A QM/MM study on the correlation between the polarisations of π and σ electrons in a hydrated benzene

In a recent work, we performed free-energy analyses for hydration of benzene by conducting QM/MM-ER simulations, where the total solvation free energy Δμ was decomposed into contributions Δμ and δμ (Δμ = Δμ + δμ). Δμ is the solvation free energy of the solute with a fixed electron density and δμ is the residual free energy due to the electron density polarisation in solution. We, further, decomposed the free energies δμ due to electron density fluctuations in aromatic solutes in aqueous solutions into contributions from π and σ orbitals. We note, however, that the decompositions will not be validated when the polarisations of π orbitals seriously couple with those of σ orbitals. In this paper, we study a correlation matrix between polarisations of π and σ orbitals through QM/MM simulations to assess the coupling strength among the orbitals. We found that the electron density polarisation is dominated by the polarisation arising from π - π * transfers between the orbitals lying in the HOMO-LUMO region. Thus, the polarisation of π electrons hardly couples with that from σ orbitals, which justifies our decomposition analyses.