Dr Alfred Msezane from the Department of Physics, Clark Atlanta University, explains ground state negative ion formation in complex heavy systems, including comment on electron affinity determination
We begin with the discussion of the ground state negative ion formation in low-energy electron collisions with complex heavy systems, such as the lanthanide and actinide atoms, as well as the fullerene molecules. The knowledge gained is essential for the determination of unambiguous and reliable electron affinities (EAs) for these systems. Generally, the low-energy electron elastic scattering total cross sections (TCSs) for complex heavy systems are characterised by Ramsauer-Townsend (R-T) minima, shape resonances and dramatically sharp resonances representing ground, metastable and excited negative ion formation.
The energy position of the sharp resonance appearing at the second R-T minimum of the ground state TCS represents the anionic binding energy (BE) of the formed ground state negative ion during the collision. This BE has been identified with the theoretically challenging to calculate electron affinity of the considered complex heavy system. Indeed, the delineation and identification of the resonance structures in the TCSs are essential for the correct interpretation of the calculated results and the determination of unambiguous and reliable EAs of the complex heavy systems.
II.1 Overview
For most of the lanthanide atoms, producing sufficient anions with known anionic BEs that can be used in photodetachment experiments is very challenging; for the actinide atoms, the situation is even worse. Due to their radioactive nature, they are difficult to handle experimentally. Theoretically, the large number of electrons involved and the presence of open d- and f-subshell electrons in both the lanthanide and actinide atoms, results in many intricate and diverse electron configurations. These lead to the computational complexity of the electronic structure calculation, making it very difficult to obtain unambiguous and reliable EAs for these systems using structure-based theoretical methods. These are notorious for their slow convergence. Indeed, many existing experimental measurements and sophisticated theoretical calculations have considered the anionic BEs of the stable metastable and/or excited negative ion formation to correspond to the EAs of the considered lanthanide and actinide atoms.
This is contrary to the usual meaning of the EAs found in the standard measurement of the EAs of such complex systems as atomic Au, Pt and most recently At as well as of the fullerene molecules, from C20 through C92. In these systems, the EAs correspond to the ground state BEs of the formed negative ions. In the electron interactions with fullerene and fullerene-like systems, simple model potentials are widely used to describe the C60 and other fullerene shells. At the heart of these model potentials are the two experimentally determined parameters, namely the fullerene radius and its EA. The lack of the appropriate parameters for other fullerene molecules is the main reason for the struggle by existing theoretical calculations to go beyond the theoretically simple C60 fullerene molecule.
Accurate and reliable atomic and molecular affinities are essential for understanding chemical reactions involving negative ions. And the EA provides a stringent test of theoretical calculations when their results are compared with those from reliable measurements. For the lanthanide atoms, the measured and/or calculated EAs are riddled with uncertainty and full of ambiguity as well. To our knowledge, there are no EA measurements available for the actinide atoms. However, the recent experimental determination with high precision of the BE of the least-bound electron in atomic No promises measurements of the EA as well. And this presentation will guide the future measurement of the EAs of the actinide atoms through the determination of their ground state negative ion BEs. Then sophisticated theoretical methods such as the Dirac R-matrix, MCHF and RCI can use the BEs of the formed negative ions during the collisions to generate target wave functions and for fine-structure determination.
Recently, our robust Regge-pole methodology achieved a theoretical breakthrough through the identification of the crucial electron-electron correlation effects and the vital core-polarization interaction as the major physical effects mostly responsible for negative ion formation in low-energy electron scattering from complex heavy systems. The novelty and generality of the Regge-pole approach is in the extraction of the anionic BEs from the calculated TCSs of the complex heavy systems; for ground state collisions these BEs yield the unambiguous and reliable theoretically challenging to calculate measured EAs.
Very recently, the ground state anionic BEs extracted from our Regge-pole calculated electron elastic TCSs for the fullerene molecules C20 through C92 have been found to match excellently the measured EAs1,2. Also, the agreement between our Regge-pole calculated ground-state anionic BEs and the measured EAs of Au3 and Pt3 as well as of C60 4 is outstanding. The Regge-pole method requires no assistance whatsoever from either experiment or other theory for the remarkable feat.
II.2 Lanthanide Atoms
The lanthanide and the Hf atoms provide clear cases of the ambiguous and confusing measured and/or calculated EA values.(5) As examples, for the Eu atom two measurements determined different EA values for its EA, viz. 0.116eV and 1.05eV. These agree excellently with the Regge-pole calculated BEs for the highest anionic excited and the metastable states, respectively; the ground state anionic BE for Eu has been determined recently to be 2.63eV5. This BE value should be considered as the EA of the Eu atom.
