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. * skotoch@temple.edu arXiv:1904.11579v2 [physics.chem-ph] 2 Dec 2019Laser cooling and trapping of atoms, enabled by the existence of closed optical cycling transitions, have revolutionized atomic physics and led to breakthroughs in several disciplines of science and technology [1]. These advances enabled the simulation of exotic phases in quantum-degenerate atomic gases, the creation of a novel generation of atomic clocks, matter-wave interferometry, and the development of other highly-sensitive sensors. Temperatures below tens of microkelvin have also allowed the confinement of diatomic molecules, built from or associated with laser-cooled atoms, in electric, magnetic, and/or optical traps, where they are isolated from their environment and can be carefully studied.Achieving similar temperatures for polyatomic molecules, however, remains challenging.Since polyatomic molecules are characterized by multiple degrees of freedom and have correspondingly more complex structures, it is far from obvious whether there exists polyatomic molecules that have the nearly-closed optical cycling transitions required for successful laser cooling. Such transitions could then repeatedly scatter photons.A diverse list of promising applications for ultracold polyatomic molecules exists. This includes creating novel types of sensors, advancing quantum information science, simulation of complex exotic materials, performing precision spectroscopy to test the Standard Model of particle physics, and, excitingly, the promise of control of quantum chemical reactions when each molecule is prepared in a unique rovibrational quantum state. Moreover, the de Broglie wavelength of colliding ultracold molecules is much larger than the range of intermolecular forces and, thus, the science of the breaking and making of chemical bonds has entered into an unexplored regime.Over the decades many spectroscopic studies of molecules consisting of an alkaline-earth metal atom (M) and a ligand have been performed [2-10], predominantly to determine their structure. The simplest polyatomic mol...