Context <p>Gas sensors with high sensitivity and selectivity are essential for industrial safety and environmental monitoring. The ongoing development of more effective sensors relies on two key aspects: the design of novel sensing materials and a deeper understanding of the underlying sensing mechanisms. Among the various materials used for the sensor fabrication, semiconducting metal oxides such as chromium and manganese oxides have garnered much recent attention. Notably, palladium-doped chromium oxide has demonstrated high efficiency in hydrogen sensing. Chromium oxides can function as single-component sensors and also in components of composite systems. Manganese oxides are likewise widely used in sensing applications, especially as electrochemical sensors either alone or in combination with other metal oxides.</p> Methods <p>All calculations were carried out by using spin-polarized density functional theory with the generalized gradient approximation as implemented in Gaussian 09. Among the numerous exchange–correlation functionals and basis sets, we chose the BPW91 functional and 6–311 + G* basis set of triple-zeta quality. We considered reactions of Cr₂O_<i>n</i> and Mn₂O_<i>n</i> with H₂ and found pathways leading from the reagents to products. All but one reaction pathways were found to have two or three transition states separated by local minima. The search of transition states was performed by using the modified conjugate gradient algorithm and the local minima were determined by applying the intrinsic reaction coordinate algorithm. It was found that some of the pathways are spin-dependent, i.e., the total spin magnetic moments of reagents do not match those of the products.</p>