def test_ewald():
cell = pbcgto.Cell()
cell.unit = 'B'
Lx = 6.
Ly = 9.
Lz = 30.
cell.a = np.array([[Lx,0.5,0.5],
[0.5,Ly,0.5],
[0.5,0.5,Lz]])
cell.gs = np.array([20,20,20])
cell.atom.extend([['He', (1, 0.5*Ly, 0.5*Lz)],
['He', (2, 0.5*Ly, 0.5*Lz)]])
# these are some exponents which are not hard to integrate
cell.basis = {'He': [[0, (1.0, 1.0)]]}
cell.verbose = 5
cell.build()
ew_eta0, ew_cut0 = cell.get_ewald_params(1.e-3)
print ew_eta0, ew_cut0
ew_cut = (20,20,20)
for ew_eta in [0.05, 0.07, 0.1, 0.3]:
print pbchf.ewald(cell, ew_eta, ew_cut) # 4.53091146255
for precision in [1.e-3, 1.e-5, 1.e-7, 1.e-9]:
ew_eta0, ew_cut0 = cell.get_ewald_params(precision)
print "precision", precision, ew_eta0, ew_cut0
print pbchf.ewald(cell, ew_eta0, ew_cut0)
def test_ewald():
cell = pbcgto.Cell()
cell.unit = "B"
Lx = Ly = Lz = 5.0
cell.a = np.diag([Lx, Ly, Lz])
cell.gs = np.array([20, 20, 20])
cell.atom.extend([["He", (2, 0.5 * Ly, 0.5 * Lz)], ["He", (3, 0.5 * Ly, 0.5 * Lz)]])
# these are some exponents which are not hard to integrate
cell.basis = {"He": [[0, (1.0, 1.0)]]}
cell.verbose = 5
cell.build()
ew_eta0, ew_cut0 = cell.get_ewald_params(1.0e-3)
print ew_eta0, ew_cut0
ew_cut = (20, 20, 20)
for ew_eta in [0.05, 0.1, 0.2, 1]:
print pbchf.ewald(cell, ew_eta, ew_cut) # -0.468640671931
for precision in [1.0e-3, 1.0e-5, 1.0e-7, 1.0e-9]:
ew_eta0, ew_cut0 = cell.get_ewald_params(precision)
print "precision", precision, ew_eta0, ew_cut0
print pbchf.ewald(cell, ew_eta0, ew_cut0)
def test_ewald():
cell = pbcgto.Cell()
cell.unit = 'B'
Lx = 6.
Ly = 9.
Lz = 30.
cell.h = np.array([[Lx,0.5,0.5],
[0.5,Ly,0.5],
[0.5,0.5,Lz]])
cell.gs = np.array([20,20,20])
cell.nimgs = [1,1,1]
cell.atom.extend([['He', (1, 0.5*Ly, 0.5*Lz)],
['He', (2, 0.5*Ly, 0.5*Lz)]])
# these are some exponents which are not hard to integrate
cell.basis = {'He': [[0, (1.0, 1.0)]]}
cell.verbose = 5
cell.build()
ew_eta0, ew_cut0 = cell.get_ewald_params(1.e-3)
print ew_eta0, ew_cut0
ew_cut = (20,20,20)
for ew_eta in [0.05, 0.07, 0.1, 0.3]:
print pbchf.ewald(cell, ew_eta, ew_cut) # 4.53091146255
for precision in [1.e-3, 1.e-5, 1.e-7, 1.e-9]:
ew_eta0, ew_cut0 = cell.get_ewald_params(precision)
print "precision", precision, ew_eta0, ew_cut0
print pbchf.ewald(cell, ew_eta0, ew_cut0)
def test_ewald():
cell = pbcgto.Cell()
cell.unit = 'B'
Lx = Ly = Lz = 5.
