Approximating the C60 shell as a collection of carbon atoms, the potential experienced by a confined atom has been calculated within the framework of the self-consistent spherical jellium model. It has been found that the potential well in this model has a cusp-shaped Lorentz-like profile. The parameters of the model Lorentz-bubble potential (depth and thickness) have been selected so that in the potential well there would be an electronic level corresponding to the experimental electron affinity of the C60 molecule. The spatial distribution of the positive charge of the C-atomic nuclei and the negative charge of the electron clouds forming the electrostatic potential of C60, as a whole, has been analyzed using the Poisson equation. It is demonstrated that the often used radial square-well potential to approximate the C60 corresponds to a non-physical charge density for the C60 molecule. This analysis demonstrates that the phenomenological potentials simulating the C60 shell potential should belong to a family of potentials with a non-flat bottom and non-parallel potential walls similar to the Lorentz-bubble potential. The photoionization cross-sections of a hydrogen atom localized at the center of the C60 shell have been calculated as well. It is found that confinement oscillations in the cross-sections are exhibited within the framework of the cusp-shaped potential model and these oscillations are essentially the same as those in the case of the potential wells with well-defined borders (parallel walls), thereby demonstrating that the inherent characteristic distances of the potential, e.g., radii of the potential walls, or the distances between potential walls, are not necessary to produce confinement resonances; this should be a general result for atoms or molecules confined in near-spherical fullerenes.

https://iopscience.iop.org/article/10.1088/0953-4075/48/18/185103/pdf

Jellium model potentials for the C 60 molecule and the photoionization of endohedral atoms, A@C 60

The hydrogen atom confined by an infinite spherical potential barrier is studied employing a variational procedure based on the p-version of the finite element method. In such a procedure, the spherical spatial confinement is imposed straightforwardly by removing a local basis function. The calculations have been performed for estimating the energy spectrum, the dipole polarizability and the effective pressure for various confinement radii. The effect of the spatial confinement on these quantities is analysed. The results obtained are compared with those previously published in the literature and the efficiency of the finite element method to treat confined quantum systems is discussed.

A study of the confined hydrogen atom using the finite element method

A perceived advantage for the replacement of a discontinuous square-well pseudo-potential, which is often used by various researchers as an approximation to the actual C60 cage potential in calculations of endohedral atoms A@C60, by a more realistic diffuse potential is explored. The photoionization of endohedral H@C60 and Xe@C60 is chosen as the case study. The diffuse potential is modelled by a combination of two Woods–Saxon potentials. It is demonstrated that photoionization spectra of A@C60 atoms are largely insensitive to the degree η of diffuseness of the potential borders, in a reasonably broad range of ηs. These spectra are found to be insensitive to discontinuity of the square-well potential as well. Both potentials result in practically identical calculated spectra. New numerical values for the set of square-well parameters, which lead to a better agreement between experimental and theoretical data for A@C60 spectra, are recommended for future studies.

Diffuse versus square-well confining potentials in modelling A@C 60 atoms

The systems of confined atoms in cages have received considerable attention for decades due to interesting phenomena arising from the effect of cage environment on the atom. For early theoretical work based on empirical model potentials, the Dirac δ-potential, i.e. the so-called bubble potential, and the attractive short-range spherical shell potential are conventionally used for the description of interaction between the valence electron of confined atom and the cage. In this work, the power-exponential potential with a flexible confining shape is proposed to model the cages. The methods of complex scaling in the finite-element discrete variable representation are implemented to investigate the hydrogen, hydrogen-like ions and alkali metals encapsulated by the cages. The energy spectrum varying with the confining well depth exhibits avoided crossings. The influence of cage on atomic photoionization leading to the oscillation behaviour or the so-called confinement resonances in cross sections is demonstrated in a variety of confined atomic systems. In comparisons with existing predictions using the Dirac δ-potential and the attractive short-range spherical shell potentials, our results show the significant influence of cage thickness and smooth shell boundary on the photoionization. The drastic changes of cross sections due to the character of cage are presented and discussed for the encaged lithium and sodium atoms. The present model is useful for clarifying the boundary effect of confining shell on the endohedral atoms.

http://iopscience.iop.org/article/10.1088/0953-4075/45/14/145001/pdf

Photoionization of atoms encapsulated by cages using the power-exponential potential

Electron‐density delocalization in many‐electron atoms confined by penetrable walls: A Hartree–Fock study

A novel model potential for modelling the environment of atoms and molecules inside fullerenes is proposed. The model takes into consideration that the electrons of the guest atom or molecule are affected by an attractive short-range Gaussian shell to simulate the Cn cage. As a test case, the present model is employed to study the electronic structure of an endohedrally confined hydrogen atom by C36 and C60 fullerenes. This study is performed using a new implementation of the p-version of the finite-element method by a self-consistent finite-element methodology. The results are then compared with previous ones obtained by using other short-range model potentials.

/pdf/a-study-of-the-electron-structure-of-endohedrally-confined-3x3c1dkr8h.pdf

A study of the electron structure of endohedrally confined atoms using a model potential

/pdf/a-study-of-the-electron-structure-of-endohedrally-confined-484a49d598.pdf

E. M. Nascimento

Papers

A study of the electron structure of endohedrally confined atoms using a model potential

A study of the electron structure of endohedrally confined atoms using a model potential