> from pyscf.pbc import gto, scf
>>> from pyscf.tools import chgcar
>>> cell = gto.M(atom='H 0 0 0; H 0 0 1', a=numpy.eye(3)*3)
>>> mf = scf.RHF(cell).run()
>>> chgcar.density(cell, 'h2.CHGCAR', mf.make_rdm1())
'''
assert (isinstance(cell, pbcgto.Cell))
cc = CHGCAR(cell, nx=nx, ny=ny, nz=nz)
coords = cc.get_coords()
ngrids = cc.get_ngrids()
blksize = min(8000, ngrids)
rho = numpy.empty(ngrids)
for ip0, ip1 in lib.prange(0, ngrids, blksize):
ao = numint.eval_ao(cell, coords[ip0:ip1])
rho[ip0:ip1] = numint.eval_rho(cell, ao, dm)
rho = rho.reshape(nx, ny, nz)
cc.write(rho, outfile)
def get_j_kpts(mydf, dm_kpts, hermi=1, kpts=np.zeros((1, 3)), kpts_band=None):
'''Get the Coulomb (J) AO matrix at sampled k-points.
Args:
dm_kpts : (nkpts, nao, nao) ndarray or a list of (nkpts,nao,nao) ndarray
Density matrix at each k-point. If a list of k-point DMs, eg,
UHF alpha and beta DM, the alpha and beta DMs are contracted
separately.
kpts : (nkpts, 3) ndarray
Kwargs:
kpts_band : (3,) ndarray or (*,3) ndarray
A list of arbitrary "band" k-points at which to evalute the matrix.
Returns:
vj : (nkpts, nao, nao) ndarray
or list of vj if the input dm_kpts is a list of DMs
'''
cell = mydf.cell
gs = mydf.gs
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
coulG = tools.get_coulG(cell, gs=gs)
ngs = len(coulG)
vR = rhoR = np.zeros((nset, ngs))
for k, aoR in mydf.aoR_loop(gs, kpts):
for i in range(nset):
rhoR[i] += numint.eval_rho(cell, aoR, dms[i, k])
for i in range(nset):
rhoR[i] *= 1. / nkpts
rhoG = tools.fft(rhoR[i], gs)
vG = coulG * rhoG
vR[i] = tools.ifft(vG, gs).real
kpts_band, single_kpt_band = _format_kpts_band(kpts_band, kpts)
nband = len(kpts_band)
vj_kpts = []
weight = cell.vol / ngs
if gamma_point(kpts_band):
vj_kpts = np.empty((nset, nband, nao, nao))
else:
vj_kpts = np.empty((nset, nband, nao, nao), dtype=np.complex128)
for k, aoR in mydf.aoR_loop(gs, kpts_band):
for i in range(nset):
vj_kpts[i, k] = weight * lib.dot(aoR.T.conj() * vR[i], aoR)
return _format_jks(vj_kpts, dm_kpts, kpts_band, kpts, single_kpt_band)
def get_vjR_kpts(cell, dm_kpts, aoR_kpts):
nkpts = len(aoR_kpts)
coulG = tools.get_coulG(cell)
rhoR = 0
for k in range(nkpts):
rhoR += 1. / nkpts * numint.eval_rho(cell, aoR_kpts[k], dm_kpts[k])
rhoG = tools.fft(rhoR, cell.gs)
vG = coulG * rhoG
vR = tools.ifft(vG, cell.gs)
if rhoR.dtype == np.double:
vR = vR.real
return vR
def get_vjR_kpts(cell, dm_kpts, aoR_kpts):
nkpts = len(aoR_kpts)
coulG = tools.get_coulG(cell)
rhoR = 0
for k in range(nkpts):
rhoR += 1./nkpts*numint.eval_rho(cell, aoR_kpts[k], dm_kpts[k])
rhoG = tools.fft(rhoR, cell.gs)
vG = coulG*rhoG
vR = tools.ifft(vG, cell.gs)
if rhoR.dtype == np.double:
vR = vR.real
return vR
def get_j_kpts(mydf, dm_kpts, hermi=1, kpts=numpy.zeros((1,3)),
kpts_band=None):
mydf = _sync_mydf(mydf)
cell = mydf.cell
mesh = mydf.mesh
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
coulG = tools.get_coulG(cell, mesh=mesh)
