Dynamic NMR

NMR is one of the few techniques that can provide dynamic information at the atomic level. It is able to do this because NMR parameters, like chemical shift, coupling constants and relaxation rates, are influenced by the immediate atomic environment. If the environment changes, then these NMR parameters are likely to change as well. The rate at which the environment changes affects how the NMR parameters appear in a spectrum. If the change is slower than the time taken to record that parameter then it is called "slow exchange", and multiple values of the NMR parameter are recorded. If the change happens faster than the time taken to record it then it is referred to as "fast exchange", and an averaged NMR parameter is detected. As an example, the temperature dependent chemical shifts of the thyroid hormone thyroxine are discussed below.

Thyroxine is an iodinated derivative of the amino acid tyrosine. It consists of a diphenyl ether with two iodines on both aromatic rings. The bulky iodines keep the rings perpendicular to each other so that the two protons on the hydroxyl-bearing ring are in very different atomic environments, as shown in the figure below. The figure shows the H2' proton above the alanyl-bearing aromatic ring, while the H6' proton lies in the plane of that ring.

The 1D ¹H NMR spectrum of thyroxine shows just two aromatic resonances. Symmetrical aromatic rings, like those in thyroxine, normally produce just one peak for symmetrical nuclei, so just two peaks from the four protons is not so unusual. If the three dimensional arrangement is considered, however, one might expect ring current effects to separate the H2' and H6' resonances. Since this is not the case either the ring currents do not affect the chemical shifts of H2' and H6', or the hydroxyl bearing ring is flipping rapidly enough about the axis  between the ether oxygen and the hydroxyl that a single averaged resonance is observed.

The stackplot below shows the aromatic region of a series of 1D ¹H spectra of thyroxine in methanol-d₄ recorded at decreasing temperatures. As the temperature is decreased the H2',6' resonance at 7.1 ppm broadens and separates into the two peaks labeled "distal" and "proximal". This indicates that the ring currents do affect the chemical shifts of H2' and H6' and that at room temperature these protons are rapidly exchanging their atomic environments. Lowering the temperature slows the exchange enough that the two chemical shifts can be measured.

The distal peak at 7.65 ppm is due to H2' or H6' when they are in the plane of the alanyl-bearing ring, while the proximal peak at 6.55 ppm is due to H2' or H6' when they are above the alanyl-bearing ring. The names indicate the positions of the protons with respect to the alanyl-bearing ring.

In the room temperature spectrum at the top of the stackplot the distal and proximal resonances are in fast exchange. Their environments exchange so rapidly that only an averaged chemical shift is recorded. For systems in fast exchange the position of the averaged resonance (δ_ave) is weighted by the populations (P) of the exchanging states (a,b...), i.e. for exchange between two sites

δ_ave = (δ_a⋅P_a + δ_b⋅P_b)/2

In the thyroxine case, there are two states in exchange, of very nearly equal populations, so the averaged resonance appears halfway between the resonances of the two states.

The spectra at the bottom of the stackplot show a system in slow exchange. Resonances are observed for each of the two states and integrating the peaks gives the relative populations of the states.

For a system like this, in which the rate of exchange can be controlled, a lot of information can be obtained. By measuring the chemical shifts of the two states and the temperature at which the resonances coalesce, the energy barrier at the coalescence temperature, ΔG^≠, can be obtained.¹ By fitting the lineshapes of the whole series of spectra to some rather complicated equations all three thermodynamic parameters ΔG^≠, ΔH^≠ and ΔS^≠, can be determined.²

You might have noticed in the stackplot that the H2,6 resonance at 7.9 ppm also starts to split as the temperature is lowered. This turns out to be due to the same exchange process that causes the H2',6' resonances to split, but it is more complicated than simple flipping of the hydroxyl bearing ring.^3,4

References
1. H. Kessler
"Detection of hindered rotation and inversion by NMR Spectroscopy"
Angew Chem Int Ed 1970 9(3):219-35

2. J. Sandström
"Dynamic NMR Spectroscopy"
Academic Press Inc, London 1982

3. B.M. Duggan and D.J. Craik
"Conformational dynamics of thyroid hormones by variable temperature nuclear magnetic resonance: the role of side chain rotations and cisoid/transoid interconversions"
J Med Chem 1997 40(14):2259-65.

4. B.M. Duggan and D.J. Craik
"¹H and ¹³C NMR relaxation studies of molecular dynamics of the thyroid hormones thyroxine, 3,5,3'-triiodothyronine, and 3,5-diiodothyronine."
J Med Chem 1996 39(20):4007-16.