  We develop a theory describing a parameter based phase diagram to be
associated with materials incorporating skipped valence ions\cite{Varma}. We
use a recently developed tight-binding approach for the bismuthates to study
the phase diagram exhibiting the crossover from a bond disproportionated (BD)
to a charge disproportionated (CD) system in addition to the presence of a new
metallic phase. We argue that three parameters determine the underlying physics
of the BD-CD crossover when electron correlation effects are small: the
hybridization between O-2$p_{\sigma}$ and Bi-6$s$ orbitals ($t_{sp\sigma}$),
the charge-transfer energy between Bi-6$s$ and O-a$_{1g}$ molecular orbitals
($\Delta$), and the width of the oxygen sublattice band ($W$). In the BD
system, we estimate an effective attractive interaction $U$ between holes on
the same O-a$_{1g}$ molecular orbital. Although here we concentrate on the
example of the bismuthates, the basic ideas can be directly transferred to
other perovskites with negative charge-transfer energy, like ReNiO$_{3}$ (Re:
rare-earth element), Ca(Sr)FeO$_{3}$, CsTIF$_{3}$ and CsTlCl$_{3}$.
