Chapter 13: Molecular Structure By Nuclear Magnetic Resonance Specroscopy

Question 1

Define spin quantum number, I

Answer 1

A fixed property of a nucleus that describes the angular momentum of the particle. It can be 0, a positive half-integer, or an integer.

Question 2

What are the possible values for spin number and what are the conditions for each?

Answer 2

Zero: even number of both protons and neutrons
Integer: odd number of both protons and neutrons
Half integer: any other case

Question 3

What are the properties of a nuclei with a spin quantum number that does not equal 0

Answer 3

• It has an angular moment with a magnitude of: |I^2 | = I · I = ħI(I + 1)
• Along the each axis, a component of the angular moment, m_I ħ, acts where -I ≤ m_I < I. The z-axis is the assumed direction of an applied magnetic field.
• It has a magnetic moment which has a constant magnetic field and orientation; this is determined by the value of m_I.

Question 4

What is the equation for the number of possible orientations for the magnetic moment of a nucleus?

Answer 4

2I + 1

I = spin quantum number

Question 5

Give the equation for the magnetic moment in terms of the angular moment

Answer 5

µ = magnetic moment
I = angular moment
γ = gyromagnetic moment

Question 6

Give the equation for the interaction energy between a magnetic moment and an external magnetic field

Answer 6

E = energy
µ = magnetic moment
B_0 = external magnetic field

Question 7

Give the equation for the interaction energy between a magnetic moment and a static external magnetic field (along the z-direction)

Answer 7

E_mz = interaction energy
µ_z = angular moment in z-direction
γ = gyromagnetic constant
B_0 = static external magnetic field
m_I = possible orientations

Question 8

The different alignments of a nucleus have different ________.

Answer 8

Energies

Question 9

Give the equation for the Larmor frequency

Answer 9

ν_L = Larmor frequency (Hz)

Question 10

Without an external magnetic field, the energies are ____ and _________ (equal energy levels for all Eigenvalues of m).

Answer 10

Zero
Degenerate

Question 11

What is the Zeeman effect?

Answer 11

The observation that the degeneracy of the energy levels is lifted (energy levels are no longer degenerate) when the nuclei are exposed to a static magnetic field.

Question 12

Describe an example of the Zeeman effect for parallel and antiparallel alignment (via an equation and graph)

Answer 12

Question 13

The polarisation of the spin system can also be calculated using the _______ ________ between the two energy levels.

Answer 13

Fractional difference

Question 14

Give the equation for the polarisation of a spin system

Answer 14

N_α = population occupying parallel alignment
N_β = population occupying antiparallel alignment
∆E = difference between two energy levels
k_B = Boltzmann constant
T = temperature
γ = gyromagnetic constant

Question 15

Outline the process of NMR spectroscopy

Answer 15

Transitions between energy levels are induced in samples that are radiated with a resonant magnetic field that oscillates with a Larmor frequency. This is done by sending a ‘radio-frequency pulse’ that matches the Larmor frequency. Pulses, known as π/2 pulses, are sent to generate a phase coherence in the population of spins. This is detected using Faraday’s law because the magnetic flux density changes, so a weak emf is generated in a coil placed around the sample.

Question 16

What is a chemical shift in NMR?

Answer 16

The shift in the external magnetic field due to a local magnetic field being generated by electrons in the sample material. This is different for different chemical groups.

Question 17

Give the equation for the field generated as a result of the interaction between the local and external magnetic fields

Answer 17

∂B = induced magnetic field
σ = shielding constant
B_0 = external magnetic field

Question 18

Give the equation for the Larmor (resonance) frequency, considering the effects of a local magnetic field

Answer 18

ν_L = Larmor frequency
B_loc = local magnetic field
B_0 = external magnetic field

Question 19

Give the equation for the chemical shift compared to a reference standard

Answer 19

∂ = chemical shift
ν_L = Larmor frequency
ν_TMS = resonant frequency of TMS

Question 20

Which factors impact the resonant frequency of a sample?

Answer 20

The number of magnetic nuclei which impacts the size of local magnetic field and the resonant frequency.

Question 21

Give the equation for the energy levels for two spins that aren’t interacting

Answer 21

m_A, m_X = secondary spin quantum numbers

Question 22

Define scalar coupling

Answer 22

The level by which spins within a sample interact defined by the scalar coupling constant, J.

Question 23

Give the energy level equation for two spins when scalar coupling exists between them

Answer 23

Question 24

How do the energy levels between two spins change when there is scalar coupling?

Answer 24

There are the same number of energy levels but they have a difference in energy. This means that complex coupling patterns and spectra are produced (which can be calculated using Pascal’s triangle).

Question 25

What is the use of NMR?

Answer 25

To acquire 2-dimensional spectra to make correlations between nuclei and their differing frequencies. This can be done for correlations between two of the same type of nuclei in different chemical environments (COSY) or two different types of nuclei in the same chemical environment (HSQC).

Question 26

What is the purpose of the Nucelar Overhauser effect?

Answer 26

To measure the distance between individual nuclei using NMR spectroscopy. The peaks in the graphs produce reflect how close two nuclei are.

Question 27

What is the difference between the NOESY and COSY techniques?

Answer 27

COSY requires J-coupling while NOESY doesn’t.

Question 28

What are the uses of NMR in biophysics?

Answer 28

To determine the structure of proteins, including the amino acid sequence and the £D configuration via distance measurements.

Question 29

How do NMR and X-ray diffraction differ?

Answer 29

NMR does not require protein crystallisation so efficiency is increased as they proteins can be measured in solution.

Question 30

Outline the Nuclear Overhauser effect (NOE) in the case where there are 4 possible energy levels and 4 possible transitions between them

Answer 30

• From Boltzmann, it is known that the lowest energy level will have the greatest population.
• The populations can be equilibrated by applying a radiofrequency pulse with a frequency, v_1.
• Relaxation will reverse the effects of the pulse and the populations will, generally, follow relaxation pathways with characteristic frequencies, v_1 and v_2, to do this.
• If strong dipolar interactions are involved, the population will take a pathway from the highest energy level directly to the lowest one.
  -If this pathway is efficient all of the populations will redistribute themselves into a new arrangement that would provide a higher signal intensity if another pulse was sent.