I wish to reproduce the results from this paper by Truhlar and co-workers, where they treat a spin-forbidden reaction by considering two effective states coupled by a semi-empirical spin-orbit coupling term $\chi$. They mention that they estimate the coupling term from a TD-DFT calculation.

(c) Singlet-triplet excitation energies are computed at the representative geometry using the ADF2016.103 program package. The spin-orbit coupling is included by employing the spin- orbit ZORA Hamiltonian. The M06-L exchange-correlation functional is used with a Slater- type ZORA/QZ4P basis set.

(d) The singlet-triplet splitting of the representative geometry is determined by averaging the corresponding singlet and triplet energies as calculated in step (c). The value of the coupling constant $\chi$ is updated accordingly such that the difference of the eigenvalues of the following 2 × 2 matrix reproduces the singlet-triplet splitting. $$\begin{pmatrix} E_1 & \chi \\ \chi & E_2 \\ \end{pmatrix}$$ Here $E_1$ and are the energies of low- and high-spin states computed from the single-point calculations using Gaussian for the representative geometry.

This is from their SI (file link here). There isn't much other explanation on this part of the publication.

However, I do not have access to ADF, and I am curious how to accomplish this TD-DFT calculation with ORCA. I have used ORCA before, but I have never dealt with spin-orbit coupling. I know that there are ZORA or DKH Hamiltonians available for relativistic effects, and TD-DFT can deal with singlet-triplet excitations. If I understand correctly, the splitting they mention in the paper is not simply the difference between converged singlet SCF and first triplet excitation from TD-DFT as they talk about averaging energies and spin-orbit coupling (so this question is not a duplicate of this).

Any help with some small explanation of what type of calculation this is referring to, and some sample ORCA input files if possible, will be very helpful.



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