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Year 3 - Chemistry > Magnetic Resonance > Flashcards

Magnetic Resonance Flashcards

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1
Q

How does magnetic field strength change gap between spin states?

A

As B increases the energy gap increases

@ high B the frequency required is higher

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2
Q

What does magnetic momentum interact with?

A

Interacts with applied field to give resonance

orbit:
μs~l = γel

e- spin: μs~g0s = 2γes

nuclear spin (with spin angular momentum, uppercase i):
μN= γI

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3
Q

How does value of I change magnetic moment of a particle?

A

Non-zero spin quantum number I required to have a non-zero spin angular momentum I and therefore a magnetic moment μ

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4
Q

What are the Zeeman Eigenstates?

A

A single-spin (1/2) has 2 eigenstates of angular momentum on z-axis

ψ = |I,mI>

ψ+/- 1/2 = |1/2, +/- 1/2>

where + is α and - is β

where I (uppercase i) = spin angular momemntum qn
mI = spin proj q.n

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5
Q

What are the eigenstates of the Zeeman eigenstates?

A

Izψ = mI hbar ψ

Izψ1/2 = +1/2 hbar ψ1/2

Izψ-1/2 = -1/2 hbar ψ-1/2

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6
Q

What is the interaction energy between a field and a spin?

A

Classic:
E = -γ(hbar)mIB

QM:
H^onespin = -γB0I^z

H^onespinψ results in
Eα = -1/2 (hbar)γB0
Eβ = 1/2 (hbar)γB0

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7
Q

What is the resonance frequency from state α -> β?

A

ν = γB0/2π

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8
Q

What are allowed transitions between spin states?

A

ΔmI = +/- 1

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9
Q

What is the difference in population between α and β states?

A

Nβ/Nα = exp(-ΔE/kT) ~ 1 - ΔE/kT

ΔE small so can make approx, and population difference is minimal

Therefore insensitive technique

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10
Q

How does population difference of spin states effect sensitivity and how is it effected by field?

A

Net absorption depends on difference in population - therefore NMR insenstitive

Population diff inreases with B or γ, and decreasing temperature

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11
Q

What is the origin of shielding?

A

Orbiting e- creates magnetic fields which can oppose or reinforce B0

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12
Q

What is difference in energy and transition freq including shielding?

A

ΔE = hbar γB0 (1-σ)

v = B0γ(1-σ)/2π

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13
Q

What is lenz’ law?

A

ε = -N(ΔφB/Δt)
Induced emf gives rise to a current whose mag field opposes original change in flux (is why -ve)

where ε is emf, and the next part is change in flux

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14
Q

What is diamagnetic and paramagnetic shielding?

A

Diamagnetic - opposes B and so causes shielding, due to spherical charge distribution

Paramagnetic - can add to B so deshield, due to non-spherical charge distribution

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15
Q

What is the Lamb formula for diamagnetic shielding?

A

σd = (μ0e2/3me) ∫ rρ(r) dr
where ρ(r) is e- density

Assumes spherical elec distribution

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16
Q

What are some features of diamagnetic shielding?

A

Caused by spherically distributed ground state atom/molecules (from s orbitals)

Opposes B0

Proportional to e- density
1/r dependence

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17
Q

What are some features of paramagnetic shielding?

A

Caused by non-spherical distribution, from p and d e-

Augments B0 (is -ve)

Proportional to 1/ΔE and 1/r3

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18
Q

What is chemical shift?

A

Measure to relative inner standard (usually TMS)

δ = 106(σref - σ) = 106 (v-vref)/vref

Independent of B0

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19
Q

How does paramagnetic cause different shifts in TM complexes?

A

Paramagnetic shielding dominates, proportional to 1/ΔE
where ΔE is usually between t2g and eg

As stronger field ligands then smaller chemical shifts

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20
Q

What are some contributions to shielding other than dia/para?

A

Neighbouring group anisotropy
Ring current effects
Elec effects
Intermolecular interactions - H bonds, solvent interactions, etc.

H is e- poor and ΔE large so must consider these effects

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21
Q

What is anisotropy?

A

Property of being directionally dependent
Includes p,d, and f orbitals

Opposite is isotropy

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22
Q

What is magnetisation dependent on?

A

M = χ H

where M is magnetisation, H is magnetic field strength, χ is susceptibility

χ is directionally dependent so magnetisation is too
chemical shielding of nucleus hence depends on it too

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23
Q

What are neighbouring group contirbutions?

A

Occur due to currents induced in nearby groups of atoms

Effect is shield/deshield nucleus depending on geometry of group/nucleus

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24
Q

How is a point dipole different in each axis?

A

Bμy = 0

Bμz is where the spin is quantised

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25
Q

What is μpar and μper?

A

μpar is parallel to symm axis (z), and is larger

μper is perpendicular to symm axis (z)

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26
Q

How do ring currents cause shielding/deshielding?

A
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27
Q

What is the neighbouring group anisotropy in alkynes?

A
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28
Q

What is the neighbouring group anisotropy in alkenes?

A

Protons are deshielded

Above/below is shielded

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29
Q

What is the shielding that occurs due to ring currents from an aromatic ring?

