Fermi and Coulomb correlation effects upon the interacting quantum atoms energy partition

Abstract

The Interacting Quantum Atoms (IQA) electronic energy partition is an important method in the field of quantum chemical topology which has given important insights of different systems and processes in physical chemistry. There have been several attempts to include Electron Correlation (EC) in the IQA approach, for example, through DFT and Hartree-Fock/Coupled-Cluster (HF/CC) transition densities. This work addresses the separation of EC in Fermi and Coulomb correlation and its effect upon the IQA analysis by taking into account spindependent one-and two-electron matrices D HF/CC pσ qσ and d HF/CC pσ qσ rτsτ wherein σ and 2 τ represent either of the α and β spin projections. We illustrate this approach by considering BeH 2 , BH, CN -, HF, LiF, NO + , LiH, H 2 O···H 2 O and HC − − − CH, which comprise non-polar covalent, polar covalent, ionic and hydrogen bonded systems. The same and different spin contributions to (i) the net, interaction and exchange-correlation IQA energy components and (ii) delocalisation indices defined in the quantum theory of atoms in molecules are carefully examined and discussed. Overall, we expect that this kind of analysis will yield important insights about Fermi and Coulomb correlation in covalent bonding, intermolecular interactions and electron delocalisation in physical chemistry.

Where Does Electron Correlation Lie? Some Answers from a Real Space Partition

“…Although these results might appear counterintuitive, they have a very precise physical origin. Under the action of Fermi correlation only, opposite spin electrons behave as statistically independent effective moieties, and they delocalize freely over larger spatial regions than when Coulomb correlation is also allowed . A very natural way to understand this starts by recalling that the Fermi hole (FH) that accompanies an electron excludes same‐spin electrons, and thus leaves free room for opposite spin ones.…”

“…Under the action of Fermi correlation only, opposite spin electrons behave as statistically independent effective moieties, and they delocalize freely over larger spatial regions than when Coulomb correlation is also allowed . A very natural way to understand this starts by recalling that the Fermi hole (FH) that accompanies an electron excludes same‐spin electrons, and thus leaves free room for opposite spin ones. This is the very nature of the Lewis pair, in which pairs of opposite spin electrons delocalize independently over common regions of space controlled by the size of the Fermi hole.…”

Contributions of IQA electron correlation in understanding the chemical bond and non-covalent interactions

“…The positive nature of the bond electron correlation is unexpected because this energy encompasses dispersion effects, which are generally stabilizing and hence come with a negative energy. However, there is a physical explanation for this observation: while only employing the Hartree-Fock field, only Fermi correlation is considered (the Fermi hole [58] follows the electron and exclude same-spin electrons), which means that there is no correlation between electrons with opposite spin states. When Møller-Plesset perturbation is applied, Coulomb correlation becomes present in the system, and opposite-spin electrons are no longer independent [59].…”

Perspective: Found in translation: Quantum chemical tools for grasping non-covalent interactions

“…The relevance of IQA for treating weak interactions will expand once a better understanding of the electronic correlation terms is achieved, for which progress is currently being made. 177,178,204 Visualization tools like NCI and DORI have a different objective than QTAIM and IQA: they were designed to be pragmatic, easy to use, and computationally efficient. As a result, they capably identify the spatial extent and the underlying nature of interactions present in molecular systems and complexes.…”