we have proposed a three-dimensional GLE approach to gas-surface reactive scattering, model H + H $${ ightarrow}$H_2/Si(100)-(2$</TEX> ${ imes}$1) system, and the implementation of 3D GLE method on the hydrogen on silicon surface has been presented. The formalism and algori thm of the 3D GLE are worked properly in the reactive scattering system. The calculated normal mode frequencies of surface vibrations were almost identical to previous harmonic slab calculations. The reaction probabilities were calculated for two energies. The calculations show that a very large amount of energy is transferred in surface in low energy scattering. Three different types of reaction mechanisms has been observed, which can not be shown in flat and rigid surface models. Further work on the reaction mechanisms and calculations of the vibrational and rotation distributions of products is in progress. The results will be reported elsewhere soon.