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Topic: Why is the Kinetic Isotope Effect (H/D) larger for OH > NH > CH  (Read 5677 times)

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Offline questor

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I'm told that the kinetic isotope effect for Hydrogen/Deuterium is more pronounced when it is attached to oxygen as OH, than nitrogen as NH, and least prnounced as CH.

I thought it might have something to do with different electronegativities and the acidity of the hydrogen decreasing from OH to NH to CH, but I'm not sure.

It would be great if anyone had a deeper understanding of this than me.  Thanks!

Offline juanrga

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Re: Why is the Kinetic Isotope Effect (H/D) larger for OH > NH > CH
« Reply #1 on: May 05, 2012, 01:08:57 PM »
I'm told that the kinetic isotope effect for Hydrogen/Deuterium is more pronounced when it is attached to oxygen as OH, than nitrogen as NH, and least prnounced as CH.

I thought it might have something to do with different electronegativities and the acidity of the hydrogen decreasing from OH to NH to CH, but I'm not sure.

It would be great if anyone had a deeper understanding of this than me.  Thanks!

Kinetic isotope effects are due to the change in the masses.
Sharing unified knowledge in pure and applied sciences

Offline cheese (MSW)

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Re: Why is the Kinetic Isotope Effect (H/D) larger for OH > NH > CH
« Reply #2 on: May 05, 2012, 02:19:35 PM »
Kinetic Isotope Effects are only distantly related to the increased mass
(reduced mass in the Schrödinger Wave Equation). KIE is a quantum mechanical
effect.
Research zero-point energy and think about the strength of the bonds involved.

Offline questor

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Re: Why is the Kinetic Isotope Effect (H/D) larger for OH > NH > CH
« Reply #3 on: May 06, 2012, 07:16:06 AM »
Kinetic Isotope Effects are only distantly related to the increased mass
(reduced mass in the Schrödinger Wave Equation). KIE is a quantum mechanical
effect.
Research zero-point energy and think about the strength of the bonds involved.


OK, well I know that the wavenumber (proportional to both frequency and energy of the vibration) varies inversely with the reduced mass.  => which would lead to a higher ZPE for H-H than for D-D for example.

Now in the case of CH, NH and OH, I totally missed the point that the reduced mass takes into account both the isotope and the atom to which it is bonded.  I have calculated the reduced masses for each of CH, CD, NH, ND, OH and OD.  I found that going from C to N to O, the reduced masses all increase, as does the difference between the reduced masses.  So for OH/OD there is a bigger difference in the reduced mass than for CH/CD.  As difference in reduced mass increases, so does difference in ZPEs (from Hooke's Law, by way of wavenumber, frequency).

Given that in each case the maximum KIE value occurs when the transition state contains no vibrational structure involving the isotope, we can assume that magnitude of maximum KIE values are dictated solely by the difference in ZPEs. => This would lead to OH having a larger maximum KIE than CH, I think.

This is what I've come up with but I don't know if it is correct.

About bond strengths, in what way are they important for the Kinetic Isotope Effect?  I have found bond energies that suggest the order of strength in these 3 bonds as OH (strongest) > CH > NH (weakest).  This does not correlate with the order of OH > NH > CH for maximum kinetic isotope effects.

http://www.kentchemistry.com/links/Kinetics/BondEnergy.htm

Do you think I have made a mistake or on the right track?  I really appreciate that people come on this to share their knowledge it's great!!

Offline juanrga

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Re: Why is the Kinetic Isotope Effect (H/D) larger for OH > NH > CH
« Reply #4 on: May 06, 2012, 09:28:58 AM »
Now in the case of CH, NH and OH, I totally missed the point that the reduced mass takes into account both the isotope and the atom to which it is bonded.  I have calculated the reduced masses for each of CH, CD, NH, ND, OH and OD.  I found that going from C to N to O, the reduced masses all increase, as does the difference between the reduced masses.  So for OH/OD there is a bigger difference in the reduced mass than for CH/CD.  As difference in reduced mass increases, so does difference in ZPEs (from Hooke's Law, by way of wavenumber, frequency).

As stated before, Kinetic isotope effects are due to the change in the masses. If you substitute an atom by another atom by the same mass, no effect is observed; if you substitute and atom by an isotope of that atom, the effect is observed.

Effectively, the reduced mass is a function of the masses of the bonded atoms X-H.

mu = mX mH / mX + mH

When the mass of X is very large the reduced mass goes to

mu :rarrow: mH

and the effect on changing H by an isotope with a different mass (e.g. mD = 2 mH) is very large and, thus, the kinetic isotope effect is the greatest possible.

This explains why the kinetic isotope effect for Hydrogen/Deuterium is greater for OH > NH> CH.
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Offline cheese (MSW)

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Re: Why is the Kinetic Isotope Effect (H/D) larger for OH > NH > CH
« Reply #5 on: May 06, 2012, 02:14:21 PM »
My apologies for not getting back to you sooner (I am not in good health).   There is a policy on this forum (that I wholeheartedly agree with) that we do not spoon-feed answers to students.  (How are they going to learn to think for themselves if we do?)   I know the answer to this problem (well I think I do!) and as I stated reduced mass of E-H plays NO part in the rationalization of KIE, but the concept crops up in the explanation where you least expect it.  I looked up the Wikipedia entry for zero point energy and it was useless! (Sorry about that.) 
But http://en.wikipedia.org/wiki/Kinetic_isotope_effect is somewhat more informative:
Heavier atoms will (classically) lead to lower vibration frequencies, or, viewed quantum mechanically, will have lower zero-point energy. With a lower zero-point energy, more energy must be supplied to break the bond, resulting in a higher activation energy for bond cleavage, which in turn lowers the measured rate (see, for example, the Arrhenius equation).
Since we are dealing with the E-H bond in its ground state (νo) the first explanation is, in my opinion, not correct.  Once again I would like you to do some research: go to the following ref:
Advanced Organic Chemistry: Structure and Mechanisms 5th ed Francis A. Carey, Richard J. Sundberg
2007 p332 (in particular Fig 3.24) (C&S is the book for physical organic chem.)   My university library has an e-version of this text that you can read on line (amazing) but even googling can bring up the relevant discussion.  So read that discussion and report back (may the force be with you).
Yes, I also noted that the bond strengths are O-H>C-H>N-H (http://www.kentchemistry.com/links/Kinetics/BondEnergy.htm) but the N-H bond can be weaker than a C-H bonds, but the KIE (rate(N-H)/rate(N-D) can still be greater than the corresponding C-H/C-D system.  I am not an expert in this area but it may be difficult comparing apples with apples: N-H rxn cannot be same as C-H rxn.


Offline Enthalpy

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Re: Why is the Kinetic Isotope Effect (H/D) larger for OH > NH > CH
« Reply #6 on: May 07, 2012, 07:12:20 AM »
I fully agree with Juanrga's answer - unless, of course, someone can give good arguments against.

Especially hydrogen bonds are weakened by the movements of the hydrogen atom, more so with protium than deuterium because the displacement is bigger, and more so if the hydrogen holds on a heavier atom - plagiarizing.

Atoms move as well in the vibration ground state, which corresponds to the quantum delocalization.

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