Discussion
The calculated photoionization of the 4e valence electrons of PF3 is examined in this animation. Electric dipole selection rules allow continua of both e and a1 symmetry to be accessed; here we look at the molecular-frame photoelectron angular distribution (MF-PAD) associated with the latter (selected by choice of light polarization).
A strong shape resonance is found at a kinetic energy ~3 eV. This can be seen, as would be anticipated, as a strong peak in the total cross-section at the resonant energy. The behaviour of the MF-PAD in this region is revealing. Below the resonance, close to threshold, the electron distribution is predominantly in a upwards direction. Passing through the resonance the PAD rapidly evolves until at energies now above the resonance the distribution falls in the opposite direction, predominantly downwards. Classical reasoning might readily suggest that an electron would find it easier to escape from one end of a molecule than the other, but this reversal in the PAD orientation and other detail observed here can only arise through a full quantum scattering treatment of the photoionization dynamics.
More specifically, the orientation in the MF-PAD direction can be attributed to interferencees between odd and even parity partial waves that make up the continuum function. This provides partial cancellation and enhancement on opposite sides of the molecular centre. When at resonance there is a near 180° phase shift in just one of these (see Shape Resonance Tutorial), the regions of constructive and destructive interference switch around, and the MF-PAD seen to reverse its direction.
Notice how richly structured (with many spherical harmonics) the MF-PAD is at any energy compared to 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. Although undoubtedly more challenging for experiment, this level of additional detail indicates how much more useful fixed-molecule photoionization studies may prove.
The Animation
This animation shows molecule-frame photoelectron angular distributions (MF-PADs) that have been calculated, using the CMS-Xα method, for photoionization of a PF3 molecule with fixed molecular axis orientation.
The 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 upwards from threshold 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 cross-section curve with a marker point that moves along the cross-section curve as the energy is scanned.