[Wien] q re: 'local coordinates' and px, py, pz

Cormac McGuinness Cormac.McGuinness at tcd.ie
Mon Aug 16 11:09:10 CEST 2004


Dear Prof. Blaha,

On Sun, 2004-08-15 at 15:46, Peter Blaha wrote:
> Have a look into case.outputs (not sgroup!). Eg. for the famous TiO2
> example you can see all relevant information:
> 
>  ATOM:          -2
> O xygen    operation #  1     1
> O xygen    operation #  6     m n z
> O xygen    operation # 13     m n -110
> O xygen    operation # 18     2 || 110
>   pointgroup is mm2 (neg. iatnr!!)
>   axes should be: 2 || z, m n y
>   z-rotation vector:  1.0000  1.0000  0.0000
>   y-rotation vector: -1.0000  1.0000  0.0000    2
> LOCAL ROT MATRIX:       NEW                                OLD
>            0.0000000-0.7071068 0.7071068      0.0000000-0.7071068 0.7071068
>            0.0000000 0.7071068 0.7071068      0.0000000 0.7071068 0.7071068
>           -1.0000000 0.0000000 0.0000000     -1.0000000 0.0000000 0.0000000
> 
> We require that the axis with the highest symmetry is the z axis. Thus the
> 2-fold rotation axis, which is in this example along (110) must be the new
> z-direction. and so on,.. (see also the UG appendix)
> 

In case.outputs I have:
 ATOM:          -4
O Oxygen   operation #  1     1                   
O Oxygen   operation #  6     m n z               
  pointgroup is m (neg. iatnr!!)
  axes should be: m n z
  z-rotation vector:  0.0000  0.0000  1.0000
  y-rotation vector:  0.7071 -0.7071  0.0000    0
LOCAL ROT MATRIX:       NEW                                OLD
           1.0000000 0.0000000 0.0000000      1.0000000 0.0000000 0.0000000
           0.0000000 1.0000000 0.0000000      0.0000000 1.0000000 0.0000000
           0.0000000 0.0000000 1.0000000      0.0000000 0.0000000 1.0000000

(This was what I meant when I said WIEN2k does not suggest a local
rotation matrix.) I take it to mean that since there is only a mirror
operation, the axis with highest symmetry is that which is perpendicular
to the mirror plane (the plane containing the Cu  2x Ti and O atoms) and
hence that is designated the z axis  ?
Further do the y and z-rotation vectors (shown above) strictly relate to
the first listed of the equivalent positions of the O atom in the
case.struct file ?

> I cannot answer your specific question (x along Cu,...?) without
> case.outputs (and case.struct), but I think it is fairly straight forward
> with the information in your case.outputs.

I attach case.outputs and case.struct and would be very grateful if you
could guide me to the answer as to the local orientations of px, py and
pz for the O atom.

