[Pw_forum] The issue of k-points in CARTESIAN coordinates obtained by XCrySDen-1.5.24.

[Hongsheng Zhao]

Dear Prof. Tone and others,

I use pre-compiled xc-1.5.24-linux_x86-semishared.tar.gz on my Debian box.

Now I use the k-path selection function to prepare k-point file used for 
pwscf.  My system is graphene.  The graphene.inp file is as follows:

-------------
      &CONTROL
calculation = 'scf'
prefix='graphene'
pseudo_dir = './'
outdir='./'
tstress=.true.
tprnfor = .true.
forc_conv_thr=1.0d-4
nstep=200
/
      &SYSTEM
ibrav=0
celldm(1)=1.889726
nat=2
ntyp=1
ecutwfc=36
/
      &ELECTRONS
mixing_beta=0.7
conv_thr =  1.0d-8
electron_maxstep=200
/
      &IONS
trust_radius_max=0.2
/
      &CELL
cell_dynamics='bfgs'
/
ATOMIC_SPECIES
     C  12.0110   C.UPF

CELL_PARAMETERS (alat)
     2.1314617179   -1.2306000020    0.0000000000
     0.0000000000    2.4612000040    0.0000000000
     0.0000000000    0.0000000000   36.9180000600

ATOMIC_POSITIONS (crystal)
   C       0.000000000     0.000000000     0.000000000
   C       0.666666671     0.333333335     0.000000000
K_POINTS {automatic}
   4 4 4  1 1 1
-------------

I select the k-path as M --> G -->K --> M , and then generate the 
corresponding files, i.e.,  graphene.pwscf and supportInfo.kpath.

In the file supportInfo.kpath, you can find the following information:

-------------
     Selected k-points in CARTESIAN coordinates:
        0.23458    0.00000    0.00000    M
        0.00000    0.00000    0.00000    G
        0.23458    0.13543    0.00000    K
        0.23458    0.00000    0.00000    M

     Selected k-points in crystal coordinates:
     (with respect to RECIPROCAL-PRIMITIVE vectors)
        0.50000    0.00000    0.00000    M
        0.00000    0.00000    0.00000    G
        0.33333    0.33333    0.00000    K
        0.50000    0.00000    0.00000    M

     Selected k-points in crystal coordinates:
     (with respect to RECIPROCAL-CONVENTIONAL vectors)
        0.50000    0.00000    0.00000    M
        0.00000    0.00000    0.00000    G
        0.33333    0.33333    0.00000    K
        0.50000    0.00000    0.00000    M
---------------

Here, I have some puzzles on the k-points in CARTESIAN coordinates 
obtained by XCrySDen.  For example, the K point in BZ has the fractional 
coordinates as this: ( 0.33333    0.33333    0.00000 ).

And in my case, I've the lattice vectors as follows:

----------
CELL_PARAMETERS (alat)
     2.1314617179   -1.2306000020    0.0000000000
     0.0000000000    2.4612000040    0.0000000000
     0.0000000000    0.0000000000   36.9180000600
-----------

So, I can obtain the reciprocal lattice like this:

B ^ T = 2*Pi* A ^ (-1),  where, A and B are 3*3 matrix whose column vectors
   are corresponding to the real space lattice vectors and reciprocal 
lattice vectors, respectively.

Thus, I obtain B as follows from within matlab:

  >>  B= 2*pi*inv([2.1314617179   -1.2306000020    0.0000000000;
     0.0000000000    2.4612000040    0.0000000000;
     0.0000000000    0.0000000000   36.9180000600])'

B =

      2.9478         0         0
      1.4739    2.5529         0
           0         0    0.1702

So the CARTESIAN coordinates for K point ( 0.33333    0.33333    0.00000 
) should be:

  >> [0.33333    0.33333    0.00000]*B

ans =

      1.4739    0.8510         0

As you can see, your XCrySDen gives the CARTESIAN coordinates for K 
point ( 0.33333    0.33333    0.00000 ) as follows:

        0.23458    0.13543    0.00000    K

I cann't figure out what's the reason.  Could you please give me some 
hints on this issue?

Attached please find all the files mentioned above.

Regards.
-- 
Hongsheng Zhao <zhaohscas at yahoo.com.cn>
School of Physics and Electrical Information Science,
Ningxia University, Yinchuan 750021, China
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