The number of singly occupied orbitals in the ground-state atomic configuration of an element defines its nominal valence. For carbon and sulfur, with two singly occupied orbitals in their (3)P ground states, the nominal valence is two. However, in both cases, it is possible to form more bonds than indicated by the nominal valence--up to four bonds for carbon and six bonds for sulfur. In carbon, the electrons in the 2s lone pair can participate in bonding, and in sulfur the electrons in both the 3p and 3s lone pairs can participate. Carbon 2s and sulfur 3p recoupled pair bonds are the basis for the tetravalence of carbon and sulfur, and 3s recoupled pair bonds enable sulfur to be hexavalent. In this paper, we report generalized valence bond as well as more accurate calculations on the a(4)Σ(-) states of CF and SF, which are archetypal examples of molecules that possess recoupled pair bonds. These calculations provide insights into the fundamental nature of recoupled pair bonds and illustrate the key differences between recoupled pair bonds formed with the 2s lone pair of carbon, as a representative of the early p-block elements, and recoupled pair bonds formed with the 3p lone pair of sulfur, as a representative of the late p-block elements.