The scattering symmetries of tetrahedral quantum structures

The electrons associated with molecules and other small quantum structures exist in states that are bound or quasibound to the molecule. The quasibound states, which can significantly affect chemical reaction dynamics, have finite lifetimes and are associated with complex energy poles of the scattering matrix. Using Wigner–Eisenbud ( R -matrix) scattering theory, we examine the symmetry properties of the quasibound states of a molecule-size tetrahedral system, and we examine the relation of quasibound states to the scattering properties. In addition, using R -matrix theory, we construct a non-Hermitian Hamiltonian whose complex energy eigenvalues coincide with the bound and quasi-bound states of the molecule. We show that each bound state and quasibound state of the tetrahedral system belongs to a distinct irreducible representation of the tetrahedral group, and that an incident electron belonging to one irreducible representation can only scatter within the same irreducible representation. Graphic Abstract