Correlation Study of Endohedrally Confined Atoms (A@C$_{60}$): Alkaline Earth Metal Elements

Effects of endohedral confinement on the correlation energy of Be, Mg, and Ca have been investigated using a modified Hartree- Fock (HF) and Multi-Configuration Hartree-Fock (MCHF) method. In this method, an atomic endohedral system (A@C$_{60}$) is approximated as an atom enclosed in an attractive spherical potential well of inner radius $r\sim5.8$ and thickness of $\Delta \sim 1.89$ a.u., and correlation energies are studied as a function of the depth of the confining potential ($0\leq U_0<2$ a.u.). In order to calculate single- and multi- configuration wave functions, we have modified the MCHF codes~ [1] by adding a well potential in addition to the internal atomic potential. Single- and multi-configuration wave functions are obtained from the solution of HF and MCHF equations with the extra potential self-consistently. In general, we have found that valance electrons diffuse outward in the presence of extra potential, which causes the electrons to be further apart. As a consequence, the electron correlations get smaller. In conclusion, our studies has showed that the correlation effects in endohedrally confined atoms gets less important than the free atoms.\\[0pt] [1] C. Froese Fischer et al., Comput. Phys. Commun. \textbf{176}, 559 (2007).