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All of the paths given by the OP can lead to discovery of catalysts. Usually, it is a combination of strategies and an accumulation of knowledge from different sources. I will give two examples, ammonia synthesis and enzymatic reactions. Ammonia synthesis $$\ce{N2(g) + 3H2(g) <=> 3NH3(g)}$$ The synthesis of ammonia from the elements is one of the ...

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Manganese(IV) oxide decomposes around 500 °C (German Wikipedia lists $\pu{450 °C},$ [1, p. 396] lists $\pu{530–585 °C}):$ $$\ce{4 MnO2 ->[\sim\pu{500 °C}] 2 Mn2O3 + O2}\label{rxn:1}\tag{R1}$$ On the other hand, according to [2, p. 12], $\ce{Mn3O4}$ reacts with oxygen only above $\pu{500 °C}$ and forms manganese(III) oxide: \ce{4 Mn3O4 + O2 ->[>\...

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Yes Not only is this possible it can be done while extracting electricity from the reaction. This is the key reaction in a hydrogen/oxygen fuel cell. Fuel cells have been known for well over a century and Hydrogen oxygen fuel cells have been used commercially since the 1930s. Platinum is often used as a catalyst for the key reaction in the cells.

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Platinum is a good catalyst for this reaction. This technique is well known. It has been developed in the 19th century by Döbereiner.

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Vitamin B-12 is a photocatalyst, see, for example, https://pubs.rsc.org/en/content/articlelanding/2018/ra/c7ra13037f#!divAbstract and also https://www.ncbi.nlm.nih.gov/pubmed/29271445 . I have used it and in sunlight, as radicals are formed, the solution gradually turns clear.

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