A couple of examples as benchmark calculations are shown below:
Si
The real part of dielectric function of Si bulk is shown for a series of kgrids in Fig. 81.
We see that as increasing kgrid from
to
,
the real part of dielectric function is getting converged.
It is found that we need to have a fine grid for the kpoints to obtain a well converged result.
In Tables 14 and 15, we show the computational time and parallel efficiency
in the calculation of the conductivity and dielectric function for supercells of Si bulk.
The results suggest that it might be possible to treat systems including 1000 atoms if 1000 CPU cores are available.
Figure 81:
The dielectric function of Si crystal (primitive cell, 2 atoms) with 6 different Kgrids:
,
,
,
,
, and
. The blue and red lines are real
and imaginary parts of dielectric function, respectively, where CDDF.FWHM=0.2 eV was used.

Table 14:
Computational time of conductivity and dielectric function of Si crystal.

# of Si atoms 
Supercell 
Diagonalization 
kGrid

 Total time (s) 

 (CPUs=128) 


 Total time (s) 

 (CPUs=256) 


 Total time (s) 

 (CPUs=512) 


 Total time (s) 

 (CPUs=1024) 


 Total time (s) 

 (CPUs=2048) 




512 atoms 
4x4x4 
Cluster 
1x1x1 
3367.16826 
1755.60797 
919.21912 
464.27761 
253.32210 



4x4x4 
ScaLAPACK 
2x1x1 
6819.30193 
3499.51872 
1838.64406 
948.87978 
513.79250 



4x4x4 
Band 
2x2x2 
15300.58350 
10217.17765 
5953.19907 
3518.84650 
1747.20171 


1000 atoms 
5x5x5 
Cluster 
1x1x1 


6900.35370 
3511.85143 
1778.33693 



5x5x5 
ScaLAPACK 
2x1x1 


12994.17818 
6817.43990 
3460.76787 



5x5x5 
Band 
2x2x2 


43676.20392 
26055.12739 
13318.14587 

Table 15:
Calculation time of conductivity and dielectric function of
Si crystal (512 atoms,
supercell, kgrid=
).
The speedup ratio with repect to the case with 128 CPU cores is shown in the last column.
 



 



 



 



 



 



PVDF
The real part of dielectric function of PVDF (polyvinylidene fluoride) is shown for a series of kgrids
in Fig. 82. We see that the kgrid of
is required to get the convergent result.
In Tables 16 and 17, we show the computational time and parallel efficiency
in the calculation of the conductivity and dielectric function for supercells of PVDF.
It is confirmed that the parallel efficiency is reasonably good, and the elapsed time is less than one hour when
the CPU cores of 256 are used. In Fig. 83, we show the , , and components of
real part of dielectric function of PVDF for your reference.
Figure 82:
The real part of dielectric function of PVDF (polyvinylidene fluoride) consisting of 6 atoms
in the
cell for a series of kgrids. CDDF.FWHM=0.2 eV was used.

Table 16:
Total time of calculating conductivity and dielectric function of PVDF (polyvinylidene fluoride)
consisting of 540 atoms which corresponds to the
supercell.
 







 







 







 







Table 17:
Calculation time of conductivity and dielectric function of PVDF (polyvinylidene fluoride)
consisting of 540 atoms which corresponds to the
supercell, where kgrid of
was used.
The speedup ratio with repect to the case with 128 CPU cores is shown in the last column.
 # of CPUs 
 Total time of calculating 

 conductivity and dielectric function (s) 


 Ratio of 

 total time by # of CPUs 

 to total time by 128 CPUs 



 128 
4215.67238 
1.000 

 256 
2086.76841 
2.020 

 512 
1061.06835 
3.973 

 1024 
565.92209 
7.449 

 2048 
329.42010 
12.797 

Figure 83:
The , , and components of real parts of dielectric function of PVDF (6 atoms,
cell).

VO in the R phase
The real and imaginary parts of dielectric function of VO in the R phase are shown for a series of kgrids
in Fig. 84. We see that the kgrid of
is required to get the convergent result.
Tables 18 and 19 show the computational time and parallel efficiency
in the calculation of the conductivity and dielectric function for supercells of VO in the R phase.
It is confirmed that the parallel efficiency is reasonably good, allowing us to treat largescale systems
in an elapsed time of 1 hour.
Figure 84:
The real and imaginary parts of dielectric function of VO (R phase, 6 atoms,
cell)
with a series of kgrids.

Table 18:
Calculation time of conductivity and dielectric function of VO (R phase, 384 atoms,
supercell)
 







 







 







 






