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Considering our lives, novel energy production is so required, and many scientists have been investigated this problem from a lot of views. One of the ways for the new energy productions is the solar power thermochemical production by an oxidation-reduction reaction of the ceramics CeO₂ (ceria). In this research, the ceria is used for obtaining an H₂ gas in vapor reaction in high-temperature thermal equipment which has a heat production system consisting by focused sun light. Nowadays technology has been also developed to keep a human living, not to harm the Earth environment. From these points, it is realized that how the H₂ gas is important for our lives, so we are trying to improve the thermochemical H₂ gas production by means of a ceria as a catalyst. Our purpose in this study is, to point out what effects occur in doped ceria-s thermal reduction (TR) reaction by using DV-Xα method. Comparing the models between the pure ceria and the Mn doped ceria, we have realized the difference by the reaction. In this appearance, one of the considerations is a view from p-DOSs (partial-Density of States), in which there are different O-2p DOSs by different crystal structures. From this view, we considered that the ceria structure would become more stable and more flexible to cut the Ce-O bonding to keep the stable cyclic thermal reaction in Mn doped ceria.