  A study of the intensity-borrowing mechanisms important to optical cycling
transitions in laser-coolable polyatomic molecules arising from non-adiabatic
coupling, contributions beyond the Franck-Condon approximation, and Fermi
resonances is reported. It has been shown to be necessary to include
non-adiabatic coupling to obtain computational accuracy that is sufficient to
be useful for laser cooling of molecules. The predicted vibronic branching
ratios using perturbation theory based on the non-adiabatic mechanisms have
been demonstrated to agree well with those obtained from variational discrete
variable representation calculations for representative molecules including
CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the
calculated transition properties, including the vibronic coupling constants,
the spin-orbit coupling matrix elements, and the transition dipole moments, and
on the calculated branching ratios have been thoroughly studied. The vibronic
branching ratios predicted using the present methodologies demonstrate that
RaOH is a promising radioactive molecule candidate for laser cooling.
