STM study of one-dimensional cluster formation of fullerenes: Dimerization ofY@C82

We have studied one-dimensional cluster formation of ${\mathrm{C}}_{60},$ ${\mathrm{Y}\mathrm{@}\mathrm{C}}_{82},$ and ${\mathrm{Gd}\mathrm{@}\mathrm{C}}_{82}$ along the step of the Cu(111) 1×1 surface using a scanning tunneling microscope. It is found that the dimer is most abundant only for ${\mathrm{Y}\mathrm{@}\mathrm{C}}_{82}$ which has one unpaired electron delocalized over the carbon cage, while the monomer is dominant in the cases of ${\mathrm{Gd}\mathrm{@}\mathrm{C}}_{82}$ and ${\mathrm{C}}_{60}.$ It was concluded that the preferential dimer formation of ${\mathrm{Y}\mathrm{@}\mathrm{C}}_{82}$ is mainly due to the interaction between the unpaired electrons. The interaction energy among fullerence molecules was estimated based on Walton’s cluster theory.