Tractable and Thermodynamically Consistent pKa Prediction via First-Dissociation Aggregation
Ionization governs molecular behavior, yet predicting aqueous pKa accurately and tractably remains a fundamental challenge. Rigorous ensemble methods require enumerating a protonation-state space that grows exponentially with the number of ionizable sites, while fast graph predictors return numbers without thermodynamic consistency. Here we derive an exact thermodynamic identity showing that the macroscopic first-dissociation constant is fully determined by protonated-microstate populations and unique first-deprotonation events, eliminating the deprotonated ensemble algebraically and reducing aggregation to O(n+E) operations. We implement this identity in DTi-pKa, a dual-head graph neural network whose free-energy and dissociation heads are coupled by thermodynamic constraints. On four external benchmarks (355 molecules), DTi-pKa achieves a pooled MAE of 0.5665 pKa units, with 0.6285 on the 169 records lacking training-cache matches, while providing site-resolved micro-pKa values and protonation-state populations. Controlled ablations show that constraint placement at the level of the reported macroscopic equilibrium matters more than microscopic label precision--a design principle transferable to physics-informed machine learning beyond chemistry. Closure diagnostics expose numerical self-consistency as an open frontier, which we report transparently. By replacing an intractable computation with a physical identity, DTi-pKa unifies macroscopic accuracy and microscopic interpretability in a single framework.