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

[Juergen Spitaler]

Dear Prof. Blaha,
thank you very much for your detailed answer!

Peter Blaha wrote:
> 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.
>   
In the meantime I could solve this issue: It was not related
to the choice of x and y!!
The problem was that in the starting struct file of the hexagonal
unit cell I had already included the identity as symmetry operation,
i.e. there was already 1 symmetry operation present
(see attached structure file).
In this case "symmetry" yielded warnings,
("nsym found by symmetry differs ...")
and in the init_lapw process no new structure file with 12
symmetry operations is proposed.
After changing the number of sym. ops. of my originial
structure file to 0, "symmetry" did not yield the warnings
any more and produced the new structure with 12 symmetries.

> 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".
>   
I see,so the problem is really that we don't deal with the
smallest possible unit cell, which would be the rhombohedral
cell, but a larger one ...

Best regards
Juergen Spitaler
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