6.1 Determination of energetics of fluxional molecules by nmr  (Page 4/4)

Diverse populations

For unequal doublets (for instance, two protons exchanging with one proton), a different treatment is needed. The difference in population can be defined through [link] , where P _i is the concentration (integration) of species i and X = 2π Δv t (counts per second). Values for Δ v t are given in [link] .

The rates of conversion for the two species, k _a and k _b , follow k _a P _a = k _b P _b (equilibrium), and because k _a = 1/t _a and k _b = 1/t _b , the rate constant follows [link] .

From Eyring’s expressions, the Gibbs free activation energy for each species can be obtained through [link] and [link]

Taking the difference of [link] and [link] gives the difference in energy between species a and b ( [link] ).

Converting constants will yield the following activation energies in calories per mole ( [link] and [link] ).

To obtain the free energys of activation, values of log (X/(2π(1 + ΔP))) need to be plotted against ΔP (values T _c and Δ v 0 are predetermined).

Example of determination of energetic parameters

Normally ligands such as dipyrido(2,3-a;3′,2′-j)phenazine (dpop’) are tridentate when complexed to transition metal centers. However, dpop’ binds to rhenium in a bidentate manner, with the outer nitrogens alternating in being coordinated and uncoordinated. See [link] for the structure of Re(CO) ₃ (dpop')Cl. This fluxionality results in the exchange of the aromatic protons on the dpop’ ligand, which can be observed via ¹ HNMR. Because of the complex nature of the coalescence of doublets, the rate constants at different temperatures were determined via computer simulation (DNMR3, a plugin of Topspin). These spectra are shown in [link] .

The activation parameters can then be obtained by plotting ln(k/T) versus 1/T (see [link] for the Eyring plot). ΔS ^‡ can be extracted from the y-intercept, and ΔH ^‡ can be obtained through the slope of the plot. For this example, ΔH ^‡ , ΔS ^‡ and ΔG ^‡ . were determined to be 64.9 kJ/mol, 7.88 J/mol, and 62.4 kJ/mol.

Limitations to the approach

Though NMR is a powerful technique for determining the energetics of fluxional molecules, it does have one major limitation. If the fluctuation is too rapid for the NMR timescale (<1 ms) or if the conformational change is too slow meaning the coalescence temperature is not observed, the energetics cannot be calculated. In other words, spectra at coalescence and at no exchange need to be observable. One is also limited by the capabilities of the available spectrometer. The energetics of very fast fluxionality (metallocenes, PF ₅ , etc) and very slow fluxionality may not be determinable. Also note that this method does not prove any fluxionality or any mechanism thereof; it only gives a value for the activation energy of the process. As a side note, sometimes the coalescence of NMR peaks is not due to fluxionality, but rather temperature-dependent chemical shifts.

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