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Charge Order at the Frontier between the Molecular and Solid States in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Ba</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>NaRu</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="bold">O</mml:mi><mml:mn>9</mml:mn></mml:msub></mml:math>
We show that the valence electrons of ${\mathrm{Ba}}_{3}{\mathrm{NaRu}}_{2}{\mathrm{O}}_{9}$, which has a quasimolecular structure, completely crystallize below 210 K. Using an extended Hubbard model, we show that the charge ordering instability results from long-range Coulomb interactions. However, orbital ordering, metal-metal bonding, and formation of a partial spin gap enforce the magnitude …