The energy profiles for the internal bond rotation of substituted methyl radicals, X-CH2 (X = BH2, CH3, NH2, and OH) were examined with B3LYP/6-31G(d) calculations. Energy evaluation of each point along the rotational coordinate was also carried out with single-point calculation at the computational levels of B3LYP/6-311+G(2df,p) and QCISD(T)/6-311+G(2df,p). The computed rotational energy profiles, as well as the calculated values for the geometrical parameters, the vibrational frequencies, and the ionization potential, were in reasonable agreement with previously reported experimental and theoretical results. Except for H3C-CH2 radical, the profiles of chemical potential and hardness along the rotational coordinates present striking contrast to those expected from the corollary of the principle of maximum hardness. Thus, there seems to be no rigorous reason for hardness to be minimum in the transition state region, in general.