# [Pw_forum] Vectors in rhombohedral cells

Marino Vetuschi Zuccolini zucco at dipteris.unige.it
Mon Nov 10 14:11:03 CET 2008

```Dear all,
working with a rhombohedral cell I've found something that appear to
me to going wrong, and I call you for a help. Probably is only my
mistake but I ask you a confirmation.

The problem arises when I compare the results of a vc-relax output as
below:

...
ibrav = 5,
celldm(1) = 10.9072,
celldm(4) = 0.67279,
....
End of BFGS Geometry Optimization

Final enthalpy =    -325.7624962652 Ry
new unit-cell volume =    666.19980 a.u.^3 (    98.72062 Ang^3 )

CELL_PARAMETERS (alat)
0.411520633  -0.237591548   0.875166762
0.000000000   0.475183096   0.875166762
-0.411520633  -0.237591548   0.875166762
...

and the few summary lines of an scf output of the optimized structure
with c=0.661301537
...
bravais-lattice index     =            5
lattice parameter (a_0)   =      10.8619  a.u.
unit-cell volume          =     661.4872 (a.u.)^3
...

crystal axes: (cart. coord. in units of a_0)
a(1) = (  0.411521 -0.237592  0.879887 )
a(2) = (  0.000000  0.475183  0.879887 )
a(3) = ( -0.411521 -0.237592  0.879887 )

You can see the difference in what concerns the volume.

To compute a0 and alpha of the optimized cell I used what is reported
in the PW manual

v1 = a(tx,-ty,tz),   v2 = a(0,2ty,tz),   v3 = a(-tx,-ty,tz).
where c=cos(alpha) is the cosine of the angle alpha between any pair
of crystallographic vectors, tc, ty, tz are defined as
tx=sqrt((1-c)/2), ty=sqrt((1-c)/6), tz=sqrt((1+2c)/3)

but...if I calculate c (as cos(alpha)) from tx, ty and tz I noticed
that tx and ty are good but tz is not.

From the vc-relax output I obtain:
c from tx ==> 0.661301537
c from ty ==> 0.661301537
c from tz ==> 0.648875292 <=== ?

From scf output I obtain, considering the truncation of the matrix'
elements
c from tx ==> 0.661300933
c from ty ==> 0.661300249
c from tz ==> 0.661301699

Thanks for any help

m.

*******************************************************
Marino Vetuschi Zuccolini
zucco at dipteris.unige.it
Researcher / Geochemist
Laboratory of Geochemistry

DIPartimento per lo studio della TErra e delle sue RISorse -
Università  di Genova
Tel. ++39 010 3538136 Fax. ++39 010 352169
Corso Europa 26, 16132 - Genova - Italy

```

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