Assessment of Kohn-Sham density-functional orbitals as approximate Dyson orbitals for the calculation of electron-momentum-spectroscopy scattering cross sections

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Abstract
One of the principal advantages of electron momentum spectroscopy (EMS) is that peaks in the binding-energy spectrum can be assigned with greater certainty than in photoelectron spectroscopy, through a comparison of the EMS triple-differential cross sections with the theoretically calculated spherically averaged momentum distributions (MD’s) of Dyson orbitals. While the target Hartree-Fock approximation is commonly used to calculate the Dyson orbital MD’s for this purpose, a computationally less demanding method would allow the advantages of EMS to be extended to larger molecules. This paper considers the use of Kohn-Sham density-functional theory for this purpose. Although Dyson orbitals are not among the quantities that can be calculated exactly (in the limit of the exact exchange-correlation functional) within the framework of Kohn-Sham density-functional theory, the Kohn-Sham equation can be regarded as an approximate form of Dyson’s quasiparticle equation, with a local self-energy. The well known shortcomings of this approach for estimating ionization potentials and band gaps do not a priori imply a corresponding problem with the orbitals. After discussing these formal considerations, we introduce the ‘‘target Kohn-Sham approximation’’ as a means of approximating Dyson orbitals by Kohn-Sham orbitals. The quality of this approximation for the calculation of MD’s is assessed by comparison with high-quality configuration-interaction calculations, the target Hartree-Fock approximation, and experiment, for several small molecules. The quality of the target Kohn-Sham approximation MD’s is found to be comparable to that of the MD’s from the target Hartree-Fock approximation, with evident practical implications for EMS.