deletions | additions       diff --git a/Delta_sigma_i__H_alpha__.tex b/Delta_sigma_i__H_alpha__.tex  index 36d2d3a..daa5836 100644  --- a/Delta_sigma_i__H_alpha__.tex  +++ b/Delta_sigma_i__H_alpha__.tex 
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$\Delta \sigma^i_{H\alpha B}$ is the effect of hydrogen bonding to the H$\alpha$ and amide O atoms of residue $i$ on the chemical shielding of the backbone atoms and C$\beta$ and has two contributions   $$\Delta \begin{equation}  \label{eqn:sigmahab}  \Delta  \sigma^i_{H\alpha B}=\Delta\sigma^i_{1^\circ H\alpha B}(r_{\mathrm{H\alpha O}},\theta_{\mathrm{H\alpha}},\rho_{\mathrm{H\alpha}})+\Delta\sigma^i_{2^\circ H\alpha B}(r_{\mathrm{OH\alpha}},\theta_{\mathrm{O}},\rho_{\mathrm{O}})$$ Here $r_{\mathrm{H\alpha O}}$ refers to the OH HB distance involving the HA and $\theta_{\mathrm{H\alpha}}$ and $\rho_{\mathrm{H\alpha}}$ are the corresponding angles (Figure \ref{fig:HAB}). Similarly, $r_{\mathrm{OH\alpha}}$ refers to the OH HB distance involving the amide O and $\theta_{\mathrm{O}}$ and $\rho_{\mathrm{O}}$ are the corresponding angles. \end{equation}  $\Delta\sigma^i_{1^\circH\alpha B}$ is computed for C’, H$\alpha$ and C$\alpha$ using the amide O of residue $i$, while for the amide  H and N it \alphaB}$  is computed using the amide O atom of the preceding ($i-1$) residue. $\Delta\sigma^i_{2^\circ H\alpha B}$ is structural models shown in Figure \ref{fig:HAB} as  the change in chemical shielding of Ala the backbone and C$\beta$  atoms in(except H$\beta$) in  Ac-A-NMe due to relative that of  the H$\alpha$ hydrogen bonding to free monomer computed at  the oxygen atom OPBE/6-31G(d,p)//PM6 level  of theory for  a NMA, methanol, or acetate molecule (Figure \ref{fig:HAB}). variety of orientations (see subsection \ref{subsec:HBscan} for more information) while the internal monomer geometries are kept fixed.  $\Delta\sigma^i_{2^\circ H\alpha B}$ HB}$  is computed as  the change in the  chemical shielding ofan atom in NMA due to the carbonyl oxygen hydrogen bonding to the HA atom in Ac-A-NMe. These value are taken from the same NMA – Ac-NMe calculations used to compute (Figure \ref{fig:HAB}a). For $\Delta\sigma^i_{2^\circ H\alpha B}$ C$\alpha$ is defined at  the methyl C bonded to top  amide C group  in the H-accepting NMA molecule and Figure \ref{fig:HAB}a. For  H$\alpha$ the chemical shielding  is taken as the average of the H chemical shielding values for that three hydrogen atom on the  methyl group. The range group  of bond lengths the acetamide. Note in this case that the amide nitrogen  and angles considered is described 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 $\Delta\sigma^i_{1^\circ HB}$. $r_\mathrm{H\alpha O}$, $\theta$, and $\rho$ are therefore labeled $r_\mathrm{OH\alpha}$, $\theta_{\mathrm{O}}$, and $\rho_{\mathrm{O}}$  in Section \ref{subsec:HBscan}. Eq \ref{eqn:sigmahab}.       
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