Efficient polarizable QM/MM using the direct reaction field Hamiltonian with electrostatic potential fitted multipole operators

Electronic polarization and dispersion are decisive actors in determining interaction energies between molecules. These interactions have a particularly profound effect on excitation energies of molecules in complex environments, especially when the excitation involves a significant degree of charge reorganisation. The direct reaction field (DRF) approach, which has seen a recent revival of interest, provides a powerful framework for describing these interactions in quantum mechanics/molecular mechanics (QM/MM) models of systems, where a small subsystem of interest is described using quantum chemical methods and the remainder is treated with a simple MM force field. In this paper we show how the DRF approach can be combined with the electrostatic potential fitted (ESPF) multipole operator description of the QM region charge density, which reduces the scaling $\mathcal{O}(N_\mathrm{MM}^3)$ of the method with MM system to $\mathcal{O}(N_\mathrm{MM}^2)$. We also show how the DRF approach can be combined with fluctuating charge descriptions of the polarizable environment, as well as previously used atom-centred dipole-polarizability based models. We further show that the ESPF-DRF method provides an accurate description of molecular interactions in both ground and excited electronic states of the QM system and apply it to predict the gas to aqueous solution solvatochromic shifts in the UV/visible absorption spectrum of acrolein.