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 Delta mu was decomposed into contributions Delta(mu) over bar and delta mu(Delta mu = Delta(mu) over bar + delta mu). Delta mu is the solvation free energy of the solute with a fixed electron density and delta mu is the residual free energy due to the electron density polarisation in solution. We, further, decomposed the free energies delta mu due to electron density fluctuations in aromatic solutes in aqueous solutions into contributions from pi and sigma orbitals. We note, however, that the decompositions will not be validated when the polarisations of pi orbitals seriously couple with those of sigma orbitals. In this paper, we study a correlation matrix between polarisations of pi and sigma 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 pi - pi* transfers between the orbitals lying in the HOMO-LUMO region. Thus, the polarisation of pi electrons hardly couples with that from sigma orbitals, which justifies our decomposition analyses.