Six possible complexes of glyphosate (O-PO(OH)-CH2NH2+CH2CO2H) with an Fe-hydroxide dimer were modeled with hybrid molecular orbital/density functional theory calculations to establish the nature of the bonds of glyphosate on goethite (alpha-FeOOH). Monodentate and bidentate coordination of the phosphonate moiety were considered, using three forms of the glyphosate molecule appropriate for different pH ranges: glyphosate with both phosphonate and amino moieties protonated, glyphosate with unprotonated phosphonates, and glyphosate with both unprotonated phosphonates and no hydrogen ion on the amino group. The calculated infrared vibrational modes were compared to experimental values, finding particularly good agreements with the monodentate complexes in all the pH ranges.