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dchamb61

Member

Registered: 2022-09-01

Posts: 4

Physical significance of SO-RASSI Transitions?

Hello all, I hope that everyone has enjoyed their holidays and is ready for the new year.

I have a question about interpreting the results of triplet photophysics calculations. More specifically, my question concerns the orbital occupancies for triplet photophysics calculations.

For reference, here is an example of singlet photophysics results. These are calculated using a four state average for singlets.

 printout of CI-coefficients larger than  0.05 for root  1
      energy=    -256.936704
      conf/sym  11111111111     Coeff  Weight
             1  22222220000  -0.93955 0.88275
             3  22222u2d000  -0.05921 0.00351
             4  22222202000   0.06790 0.00461
             6  22222022000   0.13308 0.01771
            24  22222udu0d0  -0.07656 0.00586
            26  22222uud0d0  -0.08615 0.00742
            41  22222200020   0.09460 0.00895
            43  22222020020   0.06077 0.00369
           968  u2222d2u0d0  -0.07415 0.00550

      printout of CI-coefficients larger than  0.05 for root  2
      energy=    -256.685590
      conf/sym  11111111111     Coeff  Weight
             2  222222ud000  -0.79376 0.63005
             3  22222u2d000  -0.11288 0.01274
             5  22222ud2000   0.12151 0.01476
            21  222222u00d0   0.14113 0.01992
            22  22222u200d0  -0.32157 0.10341
            23  2222220u0d0   0.21919 0.04804
            24  22222udu0d0  -0.13210 0.01745
            25  2222202u0d0  -0.17482 0.03056
            41  22222200020  -0.05833 0.00340
            42  22222ud0020  -0.13163 0.01733
            45  222220ud020   0.09640 0.00929
           109  2222u220d00  -0.08141 0.00663
           946  u222222d000   0.05013 0.00251
           947  u22222d2000   0.08971 0.00805
           948  u2222d22000   0.10896 0.01187
          3606  02222222000  -0.05146 0.00265

The first printout corresponds to the first root (ground state/S0), where all of the occupied molecular orbitals have two electrons and all of the unoccupied molecular orbitals have zero electrons. This is expected in the ground state. The second printout corresponds to the transition from the ground state (first root) to the first singlet excited state (S1). Based on the weight of the CI-coefficients, we gather that this is a transition from the highest occupied molecular orbital to the lowest unoccupied molecular orbital.

Now, the results for triplet photophysics are quite similar. These are calculated using a state average of one for singlets and four for triplets.

 printout of CI-coefficients larger than  0.05 for root  1
      energy=    -256.751714
      conf/sym  11111111111     Coeff  Weight
             1  222222uu000   0.56328 0.31728
             4  222222u00u0   0.48523 0.23545
            11  22222u2u000  -0.54235 0.29415
            12  22222uu2000   0.05513 0.00304
            20  22222u200u0  -0.18032 0.03252
            21  22222udu0u0   0.12490 0.01560
            32  22222uu0020  -0.06014 0.00362
            33  22222u0u020  -0.08091 0.00655
           261  u222222u000  -0.08616 0.00742
           270  u22222200u0   0.08921 0.00796
           314  2222202u0u0  -0.08697 0.00756
           315  222220u20u0   0.09930 0.00986
           323  222220uu020  -0.05345 0.00286

      printout of CI-coefficients larger than  0.05 for root  2
      energy=    -256.722044
      conf/sym  11111111111     Coeff  Weight
             1  222222uu000   0.54645 0.29861
             4  222222u00u0   0.14107 0.01990
             5  2222220u0u0   0.07300 0.00533
            11  22222u2u000   0.73800 0.54465
            12  22222uu2000   0.07261 0.00527
            20  22222u200u0  -0.07853 0.00617
            21  22222udu0u0  -0.07963 0.00634
            22  22222uud0u0  -0.08920 0.00796
            29  22222uuu0d0  -0.05179 0.00268
            32  22222uu0020  -0.08651 0.00748
            33  22222u0u020   0.11069 0.01225
           261  u222222u000  -0.09387 0.00881
           270  u22222200u0  -0.06578 0.00433
           271  u22222du0u0   0.05617 0.00316
           314  2222202u0u0  -0.07069 0.00500
           323  222220uu020  -0.07196 0.00518
           539  u2222d2u0u0  -0.06147 0.00378
          4143  22022u2u200  -0.05027 0.00253

In comparison to the singlet results, we see two "u's" instead of a "u" and a "d". This is to account for the spin multiplicity. What I am confused about is the physical significance of these results. For singlets, we are able to assign each printout to either the ground state, or a transition from the ground state to each of the singlet excited states. It isn't possible to directly promote from the ground state to a triplet excited state -- one would instead access the triplet excited states via intersystem crossing from a singlet excited state. So, for triplet photophysics, what do the orbital occupancies indicate here?

Ignacio

Administrator

From: Uppsala

Registered: 2015-11-03

Posts: 1,085

Re: Physical significance of SO-RASSI Transitions?

I don't understand your confusion. Of course to pass from singlet to triplet you have to "flip" one electron. Note, however, that the orbitals in the singlet calculation are not necessarily the same (or in the same order) as in the triplet calculation, you'll have to examine the "average orbitals" in each calculation to evaluate how similar they are.

dchamb61

Member

Registered: 2022-09-01

Posts: 4

Re: Physical significance of SO-RASSI Transitions?

Thank you for the response.

For example, using singlet photophysics we can easily characterize an S0 -> S1 transition. For Root 2, we observe "222222ud000" having the highest coefficient. Looking at the molecular orbitals within our active space, we can gather that this transition corresponds to promotion from the highest occupied molecular orbital (say, a non-bonding lone pair orbital) to the lowest unoccupied molecular orbital (say, a pi-antibonding orbital). From RASSI energies, we can assign an energy to the S0 -> S1 transition and characterize it as an n-pi* transition.

My confusion comes from what a similar triplet photophysics calculation would indicate. We can look at the molecular orbitals within our active space and characterize these transitions again. For Root 2 given that "22222u2u000" is an n-pi* transition (the lower u is an n orbital and the higher u is a pi-antibonding orbital), what is the physical significance of such a transition? If this is Root 2, would this be promotion from the T1 to T2? SOC values aside, would these photophysics calculations have any relevance to non-adiabatic molecular dynamics (if you could run them using Molcas)? Would it indicate promotion from S0 to T1 (which doesn't actually happen, as accessing triplet excited states is observed via intersystem crossing)?

Ignacio

Administrator

From: Uppsala

Registered: 2015-11-03

Posts: 1,085

Re: Physical significance of SO-RASSI Transitions?

If you have:

S0: 22222220000
S1: 222222ud000
T1: 22222u2u000

You could say that S0->S1 is the promotion of an electron from the 7th orbital to the 8th (whether those are HOMO/LUMO, or pi, n, etc. you can't tell from this, you have too look at the orbitals and their SCF energies). And S0->T1 is the promotion of an electron from the 6th orbital to the 8th, simultaneous with a spin flip, or S1->T1 is a promotion from 6th to 7th with spin flip.