  We perform accurate calculations of energy levels as well as fine and
hyperfine splittings of the lowest $^{1,3}\!P_J$, $^{3}\!S_1$, $^{3}\!P^e_J$,
and $^{1,3}\!D_J$ excited states of the $^9$Be atom using explicitly correlated
Gaussian functions and report on the breakdown of the standard hyperfine
structure theory. Because of the strong hyperfine mixing, which prevents the
use of common hyperfine constants, we formulate a description of the fine and
hyperfine structure that is valid for an arbitrary coupling strength and may
have wide applications in many other atomic systems.