ngrids = len(coulG)
vR = rhoR = numpy.zeros((nset,ngrids))
for ao_ks_etc, p0, p1 in mydf.mpi_aoR_loop(mydf.grids, kpts):
ao_ks = ao_ks_etc[0]
for k, ao in enumerate(ao_ks):
for i in range(nset):
rhoR[i,p0:p1] += numint.eval_rho(cell, ao, dms[i,k])
ao = ao_ks = None
rhoR = mpi.allreduce(rhoR)
for i in range(nset):
rhoR[i] *= 1./nkpts
rhoG = tools.fft(rhoR[i], mesh)
vG = coulG * rhoG
vR[i] = tools.ifft(vG, mesh).real
kpts_band, input_band = _format_kpts_band(kpts_band, kpts), kpts_band
nband = len(kpts_band)
weight = cell.vol / ngrids
vR *= weight
if gamma_point(kpts_band):
vj_kpts = numpy.zeros((nset,nband,nao,nao))
else:
vj_kpts = numpy.zeros((nset,nband,nao,nao), dtype=numpy.complex128)
for ao_ks_etc, p0, p1 in mydf.mpi_aoR_loop(mydf.grids, kpts_band):
ao_ks = ao_ks_etc[0]
for k, ao in enumerate(ao_ks):
for i in range(nset):
vj_kpts[i,k] += lib.dot(ao.T.conj()*vR[i,p0:p1], ao)
vj_kpts = mpi.reduce(vj_kpts)
if gamma_point(kpts_band):
vj_kpts = vj_kpts.real
return _format_jks(vj_kpts, dm_kpts, input_band, kpts)
def test_eval_rho(self):
cell, grids = make_grids(30)
numpy.random.seed(10)
nao = 10
ngrids = 500
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
ao = (numpy.random.random((10, ngrids, nao)) + numpy.random.random(
(10, ngrids, nao)) * 1j)
rho0 = numpy.zeros((6, ngrids), dtype=numpy.complex128)
rho0[0] = numpy.einsum('pi,ij,pj->p', ao[0], dm, ao[0].conj())
rho0[1] = numpy.einsum('pi,ij,pj->p', ao[1], dm,
ao[0].conj()) + numpy.einsum(
'pi,ij,pj->p', ao[0], dm, ao[1].conj())
rho0[2] = numpy.einsum('pi,ij,pj->p', ao[2], dm,
ao[0].conj()) + numpy.einsum(
'pi,ij,pj->p', ao[0], dm, ao[2].conj())
rho0[3] = numpy.einsum('pi,ij,pj->p', ao[3], dm,
ao[0].conj()) + numpy.einsum(
'pi,ij,pj->p', ao[0], dm, ao[3].conj())
rho0[4] += numpy.einsum('pi,ij,pj->p', ao[0], dm,
ao[4].conj()) + numpy.einsum(
'pi,ij,pj->p', ao[4], dm, ao[0].conj())
rho0[4] += numpy.einsum('pi,ij,pj->p', ao[0], dm,
ao[7].conj()) + numpy.einsum(
'pi,ij,pj->p', ao[7], dm, ao[0].conj())
rho0[4] += numpy.einsum('pi,ij,pj->p', ao[0], dm,
ao[9].conj()) + numpy.einsum(
'pi,ij,pj->p', ao[9], dm, ao[0].conj())
rho0[5] += numpy.einsum('pi,ij,pj->p', ao[1], dm, ao[1].conj())
rho0[5] += numpy.einsum('pi,ij,pj->p', ao[2], dm, ao[2].conj())
rho0[5] += numpy.einsum('pi,ij,pj->p', ao[3], dm, ao[3].conj())
rho0[4] += rho0[5] * 2
rho0[5] *= .5
rho1 = numint.eval_rho(cell, ao, dm, xctype='MGGA')
self.assertTrue(numpy.allclose(rho0, rho1))
def test_components(pseudo=None):
# The molecular calculation
mol = gto.Mole()
mol.unit = 'B'
L = 60
mol.atom.extend([['He', (L/2.,L/2.,L/2.)], ])
mol.basis = 'sto-3g'
mol.build()
m = rks.RKS(mol)
m.xc = 'LDA,VWN_RPA'
print(m.scf()) # -2.90705411168
dm = m.make_rdm1()
# The periodic calculation
cell = pbcgto.Cell()
cell.unit = 'B'
cell.a = np.diag([L,L,L])
cell.gs = np.array([80,80,80])
cell.atom = mol.atom
cell.basis = mol.basis
cell.pseudo = pseudo
cell.build()
