Dear Emil Karaev

Spin-orbit coupling is a very difficult subject. The use of numerical methods to study it is actually done by several ab initio programs.

I only can recommend you this website that will tell you about the theory of spin-orbit coupling:

https://staff.aist.go.jp/v.zayets/spin3_32_SpinOrbit.html

However, they still miss a point, i.e., the inversion point symmetry "i", the rest of the material is covered by Dr. Vadym Zayets's pedagogical website.

Now if the material is noncentrosymmetric, then it is even much harder, both ways, theoretically and numerically.

Best Regards.

Dear Emil Karaev ,

Spin-orbit couplings (SOC) are quite intriguing to obtain with Gaussian. The program only provides them for states of the same multiplicity, and using the non-blackbox CASSCF method. And it only calculates the SOC between two specified states, so you have to repeat the calculation as many times as needed to calculate several SOCs. I have attached an example input file for the calculation of the SOC between S0 and S1 states in thioformaldehyde from scratch (remove the comments before submitting the calculation, you should get a SOC of 182.2 cm-1).

There is another alternative, which allows calculating SOCs at the (TD-)DFT level, using PySOC: https://barbatti.org/2017/01/03/spin-orbit-couplings-based-on-density-functional-theory/ I have never used it, but it claims you can even calculate coupling between singlet and triplet states.

Hope you find it helpful

Gaussian calculates spin-orbit couplings between two states