  For rovibronic states corresponding to the $B$ and $B'\ ^1\Sigma_\text{u}^+$
electronic states of the hydrogen molecule, the pre-Born--Oppenheimer
(four-particle) non-relativistic energy is converged to a 1-3 parts-per-billion
relative precision. The four-particle non-relativistic energy is appended with
leading-order relativistic, leading- and estimated higher-order
quantum-electrodynamics corrections. The resulting term values referenced to
the rovibronic ground state are obtained in an excellent agreement with the
experimental results. Further results are reported and discussed for other
rovibronic states assignable to the $C\ ^1\Pi_\text{u}$ and the $EF,GK,$ and
$HH\ ^1\Sigma_\text{g}^+$ electronic states.
