The (7,7) and (10,5) carbon nanotubes were studied in the context of the Density Functional Theory (DFT) within a generalized gradient approximation (GGA). The Becke's exchange functional along with the correlation functional of Lee, Yang, and Parr (BLYP) were used with the DZVP basis set aided via auxiliary functions for the electron density. In both materials, the global indexes were calculated from the optimized structure with Kopmanns' theorem. The energy values calculated for the physisorption and chemisorption processes suggested that the physisorption process is more likely to occur for the (7,7) than for the (10,5) carbon nanotube, as well as for the achiral than chiral structure for both nanotubes and for both surface phenomena. This effect may be ascribed to the more homogeneous distribution of molecular orbital for the achiral carbon nanotube, which seems to be supported by the DOS calculations.