n_el in hfc2pms.m script

[dar_06]

Dear Support Foum, der Prof Kuprov

I have a naive question regarding the hfc2pms script and the related one hfc2pcs.

I am faily new to paramagnetic NMR calculations, so if the question is trivial, please excuse it.

I am calculating the paramagnetic NMR shifts of an iron molecule (S=1) which has a fairly complicated electronic structure. While it is not adequately described by DFT, I am relying on it for the hyperfine tensors, while the susceptibility tensor information in taken from CASSCF. For the record, both DFT and CASSCF reproduce the Mössbauer parameters well.
Phy
My workflow involves using these to components (A tensor from DFT and Chi tensor from CASSCF), together with eq 10 in Phys Chem Chem Phys 2014, 16, 20184 to calculate the sum of the FCS and PCS. For this, a purpose written python script was used.

In parallel, I wanted to test Spinach, and was surprised to see that the paramagnetic shieldings are different from the "manual" approach by a factor of 2. Trying to dig into the root of the problem, I found the following equation in Spinach, used to define a constant C

C=10^4*gamma_n*hbar*mu0*nel/(4*pi*(1e-10)^3)

Where the number of electrons is required. Since my molecule has 2 unpaired electrons, this is very likely where the difference comes from, as no where in the eq 10 in the Phys Chem Chem Phys paper, the number of electrons is required. Indeed, the triplet state is likely handled though S.

So my question is: since the full molecular susceptibility tensor in orca already takes spin into account, is it superfluous to take the n_el into account? Is n_el only necessary if the Chi tensor is constructed from simplified models (e.g from g tensor + assumed S, then scaled)?

For the record, I am using Spinach 2.10.1.

Thank you a lot in advance and thank you for making Spinach available.

Best wishes,
Dragos

[kuprov]

I had a look, yes - we did put the number of electrons in for the exact reason that you describe: on our calculations (using Gaussian) we did always have a hard-to-explain integer multiplier that was needed for the data to match up. The integer was always equal to the nominal number of unpaired electrons in the system. We also do not understand its origin, but it has likely something to do with normalisation or conventions used in the handling of those tensors. Thankfully, that was not a Spinach side issue... in the end, we simply shrugged and said, well - let the electronic structure theory peple fix their notation convention game; meanwhile, here's a multiplier option.

[dar_06]

Thank you for looking into it. I will try to look more closely then on the scripts.

I find understanding electronic structure fascinating, but when it comes it magnetism, I am not sure how the community navigates through so many differences in unit systems, conventions and notations. On top of which there are notation/convention differences between chemists and physicists and between the English literature and the German literature I guess it's all part of the fun.