[Wien] "x nn" problem
Bing Zhou
umbingz at cc.UManitoba.CA
Sat Oct 11 11:44:28 CEST 2003
Dear Kevin and Lukasz:
Thank you for your great help! Yes, I use A instead of a.u. when I input
the lattice constants using w2web. Now I attach my case.struct and
case.outputnn files with this email, could you please take a look for me
again?
Thanks!
Best wishes!
On Sat, 11 Oct 2003, Jorissen Kevin wrote:
> Hello Bing Zhou & Lukasz,
> the answer is much more simple.
>
> The "5" in "atom 5" corresponds to the number of an inequivalent atom class in case.struct. Apparently, this class contains more than one atom in the unit cell, either because there is more than one entry for atom 5 in case.struct, or your lattice type (e.g. F) generates more positions.
> Nn verifies that NO atoms in the unit cell overlap, whether they belong to the same equivalency class or not. In your case, the distance between two different atom positions both belonging to equivalency class 5 was calculated.
>
> So there is nothing strange about this.
>
> 1 a.u. is a rather small nearest neighbour distance, maybe you did input the lattice constants in A instead of a.u., as Lukasz suggested?
>
> Kevin.
>
> PS Lukasz, in fact, if you go to case.outputnn, you can find out exactly which atom positions correspond to a particular interatomic distance - nn tends to write endless lists of those.
>
> -----Oorspronkelijk bericht-----
> Van: Lukasz Plucinski [mailto:pluto at buphy.bu.edu]
> Verzonden: za 10/11/2003 1:35
> Aan: wien at zeus.theochem.tuwien.ac.at
> CC:
> Onderwerp: Re: [Wien] "x nn" problem
>
>
>
> > Why did my "init_lapw" give the distance between atom 5 and atom 5?
> >
> >
> > ERROR !!!!!!!!!!!!!!!
> > RMT( 5)=0.70000 AND RMT( 5)=0.70000
> > SUMS TO 1.40000 GT NNN-DIST= 1.05157
>
> Hello,
>
> Difficult to answer. My guess:
>
> Distance 1.05157 is related to your lattice constant (and maybe you set it
> e.g. in eV instead of Ry when typing into w2web).
>
> Maybe the problem is also related to space group and inequivalent
> positions, I am not sure.
>
> You should probably attach 'struct' file. There was a discussion few days
> ago that the users should provide more information about their problems.
> Even if Prof. Blaha and few other experts are able to answer almost every
> question with minimum information included other guys (like me) may need
> some more. And then Prof. Blaha don't have to answer almost every single
> question himself :).
>
> What is the material ? How many atoms you have in the primitive cell ? -
> if its like 2 or 4 it would be very easy to find out where the distance
> of 1.05157 comes from.
>
> Regards,
>
> Lukasz
>
> _______________________________________________
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at
> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
>
>
>
>
Bing Zhou
Dept. of Geol. Sc.
