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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)?

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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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  • $\begingroup$ The copper analog is another example $\endgroup$
    – khaverim
    Commented Mar 3, 2016 at 13:15
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Metal-metal quadruple bonds have seemingly been reported for several cases, quite often by F. A. Cotton. A short search revealed a more recent report on a species with a Cr-Cr quintuple bond: Synthesis of a Stable Compound with Fivefold Bonding Between Two Chromium(I) Centers.

Admittedly, I didn't bother to read the full article, it's just not the kind of chemistry I'm interested in. However, YMMV and you might find it helpful.

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I am a bit late to the party, but I just found this question. When I did research on the φ bond for What would follow in the series sigma, pi and delta bonds? I came across some predictions about possible φ bond in the ground state.

According to Gagliardi and Roos, there should be a φ bond in the ground state of the $\ce{U2}$ molecule. That being said, it is probably incredibly tough to synthesise this molecule.

Metal-metal multiple bonds have become fairly common as my earlier answer demonstrates.
It should be clarified that a quadruple bond does not necessarily mean that a δ bond is involved. Often enough the combination of the dz² metal orbitals lead to the formation of a second σ bond first.
It should further be explained, that a δ bond can be present, but the overall bond order could be lower than four.

Laura Gagliardi, Björn O. Roos, Nature, 2005, 433, 848-851. Available free at Archive ouverte UNIGE.

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    $\begingroup$ I figure you could make $\ce{U2}$ molecules by heating the metal enough so that becomes gaseous. Either find a chamber that resists temperatures of around $\mathrm{4000\ K}$ to get a decently high vapour pressure, or more likely, do some kind of ablation (plasma, laser, etc) on solid uranium, though there would probably be contamination with larger metallic clusters. $\endgroup$
    – Nicolau Saker Neto
    Commented Mar 3, 2016 at 9:11

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