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

Abstract

The quantum topological energy partitioning method Interacting Quantum Atoms (IQA) has been applied for over a decade resulting in an enlightening analysis of a variety of systems. In the last three years we have enriched this analysis by incorporating into IQA the two-particle density matrix obtained from Møller-Plesset (MP) perturbation theory. This work led to a new computational and interpretational tool to generate atomistic electron correlation and thus topologically based dispersion energies. Such an analysis determines the effects of electron correlation within atoms and between atoms, which covers both bonded and non-bonded "throughspace" atom-atom interactions within a molecule or molecular complex. A series of papers published by us and other groups shows that the behavior of electron correlation is deeply ingrained in structural chemistry. Some concepts that were shown to be connected to bond correlation are bond order, multiplicity, aromaticity, and hydrogen bonding. Moreover, the concepts of covalency and ionicity were shown not to be mutually excluding but to both contribute to the stability of polar bonds. The correlation energy is considerably easier to predict by machine learning (kriging) than other IQA terms. Regarding the nature of the hydrogen bond, correlation energy presents itself in an almost contradicting way: there is much localized correlation energy in a hydrogen bond system, but its overall effect is null due to internal cancelation. Furthermore, the QTAIM delocalization index has a connection with correlation energy. We also explore the role of electron correlation in protobranching, which provides an explanation for the extra stabilization present in branched alkanes compared to their linear counterparts. We hope to show the importance of understanding the true nature of the correlation energy as the foundation of a modern representation of dispersion forces for ab initio, DFT, and force field calculations.

A Comparison of the Interacting Quantum Atoms (IQA) Analysis of the Two‐Particle Density‐Matrices of MP4SDQ and CCSD

“…Over the last three years we have published a sizeable body of work on the nature of correlation energy and its implications. It is clear from our recent review [3] that most of our analyses focused on bond and interatomic correlation energies, as most chemical insight is contained in that region. Furthermore, the analyses have been limited to Møller-Plesset perturbation theory, which is neither the state-of-the-art nor the benchmark for ab initio calculations.…”

“…The set of systems investigated consists of 7 typical hydrides EH n (where n = 1, 2, 3 Figure 1 shows the configurations of these 6 complexes. Table 1 shows selected intra-atomic ("A-A") and interatomic ("A-B") electron correlation energies of all molecules studied with the exception of the complexes.…”

“…Several research groups have developed the ability [1][2][3][4][5][6] to partition the energy of a molecule, determined from the twoparticle density-matrix (2PDM), into its constituent intraatomic and interatomic contributions. The way this partitioning is achieved is by means of the gradient vector field of the electron density [7,8] as the "natural scissors" cutting the quantum mechanical system at hand.…”

“…[10] The most prevalent topological energy decomposition analysis is referred to as Interacting Quantum Atoms (IQA), [11] which was inspired by very early work of our group. [12] Our contribution [2,[13][14][15][16][17][18][19] so far, which has been reviewed [3] very recently, concentrated on the 2PDM arising from various orders of Møller-Plesset (MP) perturbation theory. However, this level of theory has an issue because MP perturbation theory correlates only the two-electron terms while leaving the electronic kinetic energy and electron-nuclear attraction terms uncorrelated.…”

Interacting Quantum Atoms—A Review

“…Using this methodology, they have been able to predict intra- [ 143 ] and interatomic energies [ 144 , 145 ], as well as correlation energy at the MP2 approximation for a previously unknown molecular geometries [ 146 ] Using. the models produced in this manner, they were able to accurately carry out geometry optimisations with chemical accuracy [ 147 ] for biomolecules [ 148 ], charged systems [ 149 ] and non-covalent interactions [ 150 ].…”