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Amines such as triaminomethane, tetraaminomethane, and many polysubstituted amines do not exist because of their degradation into ammonia. Is it possible for derivatives of these amines to exist at all? Take for example tetra(t-butylamino)methane. Will there be enhanced stability due to the tert-butyl groups or will degradation to t-butylamine still occur? Is there a point at which this degradation will stop, if so where?

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I wouldn't say that they don't exist, but there's very little to keep them from collapsing to an amidine, which makes isolation quite difficult.

This is completely analogous to orthoformic acid, which, as a tetrahedral intermediate, rapidly collapses.

Substitution helps to stabilize the tetrahedral intermediates a lot. For example, both trimethyl orthoformate and tris(dimethylamino)methane are commercially available.

EDIT: Forgot to address this in my answer, but having t-butyl groups probably makes things worse due to steric hindrance. Neopentyl is bad enough...

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