deletions | additions       diff --git a/In_the_case_of_CA__.tex b/In_the_case_of_CA__.tex  index 7cf03b4..fd5f102 100644  --- a/In_the_case_of_CA__.tex  +++ b/In_the_case_of_CA__.tex 
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In the case of C$\alpha$ none of the terms have a large effect on the chemical shielding. In the case of GB3 the results improve slightly if $\Delta \sigma_{1^\circ HB}^i$ is removed and removing $\Delta \sigma_{1^\circ H\alpha B}^i$ improves the results slightly for both proteins.   %We found that the effects are not always additive (presumably due to error cancellation) and that the overall RMSD could be lowered further (to 1.6 ppm) by also removing $\Delta \sigma_{2^\circ HB}^i$. In the case of $\Delta \sigma_{1^\circ HB}^i$ and $\Delta \sigma_{2^\circ HB}^i$ this is not particularly surprising as C$\alpha$ is approximated as a methyl group in the structural model.  Accordingly these two terms are removed from ProCS15, while all other terms are kept (note the ring current is only included for hydrogen atoms).  For C$\beta$ removing $\Delta \sigma_{1^\circ H\alpha B}^i$ decreases the RMSD by 0.2 - 0.5 ppm, while $\Delta \sigma_{BB}^{i-1}$ and $\Delta \sigma_{BB}^{i+1}$ increases and decreases the RMSD value depending on the protein. Accordingly only $\Delta \sigma_{1^\circ H\alpha B}^i$ is removed. Note that the structural models used for $\Delta \sigma_{1^\circ HB}^i$, $\Delta \sigma_{2^\circ HB}^i$ and $\Delta \sigma_{2^\circ H\alpha B}^i$ do not contain a C$\beta$ atom  so there is no such contribution for this nucleus. For C' removing $\Delta \sigma_{1^\circ H B}^i$ decreases the RMSD for GB3 by 0.1 ppm so we choose to remove this term for this atom type. Note that removing $\Delta \sigma_{2^\circ HB}^i$ increases the RMSD by 0.4 - 0.6 ppm so this term is important for accurate predictions of C' chemical shifts.   For H$^\text{N}$ and H$\alpha$ we choose to retain all the terms. Not surprisingly, the respective primary hydrogen bonding terms lower the RMSD by 0.4 - 0.6 ppm and are crucial for accurate predictions.   Finally, for N removing $\Delta \sigma_{1^\circ H\alpha B}^i$ lowers the RMSD by 0.2-0.5 ppm, so this term is removed. Note that $\Delta \sigma_{BB}^{i-1}$ and the two hydrogen bonding terms involving H lower the RMSD by as much as 1.6 ppm ($\Delta \sigma_{BB}^{i-1}$ for Ubiquitin) and is crucial for accurate predictions.  
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