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10/22/1999
Nuclear Magnetic Resonance Spectroscopy, Chapt. 2
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I. History
A. Pauli 1924: hyperfine structure of atomic spectra due to
interaction of magnetic moments of individual nuclei with moments
of electrons
B. Purcell (Harvard) found proton resonance in paraffin wax & Bloch
(Stanford) found proton resonance in water in 1946
1. they shared Nobel prize
C. Knight (1949) reported that the precise frequency of energy
absorption depends on chemical environment
D. some advantages
1. totally nondestructive
2. as fast or faster than high resolution IR
3. solids easier to run than IR
a) better choices of solvent
II. 2-1 Magnetic Properties of Nuclei
A. nucleus act like spinning charged particle
1. all nuclei have charge
2. in some nuclei, this charge "spins" on nuclear axis
3. moving charge creates a magnetic field and magnetic moment
a) circulation of nuclear charge generates magnetic
dipole along the axis
4. in absence of magnetic field, moment point in any direction
5. in magnetic field, magnetic moments align themselves either
with or against the field
a) higher energy field against field
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(1) less populated
b) observe transition from lower to higher in NMR
experiment
B. Nuclear Spin - angular moment
1.  is nuclear angular momentum
a) quantized in units of h/2
b)  = Ih/2 = Ih(bar)
2. I integer or 1/2 integer - nuclear spin quantum number
3.  magnetic moment, proportional to nuclear spin
a) nuclear magnetic moment
b) intrinsic (inherent) magnitude of generated dipole
c)  = 
4.  is the magnetogyric ratio = 2/hI
a) proportionality constant between magnetic moment 
& spin number I
5. spin based on number of protons and number of neutrons
a) odd mass number
b) or odd atomic number
c) #p + #n = even I = 0,1,2,..
d) #p + #n = odd I = 1/2,3/2,...
e) spherical distribution of charge, spin = ½
(1) C13,H1,N15,F19,Si29,P31,H3
f) nonspherical or quadrupolar distribution
(1) spin >= 1
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Nuclear Magnetic Resonance Spectroscopy, Chapt. 2
(2) 3/2 - B11,Na23,Cl35
(3) 5/2 - O17,Al27,
(4) 7/2 - Co59
(5) 1 - H2,N14
(6) 3 - B10
(7) electrical quadrupole moment
(8) effects relaxation & therefore coupling
g) #p = even, #n = even, I = 0, no spin
(1) certain nuclei not spin
(a) C12,O16,S32
6. 2I + 1 = # of orientations a nucleus may assume in an external
uniform magnetic field
a) result in
(1) quantized spin angular momentum
(2) magnetic moment
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Nuclear Magnetic Resonance Spectroscopy, Chapt. 2
C. NMR experiment
1. Terms:
a)  nuclear magnetic moment
b) I nuclear spin quantum number
c)  nuclear angular momentum
d)  magnetogyric ratio
e) h(bar) = h/2
f) Bo, Ho external magnetic field
g) B1, secondary magnetic field
h) o Larmor frequency, precessional angular velocity
2. spin of magnetic nuclei quantized
a) Iz = +1/2,-1/2 for H
3. sample between poles of magnet
a) field in Tesla Bo (10000 gauss)
b) magnetic interaction between applied magnetic field
Bo &  (magnetic dipole moment) generates a torque
that tends to tip the magnetic moment toward the
applied field
c) since nucleus spinning, it precesses or wobbles
around Bo
d) spinning nucleus precess due to Bo
(1) precess about its own axis of spin
(2) angular frequency omega 
(3) frequency dependent on magnetic field
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(4) nucleus charged
(5) therefore precession generate an oscillating electric field of
same frequency
e) frequency of precession fixed, angle of precession
related to applied energy
4. Larmor frequency o
a) precessional angular velocity
b) equal to the product of the magnetogyric ratio and
the strength of the applied magnetic field
c)  =  Bo = 2
5. Boltzmann's Law - a few more in +1/2
6. E = E2 - E1 = h(bar) Bo
a) therefore energy difference a function of
(1) Bo (Ho) external magnetic field
(2)  - the nuclide
b) h(bar) = h/2
c)  = gyromagnetic ratio
(1) collection of nuclear properties
(2) every magnetic nuclide has distinct 
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d) the higher the field Bo, the greater the difference
7. apply radiofrequency of same frequency as precession
a) radiofrequency field applied at right angle will have a
rotating magnetic component in the x-y plane that will
induce the magnetic moment  to tip to a different angle
b) apply 2nd magnetic field, B1, to detect
c) part of electromagnetic spectrum
d) frequency,  = absorption
e) this absorption referred to as resonance
