The geometric structure and optical response of gaseous endohedral magnesium—fullerenes

Using density functional theory, a jellium model for the C₆₀ molecule and a pseudopotential for the magnesium ion, we determined the energetics of the magnesium endohedral complex as a function of the magnesium ion's displacement from the fullerene's centre. The resulting Kohn—Sham equation is solved in cylindrical coordinates. Our calculation shows that the magnesium ion will reside in a very shallow energy minimium about ≈1 Å off centre. By computing the photoabsorption cross-section, or the imaginary part of the dynamic polarizability, we can correlate the displacement of the magnesium ion with a peak shift in the photoabsorption cross-section. This suggests that the location of the magnesium ion inside C₆₀ can be determined experimentally by observing the optical response of the endohedral complex.