FALDI‐based decomposition of an atomic interaction line leads to 3D representation of the multicenter nature of interactions

Abstract

Atomic interaction lines (AILs) and the QTAIM's molecular graphs provide a predominantly two-center viewpoint of interatomic interactions. While such a bicentric interpretation is sufficient for most covalent bonds, it fails to adequately describe both formal multicenter bonds as well as many non-covalent interactions with some multicenter character. We present an extension to our Fragment, Atomic, Localized, Delocalized and Interatomic (FALDI) electron density (ED) decomposition scheme, with which we can measure how any atom-pair's delocalized density concentrates, depletes or reduces the electron density in the vicinity of a bond critical point. We apply our method on five classical bonds/interactions, ranging from formal either two- or three-center bonds, a non-covalent interaction (an intramolecular hydrogen bond) to organometallic bonds with partial multicenter character. By use of 3D representation of specific atom-pairs contributions to the delocalized density we (i) fully recover previous notion of multicenter bonding in diborane and predominant bicentric character of a single covalent CC bond, (ii) reveal a multicenter character of an intramolecular H-bond and (iii) illustrate, relative to a Schrock carbene, a larger degree of multicenter MC interaction in a Fischer carbene (due to a presence of a heteroatom), whilst revealing the holistic nature of AILs from multicenter ED decomposition. © 2018 Wiley Periodicals, Inc.

FALDI‐based criterion for and the origin of an electron density bridge with an associated (3,–1) critical point on Bader's molecular graph

“…We recently introduced the FALDI ED decomposition scheme . FALDI uses concepts from the domain averaged Fermi hole (DAFH) approach to calculate pseudo‐second‐order contributions arising from electrons within QTAIM‐defined atomic basins.…”

“…However, the ED (as well as critical points in the ED) is a field influenced by all particles of a molecule, and, therefore, the notion that a DB is a diatomic property is false. In fact, we have previously shown that the ED at a (3,–1) CP is a result of contributions from delocalized electrons arising from multiple atoms, thereby concluding that a DB is inherently multicenter in nature even in the case of a classical covalent bond. A similar problem facing existing interpretations of a DB is the use of the second eigenvalue of the Hessian matrix as a measure of electron concentration for the fulfillment of Feynman's theorem (the basis for Bader's interpretation as well as the interpretation of other methods such as NCI).…”

“…This approach is flawed, as it only measures the local , relative electron concentration rather than the absolute, and resultantly shows a large dependence on the local environment. Our own fragment, atom, localized, delocalized, and interatomic (FALDI) density decomposition scheme provides absolute measures of electron concentration for 1‐ and 2‐center ED distributions. Hence, FALDI provides a much more trustworthy measure with regards to a concentration (and its origin) of ED within an internuclear region.…”

“…Our own fragment, atom, localized, delocalized, and interatomic (FALDI) density decomposition scheme provides absolute measures of electron concentration for 1‐ and 2‐center ED distributions. Hence, FALDI provides a much more trustworthy measure with regards to a concentration (and its origin) of ED within an internuclear region.…”

“…In principle, this approach can be taken with a large number of established ED decompositions. However, we have chosen our recently developed FALDI density decomposition scheme, as FALDI is (i) inherently linked to QTAIM atomic basins and populations, and (ii) FALDI can provide visualization and quantify electron exchange‐correlation channels in real 3D space.…”