Photoelectron spectroscopic studies of polyatomic molecules: Degree of orientation and ionization of rotationally state selected, oriented molecules

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Abstract
In this paper we report theoretical studies of angle-resolved photoelectron spectroscopy (ARPES) and of circular dichroism in photoelectron angular distribution (CDAD) for ionization in molecules oriented in a single ‖JKJMJ〉 rotational eigenstate. These processes have been investigated also as two of the possible alternatives to photodissociation to determine orientational distribution function of rotationally state selected, oriented molecules. Expressions are derived which can be used to calculate ARPES and CDAD for such molecular species from ab initio methods or to analyze these experimentally observed spectra for extracting information about the degree of orientation of the molecular framework. These formulas are put in their simplest possible forms using the transformation properties of the molecular point group to their full advantage. The ionization amplitude is thus shown to decompose into a sum of transitions each involving the final state wave function belonging to an irreducible representation of the point group of the target molecule. It is found that, similar to the case of photodissociation, one can determine the rotational quantum number J purely from experimental photoionization data. Expressions developed herein are used to study ARPES and CDAD for ionization in a1 orbital of those rotationally state selected and oriented spherical top molecules which transform according to the Td point symmetry group. In this case, the detection-integrated cross section, singly differential in molecular orientation, is found to be independent of the photoionization dynamics and directly gives the molecular orientational function. The other ARPES and CDAD formulas are shown to depend upon the dynamics through the integrated partial cross section σ̄, the angularly asymmetry parameter β̄, the phase shift of the continuum waves representing the photoelectron, and the phase of the dipole transition amplitudes. The formulation presented in this paper sets a methodology for the analysis of measurements and calculation of the photoelectron spectra in rotationally state selected and oriented molecules in general, spherical top Td molecules in particular. It is applied, as an example, to photoionization in 6a21 orbital of oriented CCl4 in a pure ‖JKJMJ〉 rotational state. We find, among other things, that the photoelectron angular distributions change significantly when either or both of the directions of molecular orientation and of polarization of ionizing radiation vary from parallel to perpendicular to the quantization axis.