f) energy absorbed
g) frequency of oscillating electric field component of
incoming radiation matches frequency of electric field
generated by precessing nucleus, the 2 fields couple,
energy is transferred to the nucleus, causing spin to
change (resonance)
8. observation of resonance
a) application of radiofrequency field which has a
rotating magnetic component & will tip the magnetic
moment of a particular nucleus from its precession
angle to a new angle closer to the x-y plane
b) then the magnetic moment has a greater component
in the x-y plane perpendicular to the applied field Bo
c) this is observed by a receiver coil placed in this
plane
d) the component is a rotating magnetic field which
induces a current in the receiver coil that can be
amplified and plotted
e) magnetic moment  is precessing even before the
radiofrequency field is applied but not observe some
magnetic component in the x-y plane at all times
because various 's of many molecules in sample not all
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rotating in phase. The magnetic moments cancel,
leaving a net resultant magnetic moment M parallel with
the field
f) When rotating magnetic field applied, the various
magnetic moments all begin rotating together and
become phase coherent, pointing in the same direction
at the same time
9. Range of Bo 1.4 to 14 tesla
a) 1.4 Tesla
60 MHz
H1
b) 14
600
H1
c) 2.35
10.1
N15
d) 2.35
25.2
C13
e) 2.35
100
H1
f) hertz = 1 cycle/second, frequency
g) 1 Tesla = 10000 gauss
h) energy states much further apart for H1 (overhead)
III. Chemical Shift (2-2)
A. Blocal = Bo (1 - )
1. interaction between electron cloud and applied field
2. sigma shielding - measure of ability of electron to alter Bo
B. chemical shift - variation of the resonance frequency
1. v0 = B0(1 – )/2
2. electronic shielding - lower resonance frequency
a) sigma enter as –, sigma usually positive
3. decrease shielding - resonance frequency increase
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a) electron withdrawing effect of substituents
C. 98.9% of C is C-12
D. NMR successful because
1. narrow width of resonance ( < 0.5 Hz & often < 0.1 Hz)
2. large range of resonance frequency
a) 1000 Hz for 1H at 1.41 Tesla
b) not all 1H resolved (ex. toluene)
c) but resolved in 13C
E. system of units
1. Hz – absolute frequency (ex 300.000764)
a) Changes are in millionths of hertz
b) Standard for reference TMS for protons and carbons
(1) Soluble, unreactive, volatile
(2) Low electronegativity of Si, high shielding
(3) 0 PPM
c) other internal standards in water
2.  = (vi – vtms)/vtms
a) difference in Hz, absolute frequency MHz, ppm
F. first generation NMRs
1. vary B0, hold B1 constant
a) increase in shielding require B0 to increase to keep
B1 constant
(1) right side high field or upfield end
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(2) left side low field or downfield
(3) “continuous wave, field sweep”
2. modern machines
a) B0 constant, B1 varied
(1) Right side lower frequency
(2) Left side higher frequency
IV. Excitation and relaxation
A. Boltzmann – ratio of populations
1. In 7.04 T, 50 more in + for every million spins
2. Magnitization M – sum of all the individual spins
3. Fig 2-10
a) 12 and 8
b) Spins distributed randomly around z axis
c) No net x or y magnetization
4. Fig 2-11
a) 11 and 9
b) tipping causes coherence
c) detect in x-y plane
d) rotating coordinate system
(1) x and y axis are rotating at the frequency of B1
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Nuclear Magnetic Resonance Spectroscopy, Chapt. 2
5. saturated signal
6. spin-lattice relaxation or longitudinal relaxation
a) any process that returns the z magnetization to its
equilibrium condition
b) usually a first order process with time constant T1
c) local oscillating magnetic fields in the sample that
correspond to the resonance frequency
(1) primarily from other magnetic nuclei in motion
(2) as they tumble in solution, if they have Larmor frequency,
excess spin energy of neighboring spins can pass to this
motional energy
(3) must be spatially close to resonating nucleus
(4) for13C, attached H for spin-lattice relaxation
(a) quaternary C relax very slowly
(b) more easily saturated
(c) attached to C12 atoms, nonmagnetic
(5) protons depend on nearest neighbor geminal or vicinal
d) responsible for initial excess in +1/2
(a) when placed in B0
7. spin-spin or transverse relaxation
a) returns x and y magnetizations to their equilibrium
condition of zero
b) first order with time constant T2
c) phase of nuclear spin randomized
(1) interaction of 2 nuclei with opposite spin
