Topic 1: Motional averaging of NMR interactions

Question 1

• … NMR interactions: …, … and … …
• … interactions depend on the … of the … with respect to …
• Anisotropic interactions depend on the geometry of molecules
• Motion changes … of molecules and parts of molecules influencing the … of anisotropic interactions measured with NMR

Answer 1

• Anisotropic NMR interactions: CSA, dipolar and quadrupolar couplings
• Anisotropic interactions depend on the orientation of the molecule with respect to B₀
• Anisotropic interactions depend on the geometry of molecules
• Motion changes orientation of molecules and parts of molecules influencing the magnitude of anisotropic interactions measured with NMR

Question 2

• Sketch the NMR spectra of an isotropic solution and a solid-state sample

Answer 2

• In isotropic, all anisotropic interactions averaged to 0
• In solid-state, all anisotropic interactions still present

Question 3

• How does dipolar coupling between 2 molecules vary with angle with respect to a magnetic field of a smaple in solution?

Answer 3

• If molecule samples all values of θ in a short time will result in an average of values –> isotropic tumbling (as can move in solution)

Question 4

• What is the overall average of anisotropic interactions in solution NMR? Use an equation to support your answer (don’t need to know equation, just output number)

Answer 4

• Interactions at all orientations cancel each other out with respect to magnetic field

Question 5

• In an isotropic solution only … interactions (don’t depend on … ) are retained leaving only … … and … coupling
• Anisotropic interaction (… , dipolar/… coupling) only influence spectra through … but not directly observable via …

Answer 5

• In an isotropic solution only isotropic interactions (don’t depend on B₀) are retained leaving only isotropic CS and J coupling
• Anisotropic interaction (CSA, dipolar/quadrupolar coupling) only influence spectra through relaxation but not directly observable via modulation

Question 6

• Using a sketch to describe molecular motion, describe the differences of solution and solid-state NMR

Answer 6

Question 7

• Describe the interaction in solid-state NMR and sketch the resulting powder spectra that results

Answer 7

• No overall tumbling present in solution as in static powders all orientations are present but no interchange present between them
• Pake pattern forms as sum of all orientations instead of an average
• D_c is the dipolar coupling constant

Question 8

• What can lead to averaging in solid-state NMR? How id the powder spectra effected?

Answer 8

• Local/internal motion will lead to averaging as forms an overall motion of molecules giving residual dipolar coupling (RDC)

Question 9

• Describe a method for selectively isolating interactions in solid-state NMR

Answer 9

• Magic angle spinning (MAS) simulates tumbling by spinning the sample, removing anisotropic interactions in doing so
• Recoupling uses pulses to interfere with MAS to bring back interactions of interest
• Motional averaging cannot be undone as random in nature
• RDCs can be measured under MAS

Question 10

• What parameter can be assigned to the measurement of amplitude of motion of a molecule?

Answer 10

• Order parameter (OP) is an expression for amplitude of motion which relates to how big the motion is.
• Static/rigid limit is the absence of motion (D_c), calculated from a known distance

Question 11

• An NH coupling has a measured dipolar coupling of 9230 Hz and a one-bond NH rigid limit of 11477 Hz. What is the order parameter associated with this coupling and the correlation time (τ­_c) associated with it?

Answer 11

• S² = (9230/11477)² = 0.67
• Only motion faster than the inverse of the dipolar coupling can average this coupling and contribute to the OP
• Inverse of dipolar coupling is correlation time; 1/(2π*11477) = 13 µs

Question 12

• Describe the scale of restriction of motion when varying the order parameter from one limit to the other

Answer 12

Question 13

• How can the use of deuterium help infer dynamics of systems that have indistinguishable hydrogens?

Answer 13

• Deuterium is a quadrupolar nucleus ²H (I = 1)
• Quadrupolar line shapes probe dynamics of a system, which can be compared to Hydrogen data

Question 14

• How does the source of residual dipolar coupling (RDC) vary from solid-state to solution NMR?

Answer 14

Question 15

• Is there a way to overall motion is present but not all orientations are sampled

Answer 15

• Yes, via an anisotropic solution, where molecules rotate around some but not whole 360^o axis

Question 16

• How can molecules be partially aligned to obtain solution RDCs?

Answer 16

• Different media can be used to enforce different alignment
• E.g. bicelles can be inserted to restrict the motion of proteins in a solution
• Not all orientations are samples so anisotropic interactions average to 0
• RDCs that are +ve/ -ve depending on media and direction of B₀, relate to amplitude of motions in a molecule

Question 17

• Overall motion averages … … so we observe only a fraction of …
• Amplitude of motion (… ) determines what fraction of … … is measured

Answer 17

• Overall motion averages dipolar coupling so we observe only a fraction of D_c
• Amplitude of motion (S²) determines what fraction of dipolar coupling is measured

Question 18

• How does the size of a motion relate to its order parameter?

Answer 18

• A bigger S² has a smaller amplitude of motion

Question 19

• What motions would contribute to the averaging of coupling in a system with a ¹³C-¹³C D_c ~ 2100 Hz) and a ¹H-¹³C (D_c ~ 24000 Hz) bond present? Would a motion of τ­_c = 30 µs average dipolar coupling?

Answer 19

• Only if frequency (1/ τ­_c) of motion is greater than coupling size will it contribute to averaging of coupling
• ¹³C-¹³C; only motions faster than 1/(2π*2100 Hz) = 76 µs will average
• ¹H-¹³C; only motions faster than 1/(2π*24000 Hz) = 13 µs will average
• A motion of τ­_c = 30 µs will average ¹³C-¹³C but not ¹H-¹³C dipolar coupling
• RDCs yield the amplitude of motions but only an upper bound for their timescales

Question 20

Summary of topic 1

• Motions average … interactions
• … … … (…) give cumulative amplitude of motions faster than inverse of the coupling
• Need … … in anisotropic liquids to get RDC in solution
• S² – order parameter gives generalised … … … , S² = 1, … ; S² = … , unrestricted motion; the rest is between 0-1

Answer 20

Summary of topic 1

• Motions average anisotropic interactions
• Residual dipolar coupling (RDC) give cumulative amplitude of motions faster than inverse of the coupling
• Need partial alignment in anisotropic liquids to get RDC in solution
• S² – order parameter gives generalised amplitude of motion, S² = 1, rigid; S² = 0, unrestricted motion; the rest is between 0-1