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Which would have a smaller nitrogen inversion barrier: $\ce{NMe3}$ or $\ce{N(i-Pr)2Me}?$

I think that $\ce{NMe3}$ should have a smaller inversion barrier as it is less bulky, but data shows otherwise. Are there some other effects that contribute to the inversion barrier that I might not know of?

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    $\begingroup$ You says "data shows otherwise," so would you kindly show that data? $\endgroup$ – Mathew Mahindaratne May 12 '20 at 16:19
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    $\begingroup$ @Mathew Mahindaratne: This very Question is given in MS chauhan organic chemistry book, so OP probably would have got it from there $\endgroup$ – user600016 May 20 '20 at 12:17
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So I thought about this for a bit and I think I have an answer. Be warned, I might be wrong.

The inversion process involves a conversion from $\mathrm{sp^2}$ to $\mathrm{sp^3}$. So $\mathrm{sp^2}$ hybridization increases angle between these bulky groups, which would be in fact favorable. Hence the low activation energy.

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    $\begingroup$ Yes, your thinking is correct. However, since the roughly tetrahedral ground state is ~$\ce{sp^3}$ hybridized while the planar TS for inversion is ~$\ce{sp^2}$ hybridized one would more likely say that you convert $\ce{sp^3}$ to $\ce{sp^2}$. But your argument that the steric destabilization is greater in the ground state than the TS thereby reducing the activation energy more in the di-isopropyl case is correct. $\endgroup$ – ron May 12 '20 at 19:21
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Barriers to intramolecular motions, which lead to inversion, are intimately related to the configurational identity of a molecule ($\ce{XY3}$). These barriers turn out to be most sensitive to changes in $\nu_2$ (the frequency of symmetrical deformation vibration) and $\ce{Y-X-Y}$ angle ($\alpha$) of $\ce{XY3}$ (Ref.1). The inversion is assumed to take place by a gradual increase in the amplitude of the $\nu_2$, until the molecule passes through plainer configuration (Ref.2). The values of the barriers have mostly been calculated mathematically. In fact, one of the long-standing problems of stereochemistry is that of determining barriers of nitrogen in amines, which has been assumed at time that barriers must be too small to be determined experimentally. No quantitative estimates were reported prior to the discovery that the barriers in aziridines are large enough to study by the dynamic NMR methods (Ref.3), which lying in the range $\pu{10-15 kcal/mol}$. For example, the activation energy for N-methylaziridine (1-methylaziridine) is found to be $\pu{19 \pm 3 kcal/mol}$ (Ref.4 & 5) while that of N-methyl-2,2-dimethylaziridine (1-methyl-2,2-dimethylaziridine) is found to be $\pu{10 kcal/mol}$ (pure compound; Ref.6). Further, when $\Delta E$ is measured for 1-methyl-2,2-dimethylaziridine in methanol and $\ce{CCl4}$, the values obtained are $\pu{6.8 kcal/mol}$ and $\pu{7.8 kcal/mol}$, respectively. The authors attributed this decrease of activation energy for both polar and non-polar nature of relevant solvents. The also explained the extra reduction of activation energy in methanol due to H-bonding of hydroxyl group of methanol with nitrogen lone pair in aziridine. However, the authors have admitted that they cannot explain the large difference in $\Delta E$ between 1-methylaziridine and 1-methyl-2,2-dimethylaziridine.

The mathematical estimated activation barrier of trimethylamine was found to be $\pu{7.5 kcal/mol}$ ($\pu{31.4 kJ/mol}$). The experimental value was found to be $\pu{10-11 kcal/mol}$, which was determined by indirect NMR methods (Ref.7). The first direct experimental measurement to barrier to nitrogen inversion in a simple acyclic amine, dibenzylmethylamine has been made using dynamic NMR techniques. The barrier was reported as $\pu{6.7\pm 0.2 kcal/mol}$ in vinyl chloride solution at $\pu{-135 ^\circ C}$ , which has agreed well with that of the calculated theoretical value (Ref.8).

As explained before, these barriers turn out to be most sensitive to changes in $\ce{Y-X-Y}$ angle ($\alpha$) of $\ce{NY3}$. Using any molecular modeling software, one can show that when bulkiness of $\ce{Y}$ increase the $\alpha$ increases. For example, using online software provided by ChemEd DL, one can calculate $\ce{H-N-H}$ angle of $\ce{NH3}$ as $107.2^\circ$ while $\ce{C-N-C}$ angle of $\ce{N(CH3)3}$ is $110.9^\circ$. Further, $\ce{C-N-C}$ angle of $\ce{N(CH2CH3)3}$ is $111.9^\circ$. Therefore, it is safe to assume that activation barrier of diisopropylamine is smaller than that of trimethylamine similar to competitive values of trimethylamine and dibenzylmethylamine.


References:

  1. Gerald W. Koeppl, Dalius S. Sagatys, G. S. Krishnamurthy, Sidney I. Miller, “Inversion barriers of pyramidal ($\ce{XY3}$) and related planar (($\ce{=XY}$) species,” J*. Am. Chem. Soc.* 1967, 89(14), 3396-3405 (https://doi.org/10.1021/ja00990a004).
  2. Ralph E. Weston Jr., “Vibrational Energy Level Splitting and Optical Isomerism in Pyramidal Molecules of the Type $\ce{XY3}$,” J. Am. Chem. Soc. 1954, 76(10), 2645-2648 (https://doi.org/10.1021/ja01639a012).
  3. Albert T. Bottini, John D. Roberts, “The Nitrogen Inverson Frequency in Cyclic Imines,” J. Am. Chem. Soc. 1956, 78(19), 5126-5126 (https://doi.org/10.1021/ja01600a083).
  4. H. S. Gutowsky, “Chemical Shifts and Electron-Coupled Spin-Spin Interactions,” Ann. N.Y. Acad. Sci. 1958, 70(4), 786-805 (https://doi.org/10.1111/j.1749-6632.1958.tb35431.x).
  5. J. P. Heeschen, Ph.D. Dissertation, University of Illinois, ILL, 1959.
  6. A. Loewenstein, John F. Neumer, John D. Roberts, “The Activation Energy of Inversion in Substituted 1-Methylaziridines (N-Methylethylenimines) Measured by the Nuclear Magnetic Resonance Technique,” J. Am. Chem. Soc. 1960, 82(14), 3599-3601 (https://doi.org/10.1021/ja01499a030).
  7. Martin Saunders, Fukiko Yamada, “Measurement of an Amine Inversion Rate Using Nuclear Magnetic Resonance,” J. Am. Chem. Soc. 1963, 85(12), 1882-1882 (https://doi.org/10.1021/ja00895a049).
  8. Michael J. S. Dewar, W. Brian Jennings, “Barrier to pyramidal inversion of nitrogen in dibenzylmethylamine,” J. Am. Chem. Soc. 1971, 93(2), 401-403 (https://doi.org/10.1021/ja00731a016).
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