[Pw_forum] Eigenfunctions in PWSCF

[Min Seung Kyu]

Oops, I made a mistake. :-(

You are totally right.

Thank you for your reply.

>
> 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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>
>
>