\(\Delta\sigma^{i}_{w}\) is the change in chemical shielding of an amide proton due to a hydrogen bond to a water molecule. While the backbone terms of ProCS15 is parameterized based on DFT calculations with the polarizable continuum model of solvation, this model does not account for explicit solvent effects and this term is included for amide protons that do not form hydrogen bonds to other atoms in the protein structure. \(\Delta\sigma^{i}_{w}\) is 2.07 ppm based on DFT calculations on an N-methylacetamide-water complex \cite{24391900}.