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Re^9: Help needed with the Transition density matrix determination and analysis....

Siddheshwar Chopra

Dear Alex,
Sorry for asking you again. There is a relation between transition density and transition dipole. So please pardon me if I ask:: Will extracting Transition dipole moment matrix serve the purpose of pointing out "spatial location of the transition from ground to excited state"? It is a NSTATE*NSTATE matrix as you told too.

Kind Regards,

On Mon Sep 29 '14 11:13am, Siddheshwar Chopra wrote
>Dear Alex,
>Thank you for the detailed explanation. I really need a TDDFT PUNCH file now to understand what you have suggested. I will get back once I extract this matrix.
>In the meanwhile has anyone got a program for this extraction? It would be a great help.

>Kind Regards,

>On Sun Sep 28 '14 0:20am, Alex Granovsky wrote
>>Dear Siddheshwar,

>>I'm sorry for delay with my answers.

>>As to your questions:

>>>>I would be really grateful if you could throw some light on the transition density matrix calculation. Is it possible to determine the matrix from TDDFT output file? IF yes then I would attach one file. Kindy let me know Sir.

>>No, it is impossible to compute 1-P TDM (one-particle transition
>>density matrix) based only on the information found in the output

>>>>>Dear Pavlo Sir and Alex Sir,
>>>>>Thank you so much for the useful information. Alex sir I am really happy to know that it is possible to find TDM from PUNCH file (from TDDFT calc.). I would request you to elaborate the process for the same. Right now I dont have any punch file with me. Can you explain with the help of any punch file? Once that is clear, I will look for the program.

>>The required information that can be extracted from the PUNCH file
>>is the content of the $VEC group and $TDVEC group. Each $VEC group
>>contains current molecular orbitals. The $TDVEC group contains X
>>and Y components of the TDDFT eigenvectors. For hybrid DFT, X
>>component is written first, then Y component follows. These records
>>are repeated for each root of TDDFT i.e. there are 2*NSTATE records
>>in total. As to individual record, it contains NVIR*NOC elements,
>>where NVIR is the number of virtual orbitals and NOC is the number
>>of active occupied orbitals i.e. the number of occupied orbitals
>>minus number of frozen core MOs. These numbers form matrices X
>>and Y, with virtual orbital index running first, then occupied
>>orbital index.

>>Once you extracted X and Y matrices, the transition density matrix
>>in MO basis is simply sum of X and Y blocks: Tmo = X+Y. If you need,
>>you can convert it into MO basis set using the following equation:


  Tao = S*V * Tmo * (S*V)-dagger 

>>where V are the matrix of MO coefficients and S is the matrix of
>>overlap integrals. The latter can be printed out by running
>>Firefly with exetyp=INT1

>>>>>Also, Sir I found that transition dipole moment matrix in the TDDFT o/p file is of the size NSTATE X NSTATE. Can you explain how to analyse this? I find the x,y,z data corresponding to an i,j element.

>>This is a matrix of transition dipoles between states Si and Sj.
>>This information can be used, for instance, to compute
>>two-photon absorbance (TPA)cross-sections using sum over states
>>approach (SoS)

>>> Does the magnitude of this dipole moment = sqrt(x^2+y^2+z^2)?

>>Yes it is (note in the printout atomic units are used throughout).

>>Kind regards,
>>Alex Granovsky

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