Yours
Cormac



-------------- next part --------------
CaCu3Ti4O12                                                                     
 Bravais Matrix:
       -0.50000        0.50000        0.50000
        0.50000       -0.50000        0.50000
        0.50000        0.50000       -0.50000
  ATOMIC POSITIONS:
    1     0.00000000     0.00000000     0.00000000
    2     6.97687150     0.00000000     0.00000000
    3     0.00000000     6.97687150     0.00000000
    4     0.00000000     0.00000000     6.97687150
    5     3.48843575     3.48843575     3.48843575
    6    10.46530725    10.46530725     3.48843575
    7     3.48843575    10.46530725    10.46530725
    8    10.46530725     3.48843575    10.46530725
    9     4.22798413     2.49772000     0.00000000
   10     9.72575887    11.45602300     0.00000000
   11     4.22798413    11.45602300     0.00000000
   12     9.72575887     2.49772000     0.00000000
   13     0.00000000     4.22798413     2.49772000
   14     0.00000000     9.72575887    11.45602300
   15     0.00000000     9.72575887     2.49772000
   16     0.00000000     4.22798413    11.45602300
   17     2.49772000     0.00000000     4.22798413
   18    11.45602300     0.00000000     9.72575887
   19    11.45602300     0.00000000     4.22798413
   20     2.49772000     0.00000000     9.72575887
 PGLSYM: THE CRYSTAL SYSTEM IS CUBIC       
 PGLSYM: ORDER OF LATTICE POINT GROUP (NO BASE) =            48
 PGBSYM: ORDER OF LATTICE SPACE GROUP (WITH BASE) =          24
 PGBSYM: SPACE GROUP IS SYMMORPHIC
 PGBSYM: SPACE GROUP CONTAINS INVERSION
 Symmetry operation           1
        1.00000        0.00000        0.00000
        0.00000       -1.00000        0.00000
        0.00000        0.00000       -1.00000
        0.00000        0.00000        0.00000
    1.0000    0.0000    0.0000    0.0000
    0.0000   -1.0000    0.0000    0.0000
    0.0000    0.0000   -1.0000    0.0000
           this is operation           1  in struct file
 Symmetry operation           2
        0.00000        0.00000        1.00000
       -1.00000        0.00000        0.00000
        0.00000       -1.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000   -1.0000    0.0000    0.0000
    0.0000    0.0000   -1.0000    0.0000
    1.0000    0.0000    0.0000    0.0000
           this is operation           2  in struct file
 Symmetry operation           3
        0.00000        1.00000        0.00000
        0.00000        0.00000       -1.00000
       -1.00000        0.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    0.0000   -1.0000    0.0000
    1.0000    0.0000    0.0000    0.0000
    0.0000   -1.0000    0.0000    0.0000
           this is operation           3  in struct file
 Symmetry operation           4
       -1.00000        0.00000        0.00000
        0.00000       -1.00000        0.00000
        0.00000        0.00000       -1.00000
        0.00000        0.00000        0.00000
   -1.0000    0.0000    0.0000    0.0000
    0.0000   -1.0000    0.0000    0.0000
    0.0000    0.0000   -1.0000    0.0000
           this is operation           4  in struct file
 Symmetry operation           5
        0.00000        0.00000        1.00000
        1.00000        0.00000        0.00000
        0.00000       -1.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    1.0000    0.0000    0.0000
    0.0000    0.0000   -1.0000    0.0000
    1.0000    0.0000    0.0000    0.0000
           this is operation           5  in struct file
 Symmetry operation           6
        0.00000        1.00000        0.00000
        0.00000        0.00000       -1.00000
        1.00000        0.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    0.0000    1.0000    0.0000
    1.0000    0.0000    0.0000    0.0000
    0.0000   -1.0000    0.0000    0.0000
           this is operation           6  in struct file
 Symmetry operation           7
        1.00000        0.00000        0.00000
        0.00000        1.00000        0.00000
        0.00000        0.00000       -1.00000
        0.00000        0.00000        0.00000
    1.0000    0.0000    0.0000    0.0000
    0.0000    1.0000    0.0000    0.0000
    0.0000    0.0000   -1.0000    0.0000
           this is operation           7  in struct file
 Symmetry operation           8
        0.00000       -1.00000        0.00000
        0.00000        0.00000       -1.00000
       -1.00000        0.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    0.0000   -1.0000    0.0000
   -1.0000    0.0000    0.0000    0.0000
    0.0000   -1.0000    0.0000    0.0000
           this is operation           8  in struct file
 Symmetry operation           9
        0.00000        0.00000        1.00000
       -1.00000        0.00000        0.00000
        0.00000        1.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000   -1.0000    0.0000    0.0000
    0.0000    0.0000    1.0000    0.0000
    1.0000    0.0000    0.0000    0.0000
           this is operation           9  in struct file
 Symmetry operation          10
        0.00000        0.00000       -1.00000
       -1.00000        0.00000        0.00000
        0.00000       -1.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000   -1.0000    0.0000    0.0000
    0.0000    0.0000   -1.0000    0.0000
   -1.0000    0.0000    0.0000    0.0000
           this is operation          10  in struct file
