First-principles density functional (DFT) quantum chemical calculations were carried out to understand the overall energetics for the hydrogenation of maleic anhydride to tetrahydrofuran (THF), over a Pd(111) cluster model. The calculated vapor phase structures and vibrational frequencies for maleic anhydride, succinic anhydride, gamma-butyrolactone and THF compare well with the reported experimental X-ray crystal structure data and infrared (IR) frequency measurements. The overall reaction energies for vapor phase maleic anhydride hydrogenation to THF, determined using DFT, are within 5 kcal/mol of the enthalpies of reaction, based on standard heats of formation. The adsorption structures for maleic anhydride, succinic anhydride, gamma-butyrolactone, THF water and atomic hydrogen were completely optimized on a fixed Pd(12,7) cluster model of the Pd(111) surface. The binding energies for maleic anhydride on the Pd-19 cluster in the di-sigma, pi and eta(1) adsorption modes were -83, -34 and -28 kJ/mol, respectively. The computed adsorption energy and vibrational frequencies for di-sigma bound maleic anhydride on Pd(111) are in good agreement with temperature-programmed desorption (TPD) and high resolution electron energy loss spectroscopy (HREELS) measurements of Xu and Goodman [Langmuir 12(1996) 1807-1816]. Preliminary calculations indicate that the most favorable adsorption mode for succinic anhydride, gamma-butyrolactone, THF and water on Pd(111) is eta(1), with binding energies of -28, -38, -45 and -30 kJ/mol, respectively. The energetically most stable adsorption site for atomic hydrogen on the Pd(111) surface is the 3-fold fee site, with a binding energy of -257 kJ/mol. Towards understanding the detailed reaction mechanism on Pd(111), we have postulated elementary reaction pathways for C-H bond formation in maleic anhydride hydrogenation and the ring opening reaction of maleic anhydride on Pd(111). The DFT-computed activation barrier for C-H bond formation in maleic anhydride hydrogenation to maleic anhydryl on a Pd-19 cluster is +82 kJ/mol and the energy of reaction is -9 kJ/mol. The ring opening reaction of maleic anhydride on Pd(111) has an activation barrier of +163 kJ/mol and is endothermic by 90 kJ/mol. The activation barrier on Re(0001), however, is only +80 kJ/mol, whereas the reaction is exothermic by -96 kJ/mol. These results are consistent with the observations from UHV experiments.