It is known that hydrogen stabilizes the growing diamond surface under chemical vapor deposition conditions, but a detailed, stepwise, atomic level understanding of how hydrogen atoms function in the growth mechanism is still missing. In the present work ab initio molecular orbital theory is used to address the structures and energetics of hydrogen atoms on dimer-reconstructed diamond (100)2x1 surfaces. These surfaces are modeled with clusters consisting of nine carbon atoms in four separate layers, which form the basic structural unit of the diamond lattice. Lattice constraints are modeled in the clusters in two different ways in order to determine lower and upper bounds for HC-CH, HC-C-. and C=C dimer bond lengths, carbon-hydrogen bond dissociation energies, pi bond strengths, and dehydrogenation energies on diamond (100)2x1 surfaces. Calculated lower and upper bounds for the dimer bond lengths are 1.58-1.71 Angstrom on the monohydrogenated. (100)2x1 surface, 1.55-1.68 Angstrom on the surface comprising HC-C-. radicals, and 1.38-1.44 Angstrom on the clean (100)2x1 surface. The strength of the first C-H bond (413 and 418 kJ/mol) is essentially independent of the treatment of lattice constraints. The second C-H bond is weaker than the first by 44-82 kJ/mol, due to formation of a weak pi bond on the clean surface whose strength is sensitive to the lattice constraints. The energy for the molecular desorption of hydrogen is predicted to lie in between 308 and 356 kJ/mol on diamond (100)2x1. Inclusion of the correlation energy correction is necessary for describing the energetics correctly. The calculated it bond strength on vacant surface dimers implies a substantial driving force for pairing of hydrogen atoms and dangling bonds separately on dimers on the (100)2x1 surface, and suggests that most dangling bonds are paired under diamond growth conditions.