# Special relativity and the halogen bonding

#### published 2020-01-29

In 1905, Albert Einstein formulated the theory of relativity which described the motion of objects with speeds close to the speed of light. The theory postulated that no object can move faster than light, so no process can be instataneous. About twenty years later, Paul Dirac merged the theory of relativity with the quantum mechanics and formulated what is today known as Dirac equation. The equation directly yields the spin, as a property of electron, and adjusts our understanding of chemistry of heavy elements such as gold or thallium. In our lates contribution we investigate, how the special relativity contributes to properties of halogen boding.

Halogen bonding (X-bonding) is a noncovalent interaction (just like hydrogen bonding) which involves a halogen atom and an electronegative moiety, carbonyl oxygen for instance. The strength of X-bond increases with the atomic number of the halogen, so the most attractive X-bonds often involve bromine or iodine. Astatine X-bonds are also possible, but still quite rare/bizzare. Astatine, iodine, and perhaps bromine have high enough mass to manifest relativistic effects.

When an atomic nucleus is heavy enough, the innermost electrons "move" so fast that their speed approaches the speed of light. This situation cannot be described by the (non-relativistic) Schrödinger equation. In molecules with all electrons paired, the (relativistic) Dirac equation can be simplified and typically one of the two approaches is used 1) either the inner electrons, which cause troubles due to their high velocities, are replaced by a parametrized potential, and the Schrödinger equation is solved for the remaining electrons, 2) or the electrons are described by an approximated one-electron Hamiltonian within the Douglas-Kroll-Hess theory. In the work, we compared the non-relativistic, pseudopotential and DKH quantities, where the DKH can be considered as the most accurate one among the three approaches.

The relativistic effects were shown to be about 5% for brominated and 23% for iodinated halogen-bonded complexes. σ-holes are on average more flattened and more positive, when the special relativisty is taken into account. Our results also support the use of pseudopotentials, which are easy to implement and the results differ only slightly from the DKH results. Importantnly, the relativist effects are comparable in magnitude to the effects related to the basis set.