The Univ. of Manitoba
Canada R3T 2N2
Tel: (204)474-8395
-------------- next part --------------
Ammonium Nitrate Phase 4
P LATTICE,NONEQUIV.ATOMS: 659_Pmmn
MODE OF CALC=RELA unit=ang
10.856481 10.276335 9.339030 90.000000 90.000000 90.000000
ATOM -1: X=0.75000000 Y=0.25000000 Z=0.91640000
MULT= 2 ISPLIT= 8
-1: X=0.25000000 Y=0.75000000 Z=0.08360000
N NPT= 781 R0=0.00010000 RMT= 1.1000 Z: 7.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -2: X=0.60450000 Y=0.25000000 Z=0.81020000
MULT= 4 ISPLIT= 8
-2: X=0.39550000 Y=0.75000000 Z=0.18980000
-2: X=0.10450000 Y=0.75000000 Z=0.18980000
-2: X=0.89550000 Y=0.25000000 Z=0.81020000
H NPT= 781 R0=0.00010000 RMT= 0.7000 Z: 1.0
LOCAL ROT MATRIX: 0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
1.0000000 0.0000000 0.0000000
ATOM -3: X=0.75000000 Y=0.10110000 Z=0.03240000
MULT= 4 ISPLIT= 8
-3: X=0.25000000 Y=0.89890000 Z=0.96760000
-3: X=0.25000000 Y=0.60110000 Z=0.96760000
-3: X=0.75000000 Y=0.39890000 Z=0.03240000
H NPT= 781 R0=0.00010000 RMT= 0.7000 Z: 1.0
LOCAL ROT MATRIX: 0.0000000 0.0000000 1.0000000
1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
ATOM -4: X=0.25000000 Y=0.25000000 Z=0.50670000
MULT= 2 ISPLIT= 8
-4: X=0.75000000 Y=0.75000000 Z=0.49330000
N NPT= 781 R0=0.00010000 RMT= 1.0000 Z: 7.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -5: X=0.25000000 Y=0.25000000 Z=0.76290000
MULT= 2 ISPLIT= 8
-5: X=0.75000000 Y=0.75000000 Z=0.23710000
O NPT= 781 R0=0.00010000 RMT= 1.2000 Z: 8.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -6: X=0.43420000 Y=0.25000000 Z=0.38320000
MULT= 4 ISPLIT= 8
-6: X=0.56580000 Y=0.75000000 Z=0.61680000
-6: X=0.93420000 Y=0.75000000 Z=0.61680000
-6: X=0.06580000 Y=0.25000000 Z=0.38320000
O NPT= 781 R0=0.00010000 RMT= 1.2000 Z: 8.0
LOCAL ROT MATRIX: 0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
1.0000000 0.0000000 0.0000000
8 NUMBER OF SYMMETRY OPERATIONS
-1 0 0 0.0000000
0-1 0 0.0000000
0 0-1 0.0000000
1
1 0 0 0.0000000
0 1 0 0.0000000
0 0 1 0.0000000
2
-1 0 0 0.5000000
0-1 0 0.5000000
0 0 1 0.0000000
3
-1 0 0 0.0000000
0 1 0 0.5000000
0 0-1 0.0000000
4
-1 0 0 0.5000000
0 1 0 0.0000000
0 0 1 0.0000000
5
1 0 0 0.5000000
0-1 0 0.0000000
0 0-1 0.0000000
6
1 0 0 0.0000000
0-1 0 0.5000000
0 0 1 0.0000000
7
1 0 0 0.5000000
0 1 0 0.5000000
0 0-1 0.0000000
8
-------------- next part --------------
Ammonium Nitrate Phase 4
P 6
