deletions | additions       diff --git a/Delta_sigma_i__HB_in__.tex b/Delta_sigma_i__HB_in__.tex  index 67730d2..f64e8e1 100644  --- a/Delta_sigma_i__HB_in__.tex  +++ b/Delta_sigma_i__HB_in__.tex 
...
\label{eqn:sigmahb}  \Delta \sigma^i_{HB}=\Delta\sigma^i_{1^\circ HB}(r_{\mathrm{HO}},\theta,\rho)+\Delta\sigma^i_{2^\circ HB}(r_{\mathrm{OH}},\theta_{\mathrm{O}},\rho_{\mathrm{O}})  \end{equation}  $\Delta\sigma^i_{1^\circ HB}$ is computed using the structural models shown in Figure \ref{fig:HB} as the change in chemical shielding of the backbone atoms in N-methyl acetamide relative to that of the free monomer computed at the OPBE/6-31G(d,p)//PM6 level of theory for a variety of orientations (see subsection \ref{subsec:HBscan} for more information) while the internal monomer geometries are kept fixed. For H$\alpha$ the chemical shielding is taken as the average of the three hydrogen atom on the N-methyl group. Note that the carbonyl carbon formally belongs tothe  residue $i-1$.$\Delta\sigma^i_{1^\circ HB}$.  $\Delta\sigma^i_{2^\circ HB}$ is included only when another amide or amine group is hydrogen bonded to the amide oxygen and is computed as the change in the chemical shielding of the top amide group in Figure \ref{fig:HB}a. For H$\alpha$ the chemical shielding is taken as the average of the three hydrogen atom atoms  on the methyl group of the acetamide. Note that  in this casethat  the amide nitrogen and hydrogen formally belong to residue $i+1$ and that $r_\mathrm{HO}$, $\theta$, and $\rho$ are defined relative to the carbonyl oxygen of residue $i$ rather than the amide proton as for $\Delta\sigma^i_{1^\circ HB}$. $r_\mathrm{HO}$, $\theta$, and $\rho$ are therefore labeled $r_\mathrm{OH}$, $\theta_{\mathrm{O}}$, and $\rho_{\mathrm{O}}$ in Eq \ref{eqn:sigmahb}.