NMR spectroscopy
• Not a single technique but a large set of related techniques
• “simple” 1H-NMR • 13C NMR • 2D experiments
1
Nuclear Spin Angular momentum of spinning charge described by quantum spin number “I”
I = 0, 1/2, 1, 3/2…
Intrinsic magnitude of generated dipole =
Criteria for spin: Atomic mass
even
odd
even
Atomic # even
odd or even
odd
I 0
half integer
integer
Example 12C, 16O, 34S
1H (1/2); 13C (1/2); 15N (3/2)
14N (1), 2H (1)
Spinning nucleus generates a magnetic dipole (µ)
Spin ½ nuclei in magnetic field (e.g. 1H and 13C)
In the absence of a magnetic field, these spins have the same energy and are randomly aligned
In an external magnetic field (B0) spin ½ can align with the magnetic field
or against it (2)(1/2)+1 = 2
B0
#orientations with respect to an applied B = 2I+1
4
Ene
rgy
applied magnetic field (B)
The difference in energy between the two spin states depends on B: ΔE increases with B
α-spin
β-spin
hν ΔE depends on B, so the frequency of light
needed to flip the nuclei will depend on
B
ΔE= hγB0 γ magnetogyric ratio
2π ν=
γB0
2π
ΔE energy difference
ν resonant frequency
Common NMR active nuclei
Nucleus
1H
13C
19F
31P
Natural Abundance
99.9844
1.108
100
100
γ (107 radT-1s-1)
26 753
6 728
25 179
10 840
γ = 2πµ
hI
ν C = 0.25νΗ For a B0 where ν=200 MHz (1H) ν ≈ 50 MHz (13C)
Energy difference and population
Since the α-spin state is lower in energy, it is more populated (more nuclei have α than β). The difference in energy is very small (~0.00003 kcal/mol), so the ratio of populations is α: β = 1.000000 : 0.999995 (32 ppm)
The number of nuclei in the two states α and β are determined by Boltzmann distribution:
Nupper
Nlower
= e-ΔE/kT
Sensitivity Sensitivity is partly related to Nupper/Nlower
(larger difference, larger signal)
Therefore higher B0, larger ΔE, larger signal, more sensitive
Sensitivity is also strongly dependent on g:
Sensitivity proportional to γ3 so: γ(13C) = ¼ γ(1H)
sensitivity 13C = 1/64 (1H)
And natural abundance for 13C ≈ 1% so 1H ≈ 6000 times more sensitive
Electrons have their own magnetic fields (Blocal) that “shield” the nucleus fromthe applied magnetic field (B0): the magnetic field at the nucleus (Beffective) will be less than the applied field. The more electrons around a nucleus, the higher Blocal and the lower Beffective.
Ene
rgy
magnetic field at nucleus
Beffective=B0-Blocal
B0
Blocal
Beffective
Beffective
“bare” nucleus
electrons
more electrons
Beffective=B0-Blocal E
nerg
y
magnetic field at nucleus
B0
Blocal
Beffective Beffective
The resonant frequency for spin flips depends on Beffective (not B0) so different nuclei in the same molecule will have different resonant frequencies
CC
O
O
CH
H
HH
H
H
increasing resonant frequency
chemical shift (δ) ppm
Upfield (lower ppm): higher B0 to achieve same resonant frequency Downfield (higher ppm): lower B0 to achieve resonant frequency
Acquisition of spectra
10
Classically: “continuous wave” instrument– sequentially irradiate at all frequencies in range and
determine which wavelengths are absorbed (resonance frequencies).
11
An alternative (better) approach: the sample is
simultaneously irradiated with a short pulse over all frequencies in
the range (“broad band irradiation”) and the relaxation of the molecule to the ground state
is monitored as a function of time. This results in an interferogram,
which contains all of the frequency information. To get from a “FID” to an NMR spectrum, a Fourier Transform must be applied (time
domain to frequency domain)
Table of chemical shifts Note: the effects here are additive:
e.g. δ=0.232 ppm
δ=3.05 ppm
Cl CH
ClCl
H CH
ClCl
H CH
HCl
H CH
HH
δ=5.30 ppm
δ=7.26 ppm
δ
Integration The area under a peak is proportional to the relative number of
protons that give rise to that peak. This area is called the “integration”
O C
CH3
CH3
CH3H3C
a
a
ab
int=3"
int=1"Recall that the integration only gives the ratio of the protons, not the absolute
number (9:3 = 3:1)
Chemical Shift Equivalence Two protons are said to be chemical shift equivalent (i.e.
they have the same chemical shift and do not couple to one another) if:
-they can be interconverted by a symmetry operation (rotation, reflection, or inversion center)
and/or- -they are can interconvert rapidly on the NMR timescale
int=3 CH3
NO2
H
H H
H
int=1 int=1
Splitting: signal from protons can be split into more than one peak
Ene
rgy
Bo
The presence of protons on neighbouring carbons has an additional effect: the signal for the proton gets “split” into two
signal for proton with no neighbours
signals for proton with 1 neighbour
Each nucleus has its own magnetic field; it can either increase the local field at a nearby proton (if α) or decrease it (β). Since α:β ~ 1:1, approximately half the protons will experience a higher field (be next to an α), and half a lower field (next to a β).
J = “coupling constant”
1/2 J 1/2 J
neighbour spin up
neighbour spin down
int=3: 3 H
“singlet” (not split): no protons on neighbouring carbons
CH3
NO2
H
H H
H
int=1: 1 H
“doublet”: 1 proton on neighbouring carbon
int=1: 1 H “doublet”: 1 proton on neighbouring carbon
a
b
Jab=Jba
Jab Jba
Each neighbouring proton splits the signal
Ene
rgy
Bo
+ + ++
position of unperturbed peak ∂Ha
Ene
rgy or
Bo
Jac
CCHb
Hc
Ha Jac
Jab
If Jac = Jab (often true), middle peaks overlap: triplet
“Equivalent” protons: protons that are in identical environments (e.g. on the same carbon, or equivalent because of molecular symmetry).
Equivalent protons do not split each other!
1,2-dibromoethane
BrBrH H
H H
or
3 neighbours
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
15 6 1 1 6 15 20
1 7 21 35 35 21 7 1
1 1 1
1 2 1 0 neighbours"
1 neighbour"
2 neighbours"
3 neighbours"
4 neighbours"
5 neighbours"
6 neighbours"
7 neighbours"
singlet"
doublet"
triplet"
quartet"
quintet"
sextet"
heptet"
octet"
Pascal’s triangle: each number is the sum of the numbers directly above it in the triangle