Lecture 4: NMR Flashcards
What is the physical basis of NMR?
• Nuclei have a property of spin (0, 1/2, 1, 2 etc). This depends on the isotope e.g. 1H, 13C and 15N are 1/2. If a nuclei’s spin is not zero, it has a value of I. There are multiple spin states available, the number being 2I + 1. For example, there are 2 states for I= 1/2.
• When a strong magnetic field (B0) is applied, the spin states have different energies. The magnetic field direction, is defined as the z axis. The energy differences all fall in the radio frequency range (30-1000 MHz).
• A nucleus with spin has a magnetic moment (μ). μ has the property of angular momentum, the tendency to continue spinning. μ interacts with the magnetic field, like a compass needle. This interaction leads to precession, similar to a spinning top. The precession frequency is known as ω.
ω = γB0
γ is a constant, it depends on the nucleus type.
• When I = 1/2, spins have two allowed directions, which correspond to the two energy levels. There is a slight excess (1001 vs 1000) in the lower energy state at equilibrium with net magnetization (M) along Z. M has a magnitude proportional to ng - ne. NMR detects changes in the orientation of M.
• A radio frequency is applied as pulses at right angles to B0 in resonance with the rotation spins. The pulses are at different length (t, 2t etc). The pulses induce a reorientation of M. NMR experiments are sequences of rf pulses and delays. A t pulse gives a 90 degree change to the xy plane. while 2t gives a 180-degree reorientation.
• When M moves to the xy plane, it produces a transient rf signal (free induction decay) that we can detect. The FID can be converted from the time domain to the frequency domain by a Fourier transform.
What is chemical shift?
Nuclei are shielded from the applied magnetic field by electron clouds. These clouds are sensitive to their bonding and environment. The shielding. The degree of shielding is characterised by chemical shift (δ). It is measured in ppm.
For NMR we use a reference frequency (0 ppm) for the methyl group for DSS. δ=(frequency of signal-frequency of reference )/spectrometer frequency×1,000,000 Chemical shift is sensitive to changes in chemistry and environments. This is the basis for NMR resolution. The shift is sensitive to protein structure. Each amino acids has a different environment and a unique chemical shift
What is relaxation?
After a rf pulse to the xy plane, M will eventually return to Mz.
• Recovery rate of Mz is directly proportional to 1/T1. T1 relaxation occurs along the B0 field directional (longitudinal). It can be measured using an inversion recovery experiment. M is inverted from z to -z at t = 0, but then recovers along the z direction. Recovery is exponential with a rate constant 1/T1.
• The decay rate of Mxy is directly proportional to 1/T2. T2 relaxation occurs in the xy plane (transverse). It is measured from the decay rate of the FID and linewidths. The FID contains information about the decay rate in the xy plane. The peak linewidth at half height in the frequency domain (Δv1/2) inversely depends on T2 {Δv1/2 = (1/πT2). A longer T2 means narrower peaks, so a higher spectral resolution.
Relaxation rates can tell us about distances and molecular dynamics.
- In biological systems the main relaxation mechanism arises from magnetic dipole interactions between nuclei. If two dipoles X and Y are close in space (less than 6 Angstroms) then X will create a local magnetic field (Bloc) which is felt by Y. The magnitude depends on distance (r) and the angle between B0 and X-Y. As X-Y moves through solution, Bloc at Y fluctuates.
- Slow motion gives fewer Bloc fluctuation frequencies, but the fluctuations are more intense. Fast motion creates a wide range of fluctuation frequencies. Fluctuations at the right frequency (ω0) cause transitions between energy levels and equilibrium being re-established.
- We characterise molecular tumbling in solution with tc (correlation time). The larger the molecule, the slower it tumbles. Relaxation behaviour is thus a function of tc.
- The plot of T1 vs tc goes through a minimum; T1 gets longer again at slow tc because frequency spectrum does not contain the right components (e.g. at ω0). T2 is also affected by low frequencies so it does not go through a minimum.
- Relaxation depends on the amplitude of Bloc, which depends on separation and the number of dipole neighbours. Relaxation is proportional to nf(tc) r-6. f(tc) is different for T1 and T2. This is the basis of NMR as a structural tool.
- Some system have free electrons from radicals and metal ions. The dipole moment of an electron is 658 times larger than a proton so it has a much bigger relaxation effect. There is very fast relaxation.
