[Pw_forum] K_POINTS, tpiba or crystal

Stefano Baroni baroni at sissa.it
Sun Jan 4 07:01:11 CET 2009


On Jan 4, 2009, at 12:38 AM, Paul M. Grant wrote:

> Followup on K_POINTS: tpiba vs crystal...

Hi Paul!

> As usual, Paolo is right...

he always does!

> for sc lattices (ibrav=1), tpiba or crystal give
> equal nscf outputs.

no surprise, here

> But, for fcc lattices (ibrav=2), it apparently does!

you mean it does NOT .?... no surprise here either ...

> See below comparing
> nscf k-vector outputs for tpiba and crystal, and crystal is very  
> different
> (and weird...for me anyway).

I am not sure I understand what the question really is, but I do not  
what would weird here.

My understanding is that "tpiba" means "cartesian coordinates in units  
of tipiba". By the way, it could be a good idea to replace "tpiba" (a  
word that does exist in the webster nor in any other dictionary) with  
"cartesian": this could help avoid some confusion. "crystal" means  
that the coordinates that you give are the coefficient that express a  
k-point as a linear combination of the reciprocal lattice basis g(1),  
g(2), g(3). In formulas:

k("tpiba")   =  tpiba *   (k(1)*x(1)+k(2)*x(2)+k(3)*x(3))
k("crystal") = tpiba* (k(1)*b(1)+k(2)*b(2)+k(3)*b(3)),

where x(1)= (1,0,0), x(2)=(0,1,0), x(3)=(0,0,1), and the slightly  
confusing tpiba in the second line is due to the code convention:  
g(*)=tpiba*b(*)

Let us take for instance the second vector of Paul's list. In the  
"tpiba" case, the output is just a copy of the input, as it should. In  
the crystal case, one should have:

output(*) = input(1)*b(1) + input(2)*b(2)+input(3)*b(3)
         = -1/12 (-1,-1,1) +1/12 (1,1,1)-1/12(-1,1,-1)
         = 1/12 (1+1+1,1+1-1,-1+1+1)
         = (1/4,1/12,1/12),

which is what it is. I have noot checked the other points, but I  
assume that they are what they should be according to the above argument

> BTW, whether tpiba, etc., should be enclosed
> in curly braces or parentheses or nothing on the K_POINTS card is  
> confusing.
> PW_INPUT shows braces, but parenthese work too, and probably no  
> delimiters
> as well.

sorry, no hints here ...

> My agenda here is to generate k-points grids amenable to  
> applications that
> cannot use simply MP weighted points in the irreducible BZ, such as
> epsilon.x.  I'm finding the algorithm used by Eyvaz Isaev for Fermi  
> Surface
> plotting which uniformly populate and span the fundamental reciprocal
> lattice cell works quite well...if inputted with tpiba or "blank," not
> crystal.

most probably, it give the cartesian representation of the k-points ...

hope the above is not (too) wrong and helpful to some extent ...

Happy new year to Paul, Paolo, and the whole newsgroup.

