Chapter 7 Nuclear Magnetic Resonance Spectroscopy I. Introduction 1924, W. Pauli proposed that certain atomic nuclei have spin and magnetic moment and exposure to magnetic field would lead to energy level splitting. 1946, Bloch & Purcell demonstrated that nuclei absorb EM radiation in strong field as a consequence of energy level splitting; shared Nobel prize in 1952. II. Theory of Nuclear Magnetic Resonance (A) Magnetic Properties of Nuclei i/. Nuclear Spin Certain nuclei, when placed in magnetic field, behave as spinning charged particles. Nuclei that possess this property have angular momentum, p. Spinning nuclei generate magnetic moments, µ, which orient along axis of spin. µ = γ p where γ = magnetogyric ratio TABLE 7-1. "Carrington" Table 1.1 (p. 2). 1
From quantum mechanics, maximum observable component of p is quantized and must be integral or half-integral multiple of h/2π, where h = Planck s constant. Also, values for p, depends on nuclear spin quantum number, I. i.e., µ = γ (h/2π) I Angular momentum has m = 2I + 1 states (-I, -I + 1,..., I - 1, I), where m indicates allowed orientation of magnetic moment in magnetic field, called magnetic quantum number). In absence of magnetic field, various states have identical energies. e.g., For I = ½, m = +½ and m = -½. Protons and neutrons both have spin quantum number of ½. Depending on how these particles pair up in nucleus, resultant nucleus may or may not have net non-zero nuclear spin quantum number, I. FIGURE 7-2. "Drago" Fig. 7-1 (p. 188). 1. If spins of all particles are paired, i.e., no net spin and I = 0. Nuclei with even numbers of both protons and neutrons all belong to this type, e.g., 16 O, 12C, 32 S. 2. When I is ½, one net unpaired spin which imparts nuclear magnetic moment to nucleus. Distribution of positive charge in nucleus is spherical. 3. When I 1, nucleus has spin and nuclear charge distribution is non-spherical, said to possess quadrupole moment, Q. For spherical nucleus, Q = 0. Q > 0 charge is oriented along direction of principal axis. Q < 0 charge is accumulated perpendicular to principal axis. ii/. The Nucleus in a Magnetic Field Applied magnetic field, B 0, exerts force or torque, on nucleus with magnetic moment, causing it to precess about applied field. = μ B 0 FIGURE 7-3. "Skoog" Fig. 14-2 (p. 314). From classical mechanics, ν 0 = (γ/2π) B 0 where ν 0 = Larmor frequency, frequency of nuclear moment precession in cycles/s 2
(B) The NMR Transition i/. Energy Levels in a Magnetic Field When nucleus with I = ½ is brought into external magnetic field B 0, its magnetic moment becomes oriented in one of two directions with respect to field, depending upon m. From quantum mechanics, energy levels for system is given by E = (γmh/2π) B 0 where m = ±½ Difference in energy between two states m = ±½, E = (γh/2π) B 0 Substituting E = hν 0, ν0 = (γ/2π) B 0 which is identical to Larmor frequency. ii/. The NMR Absorption Process When magnetic vector of radio-frequency radiation is same as precessional frequency of nucleus, absorption and flipping of magnetic moment occurs. FIGURE 7-4. "Skoog" Fig. 14-3 (p. 315). iii/. Distribution of Particles between Magnetic Quantum States For practical magnets, frequency for NMR absorption lies between a few KHz to present maximum of 600 MHz. i.e., Energy separation of spin states is small. For system of spin ½ nuclei, Boltzman distribution among spin states give: N h /N l = exp(-δe/kt) = exp(-γhb 0 /2πkT) where N h and N l are numbers of nuclei in high and low energy states, respectively ΔE = energy separation k = Boltzman constant T = absolute temperature At ordinary temperatures, γhb 0 << 2πkT. i.e., Populations of spin states are almost equal, and slight excess of nuclei in lower state leads to net absorption of energy. e.g., For protons in B 0 = 14,000 gauss (14 kg, 1.4 T, NMR frequency 60 MHz), excess population in lower energy level is only ca. 10-5. Since excess population B 0, sensitivity enhancement has been one of major reasons for developing larger magnets during recent years. 3
