We have performed first-principles calculations in order to understand the binding mechanism of Li atoms in disordered carbon materials that are used for negative electrodes of rechargeable lithium batteries. We used pyrene, anthracene, and phenanthrene molecules as parts of disordered carbon. We examined several binding sites for two Li atoms in these aromatics and found that they are bound with substantial negative binding energies. The most negative one was - 142.8 kJ/mol for Li-containing pyrenes, -211.0 kJ/mol for anthracenes, and -146.2 kJ/mol for phenanthrenes at the B3LYP/6-31G*//HF/6-31G* level of calculation. Li atoms are bound to interstitial (ring-over) and edge sites. In addition to these binding mechanisms, we found that Li atoms could be bound, forming a Li dimer in anthracene and phenanthrene. Their binding energies are -200.5 and -146.2 kJ/mol, respectively, being larger in magnitude than Li-2 dissociation energy. These aromatics lose their planarity when they accommodate Li atoms. We found that larger distortion brings more strong interaction between the aromatics and Li atoms. The amount of energy required for the distortion increases in the order the interstitial, edge, and Li-dimerized sites. The highest occupied molecular orbital energy, which is closely related to the electrode potential during discharge process, decreases in that order. This energy lowering may be related to the origin of the hysteresis observed during the charge/discharge cycles.