# Nuclear Magnetic Resonance Spectroscopy 1 19A. Theory of

Nuclear Magnetic Resonance Spectroscopy 1

19A. Theory of NMR 19B. Environmental effect on NMR spectra 19C. NMR spectrometer

19D. Applications of proton NMR 19E. Carbon-13 NMR 19F. Application of NMR to other nuclei 19G. Multiple pulse and multidimenasional NMR 19H. Magnetic resonance imaging 2 19A. Theory of NMR 19A-1 Quantum description of NMR

Spin of charged nuclei Total nuclear spin angular momentum: p = [I(I+1)]1/2(h/2), I = nuclear spin quantum number, h = Planks constant (6.626 x 10-34 J s) angular momentum in the direction of a magnetic field: p z = m (h/2), m = nuclear magnetic quantum number, I, ., 0, ., -I 2I + 1 discrete states

I = zero or integer, 0, 1, 2, 12C (0), 16O (0), 2H (1), 14N (1), 36Cl (2), 10B (3) I = half-integer, 1/2, 3/2, 5/2,1/2: 1H, 3H, 13C, 15N, 19F, 31P, 7 Li (3/2), 17O (5/2) Magnetic moment: = p, = gyromagnetic or magnetogric ratio Magnetic moment in the direction of a magnetic field: z = m (h/2), max. of z = I (h/2), = [eh/4mc], e = electric charge, m = mass of proton, c = light speed, nuclear magneton (Bohr magnetum) = eh/4mc = 5.05 x 10-24 gauss-1 = 5.05 x 10-24 erg/gauss

3 4 Energy levels in a magnetic field

The potential energy of nuclei: E = -(mh/2)B0, B0= an external magnetic field 1H (1/2): m = +1/2, -1/2 E+1/2 = - (h/4)B0, E-1/2 = (h/4)B0 E = (h/2)B0

E = hv = (h/2)B0, v = B0/2, v = frequency of a magnetic transition B0 = 4.69 T (tesla, 1T = 104 G) for H-1, v = B0/2= (2.68 x 10-8T-1s-1) (4.69 T)/2= 2.00x108s-1 = 200 MHz

5 6 7 8

9 Distribution of particles between magnetic quantum states

H, m = -1/2 (the lower energy state), +1/2 (the higher energy state) Boltzmann equation Nj/N0 = exp(-E/kT), Nj = the number of protons in the higher energy state. N0 = the number of protons in the lower energy state, k = Boltzmanns constant (1.38 x 10-23

JK-1), T = absolute temperature, exp = exponent E = (h/2)B0, Nj/N0 = exp(-hB0/2kT) ~ 33 ppm (small) To expand as a Maclaurin series, Nj/N0 =1- (hB0/2kT) 1 10 Example 19-2

Calculate the relative number of protons in the higher and lower magnetic states when a sample is placed in a 4.69 T field at 20 0C. Nj/N0 = exp(-hBhB0/2kT)kT) = exp[(-2.58 x 10-8 T-1 s-1)(6.63 x 10-34J s) (4.69T) ] / [2kT) x 1.38x10-23J K-1 x 293K] = e3.28x10-5 = 0.999967

N /N = 1.000033 0 j IF Nj = 106 protons No = 1,000,033 = 33 ppm excess 11

19A-2 Classical description of NMR procession of nuclei in a field angular velocity: 0 = B0 frequency of precession (Larmor frequency) v0 = B0/2

12 13 Absorption in CW experiments

the potential energy of the precessing charged particle E = - z B0 = -B0cos

= the angle between the magnetic field vector and the spin axis of the particle, = the magnetic moment, z = component of in the direction of magnetic field RF energy asorbed by a nuclei, angle of precession must change circularly polarized radiationcan be produced by an RF oscillator coil planed-polarized radiation consists of d and l circularly polarized radiation

14 15 16 Relaxation processes in NMR

To reduce saturation, relaxation (the lifetime of the excited state should be small) The inverse relationship between the lifetime of the excited state and the width of the absorption line

The optimal half-life: 0.1 to 10 s 17 Spin-lattice relaxation

Spin-lattice relaxation: a first-order exponential decay The absorbed energy increases the amplitute of the thermal vibrations or rotations Spin-lattice relaxation time (T1): average lifetime of the nuclei in the higher-energy state, strongly influenced by the mobility of the lattices, in crystalline solid and viscous liquids: low mobility, large T1

18 Spin-spin relaxation

Spin-spin relaxation time (T2): small in crystalline solid and viscous liquids (10-4 s) C-13 NMR No net change in the relative spin-state population, and thus no decrease in saturation, results , but the average lifetime of a particular excited nucleous is shortened. Line broadening is the result.

