  A new DFT+U type corrective functional is derived from first principles to
enforce the flat plane condition on localized subspaces, thus dispensing with
the need for an ad hoc derivation from the Hubbard model. The newly derived
functional as given by equation 5 yields relative errors below 0.6% in the
total energy of the dissociated s-block dimers as well as the dissociated H5+
ring system. In comparison bare PBE and PBE+U (using Dudarev's 1998 Hubbard
functional) yields relative energetic errors as high as 8.0% and 20.5%
respectively.
