The geometries and binding energies of a recent buckyball tweezers (C(60)H(28)) 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 C(60). However, due to the entropy penalty, the calculated gas-phase free energy of association of the C(60)@corannulene supramolecule is positive 3.5 kcal mol(-1); and this entropy penalty explains why it is difficult to observe C(60)@corannulene supramolecule experimentally. By using a pi-extended tetrathiafulvalene (TTF), in particular 9,10-bis(1,3-dithiol-2-ylidene)-9,10-dihydroanthracene (TTFAQ or C(20)H(10)S(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 C(60) is weaker than that between corannulene and C(60), the gas-phase binding free energy in the C(60)@C(60)H (32)S(8) supramolecular complex is smaller than that in the C(60)@C(60)H(28) supramolecule. We also discuss solvent effects.