[DFTB-Plus-User] electron phonon interaction and matrix derivative

[Gabriele Penazzi]

Hi Haimen,

it's been some time since I wrote that utility, but I think I remember.

If you apply a Loewdin orthogonalization to the Hamiltonian S^{-1/2} H 
S^{-1/2}, calculate naively the derivative and transform back to the 
original basis you obtain the same formula you see in literature, except 
for those 0.5 coefficients. Now, there must be a flaw somewhere, as you 
point out it doesn't match other references. As the code was written for 
my own sake and at some point my research on the topic stopped, that 
must be a version where I was trying to implement this formula to check 
how large was the difference or something like that. Whether I was 
seeing this in other codes or not, I can't remember.

Gabriele


On 10/28/20 5:00 AM, Haimen Mu via DFTB-Plus-User wrote:
> Hi Gabriele,
> I am also interested in the electron-phonon coupling related to dftb+. 
> I read your python code ‘elcoupl.py’which gave me much inspiration,but 
> I still have a small confusion. In your formulas ‘coupling = coupling 
> - *0.5* * work2’and ‘coupling = (coupling - *0.5* * work2) * 
> prefactor’, there is a coefficient ‘*0.5*’that did not occour in some 
> literatures. I saw formular in papers is like what Dirk Ziemann 
> written in previous mail. That is ‘ /gamma_ab^q   \approx  d H_ab / 
> d_q  -  \sum_mn  d S_am / d_q * S^-1_mn * H_nb - \sum_mn  H_am * 
> S^-1_mn * d S_nb / d_q ’./Would you explain the coefficient *0.5* here 
> is for what?
>
> Looking forward to your reply.
>
> Thank you .
>
> Haimen Mu
>
>
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