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) More on this later! 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 The presence of protons on neighbouring carbons has an additional effect: the signal for the proton gets “split” into two signal for signals for proton with no proton with 1 neighbours Each nucleus has its own neighbour 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 neighbour neighbour higher field (be next to an α), spin down spin up and half a lower field (next to Energy a β). 1/2 J 1/2 J Bo J = “coupling constant” 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".