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(2) switch in spins causes no net change in spin-lattice
relaxation – no net change in z magnetization
(3) but results in dephasing
(a) new spin state has different phase than old
d) similar result if B0 field not uniform
(1) not the same field, not the same resonance
(2) this broadens the linewidth
V. Pulsed Experiments
A. Short B1 pulse
1. Push magnetization toward y axis
2. Short pulse 450 rotation
3. Longer pulse, 900 rotation, in y axis
4. 1800 pulse
a) net magnetization in the –z direction
b) population inversion
5. angle theta determined by pulse duration tp
6. if B1 halted at 900 pulse, on y axis
a) magnetization detected over time at resonance
frequency
b) decay
c) FID free induction decay – reduction of y
magnetization with time
(1) first order process with time constant T2
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7. figure 2-14 artificial – involves only a single type of nucleus
B. benzene – single resonance
1. if xy coordinate system rotating at a frequency slightly different
from Larmor frequency
a) then nuclear magnet moves off the y axis within the
xy plane
2. only nuclei precessing at same frequency as B1 appear
stationary in the rotating coordinate system
3. magnetization continues to rotate, reaching the –y axis and
eventually returning to the +y axis
4. the detected y magnetization during this cycle first decreases,
falls to zero as it passes the y=0 point, moves to a negative value –
n the –y region and returns to a positive value
C. figure 2-16a FID for protons of acetone
1. horizontal distance between each maximum is reciprocal of
difference between the Larmor frequency and the B 1 frequency
2. intensity of maxima decrease as y magnetization is lost through
spin-spin relaxation
3. line width of spectrum determined by T 2
4. FID contains all necessary info to display a spectrum
a) frequency
b) linewidth
c) intensity
D. two resonating nuclei
1. decay pattern superimposed
a) reinforce and interfere
b) methyl acetate
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2. Fourier analysis matches FID with a series of sinusoidal curves
and obtains from them the frequencies, linewidths and intensities of
each component
3. FID is a plot in time – time domain
4. frequency domain
VI. The Coupling Constant
A. 1-chloro-4-nitrobenzene
1. Ha and Hx
a) set up 2 magnetic fields of + and – ½ each
b) roughly equally populated
c) quadrupolar nuclei Cl and N often act nonmagnetic
(1) can be ignored
(2) chloroform a singlet
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B. spin-spin splitting – influence of neighboring spins on multiplicity
of peaks
1. distance between 2 peaks of pattern – coupling constant J,
measured in Hz
2. AX pattern in 1-chloro-4-nitrobenzene
3. J the same - measure of interaction between the 2 nuclei
4. magnitude of interaction depends only on nuclear properties
and not external quantities
C. mechanism for 2 nuclei to couple
1. spin info transferred between them
2. most common – interaction of electrons along bonding path
between nuclei
a) X proton influences or polarizes spins of electrons
b) electrons polarize other electrons in C-H bond
c) through the bond interaction
(1) look at bond properties – bond strength and steric
arrangements
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D. more than one nucleus – additional splitting
1. ethyl A2X3
2. n+1 peaks
a) unless second order effects
3. intensity ratios correspond to binomial expansion
a) Pascal’s triangle – summing 2 adjacent integers and
placing the result one row lower and between the 2
integers
E. coupling between protons that have the same chemical shift does
not lead to splitting
F. vicinal protons H-C-C-H over 3 bonds
1. coupling over 4 or more bonds usually small
2. geminal can couple
a) if different chemical shift
b) ring
c) chiral center
d) alkene
G. coupling between 1H and 13C
1. 1.1% abundance
2. satellite peaks in HNMR
3. largest coupling with Hs directly attached
H. instrumental procedures – decoupling
1. irradiating one nucleus with an additional field B2
a) double resonance
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quantitation
A. signal directly proportional to number of spins present
1. relative intensity data
2. can be used to measure the relative quantities of components in
a mixture
VIII. commonly studied nuclides
A. depends on specialty
1. organic – C, H, N, O
2. biochemist add P
3. organometallic or inorganic
B. Properties
1. spin
a) zero spin
b) 1/2 best - better than quadrupolar
c) odd mass 1/2,3/2,5/2 etc.
