Recently, I calculated several isomers of a reactant. Moreover, I calculated the analogous reactions of them. Form my calculated results, the symmetry of the corresponding product is lowered as one isomer involved in the reaction. Is there a relation between the activation energy with respect to the symmetry of a reactant?
Yes, there can be a relation between symmetry and activation energy. Some reactions are classified as "symmetry forbidden." Start by reading up on the Woodward-Hoffmann rules
http://en.wikipedia.org/wiki/Woodward-Hoffmann_rules
You can also take a look at a couple of computational papers available on line. These are rather old, but the principle hasn't changed.
http://research.che.tamu.edu/groups/Seminario/publications/Secure/pubs/022_Energy%20barriers%20of%20symmetry-forbidden%20reaction.Local%20density%20functional%20calculations.pdf
http://www.qcc.ru/~tch/papers/009.pdf
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