RELA
10.856481 10.276335 9.339030 90.000000 90.000000 90.000000
-1 0.75000000 0.25000000 0.91640000
2
-1 0.25000000 0.75000000 0.08360000
N NPT= 781 R0=0.00010000 RMT= 1.1000 Z: 7.0
1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
2 0.60450000 0.25000000 0.81020000
4
2 0.39550000 0.75000000 0.18980000
2 0.10450000 0.75000000 0.18980000
2 0.89550000 0.25000000 0.81020000
H NPT= 781 R0=0.00010000 RMT= 0.7000 Z: 1.0
0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000
3 0.75000000 0.10110000 0.03240000
4
3 0.25000000 0.89890000 0.96760000
3 0.25000000 0.60110000 0.96760000
3 0.75000000 0.39890000 0.03240000
H NPT= 781 R0=0.00010000 RMT= 0.7000 Z: 1.0
0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000
4 0.25000000 0.25000000 0.50670000
2
4 0.75000000 0.75000000 0.49330000
N NPT= 781 R0=0.00010000 RMT= 1.0000 Z: 7.0
0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000
5 0.25000000 0.25000000 0.76290000
2
5 0.75000000 0.75000000 0.23710000
O NPT= 781 R0=0.00010000 RMT= 1.2000 Z: 8.0
0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000
6 0.43420000 0.25000000 0.38320000
4
6 0.56580000 0.75000000 0.61680000
6 0.93420000 0.75000000 0.61680000
6 0.06580000 0.25000000 0.38320000
O NPT= 781 R0=0.00010000 RMT= 1.2000 Z: 8.0
0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000
Bravais Matrix:
1.00000 0.00000 0.00000
0.00000 1.00000 0.00000
0.00000 0.00000 1.00000
ATOM: 1 EQUIV. 1 N AT 0.75000 0.25000 0.91640
RMT( 1)=1.10000 AND RMT( 2)=0.70000
SUMS TO 1.80000 LT. NN-DIST= 1.86517
ATOM: 2 H AT 0.6045 0.2500 0.8102 IS 1.86517 A.U. 0.98701 ANG
ATOM: 2 H AT 0.8955 0.2500 0.8102 IS 1.86517 A.U. 0.98701 ANG
ATOM: 3 H AT 0.7500 0.3989 1.0324 IS 1.87482 A.U. 0.99211 ANG
ATOM: 3 H AT 0.7500 0.1011 1.0324 IS 1.87482 A.U. 0.99211 ANG
ATOM: 1 EQUIV. 2 N AT 0.25000 0.75000 0.08360
ATOM: 2 H AT 0.3955 0.7500 0.1898 IS 1.86517 A.U. 0.98701 ANG
ATOM: 2 H AT 0.1045 0.7500 0.1898 IS 1.86517 A.U. 0.98701 ANG
ATOM: 3 H AT 0.2500 0.8989 -0.0324 IS 1.87482 A.U. 0.99211 ANG
ATOM: 3 H AT 0.2500 0.6011 -0.0324 IS 1.87482 A.U. 0.99211 ANG
ATOM: 2 EQUIV. 1 H AT 0.60450 0.25000 0.81020
RMT( 2)=0.70000 AND RMT( 1)=1.10000
SUMS TO 1.80000 LT. NN-DIST= 1.86517
ATOM: 1 N AT 0.7500 0.2500 0.9164 IS 1.86517 A.U. 0.98701 ANG
ATOM: 3 H AT 0.7500 0.1011 1.0324 IS 3.02369 A.U. 1.60007 ANG
ATOM: 3 H AT 0.7500 0.3989 1.0324 IS 3.02369 A.U. 1.60007 ANG
