pK_a calculations for tautomerizable and conformationally flexible molecules: partition function vs. state transition...

Calculations of acidities of molecules with multiple tautomeric and/or conformational states require adequate treatment of the relative energetics of accessible states accompanied by a statistical-mechanical formulation of their contribution to the macroscopic pK_a value. Here, we demonstrate rigorously the formal equivalence of two such approaches: a partition function treatment and statistics over transitions between molecular tautomeric and conformational states in the limit of a theory that does not require adjustment by empirical parameters correcting energetic values. However, for a frequently employed correction scheme, linear scaling of (free) energies and regression with respect to reference data taking an additive constant into account, this equivalence breaks down if more than one acid or base state is involved. The consequences of the resulting inconsistency are discussed on our datasets developed for aqueous pK_a predictions during the recent SAMPL6 challenge, where molecular state energetics were computed based on the "embedded cluster reference interaction site model" (EC-RISM). This method couples integral equation theory as a solvation model to quantum-chemical calculations and yielded a test set root mean square error of 1.1 pK units from a partition function ansatz. For all practical purposes, the present results indicate that a state transition approach yields comparable accuracy despite the formal theoretical inconsistency, and that an additive regression intercept, which is strictly constant in the limit of large compound mass only, is a valid approximation. Graphical abstract Embedded cluster reference interaction site model-derived vs. experimental pK_a for the test set calculated with either the partition function (blue) or the state transition approach (red), using m as a free parameter.