Calculated Electronic Behavior and Spectrum of Mg+@C60 Using a Simple Jellium-shell Model

W Even,H A Schuessler,M W Roth,J Smith

doi:10.3390/i5110333

Abstract

We present a method for calculating the energy levels and wave functions of any atom or ion with a single valence electron encapsulated in a Fullerene cage using a jelluim-shell model. The valence electron-core interaction is represented by a one-body pseudo-potential obtained through density functional theory with strikingly accurate parameters for Mg+ and which reduces to a purely Coulombic interaction in the case of H. We find that most energy states are affected little by encapsulation. However, when either the electron in the non-encapsulated species has a high probability of being near the jellium cage, or when the cage induces a maximum electron probability density within it, the energy levels shift considerably. Mg+ shows behavior similar to that of H, but since its wave functions are broader, the changes in its energy levels from encapsulation are slightly more pronounced. Agreement with other computational work as well as experiment is excellent and the method presented here is generalizable to any encapsulated species where a one-body electronic pseudo-potential for the free atom (or ion) is available. Results are also presented for off-center hydrogen, where a ground state energy minimum of -14.01 eV is found at a nuclear displacement of around 0.1 Å.

Highlights

The quantum mechanical behavior of hydrogen and hydrogen-like atoms is well understood and is standard regimen in introductory quantum mechanics texts [1,2,3]
A non-interacting spherical cage does not provide an acceptable model for a Fullerene, and a full density functional theory treatment with the intent of obtaining an effective valence electron interaction potential is exceedingly difficult
The jellium-shell model has been used to reproduce certain aspects of the photoionization cross section of C60 [8] and it has been successfully applied to other endohedral Fullerene systems [9,10,11]

Summary

Introduction

The quantum mechanical behavior of hydrogen and hydrogen-like (hydrogenic) atoms is well understood and is standard regimen in introductory quantum mechanics texts [1,2,3]. In many cases, a “jellium-shell” model is employed in order to simulate the attraction of an electron with the cage, which involves a spherical step function potential well. Such models have been utilized to calculate the photoabsorption spectrum of C60 as well as that for endohedral Xe and Ba [7]. In the interest of better understanding the behavior of species encapsulated within Fullerenes, a jellium shell model has been used in a recent study of the behavior of H confined at the center of a deformable cage [16], showing outstanding agreement with experiment and other theoretical results. The computational time and memory requirements for the two dimensional case are significantly greater than those for the one-dimensional case, mainly because the memory required for the one-dimensional simulations depends only on the number of radial grid points, while that for the two-dimensional simulations depends on the number of radial and colatitudinal grid points

Discussion and Conclusions

H Accepted

Findings

H State 1s 2s