ATOM: 2 H AT 0.8955 0.2500 0.8102 IS 3.15924 A.U. 1.67180 ANG
ATOM: 2 EQUIV. 2 H AT 0.39550 0.75000 0.18980
ATOM: 1 N AT 0.2500 0.7500 0.0836 IS 1.86517 A.U. 0.98701 ANG
ATOM: 3 H AT 0.2500 0.8989 -0.0324 IS 3.02369 A.U. 1.60007 ANG
ATOM: 3 H AT 0.2500 0.6011 -0.0324 IS 3.02369 A.U. 1.60007 ANG
ATOM: 2 H AT 0.1045 0.7500 0.1898 IS 3.15924 A.U. 1.67180 ANG
ATOM: 2 EQUIV. 3 H AT 0.10450 0.75000 0.18980
ATOM: 1 N AT 0.2500 0.7500 0.0836 IS 1.86517 A.U. 0.98701 ANG
ATOM: 3 H AT 0.2500 0.8989 -0.0324 IS 3.02369 A.U. 1.60007 ANG
ATOM: 3 H AT 0.2500 0.6011 -0.0324 IS 3.02369 A.U. 1.60007 ANG
ATOM: 2 H AT 0.3955 0.7500 0.1898 IS 3.15924 A.U. 1.67180 ANG
ATOM: 2 EQUIV. 4 H AT 0.89550 0.25000 0.81020
ATOM: 1 N AT 0.7500 0.2500 0.9164 IS 1.86517 A.U. 0.98701 ANG
ATOM: 3 H AT 0.7500 0.1011 1.0324 IS 3.02369 A.U. 1.60007 ANG
ATOM: 3 H AT 0.7500 0.3989 1.0324 IS 3.02369 A.U. 1.60007 ANG
ATOM: 2 H AT 0.6045 0.2500 0.8102 IS 3.15924 A.U. 1.67180 ANG
ATOM: 3 EQUIV. 1 H AT 0.75000 0.10110 0.03240
RMT( 3)=0.70000 AND RMT( 1)=1.10000
SUMS TO 1.80000 LT. NN-DIST= 1.87482
ATOM: 1 N AT 0.7500 0.2500 -0.0836 IS 1.87482 A.U. 0.99211 ANG
ATOM: 2 H AT 0.6045 0.2500 -0.1898 IS 3.02369 A.U. 1.60007 ANG
ATOM: 2 H AT 0.8955 0.2500 -0.1898 IS 3.02369 A.U. 1.60007 ANG
ATOM: 3 H AT 0.7500 0.3989 0.0324 IS 3.06029 A.U. 1.61944 ANG
ATOM: 3 EQUIV. 2 H AT 0.25000 0.89890 0.96760
ATOM: 1 N AT 0.2500 0.7500 1.0836 IS 1.87482 A.U. 0.99211 ANG
ATOM: 2 H AT 0.3955 0.7500 1.1898 IS 3.02369 A.U. 1.60007 ANG
ATOM: 2 H AT 0.1045 0.7500 1.1898 IS 3.02369 A.U. 1.60007 ANG
ATOM: 3 H AT 0.2500 0.6011 0.9676 IS 3.06029 A.U. 1.61944 ANG
ATOM: 3 EQUIV. 3 H AT 0.25000 0.60110 0.96760
ATOM: 1 N AT 0.2500 0.7500 1.0836 IS 1.87482 A.U. 0.99211 ANG
ATOM: 2 H AT 0.3955 0.7500 1.1898 IS 3.02369 A.U. 1.60007 ANG
ATOM: 2 H AT 0.1045 0.7500 1.1898 IS 3.02369 A.U. 1.60007 ANG
ATOM: 3 H AT 0.2500 0.8989 0.9676 IS 3.06029 A.U. 1.61944 ANG
ATOM: 3 EQUIV. 4 H AT 0.75000 0.39890 0.03240
ATOM: 1 N AT 0.7500 0.2500 -0.0836 IS 1.87482 A.U. 0.99211 ANG
ATOM: 2 H AT 0.6045 0.2500 -0.1898 IS 3.02369 A.U. 1.60007 ANG
ATOM: 2 H AT 0.8955 0.2500 -0.1898 IS 3.02369 A.U. 1.60007 ANG
ATOM: 3 H AT 0.7500 0.1011 0.0324 IS 3.06029 A.U. 1.61944 ANG
ATOM: 4 EQUIV. 1 N AT 0.25000 0.25000 0.50670
RMT( 4)=1.00000 AND RMT( 6)=1.20000
SUMS TO 2.20000 LT. NN-DIST= 2.30853
ATOM: 6 O AT 0.4342 0.2500 0.3832 IS 2.30853 A.U. 1.22162 ANG