 Symmetry operation          11
        0.00000        1.00000        0.00000
        0.00000        0.00000        1.00000
       -1.00000        0.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    0.0000   -1.0000    0.0000
    1.0000    0.0000    0.0000    0.0000
    0.0000    1.0000    0.0000    0.0000
           this is operation          11  in struct file
 Symmetry operation          12
        1.00000        0.00000        0.00000
        0.00000       -1.00000        0.00000
        0.00000        0.00000        1.00000
        0.00000        0.00000        0.00000
    1.0000    0.0000    0.0000    0.0000
    0.0000   -1.0000    0.0000    0.0000
    0.0000    0.0000    1.0000    0.0000
           this is operation          12  in struct file
 Symmetry operation          13
       -1.00000        0.00000        0.00000
        0.00000        1.00000        0.00000
        0.00000        0.00000       -1.00000
        0.00000        0.00000        0.00000
   -1.0000    0.0000    0.0000    0.0000
    0.0000    1.0000    0.0000    0.0000
    0.0000    0.0000   -1.0000    0.0000
           this is operation          13  in struct file
 Symmetry operation          14
        0.00000       -1.00000        0.00000
        0.00000        0.00000       -1.00000
        1.00000        0.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    0.0000    1.0000    0.0000
   -1.0000    0.0000    0.0000    0.0000
    0.0000   -1.0000    0.0000    0.0000
           this is operation          14  in struct file
 Symmetry operation          15
        0.00000        0.00000        1.00000
        1.00000        0.00000        0.00000
        0.00000        1.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    1.0000    0.0000    0.0000
    0.0000    0.0000    1.0000    0.0000
    1.0000    0.0000    0.0000    0.0000
           this is operation          15  in struct file
 Symmetry operation          16
        0.00000        0.00000       -1.00000
        1.00000        0.00000        0.00000
        0.00000       -1.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    1.0000    0.0000    0.0000
    0.0000    0.0000   -1.0000    0.0000
   -1.0000    0.0000    0.0000    0.0000
           this is operation          16  in struct file
 Symmetry operation          17
        0.00000        1.00000        0.00000
        0.00000        0.00000        1.00000
        1.00000        0.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    0.0000    1.0000    0.0000
    1.0000    0.0000    0.0000    0.0000
    0.0000    1.0000    0.0000    0.0000
           this is operation          17  in struct file
 Symmetry operation          18
       -1.00000        0.00000        0.00000
        0.00000       -1.00000        0.00000
        0.00000        0.00000        1.00000
        0.00000        0.00000        0.00000
   -1.0000    0.0000    0.0000    0.0000
    0.0000   -1.0000    0.0000    0.0000
    0.0000    0.0000    1.0000    0.0000
           this is operation          18  in struct file
 Symmetry operation          19
        0.00000       -1.00000        0.00000
        0.00000        0.00000        1.00000
       -1.00000        0.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    0.0000   -1.0000    0.0000
   -1.0000    0.0000    0.0000    0.0000
    0.0000    1.0000    0.0000    0.0000
           this is operation          19  in struct file
 Symmetry operation          20
        0.00000        0.00000       -1.00000
       -1.00000        0.00000        0.00000
        0.00000        1.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000   -1.0000    0.0000    0.0000
    0.0000    0.0000    1.0000    0.0000
   -1.0000    0.0000    0.0000    0.0000
           this is operation          20  in struct file
 Symmetry operation          21
        1.00000        0.00000        0.00000
        0.00000        1.00000        0.00000
        0.00000        0.00000        1.00000
        0.00000        0.00000        0.00000
    1.0000    0.0000    0.0000    0.0000
    0.0000    1.0000    0.0000    0.0000
    0.0000    0.0000    1.0000    0.0000
           this is operation          21  in struct file
 Symmetry operation          22
        0.00000       -1.00000        0.00000
        0.00000        0.00000        1.00000
        1.00000        0.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    0.0000    1.0000    0.0000
   -1.0000    0.0000    0.0000    0.0000
    0.0000    1.0000    0.0000    0.0000
           this is operation          22  in struct file
 Symmetry operation          23
        0.00000        0.00000       -1.00000
        1.00000        0.00000        0.00000
        0.00000        1.00000        0.00000
        0.00000        0.00000        0.00000
    0.0000    1.0000    0.0000    0.0000
    0.0000    0.0000    1.0000    0.0000
   -1.0000    0.0000    0.0000    0.0000
           this is operation          23  in struct file
 Symmetry operation          24
       -1.00000        0.00000        0.00000
        0.00000        1.00000        0.00000
        0.00000        0.00000        1.00000
        0.00000        0.00000        0.00000
   -1.0000    0.0000    0.0000    0.0000
    0.0000    1.0000    0.0000    0.0000
    0.0000    0.0000    1.0000    0.0000
           this is operation          24  in struct file



