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[Alex Kutana <akut@yahoo.com>]

Dear abinit developers:

I have made an observation that the Fourier coefficients of the wavefunction 
sometimes change abruptly upon moving between two points that are very close 
in the Brillouine zone.

For instance, the coefficients c_nkG at two very close points k1 and k2 
k1={-0.4375, -0.4375, 0.0000}, and k2={-0.4375,  -0.437499,   0.0000} 
(reduced units) in the BZ of 2D graphene differ significantly at some G 
vectors:

   Gx     Gy    Gz      Re(ck1)          Im(ck1)              Re(ck2)        
Im(ck2)
    0     0     0     0.0000000007   -0.0000000055         0.0000000742    
0.0000001377
    1     0     0     0.2825109211    0.0023911307        -0.2825117855   
-0.0023911581
    2     0     0     0.0143219844   -0.0243285545        -0.0143220024    
0.0243285812
    3     0     0     0.0028377926    0.0050127129        -0.0028377944   
-0.0050127170
    4     0     0     0.0023651980    0.0000200191        -0.0023652007   
-0.0000200193
    5     0     0     0.0000400059   -0.0000679573        -0.0000400061    
0.0000679577
   -5     0     0     0.0000506299    0.0000004285        -0.0000506302   
-0.0000004285
   -4     0     0    -0.0002334246    0.0003965149         0.0002334242   
-0.0003965141
   -3     0     0    -0.0011205278   -0.0019793142         0.0011205292    
0.0019793169
   -2     0     0    -0.0210765547   -0.0001783887         0.0210765632    
0.0001783903
   -1     0     0    -0.0270221905    0.0459022618         0.0270221515   
-0.0459021880
    0     1     0    -0.2825109060   -0.0023911203         0.2825100266    
0.0023911330
    1     1     0    -0.0000000039    0.0000000017         0.0000001506   
-0.0000002508

Effectively, at some G vectors ck2=-ck1. This behaviour is counterintuitive 
to the expectation that the wavefunctions should be smooth inside the 
Brillouine zone. 
If one moves even closer to k1, e.g. k2_y=-0.4374999, the difference between 
the two wavefunctions is very small, as expected. 
I am running abinit version  5.3.4 with Fritz-Haber-Institute (FHI) GGA 
pseudopotentials.
Thank you for addressing this issue.

Alex Kutana


The input file for the above problem is the following:

# Begin input file ---------------------------------------------------------
ecutsm  0.5
ixc     11
prtden  0
getden  0
ndtset 0
iscf  -2
tolwfr  1.0d-12

chkprim 1
nband   15

optcell 0
ionmov  0


acell   4.6446716832  4.6446716832  20.0

rprim  1.0  0.0  0.0
       0.5  0.8660254037844386 0.0
       0.0  0.0  1.0

# Definition of the atom types
ntypat 1          # There is only one type of atom
znucl  6          # The keyword "znucl" refers to the atomic number of the 
                  # possible type(s) of atom. The pseudopotential(s) 
                  # mentioned in the "files" file must correspond
                  # to the type(s) of atom. Here, the only type is Silicon.
                         

#Definition of the atoms
natom 2           # 
typat 1 1         # 
xred              # This keyword indicate that the location of the atoms
                  # will follow, one triplet of number for each atom
   0.0                      0.0                      0.0
   0.333333333333333333333  0.333333333333333333333  0.0



#Definition of the planewave basis set
ecut  35.0         # Maximal kinetic energy cut-off, in Hartree

kptopt 0
nkpt   2

kpt
 -0.4375  -0.4375     0.0000
 -0.4375  -0.437499   0.0000

nstep 100
diemac 12.0       # Although this is not mandatory, it is worth to
                  # precondition the SCF cycle. The model dielectric
                  # function used as the standard preconditioner
                  # is described in the "dielng" input variable section.
                  # Here, we follow the prescription for bulk silicon.

# End input file ---------------------------------------------------------


The density has been calculated in the previous run using this input:

# Begin input file ---------------------------------------------------------
ecutsm  0.5
ixc     11
prtden  1
getden  0

chkprim 1
nband   15

optcell 0
ionmov  0


acell   4.6446716832  4.6446716832  20.0

rprim  1.0  0.0  0.0
       0.5  0.8660254037844386 0.0
       0.0  0.0  1.0

# Definition of the atom types
ntypat 1          # There is only one type of atom
znucl  6          # The keyword "znucl" refers to the atomic number of the 
                  # possible type(s) of atom. The pseudopotential(s) 
                  # mentioned in the "files" file must correspond
                  # to the type(s) of atom. Here, the only type is Silicon.
                         

#Definition of the atoms
natom 2           # 
typat 1 1         # 
xred              # This keyword indicate that the location of the atoms
                  # will follow, one triplet of number for each atom
   0.0                      0.0                      0.0
   0.333333333333333333333  0.333333333333333333333  0.0



#Definition of the planewave basis set
ecut  35.0         # Maximal kinetic energy cut-off, in Hartree

kptopt 1
ngkpt   16 16 1
nshiftk 1
shiftk 0.0 0.0 0.0

nstep 100
toldfe 1.0d-11    # Will stop when, twice in a row, the difference 
                  # between two consecutive evaluations of total energy 
                  # differ by less than toldfe (in Hartree) 
diemac 12.0       # Although this is not mandatory, it is worth to
                  # precondition the SCF cycle. The model dielectric
                  # function used as the standard preconditioner
                  # is described in the "dielng" input variable section.
                  # Here, we follow the prescription for bulk silicon.
# End input file ---------------------------------------------------------