We decided to additionally include Mulliken atomic charges because they describe rearrangements in the electron densities that are not necessarily captured by the energy and the atomic forces. Although other atomic charges would be better suited because of reduced basis set dependence, Mulliken population analysis is widely implemented in quantum mechanical and QM/MM packages, ensuring consistent charge calculations across different computational frameworks. Moreover, this choice aligns naturally with GFN2-xTB's internal design, where shell-wise partitioned Mulliken charges are integral to the method's electrostatic and exchange-correlation terms, maintaining theoretical consistency in our parameter optimization approach.