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I. Introduction

By using IGMPlot you can identify, characterize, and quantify molecular interactions over a broad range: from non-covalent to covalent bonding, through metal coordination. This tool can be helpful for interpretation accessible to a wide community of chemists (organic, inorganic chemistry, including transition metal complexes and reaction mechanisms). From a practical perspective, an attractive feature of the IGM approach is to provide an automatic workflow delivering properties that provides chemists with a visual and quantitative understanding of interactions. Although IGMPlot relies on the electron density (ED) topology, no topological analysis is required like in QTAIM and an IGM analysis can be achieved with little preparation. For more detailed information on the concept please refer to the original papers:

1. Lefebvre C., Rubez G., Khartabil H., Boisson JC., Contreras-García J., Hénon E. Phys Chem Chem Phys. 2017, 19, 17928 doi: http://doi.org/10.1039/c7cp02110k
2. Lefebvre C., Khartabil H., Boisson JC., Contreras-García J., Piquemal J.-P., Hénon E. Chem. Phys. Chem. 2018, 19, 1 doi: http://doi.org/10.1002/cphc.201701325
3. Miguel Ponce-Vargas, Corentin Lefebvre, Jean-Charles Boisson, Eric Hénon J. Chem. Inf. Model. 2020, 60, 1, 268 doi: http://doi.org/10.1021/acs.jcim.9b01016
4. Johanna Klein, Hassan Khartabil, Jean-Charles Boisson, Julia Contreras-García, Jean-Philip Piquemal, Eric Hénon J. . Phys. Chem. A 2020, 124, 9, 1850 doi: http://doi.org/10.1021/acs.jpca.9b09845

Backgound

IGMPlot is based on the IGM concept and its local descriptor called δg, which can be calculated from the electron density ρ (ED). The IGM-δg approach was initially designed to work with promolecular density, to describe weak interactions. The term promolecular ED refers to an ED model prior to molecule formation. The promolecular ED is a non-relaxed electron density, the sum of spherically averaged neutral atomic densities ρi. It lacks the relaxation introduced in the SCF procedure or in DFT calculations, and then it fails to describe covalent situations for which a wavefunction description is required. In the promolecular mode, only the atomic coordinates have to be supplied and the promolecular ED estimations are fast compared to Quantum Mechanical calculations.

But in 2018, we proposed the Gradient-Based Partitioning (GBP) that extends the IGM concept to electron density derived from a wavefunction. Thus, thanks to the new IGM approach, detailed information can be directly obtained either on the covalent or on the non-covalent domain, for small and larger molecular systems.

In the absence of interactions, for instance, in an isolated atom, ρ shows an exponential decay far from the nucleus. In contrast, in molecular systems, deviations from this exponential decay can be observed. δg captures these deviations. From a practical perspective, IGMPlot employs a numeric grid and calculates local δg at each node of the grid. δg is obtained by doing the difference between the ED gradient of a reference non-interacting system (the so-called Independent Gradient Model) and the ED gradient of the real system.

More precisely, the δg local descriptor quantifies the contragradience between the two fragment ED sources. The so-called ED contragradience situation indicates the mutual penetration of electron charge densities, which is expected when fragments sources are brought closer to each other, and is also sometimes referred to hereafter as density overlap or density sharing. The IGM definition grants that positions of space with non-zero values of δg exclusively correspond to interaction situations and the greater δg, the stronger the interaction. δg is not dimensionless.

In order to better highlight peaks in δg(ρ) plots, a new qg descriptor has been devised to color points of this plot. It is the ’quotient’ twin of the 'difference' δg descriptor. It is dimensionless and it is very sensitive to ED contragradience situation, but it cannot serve to quantify the interaction since it tends to infinity as ∇ρ approaches 0 close to critical points, even for weak interactions like hydrogen-bonding. From a practical perspective, this descriptor qg serves to color IGM and NCI plots and it is also employed in IGMPlot to find critical points.

The IGM framework as described above gives rise to a number of analysing and interpretative tools in IGMPlot:

• Interaction fingerprint: the IGM-δg descriptor carries information on regions of space where the total electron density results from an overlap of individual atomic or molecular electron distributions. By plotting δg = f(ρ) collected on the nodes of a grid encompassing the molecule, a specific two-dimensional “fingerprints” emerges with peaks corresponding to chemical interactions that cover both covalent and noncovalent domains.
• Regions of interaction: Points with non-zero values of δg exclusively correspond to interaction situations. Mapping them back to real space highlights 3D regions associated with molecular interactions by chemists. Thus, constructing iso-surfaces of δg enables the identification and visualization of regions of interaction
• Quantifying interactions: the IGM reference gives a unique definition of the interaction region: non-zero values of δg exclusively correspond to overlap regions between several ED sources. As a consequence, the IGM approach overcomes difficulties to define regions within integration procedures to quantify interactions. In IGMPLot, the quantification of the detected interactions has been implemented by summing local δg quantities over the space representing the interactions, leading to different scores.
• A new way for probing bond strength : IGMPlot is able to provide a so-called Intrinsic Bond Strength Index (IBSI) stemming from a new δg_pair descriptor. The IBSI is dimensionless and is normalized to 1 for H2. Our work has shown that the IBSI is not a bond order (like Mulliken, Wiberg, Mayer, delocalization index or ELF). Thus, the values of IBSI should not be compared to those of bond orders. Rather, it is a new complementary index, related to the bond strength (not to the number of electron pair shared between two atoms).
• Pair Density Asymmetry (PDA): IGMPlot provides users with the PDA index, which captures the asymmetry of the electron density (ED) distribution attached to an atom pair. This tool provides a relatively simple way to assess inductive electronic effects in molecules.
• Atomic decomposition : IGMPlot proposes an atomic decomposition scheme in order to quantify locally the contribution of each atom At (δg_inter/At) to the interaction between two fragments A and B
• Atomic Degree Of Interaction (DOI): the DOI index captures any manifestation of electron density sharing around an atom. It reflects the strength of attachment of an atom to its molecular neighbourhood. It could be used as input in the context of artificial intelligence for predicting chemical properties, or even for predicting the outcome of reactions that require information on the strength of the bonds between atoms. In other respects, the DOI index provides an atomic-level interpretation of reaction mechanism, completing the very nice picture brought by the benchmark URVA tool based on the internal coordinates.
• Critical Point search : A feature of IGMPlot is to perform a critical point (cp) search (bonc critical points, ring critical points, cage critical points). Determining such critical points in a molecule is of high importance in many studies aiming at characterizing bonds by properties at cp like energy densities (kinetic, potential) or the ED Laplacian, or ellipticity, ...

For more detailed information we refer the interested reader to the original articles.