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

Alex Granovsky
gran@classic.chem.msu.su

Hello,

Within Tamm-Dancoff approximation Y matrix is identically zero.

> As I earlier mentioned.. the number occupied and virtual orbitals,
> is 206.

You are wrong. Look at the header of tddft computations.
You'll find something like follows:

```                    -------------------------------------
PROGRAM WRITTEN BY ALEX A. GRANOVSKY
-------------------------------------

# CORE ORBITALS      =    0
# OCCUPIED ORBITALS  =    5
# MOLECULAR ORBITALS =   19
# BASIS FUNCTIONS    =   19

NUMBER OF TDDFT SPIN-ADAPTED ANTISYMMETRIZED PRODUCTS (SAPS) IS      70

```

Here, Nocc is equal to # OCCUPIED ORBITALS,
while the number of virtual orbitals Nvir is equal to # MOLECULAR ORBITALS minus  # OCCUPIED ORBITALS minus  # CORE ORBITALS

> how did you conclude from the number of lines (22380),
> that it is non hybrid or TDA?

Because 22380 times 5 (numbers per line) is equal 111900 (the number of SAPS i.e. the number of matrix elements in X or Y matrix). If both X and Y were printed there would be 22380*2 lines per each state.

>

Kind regards,
Alex Granovsky

On Tue Aug 18 '15 9:19pm, Siddheshwar Chopra wrote
--------------------------------------------------
>Dear Sir,
>Pardon me for not mentioning earlier. Yes Tamm-Dancoff approximation was used. But again I have two questions:
>1) Relation between X and Y? I now have to construct Y from X.
>2) Dimension of X is still confusing. As I earlier mentioned.. the number ooccupied and virtual orbitals, is 206. And how did you conclude from the number of lines (22380), that it is non hybrid or TDA?

>Kind Regards,
>
>
>On Tue Aug 18 '15 8:35pm, Alex Granovsky wrote
>----------------------------------------------
>>One more comment:

>>if you performed non-hybrid DFT, then only X matrix is
>>punched as Y matrix can be computed using X matrix.
>>In your case, each of X and Y matrix has 111900 (i.e.,
>>the printed number of SAPS) elements. In total 22380 lines
>>of 5 elements each for each state means that only X matrix
>>is printed as you either performed non-hybrid DFT or Tamm-Dancoff
>>approximation to TDDFT.

>>Kind regards,
>>Alex Granovsky
>>
>>
>>On Tue Aug 18 '15 6:01pm, Alex Granovsky wrote
>>----------------------------------------------
>>>Hello,

>>>both X and Y are Nvir by Nocc matrices. Here Nvir is the number
>>>of virtual orbitals and Nocc is the number of active (i.e. non-core)
>>>occupied orbitals.

>>>Kind regards,
>>>Alex Granovsky

>>>On Wed Aug 12 '15 2:38pm, Siddheshwar Chopra wrote
>>>--------------------------------------------------
>>>>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:

>>>> \$TDVEC
>>>>    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.

>>>>Regards,
>>>>
>>>>
>>>>On Sat Oct 4 '14 7:16pm, Alex Granovsky wrote
>>>>---------------------------------------------
>>>>>Hi,

>>>>>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.

>>>>>>>>>>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

Thu Aug 20 '15 8:36pm