19 19A-3 Fourier transform NMR

In pulsed NMR measurement: RF radiation: pulse train, pulse width and time interval The length of the pulse (): usually less than 10 s, frequency: 102 to 103 MHz Free-induction decay (FID): a time-domain RF signal,

emitted by the excited nuclei as they relax FID: converted to a frequency-domain signal by fourier transformation Pulsed excitation: the extent of rotation: = B1, = gyromagnetic or magnetogric ratio, B1 = the net magnetic moment at the instant pulse of RF radiation, = the length of the pulse 20

21 22 23 24 25

19A-3 Fourier transform NMR Free-induction decay (FID): a time-domain RF signal FID: converted to a frequency-domain signal by fourier transformation

26 27 19A-4 Types of NMR spectra Wide-line spectra: useful for the quantitative determination of isotopes and for studies of the physical environment of

the absorbing species, usually obtained at relatively low magnetic field strength High-resolution spectra: collected by instruments capable of differentiating between very small frequency differences of 0.01 ppm or less

28 Fig. 19-11 A low-resolution NMR spectrum of water in a glass container, Frequency = 5 MHz 29 Fig. 19-12 NMR spectra of ethanol

(CH3CH2OH) at a frequency of 60 MHz. Resolution: (a) ~1/106; (b) ~1/107 30 19B Environmental effects on NMR spectra 19B-1 Types of environmental effects

Chemical shift the effective field: B0 = Bappl Bappl = Bappl(1-), Bappl = the applied field, = the screening constant (the shielding constant): determined by the electron density and its spatial distribution around the nucleus v0 = B0/2 = (/2) Bappl(1-) = k (1-) , k = Bappl/2

Spin-spin splitting polarization interaction: the magnetic coupling of nuclei transmitted by bonding electrons 31

Fig. 19-12 NMR spectra of ethanol (CH3CH2OH) at a frequency of 60 MHz. Resolution: (a) ~1/106; (b) ~1/107 32 Abscissa scales for NMR spectra

The internal standard: tetramethylsilane (TMS), (CH 3)4Si, inert, readily soluble in most organic liquids and easily removed from samples by distillation (bioling point = 270C), but not water soluble In aqueous media: sodium salt of 2,2-dimethyl-20silapentane-5sulfonic acid (DSS), (CH3)3SiCH2CH2CH2SO3Na, methylene groups deuterated v0 = hBB0/2kT) = (hB/2kT)) Bappl(1-) = k (1-) , k = B) = k (1-) = k (1-) , k = B) , k = hBBappl/2kT) at constant applied field, vs = k (1-) = k (1-) , k = Bs), vr = k (1-) = k (1-) , k = Br), r = TMS reference, s

= analyte sample vr - vs = k () = k (1-) , k = Bs-) = k (1-) , k = Br), (vr vs)/ vr = k () = k (1-) , k = Bs-) = k (1-) , k = Br) / (1-) = k (1-) , k = Br) ) = k (1-) , k = Br << 1, (vr vs)/ vr = k () = k (1-) , k = Bs-) = k (1-) , k = Br) chemical shift (ppm, parts per million) = = () = k (1-) , k = Bs-) = k (1-) , k = Br) x 106, most proton resonances: , 1-13, 13C: , 0-200, 19F: ~ 800,31P: ~ 300 Spin-spin coupling constant (J): in unit of hertz (Hz) 33

Ethanol (CH3CH2OH) 34 19B-2 Theory of the chemical shift

Diamagnetic shielding of a nucleus: circulating electrons, development of second field (opposite of primary field), shielding effect (diamagnetic effect) shielding effect: directly related to the electron density, to decrease with increasing electronegativity of adjacent groups, of CH3X: I (2.16) > Br (2.68) > Cl (3.05) > F (4.26)

35 36 Effect of magnetic anisotropy

: CH3-CH3 (0.9), CH2=CH2 (5.8), HCCH (2.9), RCHO (~10), benzene (~7.3) The effects of multiple bonds: explained by taking into account the anisotropic magnetic effects: shielding or

deshielding effects Armotics: ring current is similar to a current a wire loop ethyenic and carbonyl double bonds: electron circulating in a plane along the bond axix Acetylenic bond: the symmetric distribution of electrons about the bond axis permits electron to circulate around the bond 37

38 39 40 41 19B-3 Spin-spin splitting

Spin-spin splitting constant: J (Hz) First-order multiplicity: (n + 1), n = the number of magnetically equivalent protons on adjacent atoms, J/ < 0.05, /J > 0.1

Relative area: the coefficients of the terms in the expansion (a + b)n; n=1, 1:1 (doublet); n=2, 1:2:1 (triplet); n=3, 1:3:3:1 (quartet) 42 Possible spin orientations of methylene protons (-CH2-) 43

Possible spin orientations of methyl protons (-CH3) 44 45 Ethanol (CH3CH2OH)

46 Rules governing the interpretation of firstorder spectra

1. Equivalent nuclei do not interact with one another to give multiple absorption peaks. 2. Coupling constants decrease significantly with separation of groups, and

coupling is seldom observed at distances greater than four bond lengths. 3. The multiplicity of a band is determined by the number n of magnetically equivalent protons on the neighboring and is given by the quantity n+1. 4. If the protons on atom B are affected by protons on atoms A and C that are nonequivalent, the multiplicity of B is equal to (n A + 1)(nC +1), where nA and nC are the number of equivalent protons on A and C, respectively. 5. The approximate relative area of a multiplet are symmetric around the midpoint of the band and are proportional to the coefficients of the terms in the expansion (x +1)n.

