REG-MULTI: Lifting the veil on electrostatic interactions

We illustrate a proof-of-concept in the analysis of electrostatic energy with three systems: the water dimer, the benzene dimer and the phenol…toluene complex. Atomic multipole moments disentangle the electrostatic interaction and are calculated according to the quantum topological approach. This enables a connection with the exact electrostatic energy defined by an energy decomposition method called Interacting Quantum Atoms (IQA). For the first time, the Relative Energy Gradient (REG) method is used in combination with multipole moments and thus named REG-MULTI. REG is able to extract chemical insight from an energy profile controlled by a dynamical change (e.g., a rotation around a dihedral angle), both in terms of energy type (e.g., electrostatic, exchange) and atomic locale. While normally combined with IQA as REG-IQA, here REG ranks multipolar interactions according to their importance in explaining the intermolecular electrostatic energy. Charge-charge energies involving the hydrogen bond atoms mostly drive the formation of the water dimer for a large translational motion. However, analysis on the smaller β angle shift shows dependency up to charge-quadrupole and charge-hexadecapole to fully recover the water dimer global minimum. Monomeric multipole moments deliver the same ranking of REG values for translation as that of the dimeric multipole moments for certain translational and α angle motions, in the water dimer. REG-MULTI recovers the well-known Hunter-Sanders model of quadrupolar electrostatics for the benzene dimer, denoting the Qzz component as the most relevant. The addition of functional groups to the benzene dimer (leading to the phenol…toluene complex) shifts the analysis towards charges on the phenol, due to the presence of an oxygen atom, and towards dipole and quadrupole moments for the toluene, showing that the typical π-π interaction between two aromatic rings is not relevant anymore.