A random search of configuration space at the density functional theory level has been performed to explore the structures created upon chemisorption of small amounts of impurities O2 and H2 on cesiated Mo(001). Five structural models, namely clean Mo(001), surface with a low Cs coverage, surface with a saturated Cs monolayer, Mo(001) with a multilayer Cs deposition, and clean Cs(001) have been considered as substrates. The distributions of impurity atoms upon adsorption and the associated energy and the work function (ϕ) changes have been investigated. The adatoms are found to be adsorbed most strongly on sites located on the Mo surface or, in the case of thick Cs depositions, when the Mo sites are not accessible, under the uppermost Cs layer. The ϕ change due to adsorption exhibits a complex behaviour affected by both the location of the impurity particles and the Cs coverage. On average, Δϕ is positive in the case of Mo(001) with a low Cs coverage, and vanishes with increasing Cs amount. However, in cases with thick Cs depositions, when the impurities tend to reside the positions close the uppermost Cs layer, Δϕ becomes negative. Notable exceptions opposing these trends are also identified.