Discussion
The features of the MF-PAD that are so evident here are truly quantum mechanical in origin. Of particular interest in these results is the reversal in orientation or direction of the principal lobe of the MF-PAD with increasing energy. While classical reasoning might readily suggest that an electron would find it easier to escape from one end of a molecule than the other, the observed structure and rapid variations in the MF-PAD can only arise in a quantum treatment of the photoionization dynamics.
What is in fact being observed here is a shape resonance in the ka1 continuum. Resonant enhancement causes the intense peak seen in the photoionization cross-section centred at 4.5 eV. Notice, however, how the MF-PAD changes rapidly on passing through this resonant energy because of the rapidly varying resonant phase shift. The anticipated 180° phase shift at resonance causes the reversal in direction of the principal lobe, identified in the preceding paragraph, as regions of constructive and destructive interference between the resonant and non-resonant components of the continuum function switch to opposite sides of the molecule.
It may also be noted how richly structured the MF-PAD is at any energy compared the maximum cos2θ form expected for lab frame PADs; this is because of the smearing out and loss of detail caused by averaging the distribution over all possible molecular orientations in the lab frame.
(see I. Powis, J. Chem. Phys., 106 (1997), 5013.)
The Animation
This animation shows calculations made, using the CMS-Xα method, for photoionization of the (C–Cl σ-bonding electron) in CF3Cl. This is the 5a1 orbital and, with the polarization set parallel to the molecular axis, selection rules dictate that the photoelectron is a similarly symmetric ka1 continuum function.
The molecule-frame photoelectron angular distribution (MF-PAD) appears in a three dimensional representation indicating the relative probability of electron ejection in a given direction specified in the molecular coordinate frame. The orientation of the molecule can be identified from the transluscent atomic spheres; as the electron energy is scanned from threshold up to around 20 eV the molecule is allowed to rotate around its axis to help reveal the 3-D characteristics of the MF-PAD. An inset panel shows the total (integrated) photoionization with a marker point that moves along the cross-section curve as the energy is scanned.