[Wien] Understanding case.output1 with WFPNT: coefficients from interstitial region associated with reciprocal lattice vectors

[Dara Goldar]

Dear Wien2k community,

I am trying to compute the overlap between different eigenfunctions
calculated from a GaAs-run. In doing so, I've run into an issue regarding
the wavefunction from region II, which is outputted in case.output1 through
the program lapw1 (using WFPNT).

The specific issue I have is that for a given k-vector and energy band, I
am reading the same reciprocal lattice vector more than once, each time
with different values of the coefficients.

 I've copied a part from my GaAs.output1-file; an example of the above is
found for k=(0,0,0), bands 1-9, for reciprocal lattice vector (-1, -1, -1)
and (1, -1, -1) (highlighted).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

K=   0.00000   0.00000   0.00000            1
      MATRIX SIZE   166  WEIGHT= 1.00  PGR:
     EIGENVALUES ARE:
     -2.2441103   -2.2441103   -2.2441103   -2.2430406   -2.2430406
     -0.7539068   -0.7539068   -0.7539068   -0.7474829   -0.7474829
     -0.6043444    0.3329249    0.3329249    0.3329249    0.3707415
      0.6043473    0.6043473    0.6043473    0.8929301    1.0780723
      1.0780723    1.1818337    1.1818337    1.1818337    1.4052914

            0 EIGENVALUES BELOW THE ENERGY   -9.00000
       ********************************************************





   RECIPROCAL LATTICE VECTORS

                    1.ENERGY   2.ENERGY   3.ENERGY   4.ENERGY   5.ENERGY
6.ENERGY   7.ENERGY   8.ENERGY   9.ENERGY
   0   0   0
                   0.000000   0.000000  -0.000000  -0.000000   0.000000
 -0.000000   0.000000   0.000000  -0.000000       REALPART
                   0.000000   0.000000  -0.000000  -0.000000   0.000000
 -0.000000  -0.000000  -0.000000   0.000000       IMAGPART
      .
      .
      .

* -1  -1  -1*
*                   0.000321  -0.000010   0.000029  -0.000000   0.000000
0.013505   0.000959  -0.001484  -0.000000       REALPART*
*                   0.000184   0.000024  -0.000063   0.000000  -0.000000
 -0.004805   0.004760   0.000770   0.000000       IMAGPART*
*   1  -1  -1*
*                   0.000136   0.000126   0.000200  -0.000000   0.000000
0.007245  -0.004415   0.008832  -0.000000       REALPART*
*                   0.000064  -0.000120  -0.000223   0.000000  -0.000000
 -0.004644   0.003845  -0.006747   0.000000       IMAGPART*
  -1   1  -1
                   0.000104   0.000107   0.000029  -0.000000   0.000000
0.005069  -0.011615  -0.001513  -0.000000       REALPART
                   0.000091   0.000212  -0.000258   0.000000   0.000000
 -0.006230   0.005351   0.001220   0.000000       IMAGPART
*  -1  -1  -1*
*                  -0.063399  -0.008318   0.021767  -0.000000   0.000000
 -0.031423   0.031130   0.005038  -0.000000       REALPART*
*                   0.110700  -0.003450   0.009852  -0.000000   0.000000
 -0.088312  -0.006270   0.009704   0.000000       IMAGPART*
  * 1  -1  -1*
*                   0.022177  -0.041315  -0.076824   0.000000  -0.000000
0.030371  -0.025141   0.044119   0.000000       REALPART*
*                  -0.046973  -0.043376  -0.068828   0.000000   0.000000
0.047376  -0.028869   0.057754  -0.000000       IMAGPART*

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


Since each reciprocal lattice vector according to my GaAs.output1-file has
more than one set complex of coefficients, I'm not sure how to interpret
this. I've audaciously attempted to study the files 'wfpnt.f' and
'coors.f', but found no indication of mapping back to 1BZ or anything else
I can think of which would explain why each reciprocal lattice vector is
associated with more than one set of coefficients.

In particular, I'm wondering if this should happen at all, and if so, which
of the coefficients should I use when computing the overlap for a given
band and k-vector?
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