Thanks... Well... As depicted the excitation nature fro S2->T1 is pi -> pi*, and for T0->T1 it is also pi->pi*... nothing changes, yet SOC is high

Yes, just calculate difference between the two excited states and visually inspect (alternatively, examine electronic excitation nature for both S0-Sn and S0-T1, and thereby guess the nature of Sn-T1 excitation). Biorthogonalization is not relevant to this case.

Dear Tian Lu,
Apologizes. I might have forgot about your previous response. Electron density difference... So maybe difference between two excited states would be ok? (4.18.13) ...or biorthogonalization of the orbitals
The point is, I dont know why S1->T2 and S2->T1 and ->T3 have so large SOC although the symmetry of orbitals doesnt change

I have replied similar question in your previous mail. There is usually no direct way, but you may visualize electron density difference between the two states to try to identify possible orbital transition character.

Dear Tian Lu,
So how with Multiwfn I could visualize orbitals shift upon ISC from Sn to Tm state? NTOs? Though how?

This analysis is only applicable to studying transition between reference state (usually ground state) and excited state.

Hello
Can HOLE-ELECTRON analysis be used to examine how orbitals changes during intersystem crossing. I specifically means to check whether ElSayed rule applies. How to do that, would be thankful for the simple example.
Thanks.