Here, L tot refers to the total objective function and is dependent on the optimization variables k. The objective function has a hierarchical structure, and L tot is comprised of individual objective functions for each target, L T (k) individually weighted by w T . A Tikhonov regularization term is also added, with a user-determined global regularization strength w reg , here set to 1.0. In the context of this work, there are four targets for each residue / protonation state: the two QM dihedral scans, the vibrational frequency calculations, and the single-point energies and gradients from MM-optimized structures from the feedback procedure. The w T applied to the QM dihedral scans and vibrational frequencies is set to 1.0 in this work, while a w T of 4.0 was used for the MM-optimized structures to increase the contribution of this term focusing on elimination of spurious minima.