6. The coupling constant is independent of the applied field; thus, multiplets are readily distinguished from closely spaced chemical-shift peaks by running spectra at two different field strengths. 47 i-iodopropane, CH3-CH2-CH2-Cl, a = 1.02, b = 1.86, c = 3.17, Jab = 7.3, Jbc = 7.3

multiplicity = (3+1)(2+1) = 12 peaks, only six peaks are observed with relative areas of 1:5:10:10:5:1 Second-order spetra

J/ > 0.1 to 0.15: no longer apply to first-oder J ~: the lines on the inner side of two multiplets tend to be enhanced at the expense of the lines on the outer side, and the symmetry of each multiplet is thus destroyed 48 49

Example 19-3 (a) Cl-CH2-CH2-CH2-Cl, 2+1=3 (1:2:1), 4+1=5 (1:4:6:4:1), 2+1=3 (1:2:1)

(b) CH3-CHBr-CH3, 1+1=2 (1:1), 6+1=7 (1:6:15:20:15:6:1), 1+1=2 (1:1) (c) CH3-CH2-O-CH3, 2+1=3 (1:2:1), 3+1= 4 (1:3:3:1), 1 50 Effect of chemical exchange on spectra Fig. 19-19 spectrum of highly purified ethanol showing additional splitting of OH and CH2 peaks

51 The exchange of OH protons among alcohol molecules is known to be catalyzed by both acids and bses, as well as by the impurity that commonly occur in alcohol 52

19B-4 Double resonance techniques Spin decoupling Nuclear Overhauser effect Spin ticking

Internuclear double resonance 53 54 19C NMR spectrometers

1. Magnets: locking the magnetic field, shimming, sample spinning 2. The sample probe: transmitter-receiver coil, the pulse

generator, the receiver system 3. The detector and data-processing system: sampling the audio signal, signal integration 4. Sample handing: 2% to 15% solution of sample, solvents must have no resonance in the spectral region of interest, CDCl3, CD3OCD3, acetone-d6, DMSO-d6, D2O 55 19C NMR spectrometers

56 Fig. 19-23 Absorption and integral curve for a dilute ethylbenzene solution(aliphatic region) 57 19D Application of proton NMR 1. Identification of compounds

Example 19-4, C5H10O2, CH3-O-CO-CH2-CH2-CH3 Example 19-5, colorless, isomeric liquids containg only carbon and hydrogen: C6H5CH(CH3)2, C6H5C(CH3)3 Example 19-6, oragaic compound, molecular mass of 72, only carbon, hydrogen and oxygen, CH3CH2CH2CHO 2. Application of NMR to quantitative analysis 58

Example 19-4. C5H10O2, CH3-O-CO-CH2-CH2-CH3 59 C6H5CH(CH3)2 60 C6H5C(CH3)3

61 CH3CH2CH2CHO 62 19E Carbon-13 NMR

The low natural abundance of 13C: 1.1%, the small magnetogyro ratio of 13C: 0.25 of proton 13C NMR: about 6000 times less sensitive than 1H NMR 19E-1 Proton decoupling (1) Broadband decoupling: heteronuclear decoupling in which spinspin splitting of 13C lines by 1H nuclei is avoided by irradiating the sample with a broadband RF signal that encompasses the entire proton spectral, Fig. 19-27 (2) Off-resonance decoupling: the decoupling frequency is set at 1000 to 2000 Hz above the proton spectral region, which leads to a partially

decoupled spectrum in which all but the largest spin-spin shifts are absence, primary C: quartet, second C: triplet, tertiary C: doublet, quaternary C: singlet; Fig. 19-28 (3) Nuclear Overhauser effect (NOE): the enhancement of 13C by decoupling protons at neighboring 13C nucleus 63 19H Magnetic resonance imaging

Fig. 19-35 Fundamental concept of MRI Fig 19-36 Acquisition of informatio withine slices along the z-axis

Fig 19-37 Structures inside subjects may be reconstructed from the three-dimensional data arrays Fig 19-38 Brain activity in the left hemisphere resulting from naming tasks revealed by fMRI 64 65

66 19E-2 Application of 13C NMR to structure determination 67 Application of 13C NMR to solid samples 68

19F Application of NMR to other nuclei 19F-1 Phosphorus-31 69 19F-2 Fluorine-19

70 19G Multiple puse and multidimensional NMR 19G-2 Two-dimensional NMR 71 19G-3 Multidimensional NMR

72 19H Magnetic resonance imaging

Fig. 19-35 Fundamental concept of MRI Fig. 19-36 Acquisition of information whithin slices along the z-axis Fig. 19-37 Structures inside subjects may be reconstructed from the three-dimensional data arrys Fig. 19-38 Brain activity in the left hemisphere resulting from naming tasks revealed by fMRI

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