Examining a Transition from Supramolecular Halogen Bonding to Covalent Bonds: Topological Analysis of Electron Densities and Energies in the Complexes of Bromosubstituted Electrophiles

The transition from weak (noncovalent) interactions to fully developed covalent bonds is examined using the quantum theory of atoms in molecules in a series of halogen-bonded (XB) complexes of bromosubstituted electrophiles, RBr, with 1,4-diazabicyclo[2.2.2]octane (DABCO) and Cl– and Br– anions. The gradual decrease in the XB lengths in these associations, dBr···Y (where Y = Cl–, Br–, or N), was accompanied by the exponential increase in the binding energies and charge transfer, as well as electron densities and magnitudes of the kinetic and potential energy densities at the bond critical points (BCPs) on the Br···Y bond path. These indices, as well as characteristics of the adjacent bonds in the XB donor, followed remarkably close trend lines when plotted against the normalized XB length RBrY = dBr···Y/(rBr + rY) (where rBr and rY are the van der Waals radii) regardless of the methods [MP2/6-311+G(d,p) or M062X/6-311+G(d,p)], media (gas phase or dichloromethane), and nucleophiles (Cl–, Br–, or DABCO). In the systems with an RBrY higher than about 0.78, the energy densities H(r) at BCPs at the Br···Y bond path were small and positive, and XBs did not substantially affect the characteristics of the adjacent R–Br covalent bond in the XB donor. Accordingly, the XB can be identified as noncovalent in this range. In the complexes with RBrY values between about 0.67 and 0.78, energy densities H(r) at Br···Y BCPs were negative, and their magnitudes increased with the decrease in the Br···Y separation. In this range, formation of XBs was accompanied by the increase in the R–Br bond length in the XB donor and the decrease in the magnitude of the (negative) H(r) values at the BCPs of the R–Br bonds. XBs can be classified as partially covalent in this RBrY range. At an RBrY less than about 0.67, electron densities were larger, and energy densities were more negative at BCPs of the Br···Y bond than those at BCPs of the R–Br bond in the XB donor. This indicates that Br···Y bonds were stronger than R–Br bonds, and these (Br···Y) XBs can be regarded as essentially covalent. The synchronous change of a variety of (R–Br and Br···Y) bonding characteristics with RBrY suggests that the normalized XB bond length can be used as a basic parameter in the identification of the type of intermolecular interaction. A continuity of these characteristics suggests an inherent relationship between limiting (covalent and noncovalent) types of XBs and thus an onset of molecular–orbital interactions in the weaker bonds.