The Importance of Electrostatics and Polarization for Noncovalent Interactions: Ionic Hydrogen Bonds vs Ionic Halogen Bonds

Abstract

A series of 26 hydrogen-bonded complexes between Br^- and halogen, oxygen and sulfur hydrogen-bond (HB) donors is investigated at the M06-2X/6-311 + G(2df,2p) level of theory. Analysis using a model in which Br^- is replaced by a point charge shows that the interaction energy ([Formula: see text]) of the complexes is accurately reproduced by the scaled interaction energy with the point charge ([Formula: see text]).This is demonstrated by [Formula: see text] with a correlation coefficient, R² =0.999. The only outlier is (Br-H-Br)^-, which generally is classified as a strong charge-transfer complex with covalent character rather than a HB complex. [Formula: see text] can be divided rigorously into an electrostatic contribution ([Formula: see text]) and a polarization contribution ([Formula: see text]).Within the set of HB complexes investigated, the former varies between -7.2 and -32.7 kcal mol^-1, whereas the latter varies between -1.6 and -11.5 kcal mol^-1. Compared to our previous study of halogen-bonded (XB) complexes between Br^- and C-Br XB donors, the electrostatic contribution is generally stronger and the polarization contribution is generally weaker in the HB complexes. However, for both types of bonding, the variation in interaction strength can be reproduced accurately without invoking a charge-transfer term. For the Br^-···HF complex, the importance of charge penetration on the variation of the interaction energy with intermolecular distance is investigated. It is shown that the repulsive character of [Formula: see text] at short distances in this complex to a large extent can be attributed to charge penetration.

Keywords: Charge penetration; Electrostatic potential; Halogen bond; Hydrogen bond; Intermolecular interaction.

Fig. 1

The electrostatic potential [V(r)] of Br⁻ (blue line) in kcal mol⁻¹ computed at the M06-2X/6–311 + G(2df,2p) level compared to the electrostatic potential of a negative point charge of elementary charge (-e = -1 au) (red line)

Fig. 2

The graph to the left shows the linear correlation between ${\mathrm{\Delta }E}_{\mathit{Cmpl}}$ and ${\mathrm{\Delta }E}_{\mathit{Int}}^{\mathit{PC}}$ for the entire data set of HB complexes with Br⁻. The graph to the right shows the corresponding correlation between ∆E_Int and ${\mathrm{\Delta }E}_{\mathit{Int}}^{\mathit{PC}}$. The complex between HBr and Br⁻ is an outlier in both correlations

Fig. 3

The different energy components from the full quantum chemical model and the PC model as functions of the Br-H distance (R) for complexes of HF, HCl and HBr with Br⁻. The vertical dotted line marks the Br···HX distance (R₀) at the complex minimum. The corresponding structure is shown as an inset, and the X–H distance in italics is for the free hydrogen bond donor

Fig. 4

The different energy components from the full quantum chemical model and the PC model as functions of the Br-H distance (R) for complexes of CF₃OH and CF₃SH. The vertical dotted line marks the Br···H distance (R₀) of the lowest energy structure. The lowest energy structure is shown as an inset, and the X–H distance in italics refers to the free hydrogen bond donor

Fig. 5

The graph shows the effect of charge penetration on the different energy components of the PC as functions of the Br···H distance (R) for the complexes with HF. Charge penetration corrected energies are marked with superscript V and compared to the PC energies and to ${\mathrm{\Delta }E}_{\mathit{Int}}$. Similarly to ${\mathrm{\Delta }E}_{\mathit{Int}}$, the corrected energy curves, ${\mathrm{\Delta }E}_{\mathit{ES}}^V$ and ${\mathrm{\Delta }E}_{\mathit{Int}}^V$, are repulsive at short distances