  We present a generally-applicable computational framework for the efficient
and accurate characterization of molecular structural patterns and acid
properties in explicit solvent using H$_2$O$_2$ and CH$_3$SO$_3$H in phenol as
an example. In order to address the challenges posed by the complexity of the
problem, we resort to a set of data-driven methods and enhanced sampling
algorithms. The synergistic application of these techniques makes the
first-principle estimation of the chemical properties feasible without
renouncing to the use of explicit solvation, involving extensive statistical
sampling. Ensembles of neural network potentials are trained on a set of
configurations carefully selected out of preliminary simulations performed at a
low-cost density-functional tight-binding (DFTB) level. The energy and forces
of these configurations are then recomputed at the hybrid density functional
theory (DFT) level and used to train the neural networks. The stability of the
NN model is enhanced by using DFTB energetics as a baseline, but the efficiency
of the direct NN (i.e., baseline-free) is exploited via a multiple-time step
integrator. The neural network potentials are combined with enhanced sampling
techniques, such as replica exchange and metadynamics, and used to characterize
the relevant protonated species and dominant non-covalent interactions in the
mixture, also considering nuclear quantum effects.