cell.a = np.diag([Lx, Ly, Lz])
cell.gs = np.array([20, 20, 20])
cell.atom.extend([['He', (2, 0.5 * Ly, 0.5 * Lz)],
['He', (3, 0.5 * Ly, 0.5 * Lz)]])
# these are some exponents which are not hard to integrate
cell.basis = {'He': [[0, (1.0, 1.0)]]}
cell.verbose = 5
cell.build()
ew_eta0, ew_cut0 = cell.get_ewald_params(1.e-3)
print ew_eta0, ew_cut0
ew_cut = 20
for ew_eta in [0.05, 0.1, 0.2, 1]:
print pbchf.ewald(cell, ew_eta, ew_cut) # -0.468640671931
for precision in [1.e-3, 1.e-5, 1.e-7, 1.e-9]:
ew_eta0, ew_cut0 = cell.get_ewald_params(precision)
print "precision", precision, ew_eta0, ew_cut0
print pbchf.ewald(cell, ew_eta0, ew_cut0)
def test_ewald(self):
cell = pbcgto.Cell()
cell.unit = "B"
Lx = Ly = Lz = 5.0
cell.h = np.diag([Lx, Ly, Lz])
cell.gs = np.array([20, 20, 20])
cell.nimgs = [1, 1, 1]
cell.atom.extend([["He", (2, 0.5 * Ly, 0.5 * Lz)], ["He", (3, 0.5 * Ly, 0.5 * Lz)]])
# these are some exponents which are not hard to integrate
cell.basis = {"He": [[0, (1.0, 1.0)]]}
cell.verbose = 5
cell.output = "/dev/null"
cell.build()
ew_cut = (20, 20, 20)
self.assertAlmostEqual(pbchf.ewald(cell, 0.05, ew_cut), -0.468640671931, 9)
self.assertAlmostEqual(pbchf.ewald(cell, 0.1, ew_cut), -0.468640671931, 9)
self.assertAlmostEqual(pbchf.ewald(cell, 0.2, ew_cut), -0.468640671931, 9)
self.assertAlmostEqual(pbchf.ewald(cell, 1, ew_cut), -0.468640671931, 9)
def check(precision, eta_ref, ewald_ref):
ew_eta0, ew_cut0 = cell.get_ewald_params(precision)
self.assertAlmostEqual(ew_eta0, eta_ref)
self.assertAlmostEqual(pbchf.ewald(cell, ew_eta0, ew_cut0), ewald_ref, 9)
check(0.001, 4.78124933741, -0.469112631739)
check(1e-05, 3.70353981157, -0.468642153932)
check(1e-07, 3.1300624293, -0.468640678042)
check(1e-09, 2.76045559201, -0.468640671959)
def madelung(cell, kpts):
from pyscf.pbc import gto as pbcgto
from pyscf.pbc.scf.hf import ewald
Nk = get_monkhorst_pack_size(cell, kpts)
ecell = pbcgto.Cell()
ecell.atom = 'H 0. 0. 0.'
ecell.spin = 1
ecell.gs = cell.gs
ecell.precision = 1e-16
ecell.unit = 'B'
ecell.h = cell._h * Nk
ecell.build(False, False)
return -2 * ewald(ecell, ecell.ew_eta, ecell.ew_cut)
def madelung(cell, kpts):
from pyscf.pbc import gto as pbcgto
from pyscf.pbc.scf.hf import ewald
Nk = get_monkhorst_pack_size(cell, kpts)
ecell = pbcgto.Cell()
ecell.atom = 'H 0. 0. 0.'
ecell.spin = 1
ecell.gs = cell.gs
ecell.precision = 1e-16
ecell.unit = 'B'
ecell.h = cell._h * Nk
ecell.build(False,False)
return -2*ewald(ecell, ecell.ew_eta, ecell.ew_cut)
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 check(precision, eta_ref, ewald_ref):
ew_eta0, ew_cut0 = cell.get_ewald_params(precision)
self.assertAlmostEqual(ew_eta0, eta_ref)
self.assertAlmostEqual(pbchf.ewald(cell, ew_eta0, ew_cut0), ewald_ref, 9)