d) even mass, odd number 1,2,
e) quadrupolar nuclei have unique mechanism for
relaxation – extremely short relaxation times
(1) Heisenberg uncertainty principle
(2) Et ~ h(bar)
(3) lifetime of spin short – larger band frequencies
(4) quadrupole broadening
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2. Natural Abundance
a) F19, P31 100%, H1 99.%
b) C13 1.1%, N15 & O17 << 1%
c) 1.1% 1.1% = 0.00012 of 2 C13
(1) no coupling observed
3. Sensitivity
a) dependent on difference between +1/2 & -1/2 spin
states
(1) gyromagnetic ratio and energy difference
b) H1 one of the most sensitive
c) C13, N15 weak
d) H3 highly sensitive,
(1) important to biochemists,
(2) 0 abundance
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e) H2 low sensitivity but natural abundance
f) Fe, K poor sensitivity, Co high sensitivity
4. Receptivity (vs C13)
a) product of abundance * sensitivity / same for C13
5. NMR resonance frequency at 7.05 T
6. Reference substance
7. Table 2-2, p26
IX. Experimental Methods (2-8)
A. spectrometer and samples
1. Common components
a) Magnet B0
b) Generate B1 pulse
c) Receive NMR signal
d) Probe to position sample
e) Hardware to stabilize B0 and optimize signal
f) Computers for controlling and processing
2. Magnet
a) early NMR - electromagnet,
(1) low sensitivity & poor stability
b) permanent magnets
(1) cost less
(2) simpler to maintain
(3) but low sensitivity
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Nuclear Magnetic Resonance Spectroscopy, Chapt. 2
(4) Fe core used for 60 MHz H
(a) thick horseshoe magnet
(b) poles bent toward each other
c) superconducting magnet
(1) 3.5-18.8 Tesla (150-800 MHz for H)
(2) much higher sensitivity & stability
(3) very high fields - better spectral dispersion
(a) less overlap of resonances
(4) solid cylinder with hole in center for sample
(5) direction of B0 field (z) aligned with axis of cylinder
3. console
a) transmitter and receiver
(1) B1 field
(a) 1-40 mT in pulse experiment
(b) tuneable for other nuclei
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Nuclear Magnetic Resonance Spectroscopy, Chapt. 2
b) recorder
4. probe
a) most homogeneous region of field
b) holder for sample
c) mechanical means of adjusting probe
d) electronic leads for supplying B1 and B2 and
receiving signal
e) devices for improving magnetic homogeneity
5. liquid samples
a) cylindrical tube
(1) 5mm diameter for H
(2) axis parallel to z axis
(3) 300-400 l
b) microtubes available
c) proton spectrum measured on less than 1 g
d) solvent
(1) CDCl3, D2O, acetone-d6
e) record at different T
B. optimizing the signal
1. problems of sensitivity and resolution
a) peak separation of <0.5 Hz to resolve
(1) for separation of 0.3 Hz at 300 MHz, field homogeneity
must be better than 1 part in 109
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b) corrections to B0 with shim coils
(1) apply small current through a shim coil built into probe
2. Spinning side bands
a) result from inhomogeneities in magnetic field
&spinning tube
b) recognized - symmetrical appearance & distance
from peak due to spinning rate
3. “Ringing" - oscillations seen at high-field end of a strong sharp
peak
a) "beat" frequencies resulting from "fast" passage
through the absorption peak
4. ferromagnetic impurities
a) cause severe broadening of absorption peak
b) sources - tap water, steel wool, Raney nickel,
spatulas
c) remove with bar magnet, filtration, centrifugation
5. spin sample along its axis at 20-50 Hz to improve homogeneity
a) spun along z axis for superconducting magnets
(1) need shims primarily for z gradient
6. field drift
a) minimized by electronically locking the field to
resonance of substance in sample
(1) internal lock – normally at deuterium frequency
(2) external lock – used only for NMRs with specific use
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7. sensitivity dependent on natural abundance and natural
sensitivity – magnetic moment and gyromagnetic ratio
a) increase sample size
b) increase field strength – sensitivity increases with
the 3/2 power of field
c) collapse of peaks through decoupling
(1) also nuclear Overhauser effect
d) complex manipulation of pulses
