In the framework of determining system-specific long-range corrected density functionals, the question is addressed whether such functionals, tuned to satisfy the condition − ε HOMO = IP or other energetic criteria, provide accurate electron densities. A nonempirical physically motivated two-dimensional tuning of range-separated hybrid functionals is proposed and applied to the particularly challenging case of a molecular property that depends directly on the ground-state density: the copper electric field gradient (EFG) in CuCl. From a continuous range of functional parametrizations that closely satisfy − ε HOMO = IP and the correct asymptotic behavior of the potential, the one that best fulfills the straight-line behavior of E ( N ), the energy as a function of a fractional electron number N , was found to provide the most accurate electron density as evidenced by calculated EFGs. The functional also performs well for related Cu systems.