The influence of zero-flux surface motion on chemical reactivity

Abstract

Visualizing and predicting the response of the electron density, ρ(r), to an external perturbation provides a portion of the insight necessary to understand chemical reactivity. One strategy used to portray electron response is the electron pushing formalism commonly utilized in organic chemistry, where electrons are pictured as flowing between atoms and bonds. Electron pushing is a powerful tool, but does not give a complete picture of electron response. We propose using the motion of zero-flux surfaces (ZFSs) in the gradient of the charge density, ∇ρ(r), as an adjunct to electron pushing. Here we derive an equation rooted in conceptual density functional theory showing that the movement of ZFSs contributes to energetic changes in a molecule undergoing a chemical reaction. Using a substituted acetylene, 1-iodo-2-fluoroethyne, as an example, we show the importance of both the boundary motion and the change in electron counts within the atomic basins of the quantum theory of atoms in molecules for chemical reactivity. This method can be extended to study the ZFS motion between smaller gradient bundles in ρ(r) in addition to larger atomic basins. Finally, we show that the behavior of ∇ρ(r) within atomic basins contains information about electron response and can be used to predict chemical reactivity.

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

“…Furthermore, the boundary between two basins is usually set such that a bond critical point (BCP) is on the boundary, although there are exceptions . We note that Equation (1) is not the only definition for the surface of an atom in molecule (AIM) that is consistent with the mathematical requirement that the integral of the ∇ 2 ρ ( r ) over an atomic basin is zero, but it is the conventional choice, and it seems to be the most useful also. The physical consequences of this definition have been discussed elsewhere …”

Curly arrows meet electron density transfers in chemical reaction mechanisms: from electron localization function (ELF) analysis to valence-shell electron-pair repulsion (VSEPR) inspired interpretation

“…47,48,56,[68][69][70][71][72][73][74] Probing the electron density distribution during a chemical reaction can provide important insights, but this aim has required extension of the relationships between the traditional chemical concepts and the quantum mechanical ones. In this context, the catastrophe theory has been used to study the evolution along a reaction path of the topologies of the electron density, 75,76 the laplacian of the electron density 77 3 and of the electron localization function (ELF), 78 i.e. bonding evolution theory (BET).…”

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

“…In a similar manner to that used above to extract information regarding orbital evolution through a chemical process, information may be pulled from the density via gradient bundle analysis (GBA). This analytic method further decomposes the charge density into its most fundamental regions with associated well‐defined energies . Briefly, a differential gradient bundle (GB) (Figure ) is given by the locus of all gradient paths passing through a loop of radius dr, which, for purely practical purposes, is usually assumed to be located on a charge density isosurface close to a nuclear CP.…”

“…QTAIM has proven useful as a way to quantify the structure of ρ( r ) in terms of its topological and geometric properties . Quite generally, the topology of ρ( r ) can be categorized in terms of the zeros of its gradient field (∇ρ) and its associated ridge structure.…”

“…Of particular significance to the QTAIM formalism are the unique volumes bounded by gradient surfaces (zero‐flux in the gradient of the charge density) and consequently have well‐defined and additive energies, which is not true of arbitrary volumes . Every molecule and solid may be uniquely partitioned into space filling volumes containing a single nCP and bounded by 2‐ridges.…”