Near degeneracy and pseudo Jahn-Teller effects in mixed-valence ladders:   the phase transition in NaV$_2$O$_5$
  We analyze the electronic structure of a mixed-valence ladder system. We find that structural anisotropy and complex electron correlations lead to on-rung charge localization and insulating character. Charge fluctuations within the rung of the ladder interact strongly to the lattice degrees of freedom, which gives rise to large pseudo Jahn--Teller effects. The phase transition in NaV$_2$O$_5$ should be driven by this kind of mechanism. 
L. Hozoi, S. Nishimoto, and A. Yamasaki