Dimethylarsinic Acid (DMA) belongs to an important class of organoarsenical compounds commonly detected in arsenic speciation studies of environmental samples and pyrolysis products of fossil fuels. Transformation of DMA under certain conditions leads to the formation of other forms of arsenic, which could be more toxic than DMA to biota, and more efficient in deactivating catalysts used in petrochemical refining. Published surface sensitive X-ray and infrared spectroscopic work suggested that DMA simultaneously forms inner- and outer-sphere complexes with iron-(oxyhydr)oxides. Computational work on the complexation of arsenicals with various surfaces of environmental and industrial interest provides useful information that aids in the interpretation of experimental spectroscopic data as well as predictions of thermodynamic favorability of surface interactions. We report herein Gibbs free energies of adsorption, ΔG(ads), for various ligand exchange reactions between hydrated complexes of DMA and Fe-(oxyhydr)oxide clusters calculated using density functional theory (DFT) at the B3LYP/6-311+G(d,p) level. Calculations using arsenate were also performed for comparison. Calculated As-(O,Fe) distances and stretching frequencies of As-O bonds are also reported for comparison with experimental spectroscopic data. Gibbs free energies of desorption, ΔG(des), due to reactions with phosphorus species at pH 7 are reported as well. Our results indicate that the formation of both inner- and outer-sphere DMA complexes is thermodynamically favorable, with the former having a more negative ΔG(ads). Values of ΔG(des) indicate that desorption favorability of DMA complexes increases in this order: bidentate < mondentate < outersphere. The significance of our results for the overall surface complexation mechanism of DMA is discussed.