When looking at excited states of molecules, $\delta$ bonds are relatively common, but I've never come across a molecule with a $\delta$ bond in its ground state.
Are there molecules with $\delta$ bonds in their ground states?
What about even higher angular momentum states ($\phi$ and $\gamma$ bonds)?
Answer
Chromium(II) acetate has a Cr-Cr quadruple bond - and hence a $\delta$ bond - in its ground state. This sort of "paddlewheel" configuration, with four carboxylic acids coordinating a pair of metal ions, is reasonably common (see also copper(II) acetate, for instance), although the extent to which the metals can be considered covalently bonded varies.
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