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)

More on this later!

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