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Alex Granovsky
gran@classic.chem.msu.su

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
file.

>>>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