While I don't have a source (sorry...), I believe Hirshfeld charges should converge in the complete basis set limit, whereas Mulliken (and Lowdin) charges have no guarantee of this. If you want charges that reproduce atomic dipoles, perhaps you can also try CM5 charges. — Andrew Rosen yesterday

This is most likely not due to diffuse functions. Theoretically, Hirshfeld charges should never give negative f+ values, as long as the charge density of the N-1 system is uniformly smaller than or equal to that of the N system. This property however may (or may not) be broken by the dipole correction. — wzkchem5 yesterday

@wzkchem5 it looks like this is the issue, I checked with regular Hirshfeld charges and all f+ values are positive. — roma ichenko yesterday

@romaichenko Then perhaps dipole-corrected Hirshfeld charges do become unphysical when diffuse functions are added? I'm sure that Hirshfeld charges themselves converge to well-defined values in the complete basis set limit, but I don't know if this is true for the atomic dipole moment corrected Hirshfeld charges as well. — wzkchem5 yesterday