This gives derivative discontinuities at points where 𝜌𝜌 � 𝑏𝑏 passes through zero. While the earlier versions of DC functionals work reasonably well on a wide range of systems, the derivative discontinuities are unsatisfactory. We therefore experimented with alternative ways to define the unpaired density 𝐷𝐷(𝐫𝐫) and the effective spin densities 𝜌𝜌 � 𝑎𝑎 (𝐫𝐫) and 𝜌𝜌 � 𝑏𝑏 (𝐫𝐫), and we present an improved scheme in this report.