The ANANKE relative energy gradient (REG) method to automate IQA analysis over configurational change

Much chemical insight ultimately comes down to finding out which fragment of a total system behaves like the total system, in terms of an energy profile. A simple example is that of the water dimer, where this system is regarded as held together by a hydrogen bond. The hydrogen bond consists of two atoms (H···O), which energetically behave similarly to the total system (H₂O)₂. However, from a quantum mechanical point of view, each atom in the total system interacts with any other atom. Thus, the view that the hydrogen bond by itself governs the energetic stability of the water dimer needs rigorous justification. In this work, we propose a method that provides such a justification, in general, but only illustrated on the water dimer here. This method is based on the topological energy partitioning method called interacting quantum atoms (IQA). The method is implemented in the program ANANKE, which calculates correlations between the energy profile of the total system and those of subsystems (or fragments). ANANKE acts on the IQA energy contributions obtained for a sequence of full-system geometries controlled by a coordinate of interest (e.g. the O···H distance in the water dimer). Although applied only for the water dimer in this work, the method is general and able to explain the gauche effect, the torsional barrier in biphenyl, the arrow-pushing scheme of an enzymatic reaction (peptide hydrolysis in the HIV-1 Protease active site), and halogen-alkane nucleophilic substitution (S_N2) reactions. Those applications will appear elsewhere as separate and elaborated case studies; here we focus on the details of the ANANKE method and its justification, using the water dimer as a concrete case.