[DFTB-Plus-User] eigvev.out & oversqr.dat

Bálint Aradi aradi at uni-bremen.de
Thu May 13 07:59:14 CEST 2021


Dear Fengling,

Maybe you just forgot to conjugate the eigenvector on the left hand 
side? In the complex case the orthogonality relation reads as

(C_i)^* S_ij C_j = delta_ij

where C_i is the i-th eigenvector (the i-th column of the eigenvector 
matrix).

Best regards,

Bálint


On 13.05.21 03:55, 邓凤麟 via DFTB-Plus-User wrote:
> Dear DFTB developers and users,
> 
> 
> I am a new user of DFTB+. Now, I cannot understand the relation between 
> overlap matrix S in oversqr.dat and cofficients C in eigvev.out when I 
> do a calculation of Silicon crystal.
> 
> 
> In DFTB, the formula (C^T)_ij S_jk C_kl=delta_il shoud always be 
> satisfied. I do a calculation of H2O molecule and obtain the right 
> result delta_il, like the previous discussion 
> (https://mailman.zfn.uni-bremen.de/pipermail/dftb-plus-user/2017/002504.html 
> <https://mailman.zfn.uni-bremen.de/pipermail/dftb-plus-user/2017/002504.html>). 
> 
> 
> 
> However, for the Si crystal, I am puzzled when I calculate  (C^T)_ij 
> S_jk C_kl at random k point.
> 
> For the first k point and first eigen vector,
> 
> S=
> 
>       1.00855+3.40401e-20im  …     0.126487-0.0489968im
>   6.09864e-20-0.0437937im          0.115195-0.0619647im
>   1.73134e-18-0.0437937im          0.115195-0.0619647im
>    1.7415e-18-0.0437937im         0.0258335+0.120866im
>     -0.068126+0.357226im        4.68655e-17+0.0437937im
>      0.126487+0.0489968im    …    0.0338919-5.55196e-17im
>      0.126487+0.0489968im         0.0338919-5.55586e-17im
>      0.126487+0.0489968im          0.751609-4.18909e-17im
> 
> 
> C=
> 
> 
>    0.585064 - 0.000778im
>   -0.006024 + 0.041804im
>   -0.006024 + 0.041804im
>   -0.006024 + 0.041804im
>   -0.111193 - 0.574401im
>    0.039879 - 0.013912im
>    0.039879 - 0.013912im
>    0.039879 - 0.013912im
> 
> 
> C^T=
> 
> 0.585064+0.000778im  -0.006024-0.041804im  …  0.039879+0.013912im
> 
> 
> I hope I use the data from output files in a right way. The input 
> file can be found in attachments.
> 
> 
> Best regards,
> 
> Fenglin Deng
> 
> 
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-- 
Dr. Bálint Aradi
Bremen Center for Computational Materials Science, University of Bremen
http://www.bccms.uni-bremen.de/cms/people/b-aradi/


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