The potential energy surface of the H-2/S-2, system has been characterized at the full valence MRCI+Davidson/aug-cc-pV(Q+d)Z level of theory using geometries optimized at the MRCI/aug-cc-pVTZ level. The analysis includes channels occurring entirely on either the singlet or the triplet surface as well as those involving an intersystem crossing. RRKM-based multiple well calculations allow the prediction of rate constants in the temperature range of 300-2000 K between 0.1 and 10 bar. Of the SH recombined on the singlet surface, the stabilization of the rovibrationally excited adduct HSSH is at the low-pressure limit at I bar, but it has a rate comparable to that forming another major set of products H2S + S (via an intersystem crossing) at temperatures below 1000 K; at higher temperatures, HSS + H becomes the dominant product. For the reaction H2S + S, the presence of ail intersystem crossing allows the formation of the singlet excited adduct HSS, most of which rearranges and stabilizes as HSSH under atmospheric conditions. At high temperatures, the majority of excited HSSH dissociates to SH + SH and HSS + H. Compared to reported shock tube measurements of the reaction H2S + S, most of the S atom consumption can be described by the triplet abstraction route H2S + S -> SH + SH, especially at high temperatures, but inclusion of the singlet insertion channel provides a better description of the experimental data. The reaction HSS + H was found to proceed predominantly on the singlet surface without a chemical barrier. The formation of the major product channel SH + SH is very fast at room temperature (similar to 4 x 10(15) cm(3) mol(-1) s(-1)). While the formation of H2S + S or S-2 + H-2 via an isomerization or an intersystem crossing, respectively, are minor product channels, their rates are significantly higher than those of the corresponding direct triplet channels, except at elevated temperatures. Finally, due to the relatively shallow nature of its well, the stabilization of H2SS is negligible under conditions of likely interest.