  An optical cycling center (OCC) is a recently coined term to indicate two
electronic states within a complex quantum object that can repeatedly
experience optical laser excitation and spontaneous decay, while being well
isolated from its environment. Here we present a quantitative understanding of
electronic, vibrational, and rotational excitations of the polyatomic SrOH
molecule, which possesses a localized OCC near its Sr atom. In particular, we
describe the vibrationally-dependent trends in the Franck-Condon factors of the
bending and stretching modes of the molecular electronic states coupled in the
optical transition. These simulations required us to perform electronic
structure calculations of the multi-dimensional potential energy surfaces of
both ground and excited states, the determination of vibrational and bending
modes, and corresponding Franck-Condon factors. We also discuss the extent to
which the optical cycling center has diagonal Franck-Condon factors.