DETERMINATION OF POINTGROUP FOR ALL POSITIONS
CaCu3Ti4O12                                                                    
CaCalcium :   2 Atoms, Index    1 to    2
CuCopper  :   6 Atoms, Index    3 to    8
TiTitanium:   8 Atoms, Index    9 to   16
O Oxygen  :  24 Atoms, Index   17 to   40
number of atoms:  40

 ATOM:           1
CaCalcium  operation #  1     1                   
CaCalcium  operation #  2     -1                  
CaCalcium  operation #  3     2 || x              
CaCalcium  operation #  4     2 || y              
CaCalcium  operation #  5     2 || z              
CaCalcium  operation #  6     m n z               
CaCalcium  operation #  7     m n y               
CaCalcium  operation #  8     m n x               
CaCalcium  operation # 24     3 || 111            
CaCalcium  operation # 25     3 || 11-1           
CaCalcium  operation # 26     3 || -111           
CaCalcium  operation # 27     3 || 1-11           
CaCalcium  operation # 28     S6 || 111           
CaCalcium  operation # 29     S6 || -1-11         
CaCalcium  operation # 30     S6 || 1-1-1         
CaCalcium  operation # 31     S6 || 1-11          
CaCalcium  operation # 38     3 || 111            
CaCalcium  operation # 39     3 || 11-1           
CaCalcium  operation # 40     3 || -111           
CaCalcium  operation # 41     3 || 1-11           
CaCalcium  operation # 42     S6 || 111           
CaCalcium  operation # 43     S6 || -1-11         
CaCalcium  operation # 44     S6 || 1-1-1         
CaCalcium  operation # 45     S6 || 1-11          
  pointgroup is m3 (pos. iatnr!!)
  axes should be: any
  z-rotation vector:  0.0000  0.0000  1.0000
  y-rotation vector:  0.0000  0.0000  0.0000    0
LOCAL ROT MATRIX:       NEW                                OLD
           1.0000000 0.0000000 0.0000000      1.0000000 0.0000000 0.0000000
           0.0000000 1.0000000 0.0000000      0.0000000 1.0000000 0.0000000
           0.0000000 0.0000000 1.0000000      0.0000000 0.0000000 1.0000000
lm: 0 0  4 0  4 4  6 0  6 4  6 2  6 6
 ==============================================

 ATOM:          -2
CuCopper   operation #  1     1                   
CuCopper   operation #  2     -1                  
CuCopper   operation #  3     2 || x              
CuCopper   operation #  4     2 || y              
CuCopper   operation #  5     2 || z              
CuCopper   operation #  6     m n z               
CuCopper   operation #  7     m n y               
CuCopper   operation #  8     m n x               
  pointgroup is mmm (neg. iatnr!!)
  axes should be: m n z, m n y, m n x
  z-rotation vector:  0.0000  0.0000  1.0000
  y-rotation vector:  0.0000  1.0000  0.0000    2
LOCAL ROT MATRIX:       NEW                                OLD
           1.0000000 0.0000000 0.0000000      1.0000000 0.0000000 0.0000000
           0.0000000 1.0000000 0.0000000      0.0000000 1.0000000 0.0000000
           0.0000000 0.0000000 1.0000000      0.0000000 0.0000000 1.0000000
lm: 0 0  2 0  2 2  4 0  4 2  4 4  6 0  6 2  6 4  6 6
 ==============================================

