Strong correlation in polyaromatic hydrocarbons from the two-electron reduced-density-matrix method: effects of geometry and size

Polyaromatic hydrocarbons (PAHs) are a class of organic molecules with importance in several branches of science, including medicine, combustion chemistry, and astrophysics. The delocalized pi-orbital systems in PAHs require the use of highly accurate electronic structure methods to capture the effects of strong electron correlation. Wavefunction-based electronic structure methods achieve high accuracy by treating the wavefunction as a linear combination of Slater determinants, which scales exponentially with the number of electrons and is too costly to treat large PAHs. Density matrix renormalization group methods have been used effectively to capture electron correlation in linear acene chains, but are not well-suited to treat PAHs with non-linear geometries. Two-electron reduced density matrix (2-RDM) methods, in contrast, are cost effective and have no geometry restrictions, making them uniquely qualified to treat PAHs of varying sizes and geometries. In this study we apply 2-RDM theory to explore the relationship between geometry and electron correlation in PAHs. We use several metrics to assess strong correlation: natural orbital occupation numbers, Frobenius norms, correlation energy, and von Neumann entropies. When necessary, the metrics are modified to facilitate comparison between molecules. The results are as follows: (i) We confirm the trend of increasing polyradical character with increasing molecular size in linear acenes (previously noted by Hachmann et al. and Gidofalvi et al.); (ii) We find a corresponding trend of increasing correlation with increasing molecular size in the arch-shaped PAHs, indicating that the relationship between size and correlation persists in PAHs with more complex geometries; (iii) We show that PAHs of similar size but differing geometries exhibit significantly different degrees of strong correlation; (iv) We find that PAHs with a strictly linear geometry exhibit greater strong correlation than PAHs with non-linear geometries, even when they are compared to PAHs of the same size and symmetry. Our results provide strong evidence that among PAHs, electron correlation is a function of geometry as well as size.