Solution-Phase Energy Decomposition Analysis (SP-EDA): Theory and Applications.

We present an extension of our canonical energy decomposition analysis (EDA) from the gas phase to a Solution-Phase approach (SP-EDA), that is, to interactions between molecular fragments in the condensed phase, simulated using the Conductor-like Screening Model (COSMO). To this end, we have introduced different solvation states that serve to simulate particular physical phenomena that can be associated with the step from separate solvated fragments to the solvated complex of these fragments. In addition to the well-known deformation strain of the fragments, induced by complex formation, one can distinguish the desolvation of the contact points via which the fragments bind, the response of the solvent to the deformation of the fragments as well as the response of the solvent to the formation of the complex, and finally the complex formation between the partially desolvated fragments. We provide definitions of how to model these phenomena using a continuum model, such as COSMO. Finally, we analyze, for representative model systems, how the bonding and, in particular, the EDA terms of electrostatic attraction, Pauli repulsion, and stabilizing orbital interactions behave across the above steps associated with interactions in solution. An important practical conclusion is that neglecting the effect of the partial desolvation at the binding sites has, in most cases, only minor consequences for the values and trends in the EDA terms. This finding can be used to simplify investigations using SP-EDA.