Analysis of the exergy efficiency of hydrogen carriers by type requires setting of physical conditions such as pressure and temperature of the hydrogenation and dehydrogenation reactions. In determining theoretical efficiency of liquefied hydrogen as carrier, the model employed possesses a suitable parameter to work out the optimal conditions for the whole of a system after each of the refrigeration stages has been optimized. The model in this study consists of three cycles of refrigeration and a final cooling stage. Each refrigeration cycle is principally a reverse Brayton cycle comprising compressors, expanders and a heat exchanger. Trial-and-error adjustments were made to find the cycles that provide the maximum cooling heat to the next stage. The branch flow rate e, which indicates the volumetric ratio of hydrogen to be sent to the expander in the hydrogen liquefaction cycle, was found to be a suitable parameter to seek the optimal conditions of the system. Only hydrogen, helium, and neon as a pure fluid can serve as a refrigerant for cooling in the hydrogen liquefaction stage, and these three refrigerants were compared in terms of the changes in pre-cooling heat requirements and exergy loss with change in the flow rate e. The comparison brought three major findings. (i) A trade-off between pre-cooling heat requirements and exergy loss exists, and this suggests that the flow rate e is an indicator of optimal conditions. (ii) The efficiencies of hydrogen and helium as a refrigerant are very similar and better than that of neon throughout the range of the flow rate e. (iii) In a certain range of the flow rate e, the difference between hydrogen or helium and neon becomes small. This suggests the possibility of employing neon or nelium (mixed refrigerant composed of neon and helium), which have higher density than hydrogen or helium and are considered to be more efficient to rotate turbines.