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D, the kinetic isotope effect measured by comparing the rate of reaction with protonated substrate to that with deuterated substrate; and 1-D, 2-D, one-dimension, two-dimension, respectively.
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1842272427
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note
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The term "hydrogen transfer" is often used loosely to describe reactions involving hydrogen (atom), proton, or hydride particles, even though their chemical properties are remarkably different. Unless specifically mentioned, we will use the term "hydrogen" when referring to a particle that could be any one of the three - hydride, hydrogen atom, or proton.
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The area of a triangle is linearly proportional to its height, therefore for a symmetric 1-dimensional barrier the energy of activation would be proportional to an integration of the potential over the reaction pathway. In this case, the ratio of energies of activation for H and D would be given by the ratio of the respective integrated potentials, with other constants canceling out.
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56
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1842388025
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As a note, in the opposite scenario, whereby K(x) reaches a minimal value at x = 0 (i.e., a "loose transition state"), the height of the potential barrier (the "activation energy") is decreased compared to the one-dimensional model described above, and it is decreased to a greater extent for hydrogen than for deuterium. Since even the one-dimensional calculations produced isotope effects larger than the experimental results as seen in eq 7, this regime is obviously not the explanation for the isotope effects observed in the lipoxygenase reaction.
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