Hydrogen bond strengths revealed by topological analyses of experimentally observed electron densities

The halogen bond occurs when there is evidence of a net attractive interaction between an electrophilic region associated with a halogen atom in a molecular entity and a nucleophilic region in another, or the same, molecular entity. In this fairly extensive review, after a brief history of the interaction, we will provide the reader with a snapshot of where the research on the halogen bond is now, and, perhaps, where it is going. The specific advantages brought up by a design based on the use of the halogen bond will be demonstrated in quite different fields spanning from material sciences to biomolecular recognition and drug design.

The Halogen Bond

Halogen bonding refers to the non-covalent interactions of halogen atoms X in some molecules, RX, with negative sites on others. It can be explained by the presence of a region of positive electrostatic potential, the sigma-hole, on the outermost portion of the halogen's surface, centered on the R-X axis. We have carried out a natural bond order B3LYP analysis of the molecules CF(3)X, with X = F, Cl, Br and I. It shows that the Cl, Br and I atoms in these molecules closely approximate the [Formula: see text] configuration, where the z-axis is along the R-X bond. The three unshared pairs of electrons produce a belt of negative electrostatic potential around the central part of X, leaving the outermost region positive, the sigma-hole. This is not found in the case of fluorine, for which the combination of its high electronegativity plus significant sp-hybridization causes an influx of electronic charge that neutralizes the sigma-hole. These factors become progressively less important in proceeding to Cl, Br and I, and their effects are also counteracted by the presence of electron-withdrawing substituents in the remainder of the molecule. Thus a sigma-hole is observed for the Cl in CF(3)Cl, but not in CH(3)Cl.

Halogen bonding: the σ-hole

The C-H‚‚‚O hydrogen bond is so well-established in structural chemistry that it seems difficult now to believe that when Sutor proposed the existence of this type of hydrogen bond in the early 1960s,1,2 her suggestion was drowned in scepticism, if not outright hostility.3 It was only two decades later, with Taylor and Kennard’s paper, that the subject was properly revived.4 Shortly thereafter, an Account appeared from this laboratory describing the role of the C-H‚‚‚O interaction in crystal engineering.5 Subsequently, one felt confident enough to term these erstwhile “interactions” hydrogen bonds, in a second Account.6 A recent invitation to contribute another Account and the many recent efforts in this direction by my students and postdoctorals have led to the present paper. It is clearly no longer necessary to justify the relevance of C-H‚‚‚O hydrogen bonds, so widely invoked are they in small-molecule and biological crystallography. The presence of O-atoms in a large majority of organic molecules means that this hydrogen bond is widespread, even if not identified in many cases. However, other questions concerning these weak hydrogen bonds could be posed: (1) What is their upper distance limit? (2) Are very short, bent bonds significant? (3) Why do C-H‚‚‚O bonds sometimes disturb the strong O-H‚‚‚O and N-H‚‚‚O network? Alternatively, why do hydrogen bond donors and acceptors not always pair in descending order of strength? (4) How important is cooperativity for weak hydrogen bonds? (5) Are C-H‚‚‚O hydrogen bonds responsible for crystal packing, or are they the forced consequences of packing? (6) Are weak hydrogen bonds robust enough for supramolecular synthesis and crystal engineering? (7) Does the C-H‚‚‚O hydrogen bond have any biological significance? These difficult questions cannot be answered fully. This Account attempts to address some of them, but better answers can only follow from further work.

The C-h···o hydrogen bond: structural implications and supramolecular design.

The quantum mechanics of proper open systems yields the physics that governs the local behavior of the electron density, ρ(r). The Ehrenfest force F(r) acting on an element of ρ(r) and the virial field ν(r) that determine its potential energy are obtained from equations of motion for the electronic momentum and virial operators, respectively. Each is represented by a “dressed” density, a distribution in real space that results from replacing the property in question for a single electron with a corresponding density that describes its average interaction with all of the remaining particles in the system. All bond paths, lines of maximum density linking neighboring nuclei in a system in stable electrostatic equilibrium, have a common physical origin in terms of F(r) and ν(r), regardless of the nature of the interaction. Each is homeomorphically mirrored by a virial path, a line of maximally negative potential energy density linking the same nuclei. The presence of a bond path and its associated virial path...

A Bond Path: A Universal Indicator of Bonded Interactions

Properties of atoms in molecules: atomic volumes

The nature, energetics and mechanism of BASE-HF hydrogen bonding (where BASE = OC, SC, N2, HCN, H3N, O3, SCO, CO2, N2O, SO2, H2CO, H2O, HF, H3P, H2S and HCl) are examined using the theory of atoms in molecules. The results are obtained from RHF/6-311 + +G**//6-31 G** calculations. A quantitative description of the electron redistribution and changes in atomic properties, including populations, energies, volumes and moments upon hydrogen bond formation are given by the theory, information which in turn provides a qualitative understanding of the hydrogen bond. A hydrogen bond results from the interaction of two closed-shell systems and the theory quantifies the concept of the mutual penetration of the van der Waals envelopes of the acid and base molecules. It is found that the extent of this penetration and the factors which govern it are of paramount importance in determining the strength of the interaction.

An analysis of the hydrogen bond in BASE-HF complexes using the theory of atoms in molecules

The laplacian of the charge density is used to predict the structures and geometries of hydrogen-bonded gas-phase complexes of the type BASE-HF. The bases used are N2, OC, SC, OCO, SCO, HCN, N2O, HCP, H2O, H2S, H3N, H3P, O3, OSO, H2CO, HF, HCl, N2S and H2CS. Many of the weaker complexes have not been characterized experimentally, and so, results of full 6–31 G** geometry optimizations are presented. The laplacian of the charge density, ∇2ρ, determines where charge is locally concentrated and depleted. The point where ∇2ρ attains its maximum magnitude in a region of charge concentration in the base defines the site of electrophilic attack by the acidic H of HF. The angle of electrophilic attack predicted in this manner is compared with the ab initio equilibrium angle that the hydrogen of HF makes with the base. In general, the angles predicted using the laplacian are in good agreement with the ab initio and experimental results. The present results are also compared with those obtained from electrostatic m...

Marshall T. Carroll

Papers

Properties of atoms in molecules: atomic volumes

An analysis of the hydrogen bond in BASE-HF complexes using the theory of atoms in molecules

Prediction of the structures of hydrogen-bonded complexes using the laplacian of the charge density

The mechanics of hydrogen bond formation in conjugated systems

Nucleophilic addition to activated double bonds: predictions of reactivity from the Laplacian of the charge density