ATOM: 6 O AT 0.0658 0.2500 0.3832 IS 2.30853 A.U. 1.22162 ANG
ATOM: 5 O AT 0.2500 0.2500 0.7629 IS 2.39266 A.U. 1.26614 ANG
ATOM: 4 EQUIV. 2 N AT 0.75000 0.75000 0.49330
ATOM: 6 O AT 0.5658 0.7500 0.6168 IS 2.30853 A.U. 1.22162 ANG
ATOM: 6 O AT 0.9342 0.7500 0.6168 IS 2.30853 A.U. 1.22162 ANG
ATOM: 5 O AT 0.7500 0.7500 0.2371 IS 2.39266 A.U. 1.26614 ANG
ATOM: 5 EQUIV. 1 O AT 0.25000 0.25000 0.76290
RMT( 5)=1.20000 AND RMT( 4)=1.00000
SUMS TO 2.20000 LT. NN-DIST= 2.39266
ATOM: 4 N AT 0.2500 0.2500 0.5067 IS 2.39266 A.U. 1.26614 ANG
ATOM: 2 H AT -0.1045 0.2500 0.8102 IS 3.87389 A.U. 2.04997 ANG
ATOM: 2 H AT 0.6045 0.2500 0.8102 IS 3.87389 A.U. 2.04997 ANG
ATOM: 6 O AT 0.4342 0.2500 0.3832 IS 4.07104 A.U. 2.15430 ANG
ATOM: 6 O AT 0.0658 0.2500 0.3832 IS 4.07104 A.U. 2.15430 ANG
ATOM: 3 H AT 0.2500 -0.1011 0.9676 IS 4.08319 A.U. 2.16073 ANG
ATOM: 3 H AT 0.2500 0.6011 0.9676 IS 4.08319 A.U. 2.16073 ANG
ATOM: 5 EQUIV. 2 O AT 0.75000 0.75000 0.23710
ATOM: 4 N AT 0.7500 0.7500 0.4933 IS 2.39266 A.U. 1.26614 ANG
ATOM: 2 H AT 0.3955 0.7500 0.1898 IS 3.87389 A.U. 2.04997 ANG
ATOM: 2 H AT 1.1045 0.7500 0.1898 IS 3.87389 A.U. 2.04997 ANG
ATOM: 6 O AT 0.5658 0.7500 0.6168 IS 4.07104 A.U. 2.15430 ANG
ATOM: 6 O AT 0.9342 0.7500 0.6168 IS 4.07104 A.U. 2.15430 ANG
ATOM: 3 H AT 0.7500 1.1011 0.0324 IS 4.08319 A.U. 2.16073 ANG
ATOM: 3 H AT 0.7500 0.3989 0.0324 IS 4.08319 A.U. 2.16073 ANG
ATOM: 6 EQUIV. 1 O AT 0.43420 0.25000 0.38320
RMT( 6)=1.20000 AND RMT( 4)=1.00000
SUMS TO 2.20000 LT. NN-DIST= 2.30853
ATOM: 4 N AT 0.2500 0.2500 0.5067 IS 2.30853 A.U. 1.22162 ANG
ATOM: 6 O AT 0.0658 0.2500 0.3832 IS 3.99953 A.U. 2.11646 ANG
ATOM: 5 O AT 0.2500 0.2500 0.7629 IS 4.07104 A.U. 2.15430 ANG
ATOM: 2 H AT 0.6045 0.2500 0.8102 IS 4.39552 A.U. 2.32601 ANG
ATOM: 6 EQUIV. 2 O AT 0.56580 0.75000 0.61680
ATOM: 4 N AT 0.7500 0.7500 0.4933 IS 2.30853 A.U. 1.22162 ANG
ATOM: 6 O AT 0.9342 0.7500 0.6168 IS 3.99953 A.U. 2.11646 ANG
ATOM: 5 O AT 0.7500 0.7500 0.2371 IS 4.07104 A.U. 2.15430 ANG
ATOM: 2 H AT 0.3955 0.7500 0.1898 IS 4.39552 A.U. 2.32601 ANG
ATOM: 6 EQUIV. 3 O AT 0.93420 0.75000 0.61680
ATOM: 4 N AT 0.7500 0.7500 0.4933 IS 2.30853 A.U. 1.22162 ANG
ATOM: 6 O AT 0.5658 0.7500 0.6168 IS 3.99953 A.U. 2.11646 ANG
ATOM: 5 O AT 0.7500 0.7500 0.2371 IS 4.07104 A.U. 2.15430 ANG
ATOM: 2 H AT 1.1045 0.7500 0.1898 IS 4.39552 A.U. 2.32601 ANG
