# Oxygen molecule, treated with fixed occupation numbers,
# with LDA.
# This is to demonstrate a subtlety of the analysis of
# finite differences : the effect of the symmetrization.
# In dataset 1-3, one computes the total energy and forces,
# with automatic computation of symmetries, including
# symmetrization of the forces
# In dataset 4, RF is computed, and the agreement with
# finite-differences of datasets 1 and 3 is quite bad: 1.5% error
# However, the agreement with the finite differences
# of forces in datasets 5 and 6, where the symmetrization
# of forces is not done is perfect. And this is the correct
# behaviour.
# Explanation : forces in the geometry of datasets 1,3,5 and 6
# are not really symmetric, because of the underlying XC grid !!

 ndtset 6


#GS, use symmetries
 xred1  0.0 0.0  0.11545    0.0 0.0 -0.1155

 xred2  0.0 0.0  0.1155     0.0 0.0 -0.1155
 getwfk2 1

 xred3  0.0 0.0  0.11555    0.0 0.0 -0.1155
 getwfk3 2

 chksymtnons 0

#Specific for RF
 xred4  0.0 0.0  0.1155     0.0 0.0 -0.1155
  rfphon4  1
 rfatpol4  1 1
   rfdir4  0 0 1
    nqpt4  1
     qpt4  0.0 0.0 0.0
  getwfk4  2
  tolvrs4  1.0d-7

#GS, do not use symmetries
 xred5  0.0 0.0  0.11545    0.0 0.0 -0.1155
 nsym5  1
 getwfk5 1

 xred6  0.0 0.0  0.11555    0.0 0.0 -0.1155
 nsym6  1
 getwfk6 3


#Common data

 diemac 1.0d0
 diemix 1/3
 ecut 13.00
 getwfk -1
 ixc 1
  kptopt 0
 kpt   3*0.0
 natom  2
 nband 8
 nkpt 1
 nstep 30
 ntypat  1
 occopt 0
 occ 5*2 2*1 1*0
 acell  6.500  6.500  9.000
 rprim 1 0 0  0 1 0  0 0 1
 tolvrs 1.d-16
 tsmear 0.02
 typat  1 1
 wtk  1
 znucl  8.0

 pp_dirpath "$ABI_PSPDIR"
 pseudos "PseudosTM_pwteter/8o.pspnc"

#%%<BEGIN TEST_INFO>
#%% [setup]
#%% executable = abinit
#%% [files]
#%% files_to_test = 
#%%   t74.out, tolnlines = 2, tolabs = 2.0e-10, tolrel = 1.100e+00
#%% [paral_info]
#%% max_nprocs = 1
#%% [extra_info]
#%% authors = Unknown
#%% keywords = NC, DFPT
#%% description = 
#%%   O2 (non-spin-polarized, non-linear XC core correction, LDA)
#%%   Fixed occupation numbers
#%%   This is to demonstrate a subtlety of the analysis of
#%%   finite differences : the effect of the symmetrization.
#%%   In dataset 1-3, one computes the total energy and forces,
#%%   with automatic computation of symmetries, including
#%%   symmetrization of the forces (or reduced gradients).
#%%   The reduced gradients with respect to displacements
#%%   of the first atom along z in datasets 1 and 3 are
#%%   -5.705435136802 Ha and -5.692472863816 Ha, giving
#%%   the 2DTE of 129.62 Ha. 
#%%   In dataset 4, the RF 2DTE is computed, and the agreement with
#%%   finite-differences of datasets 1 and 3 is quite bad: 
#%%   127.90998027 Ha, 1.5% error !
#%%   However, the agreement with the finite differences
#%%   of forces in datasets 5 and 6 (-5.705349696912 Ha
#%%   and -5.692558689744 Ha), where the symmetrization
#%%   of forces is not done, is excellent : the finite-difference
#%%   gives 127.91007168 Ha, less than 0.0001 Ha error.
#%%   Explanation : forces in the geometry of datasets 1,3,5 and 6
#%%   are not really symmetric, because of the underlying FFT grid,
#%%   used for the evaluation of the XC functional !
#%%   This can be seen in the fulfillment of the acoustic sum rule.
#%%   With the present low-cutoff, the frequency of the acoustic mode
#%%   is 264i cm-1, a strong breaking of the sum rule. With 20Ha,
#%%   the frequency is 43.18 cm-1, much better. 
#%%   Other values : 25 Ha, 19.03i cm-1, 
#%%   30 Ha, 21.02i cm-1, 
#%%   35 Ha, 20.14i cm-1,
#%%   50 Ha,  3.57  cm-1
#%%   Note the (misleading) plateau between 25 Ha and 35 Ha : 
#%%   the convergence towards 0 cm-1 start again only beyond 35 Ha.
#%%   The influence of the FFT grid depends strongly on the pseudopotential.
#%%<END TEST_INFO>