Decomposition of energy and free energy changes by following the flow of work along reaction path

To extract mechanistic information of activated processes, we propose to decompose potential energy and free energy differences between configurations into contributions from individual atoms, functional groups, or residues. Decomposition is achieved by calculating the mechanical work associated with the displacements and forces of each atom along a path that connects two states, i.e., following the flow of work. Specifically, we focus on decomposing energy or free energy differences along representative pathways such as minimum energy paths (MEPs) and minimum free energy paths (MFEPs), and a numerical metric is developed to quantify the required accuracy of the reaction path. A statistical mechanical analysis of energy decomposition is also presented to illustrate the generality of this approach. Decomposition along MEP and MFEP is demonstrated on two test cases to illustrate the ability to derive quantitative mechanistic information for different types of activated processes. First, the MEP of alanine dipeptide isomerization in vacuum and the MFEP of isomerization in explicit water is studied. Our analysis shows that carbonyl oxygen and amide hydrogen contribute to most of the energetic cost for isomerization and that explicit water solvation modulates the free energy landscape primarily through hydrogen bonding with these atoms. The second test case concerns the formation of tetrahedral intermediate during a transesterification reaction. Decomposition analysis shows that water molecules not only have strong stabilization effects on the tetrahedral intermediate but also constitute a sizable potential energy barrier due to their significant structural rearrangement during the reaction. We expect that the proposed method can be generally applied to develop mechanistic understanding of catalytic and biocatalytic processes and provide useful insight for strategies of molecular engineering.