deletions | additions       diff --git a/Delta_sigma_i__HB_is__.tex b/Delta_sigma_i__HB_is__.tex  index f977786..d3f4600 100644  --- a/Delta_sigma_i__HB_is__.tex  +++ b/Delta_sigma_i__HB_is__.tex 
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$\Delta\sigma^i_{HB}$ is the effect of hydrogen bonding to the amide H ($\Delta\sigma^i_{1^\circ HB}$) and O ($\Delta\sigma^i_{2^\circ HB}$) atoms of residue $i$ on the chemical shielding of the backbone atoms (i.e. this term is zero for C$\beta$)   $$\Delta \sigma^i_{HB}=\Delta\sigma^i_{1^\circ HB}(r_{\mathrm{HO}},\theta},\rho)+\Delta\sigma^i_{2^\circ HB}(r_{\mathrm{HO}},\theta,\rho)+\Delta\sigma^i_{2^\circ  HB}(r_{\mathrm{OH}},\theta_{\mathrm{O}},\rho_{\mathrm{O}})$$ $\Delta\sigma^i_{1^\circ HB}$ is computed using the structural models shown in Figure \ref{fig:HB} as the change in chemical shielding relative to free N-methyl acetamide 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 the free monomer geometries. Note that the the carbonyl carbon formally belongs to the residue $i-1$. $\Delta\sigma^i_{1^\circ HB}$  Here $r_{\mathrm{HO}}$ refers to the O-H HB distance involving the amide H and $\theta_{\mathrm{H}}$ and $\rho_{\mathrm{H}}$ are the corresponding angles (Figure \ref{fig:HB}). Similarly, $r_{\mathrm{OH}}$ refers to the OH HB distance involving the amide O and $\theta_{\mathrm{O}}$ and $\rho_{\mathrm{O}}$ are the corresponding angles. For H^{N}, N, C$\alpha$, and H$\alpha$ is computed using the amide proton of residue $i$, i.e. $\Delta\sigma^i_{1^\circ HB}(r_{\mathrm{H(i)O}},\theta_{\mathrm{H}i},\rho_{\mathrm{H}i})$, while for C’, which is bonded to the N atom of the subsequent residue, $\Delta\sigma^i_{1^\circ HB}$ is computed using the amide proton of residue $i+1$. is computed for the amide C, H$\alpha$ and C$\alpha$ using the amide O of residue i, while for the amide H and N, it is computed using the amide O atom of the preceding $(i-1)$ residue.  
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