[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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