# These should match reasonably well (roughly with accuracy of normalization)
print "Kinetic energy"
tao = pbchf.get_t(cell)
tao2 = mol.intor_symmetric('cint1e_kin_sph')
print np.dot(np.ravel(tao), np.ravel(dm)) # 2.82793077196
print np.dot(np.ravel(tao2), np.ravel(dm)) # 2.82352636524
print "Overlap"
sao = pbchf.get_ovlp(cell)
print np.dot(np.ravel(sao), np.ravel(dm)) # 1.99981725342
print np.dot(np.ravel(m.get_ovlp()), np.ravel(dm)) # 2.0
# The next two entries should *not* match, since G=0 component is removed
print "Coulomb (G!=0)"
jao = pbchf.get_j(cell, dm)
print np.dot(np.ravel(dm),np.ravel(jao)) # 4.03425518427
print np.dot(np.ravel(dm),np.ravel(m.get_j(dm))) # 4.22285177049
# The next two entries should *not* match, since G=0 component is removed
print "Nuc-el (G!=0)"
if cell.pseudo:
vppao = pbchf.get_pp(cell)
print np.dot(np.ravel(dm), np.ravel(vppao))
else:
neao = pbchf.get_nuc(cell)
print np.dot(np.ravel(dm), np.ravel(neao)) # -6.50203360062
vne = mol.intor_symmetric('cint1e_nuc_sph')
print np.dot(np.ravel(dm), np.ravel(vne)) # -6.68702326551
print "Normalization"
coords = gen_uniform_grids(cell)
aoR = eval_ao(cell, coords)
rhoR = eval_rho(cell, aoR, dm)
print cell.vol/len(rhoR)*np.sum(rhoR) # 1.99981725342 (should be 2.0)
print "(Hartree + vne) * DM"
print np.dot(np.ravel(dm),np.ravel(m.get_j(dm)))+np.dot(np.ravel(dm), np.ravel(vne))
if cell.pseudo:
print np.einsum("ij,ij", dm, vppao + jao + pbchf.get_jvloc_G0(cell))
else:
print np.einsum("ij,ij", dm, neao + jao)
ew_cut = (40,40,40)
ew_eta = 0.05
for ew_eta in [0.1, 0.5, 1.]:
ew = pbchf.ewald(cell, ew_eta, ew_cut)
print "Ewald (eta, energy)", ew_eta, ew # should be same for all eta
print "Ewald divergent terms summation", ew
# These two should now match if the box is reasonably big to
# remove images, and ngs is big.
print "Total coulomb (analytic) ",
print (.5*np.dot(np.ravel(dm), np.ravel(m.get_j(dm)))
+ np.dot(np.ravel(dm), np.ravel(vne)) ) # -4.57559738004
if not cell.pseudo:
print "Total coulomb (fft coul + ewald)",
print np.einsum("ij,ij", dm, neao + .5*jao) + ew # -4.57948259115
# Exc
cell.ew_eta, cell.ew_cut = ew_eta, ew_cut
mf = pbcdft.RKS(cell)
mf.xc = 'LDA,VWN_RPA'
rks.get_veff(mf, cell, dm)
print "Exc", mf._exc # -1.05967570089
def test_components(pseudo=None):
# The molecular calculation
mol = gto.Mole()
mol.unit = 'B'
L = 60
mol.atom.extend([
['He', (L / 2., L / 2., L / 2.)],
])
mol.basis = 'sto-3g'
mol.build()
m = rks.RKS(mol)
m.xc = 'LDA,VWN_RPA'
print(m.scf()) # -2.90705411168
dm = m.make_rdm1()
# The periodic calculation
cell = pbcgto.Cell()
cell.unit = 'B'
cell.a = np.diag([L, L, L])
cell.gs = np.array([80, 80, 80])
cell.atom = mol.atom
cell.basis = mol.basis
cell.pseudo = pseudo
cell.build()
# These should match reasonably well (roughly with accuracy of normalization)
print "Kinetic energy"
tao = pbchf.get_t(cell)
tao2 = mol.intor_symmetric('cint1e_kin_sph')
