Theoretical studies in photoelectron spectroscopy. Molecular optical activity in the region of continuous absorption and its characterization by the angular distribution of photoelectrons

Abstract

The phenomenon of molecular optical activity is examined in the region of continuous absorption. When the "excited" state of the molecule describes an infinite (ionized) system, then the angular distribution of photoelectrons is the sum of coherent contributions corresponding to different magnitudes and interferences of $\hslash \overrightarrow{1}$, the angular momentum of the photoelectron. The amplitude for such a process is the sum of terms for each $l$; thus, since both even and odd values of $l$ can coexist at a single energy in the continuous spectrum, the electric and magnetic dipole matrix elements can coexist in this amplitude, making possible the existence of electric-dipole-magnetic-dipole interference in the angular distribution even for a molecule with a center or plane of symmetry. For discrete absorption, in which the intensity is the sum of incoherent contributions corresponding to the intensities for populating the fine-structure levels of a given excited state, the coexistence of the electric and magnetic dipole matrix elements in the amplitude is possible only for a molecule with a site which is asymmetric with respect to inversion or reflection; otherwise both even and odd values of $l$ could not coexist at a single energy in the discrete spectrum. The signs of the electric-dipole-magnetic-dipole interference terms are opposite for left and right circularly polarized light; thus there exists a signal for the angular distribution difference for absorption of left and right circularly polarized light of order $\alpha$ relative to the angular distribution for absorption of light of either polarization. This is just the phenomenon of "circular dichroism" which characterizes molecular "optical activity" in the region of absorption. It exists for the angular distribution of photoelectrons ejected from an oriented molecule with a center or plane of symmetry, but vanishes for isotropic systems (atoms) owing to the independence of the radial wave functions from the magnetic quantum number. This ensures the orthogonality of atomic radial wave functions belonging to states of different $m$ and is responsible for the selection rule in atomic spectroscopy that magnetic-dipole transitions are possible only between the fine-structure levels of a given multiplet. Measurement of the angular distribution characteristic for this process would provide a sensitive probe of the parameters of the initial molecular orbital. The existence of even-odd-type interferences of the partial waves of the photoelectron would provide a test of the time-reversal invariance of the wave function for the ionized system, since these interferences depend on the sine rather than the cosine of the phase-shift difference and hence on the normalization of the wave function to satisfy incoming boundary conditions. Calculations are carried out to illustrate these and other points.