A

Protons above/below ring shielded
Protons in plane of ring are deshielded

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30
Q

What are electric effects in chemcial shielding?

A

Charged/polar groups modify diamagnetic and/or paramagnetic currents by polarising local e- distributions and perturbation of ground and excisted state wavefn

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31
Q

What occurs to give splitting due to scalar spin-spin proton coupling?

A
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32
Q

What is the E difference between two spin-spin coupled atoms?

A

If two nuclei A and X
E = hJAXmAmX

where J is spin-spin coupling const (can be +ve or -ve)

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33
Q

What is the spin-spin coupling const proportional to?

A

J α γA γX

γ can be +ve/-ve, so J can be too

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34
Q

What is the splitting for A and X nulcei?

Weak coupling regime

A
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35
Q

How does J relate to Δv for two nuclei in different regimes?

A

Weak coupling: JAX &laquo_space; |vx - vA|

Mag equivalent:
JAX > |vx - vA|

Strong coupling:
JAX >= |vx - vA|

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36
Q

What is chemical equivalence?

A

2x nuclei which are:
1. spins of same isotopic species
2. molec symm which exchanges two spins

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37
Q

What is magnetic equivalence?

A

Nuclei which are:
1. Chemically equivalent
AND one of

all coupling const of nucleus i and j with all other nuclei of molecule l (this is an L)
Jil (that is an L) = Jjl
OR
No other spins in the molecule

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38
Q

What are the eigenvalues and splitting in weak coupling limit?

A

Result is two doublets

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39
Q

What are the eigenstates when there are equivalent nuclei?

A

ΔS = 0 means only two energy differences with the same frequency, gives one peak

40
Q

What is the hamiltonian for a two spin system (I and S)?

A

H^ = -ωII^z - -ωSS^z + (2πJ/hbar) I^ . S^

Where first two terms are interaction with field and 3rd is the interaction with eachother

Remember I is uppercase i

41
Q

What is the dot product of two spins I^.S^?

A

I^.S^ = I^xS^x + I^yS^y + I^zS^z

= 1/2(I^+S^-) + 1/2(I^-S^+) + I^zS^z

42
Q

How do you show the ket of a two spin system?

A

First term in ket is I and second is S
States include:
|αIαS>
|αIβS>
|βIαS>
|βIβS>

43
Q

How do operators I^z and S^z act on kets?

A

Where the ket doesnt matter

I^z|> = +1/2 | >

S^z|> = -1/2 | >

44
Q

How do the operators I^+/- and S^+/- work on different kets?

A

I^+|αI> = 0

I^-|αI> = |βI>

S^+|βS> = |αS>

S^-|βS> = 0

45
Q

What are the eigenstates in the strong coupling case?

A

|4> = |βIβS>

|3> = -sinθ|αIβS> + cosθ|βIαS>

|2> = cosθ|αIβS> + sinθ|βIαS>

|1> = αIαS>

46
Q

What is the coupling parameter?

A

tan2θ = J/δ

when θ=0 then is no coupling and when θ=3π/4

47
Q

What are the transitions seen in strong (or general) coupling?

A

Gives roofing

48
Q

What is the permutation operator and how is used for mag equivalent?

A

P^12 the hamiltonian for two mag equivalent nuclei (1&2) will remain unchanged

Exchange labels of two nuclei and then see what occurs

49
Q

What is the fermi contact interaction?

A

Is the origin of spin couplings

Mag interaction between an e- and an atomic nucleus

Crucially dependent upon s-electron char of ground and 1st excited state

50
Q

How is 3J dependent on dihedral angle?

A

3J = A + Bcosθ + Ccos2θ

This is karplus relationship

51
Q

How is the fermi contact interaction dependent on mag field and tumbling?

A

Mag field - not affected by strength or direction, so independent of spec frequency

Isotropic - no dependence on molec tumbling

52
Q

What is the range of 1J C-H coupling?

A

100-250 Hz

53
Q

What does through space coupling occur in solution and solid?

A

Solution: anisotropic quantity averages out due to tumbling
Bμx =! Bμy =! Bμz

Solids: doesn’t average out, leads to
∫ (3cos2θ-1)sinθdθ

for (3cos2θ-1) = 0, then θ=54.7 which gives a singlet

54
Q

What does the notation KAX denote?

A

Splitting in spectrum of X caused by dipolar coupling to A

55
Q

What does the fourier transform do?

A

Converts spectra from time to frequency domain

Results in product function which in peaks rather than a progression

56
Q

How does the life-time of a signal determine the signal broadness?

A

Signal broadens as lifetime decreases

57
Q

What are the advantages of fourier-transform NMR?

A
  • Increased sensitivity
  • Time saved means more spectra can be done and better signal:noise
  • Allows for using pulse-sequences
58
Q

What occurs during a pulse to spin states?

A

Phases of spins are random initially random

Mag field aligns the spins

59
Q

What is a rotating frame?

A

View spins from a frame that rotates with the field

Means the view is an apparent static field

60
Q

Why is a rotating frame required?

