Delving into Theoretical and Computational Considerations for Accurate Calculation of Chemical Shifts in Paramagnetic Transition Metal Systems using Quantum Chemical Methods

This comment refers to version 2. Please take into consideration our points below: • For Eq. (9), reference 23 is given, but the equation in 23 is different and corresponds to the physical (symmetric) susceptibility tensor. We believe that Eq. (9) corresponds to the unsymmetrical χ'; tensor that was questioned by some of us in reference 70. This connection should be highlighted. • Eq. (8) is not connected to Eq. (1). In fact, it remains unclear where Eq. (1) comes from. In our opinion, Eq. (1) can only be derived within the spin Hamiltonian approximation. It is then unclear whether it makes sense to use a χ^s tensor that is evaluated beyond the spin Hamiltonian approximation if the A tensor is still limited to this approximation. • https://doi.org/10.1063/5.0088162 should be cited together with our ref. 15. • Eq. (3) and the following derivation assumes that the energy derivatives are well defined. This is not the case for degeneracies (e.g. Kramers degeneracy at zero field). In Eq. (8), energy levels and degenerate states belonging to the same level are not distinguished. Therefore, this cannot be considered as a proper rederivation of the van den Heuvel-Soncini equation. • The last paragraph of the “Theoretical section” (before “Computational details”) is unclear to us. • The conclusion states that the "VV approach" represents the state of the art, but even better would be to evaluate the van den Heuvel-Soncini equation directly, which was already done in reference 12. It should also be mentioned that the calculated parameters that enter the different equations can have substantial error. Therefore, it is questionable to judge which equation is the best one using these parameters to reproduce the experimental data, because there might be fortuitous cancellation of errors. Lucas Lang, Enrico Ravera, Letizia Fiorucci, Giacomo Parigi, Claudio Luchinat