Relationship between the Casimir force and dark energy

There are two problems that arise here. One obvious problem is that the Casimir effect is attractive¹, while dark energy is repulsive. The other problem is one of scale.

Casimir (1948) shows that, between two particles (instead of the oft-cited case of two plates)
$$delta E propto R^{-7}$$
That's an enormous drop-off. On large scales, this should be negligible. Dark energy, however, is clearly non-negligible on these scales, while its effects are unobservable on small scales.

The Casimir effect is certainly one manifestation of vacuum energy, which may also be the cause of dark energy (in some theories), but that doesn't mean that dark energy is an example of the Casimir effect, or vice versa.

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^{1 There are exceptions, as pointed out by Stan Liou, which arise under certain conditions, but they wouldn't play a part here.}