  The TlCl molecule has previously been investigated theoretically and proposed
as promising candidates for laser cooling searches [X. Yuan et. al. J. Chem.
Phys., 149, 094306, 2018]. From these results, the cooling process, which would
proceed by transitions between a\sup{3}{\Pi}\sup{+}\sub{0} and
X\sup{1}{\Sigma}\sup{+}\sub{0} states, had as potential bottleneck the long
lifetime (6.04 {\mu}s) of the excited state a\sup{3}{\Pi}\sup{+}\sub{0} , that
would prohibit experimentally control the slowing region. Here, we revisit this
system by employing four-component Multireference Configuration Interaction
(MRCI) calculations, and investigate the effect of such approaches on the
calculated transition moments between a\sup{3}{\Pi}\sup{+}\sub{0} and
a\sup{3}{\Pi}\sub{1} excited states of TlCl as well as TlF, the latter serving
as a benchmark between theory and experiment. Wherever possible, MRCI results
have been cross-validated by, and turned out to be consistent with,
four-component equation of motion coupled-cluster (EOM-CC) and polarization
propagator (PP) calculations. We find that the results of TlF are very closed
to experiment values, while for TlCl the lifetime of the a3{\Pi}+0 state is now
estimated to be 175 ns, which is much shorter than previous calculations
indicated, thus yielding a different, more favorable cooling dynamics. By
solving the rate-equation numerically, we provide evidence that TlCl could have
cooling properties similar to those of TlF. Our investigations also point to
the potential benefits of enhancing the stimulated radiation in optical cycle
to improve cooling efficiency.