Stefano

>
>
>
> TPIBA VS CRYSTAL COMPARISON RE FCC FOLLOWS
> ===================================================
> TPIBA
> nsfc run input (partial) (Al, ibrav=2)
> K_POINTS  {tpiba}
>  2197
>  0.00000000  0.00000000  0.00000000  1.00000000
> -0.08333333  0.08333333 -0.08333333  1.00000000
> -0.16666667  0.16666667 -0.16666667  1.00000000
> -0.25000000  0.25000000 -0.25000000  1.00000000
> -0.33333333  0.33333333 -0.33333333  1.00000000
> -0.41666667  0.41666667 -0.41666667  1.00000000
> -0.50000000  0.50000000 -0.50000000  1.00000000
> -0.58333333  0.58333333 -0.58333333  1.00000000
> -0.66666667  0.66666667 -0.66666667  1.00000000
> -0.75000000  0.75000000 -0.75000000  1.00000000
> -0.83333333  0.83333333 -0.83333333  1.00000000
> -0.91666667  0.91666667 -0.91666667  1.00000000
> -1.00000000  1.00000000 -1.00000000  1.00000000
>  0.08333333  0.08333333  0.08333333  1.00000000
>  0.00000000  0.16666667  0.00000000  1.00000000
> -0.08333333  0.25000000 -0.08333333  1.00000000
> -0.16666667  0.33333333 -0.16666667  1.00000000
> -0.25000000  0.41666667 -0.25000000  1.00000000
> -0.33333333  0.50000000 -0.33333333  1.00000000
> ....................
> nsfc run output (partial) (Al, ibrav=2)
> reciprocal axes: (cart. coord. in units 2 pi/a_0)
>          b(1) = ( -1.000000 -1.000000  1.000000 )
>          b(2) = (  1.000000  1.000000  1.000000 )
>          b(3) = ( -1.000000  1.000000 -1.000000 )
> number of k points= 2197  gaussian broad. (Ry)=  0.0150     ngauss  
> =   0
>                  cart. coord. in units 2pi/a_0
>   k(    1) = (   0.0000000   0.0000000   0.0000000), wk =   0.0009103
>   k(    2) = (  -0.0833333   0.0833333  -0.0833333), wk =   0.0009103
>   k(    3) = (  -0.1666667   0.1666667  -0.1666667), wk =   0.0009103
>   k(    4) = (  -0.2500000   0.2500000  -0.2500000), wk =   0.0009103
>   k(    5) = (  -0.3333333   0.3333333  -0.3333333), wk =   0.0009103
>   k(    6) = (  -0.4166667   0.4166667  -0.4166667), wk =   0.0009103
>   k(    7) = (  -0.5000000   0.5000000  -0.5000000), wk =   0.0009103
>   k(    8) = (  -0.5833333   0.5833333  -0.5833333), wk =   0.0009103
>   k(    9) = (  -0.6666667   0.6666667  -0.6666667), wk =   0.0009103
>   k(   10) = (  -0.7500000   0.7500000  -0.7500000), wk =   0.0009103
>   k(   11) = (  -0.8333333   0.8333333  -0.8333333), wk =   0.0009103
>   k(   12) = (  -0.9166667   0.9166667  -0.9166667), wk =   0.0009103
>   k(   13) = (  -1.0000000   1.0000000  -1.0000000), wk =   0.0009103
>   k(   14) = (   0.0833333   0.0833333   0.0833333), wk =   0.0009103
>   k(   15) = (   0.0000000   0.1666667   0.0000000), wk =   0.0009103
>   k(   16) = (  -0.0833333   0.2500000  -0.0833333), wk =   0.0009103
> = 
> = 
> = 
> = 
> = 
> = 
> ======================================================================
> CRYSTAL
> nsfc run input (partial) (Al, ibrav=2)
> K_POINTS  {crystal}
>  2197
>  0.00000000  0.00000000  0.00000000  1.00000000
> -0.08333333  0.08333333 -0.08333333  1.00000000
> -0.16666667  0.16666667 -0.16666667  1.00000000
> -0.25000000  0.25000000 -0.25000000  1.00000000
> -0.33333333  0.33333333 -0.33333333  1.00000000
> -0.41666667  0.41666667 -0.41666667  1.00000000
> -0.50000000  0.50000000 -0.50000000  1.00000000
> -0.58333333  0.58333333 -0.58333333  1.00000000
> -0.66666667  0.66666667 -0.66666667  1.00000000
> -0.75000000  0.75000000 -0.75000000  1.00000000
> -0.83333333  0.83333333 -0.83333333  1.00000000
> -0.91666667  0.91666667 -0.91666667  1.00000000
> -1.00000000  1.00000000 -1.00000000  1.00000000
>  0.08333333  0.08333333  0.08333333  1.00000000
