[Pw_forum] Eigenfunctions in PWSCF

[Stefano Baroni]

On Jan 15, 2008, at 9:00 AM, Min Seung Kyu wrote:

> Dear users and developers,
>
> I have a question about eigenfunctions in PWSCF codes.
>
> I looked at PWSCF source files and I found that the 'evc' variable is
> KS eigenvectors in G-space, right?
>
> Because Hamiltonian matrix H(G,G') is hermitian, 'evc' should be real.

Who said this?

The eigenvalues of a Hermitean matrix are real, the eigenvectors not  
necessarily so. If in addition to being Hermitean the matrix is also  
real (which implies it is symmetric), the the eigenvectors CAN BE  
CHOSEN to be real. If you feed a real matrix to a complex eigenvalue  
solver, then the eigenvectors will most probably come out complex, but  
can they be easily converted to real (if needed) by an appropriate  
choice of phases (again, if the original matrix is real symmetric, not  
merely Hermitean)

Hope this helps
Stefano

>
>
> When I print out 'evc', however, 'evc' contains imaginary parts.
>
> For example, when I run 'co.rx.in' (example03 folder), I got these  
> values:
>
>  DBLE(evc(1:4,1))     0.186884     0.154551     0.154551     0.142085
> AIMAG(evc(1:4,1))     0.000000     0.000000     0.000000    -0.048560
>  DBLE(evc(1:4,2))    -0.024799    -0.021751    -0.021751    -0.068645
> AIMAG(evc(1:4,2))     0.000000     0.000000     0.000000    -0.145963
>  DBLE(evc(1:4,3))     0.000000     0.000000     0.000000     0.000000
> AIMAG(evc(1:4,3))     0.000000    -0.005668     0.152298     0.000000
>  DBLE(evc(1:4,4))     0.000000     0.000000     0.000000     0.000000
> AIMAG(evc(1:4,4))     0.000000    -0.152298    -0.005668     0.000000
>  DBLE(evc(1:4,5))    -0.299154    -0.185970    -0.185970     0.011252
> AIMAG(evc(1:4,5))     0.000000     0.000000     0.000000     0.168998
>
> ( I added 'WRITE(*,*) evc(1:4,ibnd)' in 'sum_band.f90'. )
>
> What is the problem?
>
> Thank you in advance.
>
> Sincerely, Min.
>
> -------------------------------Sig.---------------------------
> Center for Superfunctional Materials, Department of Chemistry,
> Pohang University of Science and Technology (POSTECH)
>
> Mr. Seung Kyu, Min
>
> Ph.D. Candidate
>
> E-Mail: min0220 at postech.ac.kr
> Tel.  : 82-54-279-5858
> ----------------------------------------------
>
>
>
>
>
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

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