8. s/n improved through multiple scanning or signaling averaging
a) signal proportional to n
b) noise proportional to square root of n
C. spectral parameters
1. in pulsed experiments, resolution controlled by amount of time
taken to acquire signal
a) 2 signals separated by v, acquire data at 1/v
seconds
b) sampling for longer time increase resolution
c) tail of FID mostly noise – reduce by a weighting
factor
2. after acquisition, delay time necessary to allow nuclei to relax
a) optimal – 3-5 times the spin-lattice relaxation time
(1)
13C
relaxation 10 s, total of 50s
(a) use pulse angle less than 900
(i) shorter times needed
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3. detected range of frequencies – spectral width
a) determined by FID sampling rate
(1) samples at least twice per cycle
(2) frequency N, sample at 2N Hz
(3) 13C spectral width of 15000 Hz (200 ppm at 75 MHz)
(a) signal sampled 30,000 times/sec
(4) foldover signal if not sampled enough
b) dwell time – reciprocal of sampling rate
(1) amount of time between sampling
(2) determine how much data the computer must be able to
handle
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X. Dynamic Effects
A. Averaging coupling constants
1. trace amount of acid or base or higher temperatures
a) exchange for methanol
B. Averaging for chemical shifts
1. mixture of acetic and benzoic acid
2. acetic acid in water
C. intramolecular (unimolecular) reactions
1. axial and equatorial H on cyclohexane
D. measure and examine reaction rates when system is at
equilibrium
XI. spectra of solids
A. H1 & C13 unresolved
B. J coupling - indirect spin-spin interaction between nuclei that
occurs through bonds
C. D coupling - dipole-dipole coupling
1. occurs through space
2. nuclear magnets couple directly through the interaction of their
nuclear dipoles
3. in solutions, dipoles continuously reorienting through molecular
tumbling
a) therefore in solution, no net dipolar interaction when
averaged over all mutual geometries
b) but the indirect J coupling not averaged to 0 because
tumbling cannot destroy a through-bond mechanism
4. Solids held rigidly in place
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a) D coupling much stronger than J coupling & most
chemical shifts
(1) overwhelm J coupling & shifts
(2) several hundred to a 1000 Hz
(3) featureless band
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b) remove D coupling with strong B2 field
D. Anisotropy of the chemical shielding
1. in solution, observed chemical shift average of shielding around
a nucleus for all orientations in space
2. in solid, shielding not always the same for a given type of
nucleus
3. shielding do to electrons in motion setting up opposite field
4. ability of electron to circulate vary with orientation in field
5. double irradiation not average anisotropy of chemical shielding entirely geometrical
6. overcome problem by spinning at high speeds – mimic tumbling
a) magic angle spinning 54o 44' for best results
b) angle between the edge of a cube and the adjacent
solid diagonal
c) spinning along this averages each Cartesian
direction
7. therefore combine irradiation & magic angle spinning (MAS)
a) 2-20 kHz spinning rate
E. Relaxation time extremely long
1. motion of nuclei necessary for spin-lattice relaxation
a) therefore absent
b) let atoms relax several minutes between pulses
2. Crosspolarization (CP)- same double irradiation to remove J &
D coupling also used to transfer some of H1 favorable higher
magnetization and faster relaxation to C
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a) spin locking – after protons moved onto y axis by 900
pulse, a continuous y field is applied to keep the
magnetization precessing about the y axis
b) frequency of this field hBh controlled by operator
c) When 13C channel turned on, its frequency cBc set
equal to 1H frequency – Hartmann-Hahn condition
d) both proton and carbon have same precessing
frequency and same net magnetization
e) carbon has enhanced intensity
f) when carbon achieves maximum intensity, Bc turned
off (ending contact time) and carbon magnetization is
acquired while Bh is retained for dipolar decoupling