Quantifying Fluctuations of Average Environments for Embedding Calculations

In the context of employing embedding methods to study spectroscopic properties, the viability and effectiveness of replacing an ensemble of calculations by a single calculation using an average description of the system of study are evaluated. This work aims to provide a baseline of the expected fluctuations in the average description of the system obtained in the two cases: from calculations of an ensemble of geometries, and from an average environment constructed with the same ensemble. To this end, the classical molecular dynamics simulation of a very simple system was used: a rigid molecule of acetone in a solution of rigid water. We perform a careful numerical analysis of the fluctuations of the electrostatic potential felt by the solute, as well as the fluctuations in the effect on its electronic density, measure through the dipole moment and the atomic charges derived from the corresponding potential. At the same time, we inspect the accuracy of the methods used to construct average environments. Finally, the proposed approach to generate the embedding potential from an average environment density is applied to estimate the solvatochromic shift of the first excitation of acetone. In order to account for quantum-confinement effects that may be important in certain cases, the fluctuations on the shift due to the interaction with the solvent are evaluated using Frozen-Density Embedding Theory. Our results demonstrate that, for normally-behaved environments, the constructed average environment is a reasonably good representation of a discrete solvent environment.