deletions | additions       diff --git a/Delta_sigma_i__HB_in__.tex b/Delta_sigma_i__HB_in__.tex  index 4897710..8e4074e 100644  --- a/Delta_sigma_i__HB_in__.tex  +++ b/Delta_sigma_i__HB_in__.tex 
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\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 N-methyl acetamide 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) of while  the free internal  monomer geometries. 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 to the residue $i-1$. $\Delta\sigma^i_{1^\circ HB}$. $\Delta\sigma^i_{2^\circ HB}$ is included only when another amide 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{subsec:HBscan}a. \ref{fig:HB}a.  For H$\alpha$ the chemical shielding is taken as the average of the three hydrogen atom on the methyl group of the acetamide. Note in this case that 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 $r_\mathrm{HO}$, $r_\mathrm{OH}$,  $\theta_{\mathrm{O}}$, and $\rho_{\mathrm{O}}$ in Eq \ref{eqn:sigmahb}.