KRKS with MDF fails to converge

I’m trying to run examples/pbc/21-k_points_all_electron_scf.py, but the KRHF job with MDF fails to converge. Then I tried KRKS with 6-31gs and three different DFs, and found that only KRKS with MDF fails, while GDF and RSDF works well. My input looks like

 lib.num_threads(28)

cell = gto.M(
    a = numpy.eye(3)*3.5668,
    atom = '''C     0.      0.      0.
              C     0.8917  0.8917  0.8917
              C     1.7834  1.7834  0.
              C     2.6751  2.6751  0.8917
              C     1.7834  0.      1.7834
              C     2.6751  0.8917  2.6751
              C     0.      1.7834  1.7834
              C     0.8917  2.6751  2.6751''',
    basis = '6-31gs',
    verbose = 4,
)

nk = [4,4,4]  # 4 k-poins for each axis, 4^3=64 kpts in total
kpts = cell.make_kpts(nk)

# Mixed density fitting
#
kmf = scf.KRKS(cell, kpts).mix_density_fit()
# In the MDF scheme, modifying the default mesh for PWs to reduce the cost
# The default mesh for PWs is a very dense-grid scheme which is automatically
# generated based on the AO basis. It is often not necessary to use dense grid
# for MDF method.
kmf.xc = 'bp86'
kmf.with_df.mesh = [10,10,10]
kmf.kernel()

# Density fitting
#
kmf = dft.KRKS(cell, kpts).density_fit(auxbasis='weigend')
kmf.xc = 'bp86'
kmf.kernel()

# Range-separated density fitting (RSDF)
# RSDF uses the same amount of memory & disk as GDF and achieves a similar
# accuracy as GDF but is often 5~10x faster than GDF in the DF initialization
# step. The following run should give an energy very close to the one above.
# see '35-range_separated_density_fitting.py' for more details of RSDF.
#
kmf = dft.KRKS(cell, kpts).rs_density_fit(auxbasis='weigend')
kmf.xc = 'bp86'
kmf.kernel()

The last part of output of MDF:

cycle= 48 E= -303.852099067206  delta_E= 0.000118  |g|= 5.63  |ddm|= 3.24
HOMO = 0.503518440799  LUMO = 0.650701422235
cycle= 49 E= -303.852167596699  delta_E= -6.85e-05  |g|=  5.6  |ddm|= 0.882
HOMO = 0.503541680834  LUMO = 0.650693150238
cycle= 50 E= -303.852098370327  delta_E= 6.92e-05  |g|= 5.63  |ddm|= 1.12
SCF not converged.
SCF energy = -303.852098370327

while GDF and RSDF both converges to an energy around -304.914. I’m using version d096d6f.

[sunqm]

MDF may break the symmetry between k-points. For example, integrals (i_k1,j_k2|k_k2,l_k1) should be conjugated to (i_k2,j_k1|k_k1,l_k2). If they are computed with GDF or regular FT, we can find the symmetry. This symmetry is not strictly held in MDF. It may produce large errors when computing KHF exchange . It should not affect integrals in pure DFT. I’m not clear why bp86 shows such big numerical error. So the best solution for the moment is to use GDF only in your calculations

[hebrewsnabla]

Pulling #1429 (and using odd number of mesh) resolves this problem. Thanks!