[Pw_forum] Excited State Gradients in TDDFT

yukihiro_okuno at fujifilm.co.jp yukihiro_okuno at fujifilm.co.jp
Mon Feb 6 09:50:44 CET 2012

Dear Prof. Baroni.

Thank you very much for your response.

I'm very glad.

>>by PWSCF, or are there plan to develop the excited state gradient
calculation ?

>>The implementation of TDDFT in PWSCf uses lanczos method and does not

>>explicitly calculate the excited energy, and is it difficult to extend to

>>calculate force in this formalism ?

>the present implementation of tddft is particularly suited for the
calculation of the entire spectrum of large systems, whereas excited-state
energy gradients would require the calculation of individual eigenpairs
>of the Liouvillian. That should not be difficult to implement, but it is
not considered to be a priority at this time. Should anybody be interested
in implementing this feature, we in Trieste would be delighted to help.

Thank you for your advice.

You mean  if we diagonalize the Liouvillean operator  by usual method
instead of using Lanczos chain, and get

eigenvalue and eigenvectors,  we can get excited-state gradient ?

 Are there already formalism to calculate the excited energy gradient
within occupied state only method ?

Usual Casida's matrix, the dimension of the Matrix is \Omega_{i_j, k_q}
where, i and j are occupied and unoccupied state (k and q are also occupied
and unoccupied state pair),

and the dimension is   (2*Nc*Nv) * (2* Nc * Nv) where Nc and Nv is the
number of the unoccupied and occupied states.

But your Liouvillean matrix dimension is (2*Nv) * (2 *Nv), and it is very
small than the usual Casida's one.

It seems very attractive to perform the  large molecule, because the
possibilities to calculate the large molecule's excited  state energy
gradient is very important

quantities in photochemistry.


Yukihiro Okuno.
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