In the case of GB3 the RMSD (\(r\)) value for C\(\beta\) can be reduced (increased) to 1.8 ppm (0.71) by removing a single outlier identified by the Generalized Extreme Studentized Deviate Test \cite{Rosner_1983}. The outlier is Ala20 for which ProCS15 and DFT predict a C\(\beta\) chemical shielding value of 176.8 and 167.4 ppm, respectively. Inspection of the structure shows that the C\(\beta\) atom is only 3.1 Å from the N atom of Ala26 - an interaction not taken into account in the parameterization of ProCS15.

Similarly (also for GB3), the RMSD (\(r\)) value for H\(^\text{N}\) can be reduced (increased) to 0.6 ppm (0.91) by removing a single outlier identified by the Generalized Extreme Studentized Deviate Test. The outlier is Gln2 for which ProCS15 and DFT predict a H\(^\text{N}\) chemical shielding value of 24.2 and 20.1 ppm, respectively. Inspection of the structure shows that the H\(^\text{N}\) atom is within 1.77 Å of the OE1 atom of the Gln2 side chain and within 2.54 Å of an H\(\varepsilon\) atom of the Met1 side chain. While these interactions should be included in the \(\sigma_{BB}^{i}\) and \(\Delta \sigma_{BB}^{i-1}\) term, respectively, it i possible that the latter interaction is not found in the scan due to the choice of \(\phi_{\text{std}}\) and \(\psi_{\text{std}}\) described above. This residue is also identified as an outlier for N and removing it reduces (increases) the RMSD (\(r\)) value to 4.1 ppm (0.81).