By means of density functional theory (B3LYP/6-31G*) coupled with effective cluster models, we predict that the well-known cycloaddition reactions of carbenes and nitrenes to alkenes in organic chemistry can be employed as a new type of surface reaction to organically functionalize the Si (100) and Ge (100) surfaces at low temperature. The well-established abundance of carbenes and nitrenes addition chemistry in organic chemistry provides versatile flexibility of functionalizing the surfaces of Si (100) and Ge (100), which can potentially impart new organic functionalities to the semiconductors surface for novel applications in a diversity of fields. Our predictions strongly advance the concept of using organic reactions to modify the solid surface in a controlled manner and quite intriguing chemistry can lie in the material featuring the analogous bonding motif. In further perspective, implications for other theoretical work, regarding disilenes, digermenes, silenes, and germenes that all feature the bonding motif similar to alkenes, are also discussed.