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I am working on the derivation of the equation below for the difference in activation energies for the two reactions (1) and (2).

I've done the derivation, but I am unsure on some of the approximations I have used. When considering the activation energies I have just used the zero point energy for the C-H and C-D bonds - I am not sure why I can do that, but I assume its because the rest of the zero point energies cancel out.

Secondly I am confused why I can consider the transition states as isoenergetic, as to me they look like they would different energies.

Thank you for your help.

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When you deal with energies, absolute energies never matter. Energy only makes sense when you consider it relative to some reference point. For example, for standard values, we consider standard states. You're perfectly fine declaring that both TS's have the same energy because you're not comparing them to each other; you're comparing them to two ground states.

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H and D each have 1 electron so the electronic energy can be considered to be the same. In calculating energy of the vibrational quanta then the difference in mass becomes important, as you indicate, via $E = \frac{h}{2\pi}\sqrt{k/\mu} \pu{~~(J/molecule)}$ where k is the force constant, equal for C-H and C-D bonds, and $\mu $ is the reduced mass $m_1m_2/(m_1+m_2)$.

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