2. Computational methods
All geometry optimizations and energy analyses were performed using Gaussian 03 program package [28] with density functional theory (DFT) at the level of B3LYP/6–31G(d,p). The DFT method has been chosen because of the accuracy associated [4–13,15–23,29–34]. Before energy calculations, all atoms were allowed to be relaxed. In our calculations, the periodic boundary circumstance is taken with the super-cells. A space width of 16 A is created which makes sure that the z-axis of the periodic super-cell is large sufficient so that there is no interaction between graphene sheets of bordering super-cells. Relaxed structural model of the 44 PG as well as AlG is given in Fig. 1.
The adsorption energies Eads between the analytes and PG as well as AlG are defined as eq. (1) and eq. (2) respectively: