Charge density analysis attending bond torsion: A bond bundle case study

Abstract

For nearly a century chemical understanding has been tied to the properties of bonds, although more often than not, these bond properties are rooted in molecular orbital or valence bond representations of the electronic structure. Technological advances, however, are allowing for experimental measurements of the density via high resolution X-ray diffraction, while theoretical insights are opening the door to its direct calculation using fast and potentially versatile orbital free DFT methods. Capitalizing on these emerging tools without sacrificing orbital derived understanding has spurred a search for density based representations that deliver the same information available from the orbital perspective. We show that recent extensions of the QTAIM formalism are useful as a means of recovering some of the bond properties that have become an intrinsic part of our chemical understanding. Specifically, we compute from the density the changing bond order and bond order distribution accompanying the rotation about a double bond using the well-studied fulvene molecule as a test case. We compare the picture that emerges from this density based perspective with that stemming from molecular orbital approaches and argue that the two viewpoints are compatible. K E Y W O R D S bond bundle, bond torsion, electron charge density, fulvene, quantum theory of atoms and molecules 1 | INTRODUCTION The modern view of chemical phenomena is inextricably intertwined with the orbital representation of electron movement and redistribution.Roald Hoffman has argued [1] that the orbital perspective holds a special place in chemistry because of the qualitative framework it provides for understanding. Alas, many of the more advanced and accurate methods do not easily lend themselves to orbital representations; for example: band approaches, many electron methods, orbital free approaches, and particularly the direct experimental measurement of electron density. [2] The chemistry community is thus confronted with a conundrum: How will we build on the hard-won understanding based on orbital concepts as we exploit advances in computational and experimental chemistry?Here, we show that by exploiting the quantum theory of atoms in molecules (QTAIM) [3] and its recent extensions [4][5][6][7][8] it is possible to decompose the electronic charge density into regions called bond-bundles that may be described by conventional orbital parameters. As our case study problem, we followed and characterize the evolution of the charge density accompanying the rotation of the fulvene exo-double bond. This problem was chosen because of its quintessential orbital character-the reduction of bond order accompanying the breaking of a π-bond-and because it has been well studied [9][10][11][12][13][14] yet remains relevant because of the biradical or zwitterionic character of the rotated state. Thus, it is our hope that this example might serve as a problem that allows us to focus on the charge density decomposition and characterization while remaining topical.Although w...

Observing the 3D Chemical Bond and its Energy Distribution in a Projected Space

“…Hence every trajectory through maps to a zero flux surface in ρ , and any closed loop in maps to a volume in ρ bounded by a zero flux surface and thus characterized by a well‐defined energy. Such volumes are called gradient bundles . All previously noted zero flux surface‐bounded volumes, e. g .…”

“…Such volumes are called gradient bundles. [54][55][56] All previously noted zero flux surface-bounded volumes, e. g. atomic basins, are proper subsets of the space of gradient bundles.…”

Unicorns, Rhinoceroses and Chemical Bonds

“…As has been discussed previously [ 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 ], we picture as a set of arc-length-parameterized gradient paths (G) originating from a local charge-density minimum—a cage critical point (CP)—and terminating at a maximum—almost always coincident with a nuclear CP. Imagine every nuclear CP as the center of a reference sphere (S ) of radius with a G passing through all the points on its surface.…”

Quantum theory of atoms in molecules in condensed charge density space

“…And the union of irreducible bundles sharing a common bond CP gives rise to the bond bundle-a partitioning of the charge density into unique zero flux surface-bounded volumes, each of which contains a single bond path and bond CP. Bond bundles recover traditional bond properties like bond order [14,15], and address issues like spurious bond CPs which have been shown to have tiny bond orders [16].…”