Various computational methods and predictive models have been developed to estimate HOMO-LUMO gaps and polarizabilities for organic molecules with different levels of tradeoff between accuracy and computational cost . Lately, it has became feasible to access a plethora of highly-accurate QM properties -including ∆E HL and α -for large swaths of the chemical compound space (CCS) . Comprehensive analyses of these extensive datasets may help to understand the deeper physical picture behind the inherent property-property relationships. With this motivation, we herein perform an exhaustive investigation of the two-dimensional space defined by HOMO-LUMO gap and polarizability (i.e., (∆E HL , α)-space) for small organic molecules with the aim to gain insights into the intrinsic relationship between these two properties. We find that while correlation might appear in homologous molecules, if a large enough subspace of CCS is considered, HOMO-LUMO gap and polarizability are essentially uncorrelated and their 2D space is represented as a structureless "blob". Through the analysis of diverse molecular sets, it is shown that this lack of correlation can be related to the fact that the polarizability is primarily determined by the atomic composition, while the HOMO-LUMO gap heavily depends on the arrangement of the atoms into chemical functional groups. Hence, we expect that our findings will assist the development of novel design principles in which the control of multiple electronic properties is relevant, as we finally demonstrate on the case of molecular photodetectors.