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”
Intrinsic magnitude of generated dipole = I = 0, 1/2, 1, 3/2… Spinning nucleus generates a magnetic dipole (µ) Criteria for spin: Atomic mass Atomic # I Example even even 0 12C, 16O, 34S
odd odd or even half integer 1H (1/2); 13C (1/2); 15N (3/2)
even odd integer 14N (1), 2H (1) 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
#orientations with respect to an applied B = 2I+1
B0
In an external magnetic field (B0) spin ½ can align with the magnetic field or against it (2)(1/2)+1 = 2 ΔE energy difference magnetogyric ratio hγB0 γB0 γ ΔE= ν= resonant frequency 2π 2π ν The difference in energy between the two spin states depends on B: ΔE increases with B
β-spin
hν ΔE depends on B, so the frequency of light needed to flip the nuclei will depend on Energy B α-spin applied magnetic field (B)
4 Common NMR active nuclei 2πµ γ = hI
7 -1 -1 Nucleus Natural Abundance γ (10 radT s ) 1H 99.9844 26 753
13C 1.108 6 728
19F 100 25 179
31P 100 10 840
1 13 νC = 0.25νΗ For a B0 where ν=200 MHz ( H) ν ≈ 50 MHz ( C) Energy difference and population
The number of nuclei in the two states α and β are determined by Boltzmann distribution:
N upper = e-ΔE/kT Nlower
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) 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:
3 Sensitivity proportional to γ so: γ(13C) = ¼ γ(1H)
13 1 1 sensitivity C = /64 ( H)
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. Beffective=B0-Blocal
“bare” nucleus
Blocal electrons Energy
Beffective more Beffective electrons magnetic field at nucleus B0 Beffective=B0-Blocal
The resonant frequency for spin flips depends on Beffective (not B0) so different nuclei in the same molecule will have different resonant frequencies
O H H C C H H C O H Blocal H Energy
Beffective Beffective magnetic field at B0 nucleus 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
Classically: “continuous wave” instrument– sequentially irradiate at all frequencies in range and determine which wavelengths are absorbed (resonance frequencies).
10 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)
11 Table of chemical shifts δ
Note: the effects here are additive: e.g. H H C H δ=0.232 ppm H
H H C Cl δ=3.05 ppm H
H H C Cl δ=5.30 ppm Cl
H Cl C Cl δ=7.26 ppm Cl 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”
a int=3 CH3 a O C CH3 Recall that the integration int=1 only gives the ratio of the b H3C CH a 3 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 Splitting: signal from protons can be split into more than one peak
int=3 CH3 H H
H H
NO2
int=1 int=1 Energy two into gets “split” for the proton signal effect: additional an has carbons neighbouring on of protons The presence the spin down down spin neighbour neighbour neighbour 1 with proton for signals J J = “coupling constant” 1/2 B J o proton with no no with proton for signal neighbours neighbours 1/2 spin up up spin neighbour J a (next to field a lower half and next toα (be an field higher a experience will protons the half 1:1, approximately it ( decrease (if proton nearby at a field the local increase it either field; can magnetic its has own nucleus Each β ). β ). Since α ) or α : β ~ ) , int=3: 3 H CH3 a H H “singlet” (not split): no protons on neighbouring carbons b H H
NO2
Jab Jba int=1: 1 H int=1: 1 H “doublet”: 1 proton on “doublet”: 1 proton on neighbouring carbon neighbouring carbon
Jab=Jba position of unperturbed peak ∂Ha Each neighbouring proton splits the + signal + + + Energy Ha Jac Jac Hb C Jab C Bo Hc
If Jac = Jab (often true), middle peaks overlap: or triplet Energy
Bo “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
H H Br Br H H or 3 neighbours 1 Pascal’s triangle: each number is the sum of the numbers directly above it in 1 1 the triangle 1 2 1 singlet 1 0 neighbours doublet 1 1 1 neighbour triplet 1 2 1 2 neighbours quartet 1 3 3 1 3 neighbours quintet 1 4 6 4 1 4 neighbours sextet 1 5 10 10 5 1 5 neighbours heptet 1 6 15 20 15 6 1 6 neighbours octet 1 7 21 35 35 21 7 1 7 neighbours