Using first-principles density-functional calculations, we investigated two competing pathways for the dissociation of water and ammonia on a Si(001) surface. For both systems, we found that, in addition to the conventionally accepted intradimer transfer of the H atom, the interdimer transfer of the H atom can be equally probable with the same reaction mechanism. Our analysis shows that the two dissociation pathways occur through the Lewis acid-base reaction between the partially positive H ion and the electron-abundant up atom of the buckled Si dimer. The result of the interdimer H transfer not only supports a recently proposed model for C-defect on Si(001) but also corresponds to the recent scanning tunneling microscopy data of ammonia dissociation on Si(001).