Dihydrogen Transfer and Symmetry: The Role of Symmetry in the Chemistry of Dihydrogen Transfer in the Light of NMR Spectroscopy

Abstract

The concept of symmetry is one of the basic pillars of modern chemistry and physics. Many fundamental phenomena and laws of nature are related to symmetry or are describable with the help of symmetry arguments. Accordingly, the mathematical description of symmetry, the so-called group theory, is at the heart of both classical mechanics and quantum mechanics. Since the latter field is the basis of modern chemistry, symmetry is also of great importance for chemists. They employ symmetry arguments on a regular basis to help in the understanding of spectra or molecular structures and courses on group theory are a regular part of the chemical education syllabus. It is less well known that symmetry effects also play an important role in chemical kinetics, in particular when low mass particles like hydrogen or deuterium are involved in the reaction and quantum mechanical tunneling processes are present. Especially when dihydrogen exchange reactions are studied, the exchange of the two hydrogen atoms or more generally hydrons (i.e. 1H, 2H or 3H) is a perfect symmetry operation. This apparently trivial symmetry has far fetching consequences for the reaction dynamics. These consequences stem from two different aspects of symmetry: On the one hand basic quantum mechanics tells us that the wavefunctions of the hydrogen or deuterium atoms have to obey the spin dependent Fermi symmetrization rules: They have to be either symmetric (deuterium, spin 1) or anti-symmetric (hydrogen, spin 1⁄2). The result of this symmetrization is the formation of paraand orthostates, which are the spin isotopomers of dihydrogen and dideuterium [1]. On the other hand group theory tells us that the eigenfunctions of the spatial Hamilton operator are now also eigenfunctions of the operator which exchanges the two hydrogen atoms. This implies that the eigenfunctions are either even or odd functions. As a consequence of this, the whole system behaves quantum mechanically. This is particularly visible at low temperatures when only the rotational ground states of the molecules are occupied.