(C) The Magnetic Field at the Nucleus i/. Effects due to the Molecule External magnetic field induces motion of electron cloud in atom or molecule such that a current loop is set up. FIGURE 7-5. "Skoog" Fig. 14-14 (p. 326). Secondary field produced by this current loop opposes main field at nucleus. Since magnitude of current B 0, magnitude of field seen at nucleus, B N, is different from applied field, B 0 : B N = B 0 (1 - σ) where σ = shielding constant, dimensionless quantity i.e., Nucleus is screened (or shielded) from applied field by its electrons. Magnitude of effect also depends upon density of electrons in current loop. This is maximum for free atom where electrons can circulate freely. ii/. Effect of Magnetic Anisotropy If source of magnetism is anisotropic, e.g., anisotropic magnets are formed in chemical bonds in molecule, then nuclei in some parts of space near a bond are descreened while in other parts screening increases. e.g., FIGURE 7-6. "Skoog" Fig. 14-15 & 14-16 (p. 326). Thus, two contributions to that are opposite in sign. iii/. The Chemical Shift For two nuclei in different environments with screening constants σ 1 and σ 2, then the two nuclear frequencies in magnetic field B 0 are: v 1 = (B 0 /2Π) (1 - σ 1 ) (1) v 2 = (B 0 /2Π) (1 - σ 2 ) (2) v 1 -v 2 = (B 0 /2Π) (σ 2 - σ 1 ) (3) From (1) and (3), (v 1 -v 2 )/1 = (σ 2 - σ 1 )/(1 - σ 1 ) Since σ1 << 1, (v 1 -v 2 )/1 = σ 2 - σ 1 In practice, impossible to determine σ. Instead, a reference compound is employed. 4
Thus, for measurements made at constant applied field where frequency is varied, chemical shift is defined by δ = (v s v r )/ v r 10 6 ppm where v s = frequency of absorption for a given nucleus in sample v r = frequency of absorption for reference Alternately, for measurements made at constant frequency, chemical shift is defined by δ = (B r -B s )/B r 10 6 ppm where B s = applied field for absorption of a given nucleus in sample B r = applied field for absorption of reference Standard for proton ( 1 H) or carbon ( 13 C) spectra is tetramethylsilane, (CH 3 ) 4 Si, usually abbreviated as TMS, since it gives a single absorption band at higher applied field than most other proton or carbon absorptions. FIGURE 7-7. Skoog Fig. 14-13 (p. 324). (D) Internuclear Spin-Spin Coupling Some spectra contained multiplets that could not be accounted for on basis of number of chemically different nuclei in sample. This multiple splitting of resonance lines does not depend upon magnetic field strength and results from interaction of nuclei in same molecule which causes splitting of energy levels and hence multiple transitions. e.g., Consider CHCl 2 CH 2 Cl and its proton resonance. Two sorts of hydrogen, CHCl 2 and CH 2 Cl. 1. CH 2 Cl resonance is split into 1:1 doublet. 2. CHCl 2 is split by two CH 2 Cl protons. Two CH 2 Cl protons have four possible spin states. FIGURE 7-8. "Akitt" Fig. 3.2 (p. 33). If spins are paired and opposed to external field, effective applied field on CHCl 2 proton is lessened and upfield shift results. If spins are paired and aligned with external field, downfield shift results. Opposite spins has no effect on resonance of CHCl 2 proton. Appear as 1:2:1 triplet, spacing between lines called coupling constant, J. 5
e.g., Consider ethyl group CH 3 CH 2 - and its proton resonance. CH 3 protons resonates as 1:2:1 triplet. Splitting of CH 2 - resonance by CH 3 group is 1:3:3:1 quartet. FIGURE 7-9. "Akitt" Fig. 3.4 (p. 35). Rules: 1. Equivalent nuclei do not interact with one another to give multiple absorption peaks. 2. Coupling constant decreases with separation of groups. 3. Number of lines due to coupling to n equivalent spin ½ nuclei is n + 1. Intensities of lines are given by binomial coefficients of (x + 1) n or by Pascal s triangle. FIGURE 7-10. "Akitt" Fig. 3.6 (p. 36). 4. Number of lines due to coupling to n equivalent nuclei of spin I is 2nI + 1. 5. If protons on atom B are affected by protons on atoms A and C that are nonequivalent, multiplicity of B is equal to (n A + 1) (n C + 1), where n A and n C are number of equivalent protons on A and C, respectively. 6. Coupling constant is independent of applied field. (E) Relaxation Processes in NMR When perturbing influence is removed, system will take finite time to return to equilibrium condition, called relaxation. Lifetime of spin state influences spectral line width via Uncertainty Principle, E t h/2π Since E = h ν and t = T, lifetime of excited state, ν 1/T i/. Spin-Lattice Relaxation Nuclei undergo thermal motion and interact with their surroundings (lattice) to provide mechanism for energy transfer between spin system and lattice. Characterized by spin-lattice relaxation time T 1. ii/. Spin-Spin Relaxation Occur when two nuclei interact where neighboring nuclei exchange spin orientations by interaction between their magnetic moments. This process results in no net change in spin and total energy of system. Characterized by spin-spin relaxation time T 2. T 1 T 2 6
