Exchange and Superexchange

Abstract

The essential fundament of the exchange (or the superexchange) interaction is the formation of a weak bond. It is well known that spin pairing characterizes bond formation:two isolated hydrogen atoms have a spin S=1/2 each, but when they couple to form a molecule, H2, the result is a spin singlet state, because the two electrons must pair their spins to obey the Pauli principle. If the bond is strong enough, the possibility of having the two electrons with parallel spins is very low, and the triplet state has a much higher energy than the singlet (ΔE, the singlet-triplet separation, is much larger than kT at room temperature). However, if the bonding interaction is weak, the singlet-triplet energy separation becomes smaller, and eventually of the same order of magnitude as kT. It must be recalled here that although the exchange interaction is a bond interaction, therefore, acting only on the orbital coordinates of the electrons, the spin coordinates are extremely useful for the characterization of the wave functions of the pair. In fact, the Pauli principle imposes that the complete wave function of a system is antisymmetric with respect to the exchange of electrons:in the above example of the hydrogen molecule the symmetric orbital function must be coupled to the antisymmetric spin singlet function, and the antisymmetric orbital function is coupled to the symmetric spin triplet. Therefore, spins act as indicators of the nature of the orbital states.