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

Siddheshwar Chopra

Dear Sir,
I have got the PUNCH file now from TDDFT output file.
I was seeing the $TDVEC group. It was told that there are 2*NSTATE records in the PUNCH file. In my case, NSTATE=10. I found only 10 records. Some of the text is below:

   111900 SAPS,  10 STATES
STATE   1 ENERGY=    -3138.3278180436
 1.020442E-04 -5.608704E-05  2.396080E-05 -9.260984E-06 -6.636264E-05
-2.286013E-05  9.396216E-06  4.878278E-06 -1.852484E-06  7.472925E-06
-1.400424E-05  1.178049E-06 -1.364119E-05 -2.155512E-05 -5.376085E-07
 2.311168E-05  2.947819E-05 -1.013776E-05 -1.373176E-05  5.238495E-05
-1.988428E-05 -4.153096E-05  1.564358E-06 -2.853384E-05  2.364293E-05
 8.782922E-06  1.376641E-05  7.302916E-07 -1.307850E-05 -2.573553E-05
-2.404907E-05 -4.533857E-05  1.029407E-05 -5.705214E-06  1.335178E-05
-1.349594E-05  1.777842E-05  2.651136E-05 -1.773483E-05  1.564974E-05
 1.235830E-05  6.562604E-06 -5.306053E-06  1.476717E-05  3.225120E-06
..................... (in total 22380 lines for one state)

Here as you said, "X" and "Y" are mentioned alternatively, X from 1st line onwards. I am unable to understand the size of the matrix (X or Y). Here "X" has 5 numbers. How to visualize this matrix?
Also, NVIR and NOC were talked about. Are these the "number of alpha and beta orbitals"? In this case it is 206 then?
Please elaborate about the construction of matrix. In case if PUNCH file is needed, I will send it privately, if only you permit.


On Sat Oct 4 '14 7:16pm, Alex Granovsky wrote

>no, transition dipole moment matrix does not serve your purposes.

>Kind regards,
>Alex Granovsky
>On Mon Sep 29 '14 11:49am, Siddheshwar Chopra wrote
>>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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