print np.dot(np.ravel(tao), np.ravel(dm)) # 2.82793077196
print np.dot(np.ravel(tao2), np.ravel(dm)) # 2.82352636524
print "Overlap"
sao = pbchf.get_ovlp(cell)
print np.dot(np.ravel(sao), np.ravel(dm)) # 1.99981725342
print np.dot(np.ravel(m.get_ovlp()), np.ravel(dm)) # 2.0
# The next two entries should *not* match, since G=0 component is removed
print "Coulomb (G!=0)"
jao = pbchf.get_j(cell, dm)
print np.dot(np.ravel(dm), np.ravel(jao)) # 4.03425518427
print np.dot(np.ravel(dm), np.ravel(m.get_j(dm))) # 4.22285177049
# The next two entries should *not* match, since G=0 component is removed
print "Nuc-el (G!=0)"
if cell.pseudo:
vppao = pbchf.get_pp(cell)
print np.dot(np.ravel(dm), np.ravel(vppao))
else:
neao = pbchf.get_nuc(cell)
print np.dot(np.ravel(dm), np.ravel(neao)) # -6.50203360062
vne = mol.intor_symmetric('cint1e_nuc_sph')
print np.dot(np.ravel(dm), np.ravel(vne)) # -6.68702326551
print "Normalization"
coords = gen_uniform_grids(cell)
aoR = eval_ao(cell, coords)
rhoR = eval_rho(cell, aoR, dm)
print cell.vol / len(rhoR) * np.sum(rhoR) # 1.99981725342 (should be 2.0)
print "(Hartree + vne) * DM"
print np.dot(np.ravel(dm), np.ravel(m.get_j(dm))) + np.dot(
np.ravel(dm), np.ravel(vne))
if cell.pseudo:
print np.einsum("ij,ij", dm, vppao + jao + pbchf.get_jvloc_G0(cell))
else:
print np.einsum("ij,ij", dm, neao + jao)
ew_cut = (40, 40, 40)
ew_eta = 0.05
for ew_eta in [0.1, 0.5, 1.]:
ew = pbchf.ewald(cell, ew_eta, ew_cut)
print "Ewald (eta, energy)", ew_eta, ew # should be same for all eta
print "Ewald divergent terms summation", ew
# These two should now match if the box is reasonably big to
# remove images, and ngs is big.
print "Total coulomb (analytic) ",
print(.5 * np.dot(np.ravel(dm), np.ravel(m.get_j(dm))) +
np.dot(np.ravel(dm), np.ravel(vne))) # -4.57559738004
if not cell.pseudo:
print "Total coulomb (fft coul + ewald)",
print np.einsum("ij,ij", dm, neao + .5 * jao) + ew # -4.57948259115
# Exc
cell.ew_eta, cell.ew_cut = ew_eta, ew_cut
mf = pbcdft.RKS(cell)
mf.xc = 'LDA,VWN_RPA'
rks.get_veff(mf, cell, dm)
print "Exc", mf._exc # -1.05967570089
def _eval_rhoG(mydf, dm_kpts, hermi=1, kpts=numpy.zeros((1, 3)), deriv=0):
log = lib.logger.Logger(mydf.stdout, mydf.verbose)
cell = mydf.cell
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
tasks = getattr(mydf, 'tasks', None)
if tasks is None:
mydf.tasks = tasks = multi_grids_tasks(cell, log)
log.debug('Multigrid ntasks %s', len(tasks))
assert (deriv <= 2)
if abs(dms - dms.transpose(0, 1, 3, 2).conj()).max() < 1e-9:
def dot_bra(bra, aodm):
rho = numpy.einsum('pi,pi->p', bra.real, aodm.real)
if aodm.dtype == numpy.complex:
rho += numpy.einsum('pi,pi->p', bra.imag, aodm.imag)
return rho
if deriv == 0:
xctype = 'LDA'
rhodim = 1
def make_rho(ao_l, ao_h, dm_lh, dm_hl):
c0 = lib.dot(ao_l, dm_lh)
rho = dot_bra(ao_h, c0)
return rho * 2
elif deriv == 1:
xctype = 'GGA'
rhodim = 4
def make_rho(ao_l, ao_h, dm_lh, dm_hl):
ngrids = ao_l[0].shape[0]
