Halogen bonding is a recently rediscovered secondary interaction that shows potential to become a complementary molecular tool to hydrogen bonding in rational drug design and in material sciences. Whereas hydrogen bond symmetry has been the subject of systematic studies for decades, the understanding of the analogous three-center halogen bonds is yet in its infancy. The isotopic perturbation of equilibrium (IPE) technique with (13)C NMR detection was applied to regioselectively deuterated pyridine complexes to investigate the symmetry of [N-I-N](+) and [N-Br-N](+) halogen bonding in solution. Preference for a symmetric arrangement was observed for both a freely adjustable and for a conformationally restricted [N-X-N](+) model system, as also confirmed by computation on the DFT level. A closely attached counterion is shown to be compatible with the preferred symmetric arrangement. The experimental observations and computational predictions reveal a high energetic gain upon formation of symmetric, three-center four-electron halogen bonding. Whereas hydrogen bonds are generally asymmetric in solution and symmetric in the crystalline state, the analogous bromine and iodine centered halogen bonds prefer symmetric arrangement in solution.

For the first time, a complete implementation of coupled perturbed density functional theory ͑CPDFT͒ for the calculation of NMR spin-spin coupling constants ͑SSCCs͒ with pure and hybrid DFT is presented. By applying this method to several hydrides, hydrocarbons, and molecules with multiple bonds, the performance of DFT for the calculation of SSCCs is analyzed in dependence of the XC functional used. The importance of electron correlation effects is demonstrated and it is shown that the hybrid functional B3LYP leads to the best accuracy of calculated SSCCs. Also, CPDFT is compared with sum-overstates ͑SOS͒ DFT where it turns out that the former method is superior to the latter because it explicitly considers the dependence of the Kohn-Sham operator on the perturbed orbitals in DFT when calculating SSCCs. The four different coupling mechanisms contributing to the SSCC are discussed in connection with the electronic structure of the molecule.

DFT calculations provide a reliable description of the Bergman reaction of (Z)-hex-3-ene-1,5-diyne 1 provided the following are considered. (a) Restricted DFT (RDFT) calculations along the reaction path have to be replaced by unrestricted DFT (UDFT) calculations at those locations where the former description becomes unstable. This is the case in the region of the p-didehydrobenzene biradical 2, which possesses significant multireference character. (b) LSD and pure GGA functionals are more stable than hybrid functionals, which can be directly related to the composition of these functionals. With increasing instability, RDFT calculations lead to increasing errors in the S−T splitting and the geometry of 2 as well as in the energetics of the Bergman reaction. (c) LSD and GGA functionals underestimate the energy barrier of the Bergman reaction of 1. This becomes obvious when the correct experimental barrier is considered, which was not done in previous DFT investigations. (d) The best description of the Bergman reaction is provided by a mixed RDFT/UDFT description using the B3LYP functional (average error of 2.7 kcal/mol). Although the B3LYP functional is rather unstable, its semiempirical calibration helps to compensate for the typical underestimation of barriers by GGA functionals, which demonstrates that the performance of a hybrid functional does not necessarily have to do with its stability. (e) Application of the sum formula to the UB3LYP energy of biradical 2 improves the description of the Bergman reaction so that the most reliable data are obtained at RB3LYP-UB3LYP(sum)/6-311+G(3df,3pd). Activation enthalpies at 470 K for forward and backward reaction are 29.9 and 21.4 kcal/mol, respectively (exptl values, 28.23 ± 0.5 and 19.75 ± 0.7 kcal/mol), while the calculated reaction enthalpy at 298 K is 8.5 kcal/mol (exptl value, 8.5 ± 1.0 kcal/mol) in reasonable agreement with experiment. The calculated S−T splitting is 2.6 kcal/mol (after correction, 4.9 kcal/mol; exptl value, 3.8 ± 0.5 kcal/mol at 298 K). It is shown that the UDFT description covers static correlation effects needed for the correct treatment of 2S. Total and on-top pair density reflect this, while Kohn−Sham orbitals and spin density have to be considered as physically not meaningful intermediates in line with the interpretation given by Perdew, Savin, and Burke (Phys. Rev. A 1995, 51, 4531).

We have investigated the influence of electron density on the three-center [N–I–N]+ halogen bond. A series of [bis(pyridine)iodine]+ and [1,2-bis((pyridine-2-ylethynyl)benzene)iodine]+ BF4– complexes substituted with electron withdrawing and donating functionalities in the para-position of their pyridine nitrogen were synthesized and studied by spectroscopic and computational methods. The systematic change of electron density of the pyridine nitrogens upon alteration of the para-substituent (NO2, CF3, H, F, Me, OMe, NMe2) was confirmed by 15N NMR and by computation of the natural atomic population and the π electron population of the nitrogen atoms. Formation of the [N–I–N]+ halogen bond resulted in >100 ppm 15N NMR coordination shifts. Substituent effects on the 15N NMR chemical shift are governed by the π population rather than the total electron population at the nitrogens. Isotopic perturbation of equilibrium NMR studies along with computation on the DFT level indicate that all studied systems possess static, symmetric [N–I–N]+ halogen bonds, independent of their electron density. This was further confirmed by single crystal X-ray diffraction data of 4-substituted [bis(pyridine)iodine]+ complexes. An increased electron density of the halogen bond acceptor stabilizes the [N···I···N]+ bond, whereas electron deficiency reduces the stability of the complexes, as demonstrated by UV-kinetics and computation. In contrast, the N–I bond length is virtually unaffected by changes of the electron density. The understanding of electronic effects on the [N–X–N]+ halogen bond is expected to provide a useful handle for the modulation of the reactivity of [bis(pyridine)halogen]+-type synthetic reagents.

Unrestricted density functional theory (UDFT) can be used for the description of open-shell singlet (OSS) biradicals provided a number of precautions are considered. Biradicals that require a two-determinantal wave function (e.g. OSS state of carbenes) cannot be described by UDFT for principal reasons. However, if the overlap between the open-shell orbitals is small (the single electrons are located at different atomic centers) errors become small and, then, the principal failure of UDFT in these cases is not apparent and may even be disguised by the fact that UDFT has the advantage of describing spin polarization better than any restricted open shell DFT method. In the case of OSS biradicals with two-or multiconfigurational character (but a onedeterminantal form of the leading configuration), reasonable results can be obtained by broken-symmetry (BS)-UDFT, however in each case this has to be checked. In no case is it reasonable to lower the symmetry of a molecule to get a suitable UDFT description. Hybrid functionals such as B3LYP perform better than pure DFT functionals in BS-UDFT calculations because the former reduce the self-interaction error of DFT exchange functionals, which mimics unspecified static electron correlation effects, so that the inclusion of specific static electron correlation effects via the form of the wavefunction becomes more effective.

Counterions influence three-center halogen bonds differently than coordination bonds of transition metals.

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The solution symmetry of [N–Cl–N]+and [N–F–N]+halogen bonds is discussed, in comparison to the iodine and bromine-centered bonds as well as to the corresponding three-center [N–H–N]+hydrogen bond.