 ATOM:          -3
TiTitanium operation #  1     1                   
TiTitanium operation #  2     -1                  
TiTitanium operation # 24     3 || 111            
TiTitanium operation # 28     S6 || 111           
TiTitanium operation # 38     3 || 111            
TiTitanium operation # 42     S6 || 111           
  pointgroup is -3 (neg. iatnr!!)
  axes should be: -3 || z
  z-rotation vector:  1.0000  1.0000  1.0000
  y-rotation vector:  1.0000  0.0000  0.0000    0
LOCAL ROT MATRIX:       NEW                                OLD
           0.7071068 0.4082483 0.5773503      0.7071068 0.4082483 0.5773503
          -0.7071068 0.4082483 0.5773503     -0.7071068 0.4082483 0.5773503
           0.0000000-0.8164966 0.5773503      0.0000000-0.8164966 0.5773503
lm: 0 0  2 0  4 0  4 3 -4 3  6 0  6 3 -6 3  6 6 -6 6
 ==============================================

 ATOM:          -4
O Oxygen   operation #  1     1                   
O Oxygen   operation #  6     m n z               
  pointgroup is m (neg. iatnr!!)
  axes should be: m n z
  z-rotation vector:  0.0000  0.0000  1.0000
  y-rotation vector:  0.7071 -0.7071  0.0000    0
LOCAL ROT MATRIX:       NEW                                OLD
           1.0000000 0.0000000 0.0000000      1.0000000 0.0000000 0.0000000
           0.0000000 1.0000000 0.0000000      0.0000000 1.0000000 0.0000000
           0.0000000 0.0000000 1.0000000      0.0000000 0.0000000 1.0000000
lm: 0 0  1 1 -1 1  2 0  2 2 -2 2  3 1 -3 1  3 3 -3 3  4 0  4 2 -4 2  4 4 -4 4  5 1 -5 1  5 3 -5 3  5 5 -5 5  6 0  6 2 -6 2  6 4 -6 4  6 6 -6 6
 ==============================================
-------------- next part --------------
CaCu3Ti4O12                                                 
B   LATTICE,NONEQUIV.ATOMS:  4204_Im-3                      
MODE OF CALC=RELA unit=ang 
 13.953743 13.953743 13.953743 90.000000 90.000000 90.000000
ATOM   1: X=0.00000000 Y=0.00000000 Z=0.00000000
          MULT= 1          ISPLIT= 2
CaCalcium  NPT=  781  R0=0.00010000 RMT=    1.9000   Z: 20.0
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
ATOM  -2: X=0.50000000 Y=0.00000000 Z=0.00000000
          MULT= 3          ISPLIT= 8
ATOM  -2:X= 0.00000000 Y=0.50000000 Z=0.00000000
ATOM  -2:X= 0.00000000 Y=0.00000000 Z=0.50000000
CuCopper   NPT=  781  R0=0.00010000 RMT=    1.9000   Z: 29.0
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
ATOM  -3: X=0.25000000 Y=0.25000000 Z=0.25000000
          MULT= 4          ISPLIT= 4
ATOM  -3:X= 0.75000000 Y=0.75000000 Z=0.25000000
ATOM  -3:X= 0.25000000 Y=0.75000000 Z=0.75000000