rho = numpy.empty((4, ngrids))
c0 = lib.dot(ao_l[0], dm_lh)
rho[0] = dot_bra(ao_h[0], c0)
for i in range(1, 4):
rho[i] = dot_bra(ao_h[i], c0)
c0 = lib.dot(ao_h[0], dm_hl)
for i in range(1, 4):
rho[i] += dot_bra(ao_l[i], c0)
return rho * 2 # *2 for dm_lh+dm_hl.T
elif deriv == 2:
xctype = 'MGGA'
rhodim = 6
def make_rho(ao_l, ao_h, dm_lh, dm_hl):
ngrids = ao_l[0].shape[0]
rho = numpy.empty((6, ngrids))
c = [lib.dot(ao_l[i], dm_lh) for i in range(4)]
rho[0] = dot_bra(ao_h[0], c[0])
rho[5] = 0
for i in range(1, 4):
rho[i] = dot_bra(ao_h[i], c[0])
rho[i] += dot_bra(ao_h[0], c[i])
rho[5] += dot_bra(ao_h[i], c[i]) * 2
XX, YY, ZZ = 4, 7, 9
ao2 = ao_h[XX] + ao_h[YY] + ao_h[ZZ]
rho[4] = dot_bra(ao2, c[0])
ao2 = lib.dot(ao_l[XX] + ao_l[YY] + ao_l[ZZ], dm_lh)
rho[4] += dot_bra(ao2, ao_h[0])
rho[4] += rho[5] * 2
rho[5] *= .5
return rho * 2 # *2 for dm_lh+dm_hl.T
else:
raise NotImplementedError('Non-hermitian density matrices')
ni = mydf._numint
nx, ny, nz = cell.mesh
rhoG = numpy.zeros((nset * rhodim, nx, ny, nz), dtype=numpy.complex)
for grids_high, grids_low in tasks:
cell_high = grids_high.cell
mesh = grids_high.mesh
coords_idx = grids_high.coords_idx
ngrids0 = numpy.prod(mesh)
ngrids1 = grids_high.coords.shape[0]
log.debug('mesh %s, ngrids %s/%s', mesh, ngrids1, ngrids0)
idx_h = grids_high.ao_idx
dms_hh = numpy.asarray(dms[:, :, idx_h[:, None], idx_h], order='C')
if grids_low is not None:
idx_l = grids_low.ao_idx
dms_hl = numpy.asarray(dms[:, :, idx_h[:, None], idx_l], order='C')
dms_lh = numpy.asarray(dms[:, :, idx_l[:, None], idx_h], order='C')
rho = numpy.zeros((nset, rhodim, ngrids1))
if grids_low is None:
for ao_h_etc, p0, p1 in mydf.aoR_loop(grids_high, kpts, deriv):
ao_h, mask = ao_h_etc[0], ao_h_etc[2]
for k in range(nkpts):
for i in range(nset):
rho_sub = numint.eval_rho(cell_high, ao_h[k],
dms_hh[i, k], mask, xctype,
hermi)
rho[i, :, p0:p1] += rho_sub.real
ao_h = ao_h_etc = None
else:
for ao_h_etc, ao_l_etc in zip(
mydf.aoR_loop(grids_high, kpts, deriv),
mydf.aoR_loop(grids_low, kpts, deriv)):
p0, p1 = ao_h_etc[1:3]
ao_h, mask = ao_h_etc[0][0], ao_h_etc[0][2]
ao_l = ao_l_etc[0][0]
for k in range(nkpts):
for i in range(nset):
rho_sub = numint.eval_rho(cell_high, ao_h[k],
dms_hh[i, k], mask, xctype,
hermi)
rho[i, :, p0:p1] += rho_sub.real
rho_sub = make_rho(ao_l[k], ao_h[k], dms_lh[i, k],
dms_hl[i, k])
rho[i, :, p0:p1] += rho_sub.real
ao_h = ao_l = ao_h_etc = ao_l_etc = None
rho *= 1. / nkpts
rhoR = numpy.zeros((nset * rhodim, ngrids0))
rhoR[:, coords_idx] = rho.reshape(nset * rhodim, ngrids1)
gx = numpy.fft.fftfreq(mesh[0], 1. / mesh[0]).astype(int)
gy = numpy.fft.fftfreq(mesh[1], 1. / mesh[1]).astype(int)
gz = numpy.fft.fftfreq(mesh[2], 1. / mesh[2]).astype(int)
rho_freq = tools.fft(rhoR, mesh) * cell.vol / ngrids0
for i in range(nset * rhodim):
rhoG[i, gx[:, None, None], gy[:, None],
gz] += rho_freq[i].reshape(mesh)
return rhoG.reshape(nset, rhodim, ngrids0)