ATOM: 6 EQUIV. 4 O AT 0.06580 0.25000 0.38320
ATOM: 4 N AT 0.2500 0.2500 0.5067 IS 2.30853 A.U. 1.22162 ANG
ATOM: 6 O AT 0.4342 0.2500 0.3832 IS 3.99953 A.U. 2.11646 ANG
ATOM: 5 O AT 0.2500 0.2500 0.7629 IS 4.07104 A.U. 2.15430 ANG
ATOM: 2 H AT -0.1045 0.2500 0.8102 IS 4.39552 A.U. 2.32601 ANG
SHELL STRUCTURE for all ATOMS:
ATOM | DISTANCE #of NEIGHBORS Z |
1 | 1.865 2 1.0| 1.875 2 1.0| 5.546 2 8.0| 5.614 2 8.0|
2 | 1.865 2 1.0| 1.875 2 1.0| 5.546 2 8.0| 5.614 2 8.0|
3 | 1.865 1 7.0| 3.024 2 1.0| 3.159 1 1.0| 3.874 1 8.0|
4 | 1.865 1 7.0| 3.024 2 1.0| 3.159 1 1.0| 3.874 1 8.0|
5 | 1.865 1 7.0| 3.024 2 1.0| 3.159 1 1.0| 3.874 1 8.0|
6 | 1.865 1 7.0| 3.024 2 1.0| 3.159 1 1.0| 3.874 1 8.0|
7 | 1.875 1 7.0| 3.024 2 1.0| 3.060 1 1.0| 4.083 1 8.0|
8 | 1.875 1 7.0| 3.024 2 1.0| 3.060 1 1.0| 4.083 1 8.0|
9 | 1.875 1 7.0| 3.024 2 1.0| 3.060 1 1.0| 4.083 1 8.0|
10 | 1.875 1 7.0| 3.024 2 1.0| 3.060 1 1.0| 4.083 1 8.0|
11 | 2.309 2 8.0| 2.393 1 8.0| 4.780 2 1.0| 5.617 2 1.0|
12 | 2.309 2 8.0| 2.393 1 8.0| 4.780 2 1.0| 5.617 2 1.0|
13 | 2.393 1 7.0| 3.874 2 1.0| 4.071 2 8.0| 4.083 2 1.0|
14 | 2.393 1 7.0| 3.874 2 1.0| 4.071 2 8.0| 4.083 2 1.0|
15 | 2.309 1 7.0| 4.000 1 8.0| 4.071 1 8.0| 4.396 1 1.0|
16 | 2.309 1 7.0| 4.000 1 8.0| 4.071 1 8.0| 4.396 1 1.0|
17 | 2.309 1 7.0| 4.000 1 8.0| 4.071 1 8.0| 4.396 1 1.0|
18 | 2.309 1 7.0| 4.000 1 8.0| 4.071 1 8.0| 4.396 1 1.0|
LISTING of INDEX of all EQUIVALENT ATOMS:
ATOM: 1 and ATOM: 1 are equivalent
ATOM: 1 and ATOM: 2 are equivalent
ATOM: 3 and ATOM: 3 are equivalent
ATOM: 3 and ATOM: 4 are equivalent
ATOM: 3 and ATOM: 5 are equivalent
ATOM: 3 and ATOM: 6 are equivalent
ATOM: 7 and ATOM: 7 are equivalent
ATOM: 7 and ATOM: 8 are equivalent
ATOM: 7 and ATOM: 9 are equivalent
ATOM: 7 and ATOM: 10 are equivalent
ATOM: 11 and ATOM: 11 are equivalent
ATOM: 11 and ATOM: 12 are equivalent
ATOM: 13 and ATOM: 13 are equivalent
ATOM: 13 and ATOM: 14 are equivalent
ATOM: 15 and ATOM: 15 are equivalent
ATOM: 15 and ATOM: 16 are equivalent
ATOM: 15 and ATOM: 17 are equivalent
ATOM: 15 and ATOM: 18 are equivalent
ATOM KIND: 1 OLD and NEW MULTIPLICITY: 2 2
ATOM KIND: 2 OLD and NEW MULTIPLICITY: 4 4
ATOM KIND: 3 OLD and NEW MULTIPLICITY: 4 4
ATOM KIND: 4 OLD and NEW MULTIPLICITY: 2 2
ATOM KIND: 5 OLD and NEW MULTIPLICITY: 2 2
ATOM KIND: 6 OLD and NEW MULTIPLICITY: 4 4
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