We are currently performing TD-DFT calculations on silicon quantum dots. We would like to discuss the magnitude of the transition dipole moments between the singlet ground state and our excited singlet states. Is there a way to compute the actual overlap between the involved molecular orbitals? Or is it already present somewhere in the .out or .chk file?
This is a typical input for those calculations:
$molecule
0 1
Si 1.360840082155 -1.360840082155 1.360840082155
Si 1.360840082155 1.360840082155 -1.360840082155
Si -1.360840082155 1.360840082155 1.360840082155
Si 0.000000000000 0.000000000000 0.000000000000
Si -1.360840082155 -1.360840082155 -1.360840082155
H 2.226738769514 -0.522677592846 2.226738769514
H 2.226738769514 -2.226738769514 0.522677592846
H 0.522677592846 -2.226738769514 2.226738769514
H 2.226738769514 2.226738769514 -0.522677592846
H 0.522677592846 2.226738769514 -2.226738769514
H 2.226738769514 0.522677592846 -2.226738769514
H -0.522677592846 2.226738769514 2.226738769514
H -2.226738769514 0.522677592846 2.226738769514
H -2.226738769514 2.226738769514 0.522677592846
H -2.226738769514 -0.522677592846 -2.226738769514
H -2.226738769514 -2.226738769514 -0.522677592846
H -0.522677592846 -2.226738769514 -2.226738769514
$end
It’s not exactly clear to me what you want. The overlap between MOs is zero (because they are orthogonal), as is the overlap between ground- and excited-state wave functions (for the same reason). If you are trying to interpret the magnitude of the transition dipole, you could try looking at transition charges (i.e., how Mulliken or Loewdin atomic charges change between ground and excited state. That information can be obtained by setting CIS_AMPL_ANAL = TRUE.
When spatial and spin symmetries allow it, the transition moment integral between psi_1 and psi_2 should be non-zero :
I am referring to the overlap between the psi_1 and psi_2 wavefunctions. Since TD-DFT only considers simple excitations and always uses the ground state orbitals, those functions only differ by one orbital. The overlap between those two functions should then be directly linked to the overlap between the two orbitals involved. That is the orbitals overlap I am talking about.
The intensity of the transition depends on the transition dipole moments as given by your equation. These are printed out if the STS_MOM rem is set, which you have done. If you look through your output file you should see the following block:
Transition Moments Between Ground and Singlet Excited States
--------------------------------------------------------------------------------
States X Y Z Strength(a.u.)
--------------------------------------------------------------------------------
0 7 0.000000 0.000000 0.000000 7.194022E-19
0 8 -0.000000 0.000000 -0.000000 2.367228E-18
0 9 0.000000 -0.000000 0.000000 4.765984E-19
0 10 0.000001 0.108407 0.000000 0.001917013
0 11 -0.108407 0.000001 -0.000001 0.001917013
0 12 -0.000001 -0.000000 0.108407 0.001917014
--------------------------------------------------------------------------------
The ground state is 0 and the first six excited states are all triplets, so they are spin-forbidden. This is why you only see overlaps from state 7 onwards. The overlap integrals (without the dipole moment operator) are not very interesting as the states and orbitals are all orthogonal, as John said. You only see non-zero values if you allow the excited state orbitals to relax, such as in the Maximum Overlap Method.
Yes, I did found the values for the transition dipole moments. It’s just that I want to discuss why those values are big for some molecules, while they are small for others.
For example, this is the values I obtained for the transition dipole moments from the ground state to each of the first six singlet excited states :
As you can see, for the molecule Si47H60, the 4th, 5th and 6th singlet excited states have a 0.66 a.u. transition dipole moment with the ground state. For the molecule Si87H76, the first three excited singlets have a 0.012 a.u. moment. Selection rules can explain why the values are zero or non-zero, but they don’t explain how big those values are.
Is there a way to explain why those values are what they are?
The overlap between your functions psi1 and psi2 is zero, because they are orthogonal. That is the point that I was trying to make above - that you can’t rely on overlap so you need to look to alternative means to get a qualitative understanding of what is going on.
If you google for “Transition Density Cube” method you will find literature on rationalizing energy transfer couplings using full transition densities instead of dipole approximations, which is not exactly what you want but might lead you to something that is helpful. Along those lines, I would suggest that perhaps looking at difference densities or natural transition orbitals for the transition(s) in question might help to gain qualitative understanding of how charge is redistributed upon excitation. Both difference densities and NTOs can be obtained using Q-Chem.
