The Distance between Minima of Electron Density and Electrostatic Potential as a Measure of Halogen Bond Strength

Abstract

In this study, we present results of a detailed topological analysis of electron density (ED) of 145 halogen-bonded complexes formed by various fluorine-, chlorine-, bromine-, and iodine-containing compounds with trimethylphosphine oxide, Me₃PO. To characterize the halogen bond (XB) strength, we used the complexation enthalpy, the interatomic distance between oxygen and halogen, as well as the typical set of electron density properties at the bond critical points calculated at B3LYP/jorge-ATZP level of theory. We show for the first time that it is possible to predict the XB strength based on the distance between the minima of ED and molecular electrostatic potential (ESP) along the XB path. The gap between ED and ESP minima exponentially depends on local electronic kinetic energy density at the bond critical point and tends to be a common limiting value for the strongest halogen bond.

Keywords: 31P NMR; QTAIM; bond strength; density functional theory; electron density; electrostatic potential; halogen bond; interaction energy; phosphine oxide.

Figure 1

Schematic representation of a halogen bond (X—halogen atom, A—nucleophilic site), ED (blue) and ESP (red) distributions along the bond path. The graphical definition of d(ED_min) (blue), d(ESP_min) (red), and Δd (black) are given.

Figure 2

Schematic representation of halogen-bonded complexes formed between R–X (X = F, Cl, Br and I) and Me₃PO. In blue are given geometric (interatomic distance R(X⋯O)), energetic (complexation enthalpy ΔH), and electronic (ρ stands for electron density, ∇²ρ for its Laplacian, V, G and K stand for local electron potential, kinetic and total energy densities at the bond critical point, BCP) parameters that were correlated with Δd in this work (see Figure 1 for the definition of Δd).

Figure 3

Some examples of optimized geometries of halogen-bonded complexes formed between (a) F₂; (b) I₂; (c) ClF; (d) BrF; (e) IF; (f) FCN; (g) ClCN; (h) BrCN; (i) ICN; (j) CF₃Cl; (k) CF₃Br; (l) CF₃I; (m) C₆F₅Cl; (n) C₆F₅Br; (o) C₆F₅I and Me₃PO considered in this work. Blue dot marks the position of the X⋯O bond critical point.

Figure 4

(a) Distances from oxygen atom to minima of molecular electrostatic potential d(ESP_min) (lighter colors) and electron density d(ED_min) (darker colors) along the X⋯O (X = F, Cl, Br and I) bond path; (b) distances between ED and ESP minima Δd as a function of G(r_BCP) for a series of halogen-bonded complexes formed between R–X and Me₃PO. The solid curves correspond to Equation (2) with fitted parameters listed in Table 1.

Figure 5

Examples of additional non-covalent interactions (red dashed lines) present in some halogen-bonded (black dashed line) R–X⋯OPMe₃ complexes: hydrogen bonds between methyl protons of the Me₃PO moiety and electronegative atoms of the halogen donor; (а) two H-bonds with two proton acceptors; (b) two H-bonds with one proton acceptor; (c) two H-bonds with the halogen donating atom.

Figure 6

Distances between ED and ESP minima Δd as a function of normalized interatomic distances R_norm between X (X = F, Cl, Br and I) and O (see definition in Equation (5)).

Figure 7

The correlation of Δδ³¹P on Δd for a series of R–X⋯OPMe₃ complexes. The solid lines are guides for the eye added for Cl- and Br-bonded complexes.