Other examples where the measurements of the EAs correspond to the BEs of the metastable and/or excited states include the lanthanide atoms Tb, Tm, Gd and Yb as well as the Nb and Hf atoms.5 For Hf the Relativistic Configuration Interaction (RCI) calculated EA agrees excellently with the Regge-pole calculated BE of an excited state and not with that of the ground state. These results demonstrate the importance of obtaining the ground, metastable and excited ionic states BEs. It is noted here that the determination of the ground state negative ion BE of complex heavy systems is a great challenge for the structure-type calculations.
II.3 Actinide Atoms
In6 the low-energy electron scattering from the actinide atoms Th, Pa, U, Np and Pu was investigated through the elastic TCSs calculations. The objective was to delineate and identify the characteristic resonance structures as well as to understand and assess the reliability of the existing theoretical EAs. Particularly interesting in the study6 is the finding for the first time that the TCSs for atomic Pu exhibited fullerene molecular behaviour(1) near- threshold through the TCS of the highest excited state, while maintaining the atomic character through the ground state TCS. Very recently, the low-energy electron scattering TCSs for Cm to Lr actinide atoms were explored. We discovered new manifestations in the TCSs of Cm to Lr actinide atoms; namely, atomic and fullerene molecular behaviour near threshold. We have attributed these peculiar tunable behaviours in the TCSs to size effects impacting significantly the polarization interaction.
This provides a novel mechanism of tuning a shape resonance and R-T minimum through the polarization interaction via the size effect. The comparison between the Regge-pole calculated ground, metastable and excited states anionic BEs with the existing theoretical EAs demonstrates that the existing calculations tend to obtain metastable and/or excited states BEs and equate them incorrectly with the EAs. Indeed, this leads to an ambiguous and unreliable determination of the EAs of complex heavy systems; they are already populating the literature.(7) For an unambiguous and a definitive meaning of the EA, we recommend using the ground state anionic BE as the EA of complex heavy systems, consistent with the use in the determination of the EAs of such atoms as Au and Pt as well as of the fullerene molecules. (1,2)
II.4 Fullerene Molecules
For fullerene molecules, excellent measured EAs are available in the literature from C20 through C92. Benchmarked on the measured EAs of C60 4, the Regge-pole methodology was used to calculate the ground state anionic BEs of the fullerene molecules negative ions from C20 through C240. Our calculated ground state anionic BEs agreed excellently with the available measured EA values of C20 through C92. Indeed, these results provided great credence to the ability of the Regge-pole methodology to extract from the calculated TCSs reliable EAs for the fullerene molecules for the first time.
The obtained agreement represented an unprecedented accomplishment by the Regge-pole methodology in electron-cluster/fullerene collisions. For the fullerene molecules, other theories are still struggling to go beyond the theoretically simple C20 and C60 fullerene molecules. It is noted here that the fullerene TCSs are very rich in metastable and excited anionic resonances, revealed for the first time in 1,2. Thus, careful delineation and identification of the various resonances in the TCSs, particularly for the anionic ground states are essential for reliable calculation of their EAs. These fullerene negative ions could be useful in catalysis.
Indeed, many existing experimental measurements and sophisticated theoretical calculations have considered the anionic BEs of the stable metastable and/or excited negative ion formation to correspond to the EAs of the considered lanthanide and actinide atoms(7). This is contrary to the usual meaning of the EAs found in the standard measurement of the EAs of such complex systems as atomic Au, Pt and At as well as of the fullerene molecules. In these systems, the EAs correspond to the ground state BEs of the formed negative ions. For fullerenes, existing theories continue to struggle to obtain reliable EAs.
References
1 A. Z. Msezane and Z. Felfli, Chem. Phys. 503, 50 (2018).
2 Z. Felfli and A. Z. Msezane, Euro Phys. J. D 72, 78 (2018).
3 H. Hotop and W. C. Lineberger, J. Chem. Phys. 58, 2379 (2003).
4 D.-L. Huang, P. D. Dau, H. T. Liu and L.-S. Wang, J. Chem. Phys. 140, 224315 (2014).
5 Z. Felfli and A. Z. Msezane, J. of Atomic, Molecular, Condensate & Nano Phys. 5, 73 ( 2018).
6 Z. Felfli and A. Z. Msezane, Applied Physics Research 11, 52 (2019)
7 A. Z. Msezane, Journal of Atomic, Molecular, Condensate & Nano Physics 5, 195 (2018).
This research is supported by U.S. DOE, Office of Basic Energy Sciences, Office of Energy Research.
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