ATOM  -3:X= 0.75000000 Y=0.25000000 Z=0.75000000
TiTitanium NPT=  781  R0=0.00010000 RMT=    1.9000   Z: 22.0
LOCAL ROT MATRIX:    0.7071068 0.4082483 0.5773503
                    -0.7071068 0.4082483 0.5773503
                     0.0000000-0.8164966 0.5773503
ATOM  -4: X=0.30300000 Y=0.17900000 Z=0.00000000
          MULT=12          ISPLIT= 9
ATOM  -4:X= 0.69700000 Y=0.82100000 Z=0.00000000
ATOM  -4:X= 0.30300000 Y=0.82100000 Z=0.00000000
ATOM  -4:X= 0.69700000 Y=0.17900000 Z=0.00000000
ATOM  -4:X= 0.00000000 Y=0.30300000 Z=0.17900000
ATOM  -4:X= 0.00000000 Y=0.69700000 Z=0.82100000
ATOM  -4:X= 0.00000000 Y=0.69700000 Z=0.17900000
ATOM  -4:X= 0.00000000 Y=0.30300000 Z=0.82100000
ATOM  -4:X= 0.17900000 Y=0.00000000 Z=0.30300000
ATOM  -4:X= 0.82100000 Y=0.00000000 Z=0.69700000
ATOM  -4:X= 0.82100000 Y=0.00000000 Z=0.30300000
ATOM  -4:X= 0.17900000 Y=0.00000000 Z=0.69700000
O Oxygen   NPT=  781  R0=0.00010000 RMT=    1.8000   Z:  8.0
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
  24      NUMBER OF SYMMETRY OPERATIONS
 1 0 0 0.0000000
 0-1 0 0.0000000
 0 0-1 0.0000000
       1
 0-1 0 0.0000000
 0 0-1 0.0000000
 1 0 0 0.0000000
       2
 0 0-1 0.0000000
 1 0 0 0.0000000
 0-1 0 0.0000000
       3
-1 0 0 0.0000000
 0-1 0 0.0000000
 0 0-1 0.0000000
       4
 0 1 0 0.0000000
 0 0-1 0.0000000
 1 0 0 0.0000000
       5
 0 0 1 0.0000000
 1 0 0 0.0000000
 0-1 0 0.0000000
       6
 1 0 0 0.0000000
 0 1 0 0.0000000
 0 0-1 0.0000000
       7
 0 0-1 0.0000000
-1 0 0 0.0000000
 0-1 0 0.0000000
       8
 0-1 0 0.0000000
 0 0 1 0.0000000
 1 0 0 0.0000000
       9
 0-1 0 0.0000000
 0 0-1 0.0000000
-1 0 0 0.0000000
      10
 0 0-1 0.0000000
 1 0 0 0.0000000
 0 1 0 0.0000000
      11
 1 0 0 0.0000000
 0-1 0 0.0000000
 0 0 1 0.0000000
      12
-1 0 0 0.0000000
 0 1 0 0.0000000
 0 0-1 0.0000000
      13
 0 0 1 0.0000000
-1 0 0 0.0000000
 0-1 0 0.0000000
      14
 0 1 0 0.0000000
 0 0 1 0.0000000
 1 0 0 0.0000000
      15
 0 1 0 0.0000000
 0 0-1 0.0000000
-1 0 0 0.0000000
      16
 0 0 1 0.0000000
 1 0 0 0.0000000
 0 1 0 0.0000000
      17
-1 0 0 0.0000000
 0-1 0 0.0000000
 0 0 1 0.0000000
      18
 0 0-1 0.0000000
-1 0 0 0.0000000
 0 1 0 0.0000000
      19
 0-1 0 0.0000000
 0 0 1 0.0000000
-1 0 0 0.0000000
      20
 1 0 0 0.0000000
 0 1 0 0.0000000
 0 0 1 0.0000000
      21
 0 0 1 0.0000000
-1 0 0 0.0000000
 0 1 0 0.0000000
      22
 0 1 0 0.0000000
 0 0 1 0.0000000
-1 0 0 0.0000000
      23
-1 0 0 0.0000000
 0 1 0 0.0000000
 0 0 1 0.0000000
      24


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