Rotational spectroscopy of H[sub 3]P⋯BrCl and the systematics of intermolecular electron transfer in the series B⋯BrCl, where B=CO, HCN, H[sub 2]O, C[sub 2]H[sub 2], C[sub 2]H[sub 4], H[sub 2]S, NH[sub 3], and PH[sub 3]

The Electrophilicities of XCF3 and XCl (X=H, Cl, Br, I) and the Propensity of These Molecules To Form Hydrogen and Halogen Bonds with Lewis Bases: An Ab Initio Study

Equilibrium dissociation energies, De , of four series of halogen- and hydrogen-bonded complexes B⋅⋅⋅XCF3 (X=H, Cl, Br and I) are calculated ab initio at the CCSD(T)(F12c)/cc-pVDZ-F12 level. The Lewis bases B involved are N2 , CO, PH3 , C2 H2 , C2 H4 , H2 S, HCN, H2 O and NH3 . Plots of De versus NB , where the NB are the nucleophilicities assigned to the Lewis bases previously, are good straight lines through the origin, as are those for the corresponding set of complexes B⋅⋅⋅XCl. The gradients of the De versus NB plots define the electrophilicities EXCF3 and EXCl of the various Lewis acids. The determined values are: EXCF3 =2.58(22), 1.40(9), 2.15(2) and 3.04(9) for X=H, Cl, Br and I, respectively, and EXCl =4.48(22), 2.31(9), 4.37(27) and 6.06(37) for the same order of X. Thus, it is found that, for a given X, the ratio EXCl / EXCF3 is 2 within the assessed errors, and therefore appears to be independent of the atom X and of the type of non-covalent interaction (hydrogen bond or different varieties of halogen bond) in which it is involved. Consideration of the molecular electrostatic surface potentials shows that De and the maximum positive electrostatic potential σmax (the most electrophilic region of XCF3 and XCl, which lies on the symmetry axes of these molecules, near to the atom X) are strongly correlated.

Systematic behaviour of electron redistribution on formation of halogen-bonded complexes BXY, as determined via XY halogen nuclear quadrupole coupling constants

Equilibrium nuclear quadrupole coupling constants associated with the di-halogen molecule XY in each of 60 complexes BXY (where B is one of the Lewis bases N₂, CO, HCN, H₂O, H₂S, HCCH, C₂H₄, PH₃, NH₃ or (CH₃)₃N and XY is one of the di-halogens Cl₂, BrCl, Br₂, ICl, IBr or I₂) have been calculated ab initio. The Townes-Dailey model for interpreting the changes in the coupling constants when XY enters the complex was used to describe the electron redistribution in the di-halogen molecule in terms of the fraction δ_i of an electron transferred from the Lewis base B to atom X and the fraction δ_p of an electron transferred simultaneously from atom X to atom Y. Systematic relationships between the δ_i values for the six series are established. It is shown that, in reasonable approximation, δ_i decays exponentially as the first ionisation energy I_B of the Lewis base B increases, that is δ_i = A exp(-bI_B). It is concluded from the results for the series BBrCl, BBr₂, BICl, BIBr and BI₂ that the coefficients A and b in regression fits to the corresponding logarithmic version ln(δ_i) = ln(A) -b(I_B) of the equation are not strongly dependent on either the halogen atom X directly involved in the halogen bond in BXY or, for a given X, on the nature of Y. The behaviour of PH₃ as a Lewis base appears to be anomalous. Values of δ_i and δ_p calculated by the quantum theory of atoms-in-molecules and natural bond orbital methodologies are very close to those from application of the Townes-Dailey approach described.

Halogen Bonding: A Halogen-Centered Noncovalent Interaction Yet to Be Understood

In addition to the underlying basic concepts and early recognition of halogen bonding, this paper reviews the conflicting views that consistently appear in the area of noncovalent interactions and the ability of covalently bonded halogen atoms in molecules to participate in noncovalent interactions that contribute to packing in the solid-state. It may be relatively straightforward to identify Type-II halogen bonding between atoms using the conceptual framework of σ-hole theory, especially when the interaction is linear and is formed between the axial positive region (σ-hole) on the halogen in one monomer and a negative site on a second interacting monomer. A σ-hole is an electron density deficient region on the halogen atom X opposite to the R–X covalent bond, where R is the remainder part of the molecule. However, it is not trivial to do so when secondary interactions are involved as the directionality of the interaction is significantly affected. We show, by providing some specific examples, that halogen bonds do not always follow the strict Type-II topology, and the occurrence of Type-I and -III halogen-centered contacts in crystals is very difficult to predict. In many instances, Type-I halogen-centered contacts appear simultaneously with Type-II halogen bonds. We employed the Independent Gradient Model, a recently proposed electron density approach for probing strong and weak interactions in molecular domains, to show that this is a very useful tool in unraveling the chemistry of halogen-assisted noncovalent interactions, especially in the weak bonding regime. Wherever possible, we have attempted to connect some of these results with those reported previously. Though useful for studying interactions of reasonable strength, IUPAC’s proposed “less than the sum of the van der Waals radii” criterion should not always be assumed as a necessary and sufficient feature to reveal weakly bound interactions, since in many crystals the attractive interaction happens to occur between the midpoint of a bond, or the junction region, and a positive or negative site.

A Simple Model for Halogen Bond Interaction Energies

Halogen bonds are prevalent in many areas of chemistry, physics, and biology. We present a statistical model for the interaction energies of halogen-bonded systems at equilibrium based on high-accuracy ab initio benchmark calculations for a range of complexes. Remarkably, the resulting model requires only two fitted parameters, X and B—one for each molecule—and optionally the equilibrium separation, R e , between them, taking the simple form E = X B / R e n . For n = 4 , it gives negligible root-mean-squared deviations of 0.14 and 0.28 kcal mol - 1 over separate fitting and validation data sets of 60 and 74 systems, respectively. The simple model is shown to outperform some of the best density functionals for non-covalent interactions, once parameters are available, at essentially zero computational cost. Additionally, we demonstrate how it can be transferred to completely new, much larger complexes and still achieve accuracy within 0.5 kcal mol - 1 . Using a principal component analysis and symmetry-adapted perturbation theory, we further show how the model can be used to predict the physical nature of a halogen bond, providing an efficient way to gain insight into the behavior of halogen-bonded systems. This means that the model can be used to highlight cases where induction or dispersion significantly affect the underlying nature of the interaction.

A reduced radial potential energy function for the halogen bond and the hydrogen bond in complexes B···XY and B···HX, where X and Y are halogen atoms

It is shown by considering 76 halogen- and hydrogen-bonded complexes BXY and BHX (where B is a Lewis base N2, CO, C2H2, C2H4, H2S, HCN, H2O, PH3 or NH3 and X, Y are F, Cl, Br or I) that the intermolecular stretching force constants kσ (determined from experimental centrifugal distortion constants via a simple model) and the intermolecular dissociation energies Dσ (calculated at the CCSD(T)(F12*)/cc-pVDZ-F12 level of theory) are related by Dσ = Cσkσ, where Cσ = 1.50(3) × 10(3) m(2) mol(-1). This suggests that one-dimensional functions implying direct proportionality of Dσ and kσ, (e.g. a Morse or Rydberg function) might serve as reduced radial potential energy functions for such complexes.