5 Time-Resolved Photoelectron Spectroscopy for Excited State Dynamics
103
is in these Type II situations that measuring the time-resolved photoelectron angular
distribution can be of real benefit—as discussed below, the photoelectron angular
distribution reflects the evolution of the molecular electronic symmetry.
5.2.2 Photoelectron Angular Distributions: Using the Free
Electron to Map Excited State Dynamics
The electronic states of the free electron, usually described as scattering states, are
also responsible for electronic structure in the continuum. The free electron states
populated during photoionization reflect angular momentum correlations and are
therefore sensitive to the evolving electronic configuration and symmetry of the neutral molecule. This sensitivity is expressed in the form of the photoelectron angular
distribution (PAD). As the electron leaves the molecule, it scatters from the molecular potential. As such, the scattering wave function reflects the electronic and nuclear configuration of the neutral molecule at the moment of ionization [26, 38, 39].
Hence, the PAD measured (in the molecular frame) also reflects the electronic and
nuclear structure of the neutral at the moment of ionization. However, the PAD is
usually measured in the laboratory frame, where the direction of electron ejection
is measured in a frame which is referenced to the polarization of the probe pulse,
rather than directly in the molecular frame. Although such laboratory-frame measurements carry a great deal of information, they are an average over all molecular
orientations present and therefore carry less information than a measurement of the
PAD in the molecular frame. Using coincidence techniques, it is possible to measure the PAD relative to a recoiling photofragment, which approaches a molecular
frame PAD measurement [40–42]. A more generally applicable method for making molecular-frame PAD measurements exploits strong non-resonant laser fields
to align the molecular axis, thus defining the molecular orientation prior to ionization [43].
The continuum state accessed by the probe pulse may be written as a direct product of the cation and free electron states. As with any optical transition, there are
symmetry based ‘selection rules’ for the photoionization step. For photoionization,
the requirement is that the direct product of the irreducible representations of the
free electron wave function (Γ e − ), the state of the ion (Γ M + ), the molecular frame
transition dipole moment (Γ μ ) and the neutral state (Γ M ) contains the totally symmetric irreducible representation of the molecular point group (Γ TS ),
Γ e − ⊗ Γ M + ⊗ Γ μ ⊗ Γ M ⊂ Γ TS .
(5.1)
Clearly, the symmetries of the contributing photoelectron partial waves will be determined by the electronic symmetry of the electronic state undergoing ionization,
as well as the molecular frame direction of the ionization transition dipole moment
(which determines the possible Γ μ ), and the electronic symmetry of the cation. As
103
is in these Type II situations that measuring the time-resolved photoelectron angular
distribution can be of real benefit—as discussed below, the photoelectron angular
distribution reflects the evolution of the molecular electronic symmetry.
5.2.2 Photoelectron Angular Distributions: Using the Free
Electron to Map Excited State Dynamics
The electronic states of the free electron, usually described as scattering states, are
also responsible for electronic structure in the continuum. The free electron states
populated during photoionization reflect angular momentum correlations and are
therefore sensitive to the evolving electronic configuration and symmetry of the neutral molecule. This sensitivity is expressed in the form of the photoelectron angular
distribution (PAD). As the electron leaves the molecule, it scatters from the molecular potential. As such, the scattering wave function reflects the electronic and nuclear configuration of the neutral molecule at the moment of ionization [26, 38, 39].
Hence, the PAD measured (in the molecular frame) also reflects the electronic and
nuclear structure of the neutral at the moment of ionization. However, the PAD is
usually measured in the laboratory frame, where the direction of electron ejection
is measured in a frame which is referenced to the polarization of the probe pulse,
rather than directly in the molecular frame. Although such laboratory-frame measurements carry a great deal of information, they are an average over all molecular
orientations present and therefore carry less information than a measurement of the
PAD in the molecular frame. Using coincidence techniques, it is possible to measure the PAD relative to a recoiling photofragment, which approaches a molecular
frame PAD measurement [40–42]. A more generally applicable method for making molecular-frame PAD measurements exploits strong non-resonant laser fields
to align the molecular axis, thus defining the molecular orientation prior to ionization [43].
The continuum state accessed by the probe pulse may be written as a direct product of the cation and free electron states. As with any optical transition, there are
symmetry based ‘selection rules’ for the photoionization step. For photoionization,
the requirement is that the direct product of the irreducible representations of the
free electron wave function (Γ e − ), the state of the ion (Γ M + ), the molecular frame
transition dipole moment (Γ μ ) and the neutral state (Γ M ) contains the totally symmetric irreducible representation of the molecular point group (Γ TS ),
Γ e − ⊗ Γ M + ⊗ Γ μ ⊗ Γ M ⊂ Γ TS .
(5.1)
Clearly, the symmetries of the contributing photoelectron partial waves will be determined by the electronic symmetry of the electronic state undergoing ionization,
as well as the molecular frame direction of the ionization transition dipole moment
(which determines the possible Γ μ ), and the electronic symmetry of the cation. As