Nuclear Magnetic Resonance (NMR) E E increases with increasing magnetic field strength Boltzmann distribution at thermal equilibrium: N (m=-1/2) /N (m=+1/2) = e ( E/kT) with E = γ(h/2π)b o
NMR Physical Priciples Requirements Molecules must contain nuclei that have a nuclear angular momentum (or nuclear spin) quantum number I >0 which results in (2I + 1) magnetic quantum numbers (eigen states) m = + I, I -1, I -2,, - I +1,- I. All nuclei with odd mass, odd atomic number or both are NMR active: I = ½ for 1 1 H,13 6 C, 19 9 F, 31 15 P and I = 1 for 2 1 H, 14 7 N For NMR measurements magnetic nuclei must be in a magnetic field as the eigen states of m are degenerated in an non-magnetic environment. hν = E = γ(h/2π)b o E is the energy difference between the generated states and depends on the applied external magnetic field B o and the nucleus specific gyro-magnetic ratio γ. The energy differences, however, are very small for all nuclei and electromagnetic radiation of radio frequency is sufficient for their excitation (5-100 MHz at a field of 2.3 T).
Sample Preparation and Measurement The resonance frequency ν o for protons in 1 H-NMR are at 60 MHz in a 1.41 T magnetic field (100 MHz at 2.34 T, 300 MHz at 7.05 T, and 500 MHz at 11.7 T. The sample is dissolved in a solvent that does not contain the magnetic nucleus of interest and this is why deuterated solvents are used in 1 H-NMR: e.g. C 6 D 6, CDCl 3,or CCl 4. An NMR tube of 5 mm diameter is typically filled with 2 mg of compound dissolved in 0.5 ml of solvent ( 1 H-NMR) and spun in the magnetic field to average out field inhomogeneities.
Chemical Shift NMR would be useless if all protons in a sample had the same resonance frequency. Fortunately, the resonance frequency is slightly varied by the chemical environment of each proton. The frequency difference ν of a nucleus is measured relative to a standard (tetramethylsilane (TMS) for 1 H- and 13 C-NMR) and has been named chemical shift δ. δ is given in ppm. δ(x) = 10 6 ν/ν with δ(tms) = 0 H 3 C H 3 C TMS Example: The protons of a methyl group have a resonance frequency of 126 Hz lower than TMS at an observation frequency of 60 MHz. δ H (CH 3 ) = 10 6 (126/60*10 6 ) = 2.10 ppm Si CH 3 CH 3
NMR Scale The advantage of using the dimensionless ppm unit is that the scale is independent of the external magnetic field. Examples: 1 H-NMR with TMS as reference and 60 MHz resonance frequency. 1 H-NMR with TMS as reference and 300 MHz resonance frequency. 1 H-NMR with TMS as reference and 600 MHz resonance frequency. 600 Hz 0 Hz 3000 Hz 0 Hz 6000 Hz 0 Hz 10 ppm 0 ppm
NMR Scales ( 1 H-NMR) 3000 Hz 10 ppm 300 MHz, 7.05 T 0 Hz 0 ppm (downfield) higher frequency-less shielded (upfield) lower frequency-more shielded higher resolution 6000 Hz 10 ppm 600 MHz, 14.1 T 0 Hz 0 ppm
Field Strength Effect ( 1 H-NMR) 300 MHz H b H a H x CN 60 MHz
Chemical Shift and Molecular Structure The resonance position of a given nucleus is determined by its shielding constant σ. σ is made up of four terms, the diamagnetic shielding (σ dia,sorbitals), the paramagnetic shielding (σ para, p-orbitals), shielding due to neighbouring groups (σ intra ), and shielding due to intermolecular effects (σ inter ). σ can possess positive and negative values and is given by: σ = σ dia + σ para + σ intra + σ inter ν eff = (γ/2π)b o (1-σ) Shielding and deshielding effects are produced by local magnetic fields generated by circulating electron densities. Thus, changes in the local electron density will influence the chemical shift δ. A positive value of δ is left of TMS and means the nuclei under observation are deshielded relative to TMS. TMS has a high electron density around its protons and, thus, most protons in other compounds are less shielded and their chemical shift is positive.
Chemical Shift in 1 H-NMR diamagentic shielding σ dia diamagentic shielding anisotropy add electrons (not centrosymmetric) E = hν 0 = γb 0 h/2π, ν 0 = γb 0 /2π, with B local = B o (1-σ) σ is the electronic shielding of a specific proton and its resonance frequency with shielding is termed chemical shift δ; ν 0 = γb 0 (1-σ)/2π An increase in δ means a 1 H nucleus is deshielded relative to TMS and vice versa;
As δ depends on electron density around nuclei, the electronegativity of atoms close to the nuclei will affect the chemical shifts; The chemical shifts δ for H in H 3 CX with X = F, HO, H 2 N, H, Me 3 Si, or Li are 4.26, 3.38, 2.47, 0.23, 0.0, and -0.4 (very solvent depending), respectively; For example, we can deduced from the increasing ppm values in 1 H-NMR given below that Cl and C are more electronegative than H: H 3 CCl > H 2 CCl 2 > HCCl 3 R 3 CH >R 2 CH 2 > RCH 3 > CH 4 δ(ppm) 3.05 5.30 7.27 1.6 1.2 0.8 0.23
Electron Density and δ Electron density and, consequently, δ are influenced by hybridization (s- and p-character), the inductive effect (±i), and resonance (mesomerism) (±m); 4.18 H +m -i O 3.50 CH 3 1.30 CH 3 5.03 1.71 H sp 3 CH 3 sp 2 H H 4.97 5.70 hybridization H H 4.04 6.47 6.88 H -m H 3 C 1.71 -i CH 2 O O H 5.83 4.19
Electron Density and δ Hybridization of the carbon to which a proton is attached also influences the electron density around the proton; As the proportion of s-character increases form sp 3 to sp hybridization, bonding electrons move closer to the carbon and the proton becomes more deshielded; CH 4 0.23 0.86 0.86 5.25 5.25 1.96 1.96 1.96 1.96 sp 3 but very deshielded 4.00