Access to cold molecules is critical for quantum information science, design of new sensors, ultracold chemistry, and search of new phenomena. These applications depend on the ability to laser-cool molecules. Theory and qualitative models can play a central role in narrowing down the vast pool of potential candidates amenable to laser cooling. We report a systematic study of structural and optical proper- ties of alkaline earth metal derivatives in the context of their applicability in laser cooling using equation-of-motion coupled-cluster methods. To rationalize and gen- eralize the results from high-level electronic structure calculations, we develop an effective Hamiltonian model. The model explains the observed trends and suggests new principles for the design of laser-coolable molecules.