[2+2] and [4+2] cycloaddition reactions of 1,3-cyclohexadiene on the Si(001) surface were studied. It is shown that not only the [4+2] cycloaddition reaction but also the [2+2] cycloadditions can occur on the Si(001) surface. Surface isomerization reactions connecting [4+2] and [2+2] are very unlikely due to a high energy barrier, implying that the surface reactions are kinetically controlled. Therefore the final surface reaction products are determined during the initial stage of the reactions in contrast with earlier assumptions that the "product distribution is thermodynamically determined". Our interpretations are consistent with the new experimental results by the Hamers group. According to our CASSCF(6,6) calculations, the nonsymmetric ct-complex transition states along the [2+2] cycloaddition mechanism, which has been suggested by many theoretical studies, seem to be an artifact. Nevertheless, the very soft Si dimer buckling motion of the Si(001) surface certainly facilitates the [2+2] reaction.