[Wien] Transformation from rhombohedral to hexagonal coordinates - swapping of x and y components

[Peter Blaha]

Now I looked briefly into the code and apparently I've made this change
(some 20 years ago for reasons I cannot remember at all).

Naively, I'd say that interchanging h1 and h2 must not matter at all.
Maybe it was done because I wanted that the first position of the
hex setting 18e (x,0,.25) matches the first rhomb setting 6e (x,.5-x,.25)
of the int.Tables of Cryst.

Can you send me the two struct files (or the basic data), when you say
that symmetry does not work at all (finds zero symmetry) ? I do not understand
this, because your interchanged H1/H2 matric would lead for the example above
to a position (.5-x,.25,x), which is a valid 6e position and in WIEN it should
not matter which of the 6 "6e" positions you enter.

The answer to the question: 12 vs. 36 symmetry operations is the same
as for FCC Cu: Do we have 48 or 4.48=192 symmetry operations?
The "primitive" cell always has 48 (or 12 for Rhomb) symops, the
"simple-cubic (or hexagonal) "supercell" has 4 (3) times more. But
WIEN uses always a primitive cell.

Take a primitive cubic cell with one atom. There are 48 operations.
Now create a 10x10x10 supercell. This produces 1000 atoms and of course,
these 1000 atoms are still equivalent. Thus a "generalized" symmetry-
program should find at least 1000 symmetry operations, which transform
these atoms among each other.

WIEN does not do it, but requires that you define the smallest possible cell
(the "primitive" one; and sgroup will do this for you); or you have to
"break symmetry" and make some atoms "non-equivalent".


> Dear Prof. Blaha,
> it is true that hex2rho and rho2hex are compatible,
> since both of them use the same hexagonal Bravais matrix
> with the swapped two lines.
> Writing the hexagonal lattice vectors in rows, they both use
>     H1 = (0         1     0)
>     H2 = (0.866  -0.5     0)
>     H3 = (0         0     1)
>     (I will call this rhomb2hex setting)
> instead of
>     H1 = (0.866  -0.5     0)
>     H2 = (0         1     0)
>     H3 = (0         0     1)
>   (I will call this usersguide setting) 
> 
> There are 4 points about this lattice choice:
> - The change of the Bravais matrix cannot be
>   a matter of row/column vectors. That would
>   leave, eg., the H(1,1) component unchanged
> - The coordinate system defined in the rhomb2hex
>   setting is left-handed, and not right-handed anymore.
>   Apart from that, the order of H1 and H2 should
>   not change the "physics".
> - In both cases, "nn" yields exactly the same nearest
>  neighbor distances, as one could expect, and in both
>  cases it is found that all 12 Al atoms are  equivalent,
>  and all 18 O atoms equivalent.
> - "symmetry" finds 12 symmetries in the rhomb2hex setting,
>   but no symmetry at all for the usersguide setting.
> 
> In this context it would also be interesting why even in
> the rhomb2hex setting only 12 symmetry operations are found,
> instead of 36; this problem was already described
> Swati Chaudhury in Aug 2007, but to my understanding it has
> not been answered so far.
> 
> Best wishes,
> Juergen
> 
> 
> 
>  
>  
> 
>> I cannot answer this in general.
>> All I see from simple tests is that hex2rho and rho2hex are converting coordinates
>> into each other properly.
>> WIEN takes sometimes row, sometimes column vectors ....
>>
>> We would need to look into a specific example where you have some structural
>> data and need to set them into WIEN2k-format. Then check eg. the nn-distances,
>> symmetry,....
>>
>> Juergen Spitaler schrieb:
>>   
>>> Dear Prof. Blaha!
>>> Recently I have been dealing with the conversion from rhombohedral to
>>> hexagonal coordinates. I was surprised that the x and y  values I
>>> obtained for the hexagonal coordinates were just swapped with
>>> respect to the ones "expected" by sgroup/symmetry
>>> and the ones obtained by rhomb2hex.
>>> When I looked into the source of rhomb2hex I found that
>>> the first and second line of the Bravais matrix for the hexagonal
>>> lattice are swapped with respect to the lattice vectors given in
>>> the usersguide. Now my questions are:
>>> - How can this swapping be explained?
>>> - Are the coordinates I obtain using the "swapped" hexagonal Bravais matrix
>>>   compatible with all other parts of the Wien-code?
>>>
>>> Best regards,
>>> Juergen Spitaler
>>>
>>>     
>>
>>   
> 
> 
> -- 
> Dr. Jürgen Spitaler
> Material Center Leoben and
> Chair of Atomistic Modelling and Design of Materials, Leoben University
> Franz-Josef-Straße 18    
> 8700 Leoben
> Tel.: ++43 (0)3842 402 4404
> E-Mail: juergen.spitaler at unileoben.ac.at
> 
> 
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-- 

                                       P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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