We explore various design principles for efficient excitation energy transport in complex quantum systems. We investigate energy transfer efficiency in randomly disordered geometries consisting of up to 20 chromophores to explore spatial and spectral properties of small natural/artificial Light-Harvesting Complexes (LHC). We find significant statistical correlations among highly efficient random structures with respect to ground state properties, excitonic energy gaps, multichromophoric spatial connectivity, and path strengths. These correlations can even exist beyond the optimal regime of environment-assisted quantum transport. For random configurations embedded in spatial dimensions of 30 Å or 50 Å, we observe that the transport efficiency saturates to its maximum value if the systems contain around 7 or 14 chromophores, respectively. Remarkably, these optimum values coincide with the number of chlorophylls in the Fenna-Matthews-Olson protein complex and LHC II monomers, respectively, suggesting a potential natural optimization with respect to chromophoric density.

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