Powis Group

For visualisation it is convenient to use the real, so-called eigenchannel functions. This animation commences with a view showing the eigenphase sum ( ∑μ_a —a combined continuum phase shift) and how the phase is distributed over a few of the more significant eigenchannels. The rapid rise of almost π radians at ~15 eV is a signature of a shape resonance, and it can be seen that, although a multichannel phenomenon, the γ_E eigenchannel (highlighted in blue) is the principal carrier of the resonance. The bulk of the animation then shows this resonant channel.

Accompanying the resonant phase rise is an obvious increase in amplitude of the wave function in the inner, molecular regions at the shape resonance energy. This enhanced amplitude around the molecular interior provides greater overlap with the initial bound electron wave function in this region, and so an increased transition probability can be anticipated. It can also be seen from the little bar (to the left) that the asymptotic phase, μ_a, varies very rapidly at the resonance and this can be expected to influence the photoelectron angular distribution.

The contour plot shows the continuum wave function contracting inwards as the energy increases (decreasing de Broglie wavelength) and the resonance closely resembles a p-type wave that is centered on the I atom. In this instance at least it seems reasonable to associate the molecular shape resonance with a predominant atomic iodine character. For further discussion see D.M.P. Holland et al, Chem. Phys. 297 (2004) 55.

In principle the continuum for a given electron energy has an infinite degeneracy, and so an infinite number of alternate solutions. In practice this set is truncated when using a limited partial wave expansion. The animation shows one such eigenchannel function, selected as it largely carries the π symmetry shape resonance found in ICN photoionization.

The principal part of the animations is then a surface representing the real value of the function across the XZ plane that includes the three nuclei, showing its variation as the electron energy is scanned through the ~15 eV resonance. Contour map projections of this eigenchannel onto the top and bottom planes of the box, are also included and on the lower plane the positions of the nuclei along the Z axis are marked in white (I atom central). Alongside is a little bar that show the rate of change in asymptotic phase of this continuum function.