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Three different clusters, Si_9H_12, Si_15H_16, and Si_21H_20, are used indensity-functional theory calculations in conjunction with ab initiopseudopotentials to study how the energetics of H_2 dissociativ e adsorption onand associative desorption from Si(001) depends on the cluster size. Theresults are compared to five-layer slab calculations using the samepseudopotentials and high qu ality plane-wave basis set. Severalexchange-correlation functionals are employed. Our analysis suggests that thesmaller clusters generally overestimate the activation barriers and reactionenergy. The Si_21H_20 cluster, however, is found to predict reactionenergetics, with E_{a}^{des}=56 +- 3 kcal/mol (2.4 +- 0.1 eV), reasonably close(though still different) to that obtained from the slab calculations.Differences in the calculated activation energies are discussed in relation tothe efficiency of clusters to describe the properties of the clean Si(001)-2x1surface.Comment: 10 pages, 6 figures, submitted to J. Chem. Phy

Effect of the cluster size in modeling the H2 desorption and dissociative adsorption on Si(001)