Assessment of Scalar Relativistic Effects on Halogen Bonding and $\sigma$-Hole Properties

Halogen bond (X-bond) is a noncovalent interaction between a halogen atom and an electron donor. It is often rationalized by a region of the positive electrostatic potential on the halogen atom, so-called $\sigma$-hole. The X-bond strength increases with the atomic number of the halogen involved, thus for heavier halogens, relativistic effects become of concern. This poses a challenge for the quantum chemical description of X-bonded complexes. To quantify scalar relativistic effects (SREs) on the interaction energies and $\sigma$-hole properties, we have performed highly accurate coupled-cluster calculations at the complete basis set limit of several X-bonded complexes and their halogenated monomers. The SREs turned to be comparable in magnitude to the effect of basis set. The nonrelativistic calculations typically underestimate the attraction by up to 5% or 23% for brominated and iodinated complexes, respectively. Counter-intuitively, the electron densities at the bond critical points are larger for SRE-free calculations than for the relativistic ones. SREs yield smaller, flatter, and more positive $\sigma$-holes. Finally, we highlight the importance of diffuse functions in the basis sets and provide quantitative arguments for using basis sets with pseudopotentials as an affordable alternative to a more rigorous Douglas-Kroll-Hess relativistic theory.