  A way to improve the accuracy of the spectral properties in density
functional theory (DFT) is to impose constraints on the effective, Kohn-Sham
(KS), local potential [J. Chem. Phys. {\bf 136}, 224109 (2012)]. As
illustrated, a convenient variational quantity in that approach is the
``screening'' or ``electron repulsion'' density, $\rho_{\rm rep}$,
corresponding to the local, KS Hartree, exchange and correlation potential
through Poisson's equation. Two constraints, applied to this minimization,
largely remove self-interaction errors from the effective potential: (i)
$\rho_{\rm rep}$ integrates to $N-1$, where $N$ is the number of electrons, and
(ii) $\rho_{\rm rep}\geq 0$ everywhere. In the present work, we introduce an
effective ``screening'' amplitude, $f$, as the variational quantity, with the
screening density being $\rho_{\rm rep}=f^2$. In this way, the positivity
condition for $\rho_{\rm rep}$ is automatically satisfied and the minimization
problem becomes more efficient and robust. We apply this technique to molecular
calculations employing several approximations in DFT and in reduced density
matrix functional theory. We find that the proposed development is an accurate,
yet robust, variant of the constrained effective potential method.
