Notably, we have not attempted the empirical adjustment of the regularization to the scrutinized systems. Instead, the literature reported κ parameter (adjusted to molecular thermochemistry) was used, while xBW2 is a non-empirical method (though it could be converted into an empirical one by scaling the regularization term). Fitting the regularization parameter to a representative set of condensed matter systems would certainly lead to even better performance. Indeed, even a systemspecific choice of the regularization parameter would be possible, in analogy to the DFT+U method. However, this would require an objective and transferable protocol for determining this value.