(F) Effect of Exchange Processes on NMR Spectra e.g., ROH* + HA ROH + H*A 1. If H* is exchanging at fast rate, nucleus will experience an average of magnetic field at individual exchange sites and will exhibit single, sharp absorption, i.e., average absorption frequency observed. 2. If rate of exchange is slow, separate absorptions characteristic of each individual site observed. 3. At intermediate rates of exchange, may observe spectra ranging from single, broadened peak to broadened peaks slightly offset in frequency from absorptions of individual exchange sites. FIGURE 7-11. "Skoog" Fig. 14-12 (p. 323). (G) Pulsed FT-NMR Pulsed FT technique uses short, intense pulse of rf energy to excite nuclei in sample within a given frequency range. FIGURE 7-12. "Skoog" Fig. 14-5 (p. 317). FIGURE 7-13. "Skoog" Fig. 14-6 (p. 318). At equilibrium, magnetization M of sample lies parallel to B 0 along z axis. If rf field B 1, with frequency ν = ν 0 is applied along x axis for time τ, M will experience a torque that will tip it off z axis around x axis. Extent of rotation, α (in radians), is given by α = τγb 1 If τ is chosen such that α = π /2, M will precess from along z axis to y axis. This pulse is called a 90 pulse. Once pulse is terminated, nuclei begin to relax and return to their equilibrium position. Relaxation involves decrease in magnetic moment along y axis and increase in magnetic moment along z axis. This motion constitute rf signal that can be detected by a coil along x axis. The signal, a time-domain signal, is called free induction decay (FID) signal. FIGURE 7-14. "Leyden" Fig. 3.11 (p. 79). If nuclei under consideration are spin coupled to another type of nuclear species, FID will appear as beat pattern which is modulated with a frequency of J Hz, where J is coupling constant between two nuclei. 7
For complex beat pattern, FID must be Fourier transformed to obtain chemical shifts (frequency differences) and coupling constants (modulation frequencies). FIGURE 7-15. "Skoog" Fig. 14-10 (p. 322). III. NMR Spectrometers i/. Types of NMR spectrometers a) Continuous wave NMR spectrometers. b) FT-NMR spectrometers. ii/. Components of FT-NMR Spectrometers FIGURE 7-16. "Skoog" Fig. 14-22 (p. 335). a) Magnets Field strength sensitivity and resolution. Must be highly homogeneous and reproducible. Superconducting magnets (as great as 14 T or 600 MHz) are used in most high-resolution instruments. Shim coils (pairs of wire loops) to provide small magnetic fields to compensate for inhomogeneities in primary magnetic field. Field inhomogeneities are also counteracted by sample spinning (20 to 50 cycles/s). b) Sample Probe 1. Houses sample. 2. Houses transmitter/receiver coils. c) Detector and Data Processing System IV. Applications i/. Identification of compounds and Structure Determination ii/. Quantitative Analysis a) Analysis of multicomponent mixtures b) Quantitative organic functional group analysis c) Elemental analysis. 8
TABLE 7-1. "Carrington" Table 1.1 (p. 2). FIGURE 7-2. "Drago" Fig. 7-1 (p. 188). 9
FIGURE 7-3. "Skoog" Fig. 14-2 (p. 314). FIGURE 7-4. "Skoog" Fig. 14-3 (p. 315). 10
FIGURE 7-5. "Skoog" Fig. 14-14 (p. 326). e.g., FIGURE 7-6. "Skoog" Fig. 14-15 & 14-16 (p. 326). 11
FIGURE 7-7. Skoog Fig. 14-13 (p. 324). FIGURE 7-8. "Akitt" Fig. 3.2 (p. 33). 12
all multiplets with an even number of lines. FIGURE 7-9. "Akitt" Fig. 3.4 (p. 35). FIGURE 7-10. "Akitt" Fig. 3.6 (p. 36). 13
FIGURE 7-11. "Skoog" Fig. 14-12 (p. 323). FIGURE 7-12. "Skoog" Fig. 14-5 (p. 317). 14
FIGURE 7-13. "Skoog" Fig. 14-6 (p. 318). FIGURE 7-14. "Leyden" Fig. 3.11 (p. 79). 15
FIGURE 7-15. "Skoog" Fig. 14-10 (p. 322). FIGURE 7-16. "Skoog" Fig. 14-22 (p. 335). 16