Angular distributions and dichroism of photoelectrons ejected from fixed-in-space molecules of definite symmetry: Application to the C2v symmetry group

Chirality in the Solid State: Chiral Crystal Structures in Chiral and Achiral Space Groups

Chirality depends on particular symmetries. For crystal structures it describes the absence of mirror planes and inversion centers, and in addition to translations, only rotations are allowed as symmetry elements. However, chiral space groups have additional restrictions on the allowed screw rotations as a symmetry element, because they always appear in enantiomorphous pairs. This study classifies and distinguishes the chiral structures and space groups. Chirality is quantified using Hausdorff distances and continuous chirality measures and selected crystal structures are reported. Chirality is discussed for bulk solids and their surfaces. Moreover, the band structure, and thus, the density of states, is found to be affected by the same crystal parameters as chirality. However, it is independent of handedness. The Berry curvature, as a topological measure of the electronic structure, depends on the handedness but is not proof of chirality because it responds to the inversion of a structure. For molecules, optical circular dichroism is one of the most important measures for chirality. Thus, it is proposed in this study that the circular dichroism in the angular distribution of photoelectrons in high symmetry configurations can be used to distinguish the handedness of chiral solids and their surfaces.

Circular dichroism in photoionization of degenerate orbitals: Spin-polarized photoelectrons and spontaneous separation of oriented photoions

This work investigated the circular dichroic effect on the photoionization integral cross section of molecules in conjunction with irreducible tensor theory and effective operator formalism. The results show that the dichroic effect can be non-zero for complex orbitals, but becomes zero for all real orbitals due to time-reversal symmetry, within the electric dipole and Born-Oppenheimer approximations. Calculations were performed for carbon monoxide, boric acid, and fullerene, and implications of the first-order coefficient for the spin polarization of photoelectrons and the molecular axis orientation of photoions are discussed herein. The results of this work demonstrate that the photoionization of complex orbitals can cause photoions to become oriented such that photoions originating from complex conjugate orbitals are oriented opposite to one another. Due to electron-ion recoil, the spontaneous separation of these two kinds of photoions is expected for the point groups C _n , C n v , C ∞ v , C _nh , and S _n with n ≥ 3.

Communication: Photoionization of degenerate orbitals for randomly oriented molecules: The effect of time-reversal symmetry on recoil-ion momentum angular distributions

The photoelectron asymmetry parameter β, which characterizes the direction of electrons ejected from a randomly oriented molecular ensemble by linearly polarized light, is investigated for degenerate orbitals. We show that β is totally symmetric under the symmetry operation of the point group of a molecule, and it has mixed properties under time reversal. Therefore, all degenerate molecular orbitals, except for the case of degeneracy due to time reversal, have the same β (Wigner-Eckart theorem). The exceptions are e-type complex orbitals of the C_n, S_n, C_nh, T, and T_h point groups, and calculations on boric acid (C_3h symmetry) are performed as an example. However, including those point groups, all degenerate orbitals have the same β if those orbitals are real. We discuss the implications of this operator formalism for molecular alignment and photoelectron circular dichroism.

Symmetry of valence states of Heusler compounds explored by linear dichroism in hard-x-ray photoelectron spectroscopy

This study reports on the linear dichroism in angular-resolved photoemission from the valence band of the Heusler compounds NiTi0.9Sc0.1Sn and NiMnSb. High-resolution photoelectron spectroscopy was performed with an excitation energy of hν = 7.938  keV. The linear polarization of the photons was changed using an in-vacuum diamond phase retarder. The valence band spectra exhibit the typical structure expected from first-principles calculations of the electronic structure of these compounds. Noticeable linear dichroism is found in the valence band of both materials, and this allows for a symmetry analysis of the contributing states. The differences in the spectra are found to be caused by symmetry-dependent angular asymmetry parameters, and these occur even in polycrystalline samples without preferential crystallographic orientation.