deletions | additions       diff --git a/section_Introduction_A_large_proportion__.tex b/section_Introduction_A_large_proportion__.tex  index be22df7..d58c762 100644  --- a/section_Introduction_A_large_proportion__.tex  +++ b/section_Introduction_A_large_proportion__.tex 
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where $\Delta G^\circ$ denotes the change in standard free energy for the reaction  \begin{equation}  \mathrm{ BH^+ + B_{ref} \rightleftharpoons B + B_{ref}H^+  } \end{equation}  and is approximated as the sum of the electronic and solvation free energy. NC $N_C$  - 1 is an empirical correction accounting for the observation that the the method systematically underestimated the pKa of secondary (NC ($N_C$  = 2) and tertiary (NC ($N_C$  = 3) amines by ca 1 and 2 pH units, respectively. Using this approach the pKa values of 58 drug-like molecules containing one or more ionizable N atoms could be reproduced with a root mean square deviation (RMSD) of 0.7. 0.7 pH units.  However, the method relies on conformer search at the BP/TZVP level of theory which is computationally too expensive for routine use in screening and design. Semiempirical QM (SQM) methods are many orders of magnitude faster than conventional QM but their application to small molecule pKa prediction has been very limited and have focussed focused  mainly indirect prediction using atomic charges.4,5 charges \cite{Stewart_2008,Ugur_2014}.  The most likely reason for this is that SQM methods give significantly worse pKa predictions if used with an arbitrary reference molecule such as H2O (Rxn 1). However, we6 we \cite{Li_2004}  and others7,8 others \cite{Li_1997,Govender_2010,Sastre_2012}  have shown that a judicious choice of reference molecule is a very effective way of reducing the error in pKa predictions. Here we show that this approach is the key to predict accurate pKa values using our PM6-D3H+ SQM method9 combined with the SMD solvation method.