>  0.00000000  0.16666667  0.00000000  1.00000000
> -0.08333333  0.25000000 -0.08333333  1.00000000
> -0.16666667  0.33333333 -0.16666667  1.00000000
> -0.25000000  0.41666667 -0.25000000  1.00000000
> -0.33333333  0.50000000 -0.33333333  1.00000000
> -0.41666667  0.58333333 -0.41666667  1.00000000
> ...................
> nsfc run output (partial) (Al, ibrav=2)
> reciprocal axes: (cart. coord. in units 2 pi/a_0)
>          b(1) = ( -1.000000 -1.000000  1.000000 )
>          b(2) = (  1.000000  1.000000  1.000000 )
>          b(3) = ( -1.000000  1.000000 -1.000000 )
> number of k points= 2197  gaussian broad. (Ry)=  0.0150     ngauss =
>                   cart. coord. in units 2pi/a_0
>    k(    1) = (   0.0000000   0.0000000   0.0000000), wk =   0.0009103
>    k(    2) = (   0.2500000   0.0833333   0.0833333), wk =   0.0009103
>    k(    3) = (   0.5000000   0.1666667   0.1666667), wk =   0.0009103
>    k(    4) = (   0.7500000   0.2500000   0.2500000), wk =   0.0009103
>    k(    5) = (   1.0000000   0.3333333   0.3333333), wk =   0.0009103
>    k(    6) = (   1.2500000   0.4166667   0.4166667), wk =   0.0009103
>    k(    7) = (   1.5000000   0.5000000   0.5000000), wk =   0.0009103
>    k(    8) = (   1.7500000   0.5833333   0.5833333), wk =   0.0009103
>    k(    9) = (   2.0000000   0.6666667   0.6666667), wk =   0.0009103
>    k(   10) = (   2.2500000   0.7500000   0.7500000), wk =   0.0009103
>    k(   11) = (   2.5000000   0.8333333   0.8333333), wk =   0.0009103
>    k(   12) = (   2.7500000   0.9166667   0.9166667), wk =   0.0009103
>    k(   13) = (   3.0000000   1.0000000   1.0000000), wk =   0.0009103
>    k(   14) = (  -0.0833333   0.0833333   0.0833333), wk =   0.0009103
>    k(   15) = (   0.1666667   0.1666667   0.1666667), wk =   0.0009103
>    k(   16) = (   0.4166667   0.2500000   0.2500000), wk =   0.0009103
>    k(   17) = (   0.6666667   0.3333333   0.3333333), wk =   0.0009103
>    k(   18) = (   0.9166667   0.4166667   0.4166667), wk =   0.0009103
>    k(   19) = (   1.1666667   0.5000000   0.5000000), wk =   0.0009103
>    k(   20) = (   1.4166667   0.5833333   0.5833333), wk =   0.0009103
>    k(   21) = (   1.6666667   0.6666667   0.6666667), wk =   0.0009103
>
> Paul M. Grant, PhD
> Principal, W2AGZ Technologies
> Visiting Scholar, Applied Physics, Stanford (2005-2008)
> EPRI Science Fellow (Retired)
> IBM Research Staff Member Emeritus
> w2agz at pacbell.net
> http://www.w2agz.com
>
>
>
>
> -----Original Message-----
> From: pw_forum-bounces at pwscf.org [mailto:pw_forum-bounces at pwscf.org]  
> On
> Behalf Of Paolo Giannozzi
> Sent: Tuesday, December 30, 2008 5:21 AM
> To: PWSCF Forum
> Subject: Re: [Pw_forum] K_POINTS, tpiba or crystal
>
> On Tuesday 30 December 2008 05:56, Paul M. Grant wrote:
>
>>               b(1) = (  1.000000  0.000000  0.000000 )
>>               b(2) = (  0.000000  1.000000  0.000000 )
>>               b(3) = (  0.000000  0.000000  1.000000 )
>
> these are the lattice vectors generating a simple cubic lattice
>
>> Now, I want to input this grid to an nscf run via K_POINTS...is my  
>> grid
>> "tpiba" or "crystal?"
>
> in this particular case, it shouldn't matter, since the crystal and
> cartesian axis are the same, and the length of crystal axis is 2pi/a .
>
> Paolo
> -- 
> Paolo Giannozzi, Democritos and Udine University
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
http://www.sissa.it/~baroni / [+39] 040 3787 406 (tel) -528 (fax) /  
stefanobaroni (skype)

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