deletions | additions       diff --git a/Delta_sigma_i__HB_is__.tex b/Delta_sigma_i__HB_is__.tex  index 2d3a867..0d7c612 100644  --- a/Delta_sigma_i__HB_is__.tex  +++ b/Delta_sigma_i__HB_is__.tex 
...
$\Delta\sigma^i_{HB}$ is the effect of hydrogen bonding to the H$^\mathrm{N}$ amide H  and O$^{\mathrm{C'}}$ O  atoms of residue $i$, respectively, on the chemical shielding of the backbone amide atoms (i.e. this term is zero for C$\beta$) and has two contribution. $$\Delta \sigma^i_{HB}=\Delta\sigma^i_{1^\circ HB}(r_{\mathrm{HO}},\theta_{\mathrm{H}},\rho_{\mathrm{H}})+\Delta\sigma^i_{2^\circ HB}(r_{\mathrm{OH}},\theta_{\mathrm{O}},\rho_{\mathrm{O}})$$  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 2). 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$^\mathrm{N}$, 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 C’, H$\alpha$ and C$\alpha$ using the O$^{\mathrm{C'}}$ of residue i, while for H$^\mathrm{N}$ the amide H  and N, it is computed using the O$^{\mathrm{C'}}$ amide O  atom of the preceding $(i-1)$ residue.