  The exact eigenenergies of the $T_{4c}=[cc][\bar{c}\bar{c}]$,
$T_{4b}=[bb][\bar{b}\bar{b}]$, and $T_{2[bc]}=[bc][\bar{b}\bar{c}]$ tetraquarks
are calculated within the extended transitional Hamiltonian approach, in which
the so-called Bethe \emph{ansatz} within an infinite-dimensional Lie algebra is
used. We fit the parameters appearing in the transitional region from
phenomenology associated with potential candidates of tetraquarks. The rotation
and vibration transitional theory seems to provide a better description of
heavy tetraquarks than other attempts within the same formalism. Our results
indicate that the pairing strengths are large enough to provide binding; an
extended comparison with the current literature is also performed.
