The present disclosure relates to methods for more efficiently recycling reduced electron carriers in a hydrogen-oxidizing microorganism with an operable Calvin-Benson cycle; synthetic carbon fixation pathways that recycle reduced electron carriers more efficiently than the Calvin-Benson cycle, such as methods for enzymatically converting carbon dioxide to formate and assimilating the resulting formate into central carbon metabolism; methods for producing biochemical products; and recombinant hosts utilizing one or more synthetic carbon fixation pathways.