A

Freq of applied RF-field B1(t) close to spin resonance freq

The effect of the pulse tilts magnetisation vector away from z axis

B1(t) oscillates itself so rotating frame to view B1(t) required

61
Q

How does the rotating frame work?

A

Detail linear field as sum of counter-rotating circularly polarised components

Only component that rotates in same sense as Larmor preccesion of the spins is retained

62
Q

What occurs to magnetisation during a pulse in the rotating frame?

A

Rotates about z-axis with ang freq ωrf, a field B1

63
Q

What is nutation freq?

A

Angular freq of precession
ω1 = -γB1

64
Q

What is the angle through which M rotates?

A

β = -ω1tp

where tp is the length of pulse

65
Q

What is a 90-degree pulse?

A
66
Q

What is a 180-degree pulse?

A
67
Q

How do spins cause coherence?

A

Coherent EM radiation induces coherence amongst spins and causes orientations of individual mag moments in the x-y plane to not be random

68
Q

What is relaxation in NMR?

A

The population after a pulse returning to thermal eqm

69
Q

How does magnetisation increase with time?

A

Mz(t) = Meq (1 - exp[-(t-ton)/T1]

where T1 is the spin-lattice or longitudinal relaxation time in same direction as field (z)

70
Q

How does magnetisation decreases to eqm?

A

Mz(t) = Meq (1 - exp[-(t-toff)/T1]

where T1 is the spin-lattice or longitudinal relaxation time in same direction as field (z)

71
Q

What is the dependence of emission (relaxation) in NMR?

A

From Einstein coefficient:
A α v3

Therefore very slow for NMR

72
Q

How does magnetic interactions effect spin-lattice relaxation?

A

Instant local mag field might induce a radiationless transition if @ correct freq

Therefore can cause spin-lattice relaxation

73
Q

What is rotational correlation time, τc?

A

Time taken for root-mean-square deflection of the molecules to be about 1 radian

t &laquo_space;τc - close to original position
t&raquo_space; τc - lost all memory of position

74
Q

What is τc-1?

A

Root-mean square rotational frequency to reach 1 radian

75
Q

What is spectral density function, J(ω)?

A

J(ω) = 2τc/(1 + ω2τc2)

Chance that molecular tumbling leads to right freq to make a transition between energy levels

76
Q

What is the plot of spectral density function and tumbling rate?

A

Intermediate tumbling causes fastest relaxation

77
Q

What does spin-lattice relaxation time, T1, depend on?

A

Prob that local mag fields are oscillating at resonant NMR freq J(ω)

78
Q

What is spin-spin relaxation time, T2?

A

Time quantifies rate of decay of manetization within xy plane

Doesnt affect total amount of z-magnetization

79
Q

How do T1 and T2 depend on τc?

A

Same when fast tumbling wrt frequency

T1 >= T2
As full magnetization along z cannot be recovered unless all phase coherence has gone with T2

80
Q

What is observed orbital-wise when I > 1/2?

A

Nucleus possesses an electric quadrupolar moment additional to magnetic dipole moment

Leads to distribution of nuclear charge being ellipsoidal, so elec energy varies with orientation

81
Q

What do electric quadrupoles interact with?

A

Interacts with field gradients

NOT with uniform elec field

82
Q

What occurs to quadrupolar interaction in high symm?

A

High symm environ causes electric field gradients to cancel

Means no net quad interaction, so no effect seen

83
Q

How does quadrupolar effect spins?

A

Induces spin relaxation so causes line broadening

Loses multiplet splitting

84
Q

How can you measure spin-lattice relaxation?

A

Inversion-recovery experiment

85
Q

What is the pulse sequence in an inversion-recovery experiment?

A

Can measure τ1,2,3,4

Plot NMR signal vs τ

86
Q

How can you get T1 from an inversion-recovery measurement?

A

Plot ln[I - I(τ)] against τ
where I is the fully relaxed signal intensity

Then use following to get T1:
Mz(τ) = M0(1-2exp[-τ/T1])

87
Q

How can you measure the spin-spin relaxation time (T2)?

A

Spin-echo experiment

88
Q

What is the pulse sequence in a spin-echo experiment?

A
89
Q

What is the intensity of signal from a spin-echo experiment?

A

I(2τ) = I(0) exp(-2τ/T2)

90
Q

How does relaxation change the echo amplitude?

A

Random mag fields destroy phase coherence (which due to random molec motion)

Not refocused by p pulse

91
Q

What is the equation for line broadening according to spin-lattice relaxation?

A

Δv = 1/πT1

92
Q

What is the line broadening due to spin-spin relaxation?

A

Δv = 1/πT2

93
Q

What occurs to broadening at slow exchange rate?

A

Δv = kex = 1/πτ

2 separate sharp peaks observed

94
Q

What occurs to line broadening in intermediate exchange?

A

kex = πδv/Sqrt[2] ~ 2.2δv

A broad peak is observed (two lines merged)

95
Q

What occurs to line broadening in fast exchange?

A

Δv = π(δv)2/2kex = (π/2)(δv)2τ

Gives one sharp line (for two environments)

Year 3 - Chemistry (12 decks)

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