Correlation study of endohedrally confined alkaline-earth-metal atoms ( A @ C 60 )

The effects of endohedral confinement on the correlation energy of Be, Mg, and Ca atoms have been investigated using modified Hartree-Fock and multiconfiguration Hartree-Fock methods where the endohedral system $(A@{\text{C}}_{60})$ is approximated as an atom enclosed in an attractive spherically symmetric potential well of inner radius $r\ensuremath{\sim}5.8$ a.u. and thickness of $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}1.89$ a.u., and correlation energies are studied as a function of the depth of the confining potential ($0\ensuremath{\le}{U}_{0}\ensuremath{\le}1$ a.u.) to give some idea as to how the correlation energy behaves in different endohedral environments. In general, we have found that as a function of well depth, starting from the free atom, valence electrons diffuse outward in the presence of the confining potential, which causes the electrons to be further apart, thereby decreasing the correlation energy; however, with further increase of well depth, the valence electrons become trapped in the confining well and, as a result of their being closer together, the correlation energy increases.