The geometries and binding energies of a recent buckyball tweezers (C 60H28) and its supramolecular complexes are investigated using recently developed density functionals (M06-L and M06-2X) that include an accurate treatment of medium-range correlation energy. The pincer part of the tweezers, corannulene, has a strong attractive interaction with C60. However, due to the entropy penalty, the calculated gas-phase free energy of association of the C60@corannulene supramolecule is positive 3.5 kcal mol-1; and this entropy penalty explains why it is difficult to observe C60@corannulene supramolecule experimentally. By using a π-extended tetrathiafulvalene (TTF), in particular 9,10-bis(1,3-dithiol-2- ylidene)-9,10-dihydroanthracene (TTFAQ or C20H10S 4), as the pincer part, we modeled a new buckyball tweezers. The geometries and binding energies of the new buckyball tweezers and its supramolecular complexes are also calculated. Due to fact that the attractive interaction between TTFAQ and C60 is weaker than that between corannulene and C60, the gas-phase binding free energy in the C 60@C60H 32S8 supramolecular complex is smaller than that in the C60@C60H28 supramolecule. We also discuss solvent effects.