# Halogen bonding: the σ-hole

TL;DR: In this paper, the authors carried out a natural bond order B3LYP analysis of the molecules CF(3)X, with X = F, Cl, Br and I. The results showed that the Cl and Br atoms in these molecules closely approximate the [Formula: see text] configuration, where the z-axis is along the R-X bond.

Abstract: 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.

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TL;DR: Five practical examples involving a wide variety of systems and analysis methods are given to illustrate the usefulness of Multiwfn, a multifunctional program for wavefunction analysis.

Abstract: Multiwfn is a multifunctional program for wavefunction analysis. Its main functions are: (1) Calculating and visualizing real space function, such as electrostatic potential and electron localization function at point, in a line, in a plane or in a spatial scope. (2) Population analysis. (3) Bond order analysis. (4) Orbital composition analysis. (5) Plot density-of-states and spectrum. (6) Topology analysis for electron density. Some other useful utilities involved in quantum chemistry studies are also provided. The built-in graph module enables the results of wavefunction analysis to be plotted directly or exported to high-quality graphic file. The program interface is very user-friendly and suitable for both research and teaching purpose. The code of Multiwfn is substantially optimized and parallelized. Its efficiency is demonstrated to be significantly higher than related programs with the same functions. Five practical examples involving a wide variety of systems and analysis methods are given to illustrate the usefulness of Multiwfn. The program is free of charge and open-source. Its precompiled file and source codes are available from http://multiwfn.codeplex.com.

17,273 citations

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TL;DR: 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.

Abstract: 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.

2,582 citations

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TL;DR: In this article, the energy and geometrical features of the interaction are described along with the atomic characteristics that confer molecules with the specific ability to interact through this interaction, and some principles are presented for crystal engineering based on halogen-bonding interactions.

Abstract: Halogen bonding is the noncovalent interaction where halogen atoms function as electrophilic species. The energetic and geometrical features of the interaction are described along with the atomic characteristics that confer molecules with the specific ability to interact through this interaction. Halogen bonding has an impact on all research fields where the control of intermolecular recognition and self-assembly processes plays a key role. Some principles are presented for crystal engineering based on halogen-bonding interactions. The potential of the interaction is also shown by applications in liquid crystals, magnetic and conducting materials, and biological systems.

1,358 citations

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TL;DR: Experimental as well as computational studies indicate that halogen and other sigma-hole interactions can be competitive with hydrogen bonding, which itself can be viewed as a subset of s Sigma-hole bonding.

Abstract: A halogen bond is a highly directional, electrostatically-driven noncovalent interaction between a region of positive electrostatic potential on the outer side of the halogen X in a molecule R–X and a negative site B, such as a lone pair of a Lewis base or the π-electrons of an unsaturated system. The positive region on X corresponds to the electronically-depleted outer lobe of the half-filled p-type orbital of X that is involved in forming the covalent bond to R. This depletion is labeled a σ-hole. The resulting positive electrostatic potential is along the extension of the R–X bond, which accounts for the directionality of halogen bonding. Positive σ-holes can also be found on covalently-bonded Group IV–VI atoms, which can similarly interact electrostatically with negative sites. Since positive σ-holes often exist in conjunction with negative potentials on other portions of the atom's surface, such atoms can interact electrostatically with both nucleophiles and electrophiles, as has been observed in surveys of crystallographic structures. Experimental as well as computational studies indicate that halogen and other σ-hole interactions can be competitive with hydrogen bonding, which itself can be viewed as a subset of σ-hole bonding.

1,332 citations

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TL;DR: A σ-hole bond is a noncovalent interaction between a covalently-bonded atom of Groups IV-VII and a negative site, e.g. a lone pair of a Lewis base or an anion.

Abstract: A σ-hole bond is a noncovalent interaction between a covalently-bonded atom of Groups IV–VII and a negative site, e.g. a lone pair of a Lewis base or an anion. It involves a region of positive electrostatic potential, labeled a σ-hole, on the extension of one of the covalent bonds to the atom. The σ-hole is due to the anisotropy of the atom's charge distribution. Halogen bonding is a subset of σ-hole interactions. Their features and properties can be fully explained in terms of electrostatics and polarization plus dispersion. The strengths of the interactions generally correlate well with the magnitudes of the positive and negative electrostatic potentials of the σ-hole and the negative site. In certain instances, however, polarizabilities must be taken into account explicitly, as the polarization of the negative site reaches a level that can be viewed as a degree of dative sharing (coordinate covalence). In the gas phase, σ-hole interactions with neutral bases are often thermodynamically unfavorable due to the relatively large entropy loss upon complex formation.

1,294 citations

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TL;DR: In this article, a semi-empirical exchange correlation functional with local spin density, gradient, and exact exchange terms was proposed. But this functional performed significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.

Abstract: Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.

87,732 citations

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TL;DR: Numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, show that density-functional formulas for the correlation energy and correlation potential give correlation energies within a few percent.

Abstract: A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.

84,646 citations

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15,091 citations

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TL;DR: In this article, two extended basis sets (termed 5-31G and 6 -31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine.

Abstract: Two extended basis sets (termed 5–31G and 6–31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine. These basis functions are similar to the 4–31G set [J. Chem. Phys. 54, 724 (1971)] in that each valence shell is split into inner and outer parts described by three and one Gaussian function, respectively. Inner shells are represented by a single basis function taken as a sum of five (5–31G) or six (6–31G) Gaussians. Studies with a number of polyatomic molecules indicate a substantial lowering of calculated total energies over the 4–31G set. Calculated relative energies and equilibrium geometries do not appear to be altered significantly.

13,036 citations

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TL;DR: In this paper, a split-valence extended gaussian basis set was used to obtain the LCAO-MO-SCF energies of closed shell species with two non-hydrogen atoms.

Abstract: Polarization functions are added in two steps to a split-valence extended gaussian basis set: d-type gaussians on the first row atoms C. N, O and F and p-type gaussians on hydrogen. The same d-exponent of 0.8 is found to be satisfactory for these four atoms and the hydrogen p-exponent of 1.1 is adequate in their hydrides. The energy lowering due to d functions is found to depend on the local symmetry around the heavy atom. For the particular basis used, the energy lowerings due to d functions for various environments around the heavy atom are tabulated. These bases are then applied to a set of molecules containing up to two heavy atoms to obtain their LCAO-MO-SCF energies. The mean absolute deviation between theory and experiment (where available) for heats of hydrogenation of closed shell species with two non-hydrogen atoms is 4 kcal/mole for the basis set with full polarization. Estimates of hydrogenation energy errors at the Hartree-Fock limit, based on available calculations, are given.

12,669 citations