The formation and transformation of adsorbed alkoxide intermediates to active carbenium-ion species over solid acid catalysts are essential steps that determine the rate and selectivity of many hydrocarbon conversion processes. Herein, density functional theory is used to examine these processes for a t-butyl species adsorbed to phosphotungstic acid, a Keggin structured polyoxometalate. The tertiary carbenium ion is found to be a meta-stable intermediate state. The conversion of a physisorbed, pi-bound isobutene state to the t-butyl alkoxide state occurs in a two-step process through formation of this tertiary carbenium-ion intermediate. Both the intermediate and transition states contain a positive charge and are properly termed carbenium ions, and the interaction with the catalyst surface is mainly Coulombic. The dehydrogenation of isobutane and the dehydration of 2-methyl-2-propanol are also examined. Tertiary carbenium ions are found to be transition states for both of these processes as well. (C) 2006 Elsevier B.V. All rights reserved.