Author: Fred J' Grieman

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Magnetic Field Interaction Nuclear Magnetic
Resonance Spectroscopy
Author Fred J. Grieman
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• External Magnetic Field and Spectroscopy (K
  P, 7-12)
• Magnetic dipole created by motion of charge (e.g.
  e- orbital motion, e- spin)
• External magnetic field B k Bo(z)
  (Physics of magnetic fields Physics course)
• Orbital Angular Momentum
• A. Splitting of levels due to electric field
  Stark Effect
• B. Splitting of levels due to magnetic filed
  Zeeman effect
• 1) Magnetic field from small loop of current
  from a large distance
• magnetic dipole. E.g. Atom e- orbit ? ?L -
  ?LL -e/(2me)L (See MS
• 
  
  magnetogyric ratio problems 6
  43-46)
• 2) Interaction with external magnetic field
  Perturbing Hamiltonian
• Hm ?L B - ?LBoLz (external field
  along z axis)
• ßB h?L Bohr Magneton
• Hm?atom -(ßB/h)Bo(z)MLh?atom
• -(ßB)Bo(z)ML?atom

H atom
-1 0 ml 1
E
2s,2p
Bo(z)
3
II. Electron Spin Angular Momentum Analogous to
orbital ?s - ?sS -go ßBS go 2.0023
(electron g value from relativistic q. m.) In
external magnetic field Em - ? sBo (z) ms -go
ßBmsBo Interactions 1) In atom ?LL ?SS
spin-orbit coupling 2) External field ESR (EPR)
Spectroscopy of Radical species
III. Nuclear Spin (analogous to electron spin)
Spin q. I (integer or ½ integer) mI is z
component mI ?I, ?(I - 1), ?½ or 0
e.g., 1H, 13C, 19F - I ½ mI ?½
2H, 14N - I 1 mI ? 1, 0 Em
-gNßNBo(z)mI gN 1 (must be measured for
each nucleus found in table) ßN me/mNßB )
nuclear magneton 5.0508 x 10-27 JT-1
4
D nucleus I 1
E
Bo(z)
IV. Nuclear Magnetic Resonance Spectroscopy Trans
itions between nuclear spin levels Selection
Rules ?mI ?1 (-1 for absorption)
Transition ?E/h ?o gN ßN Bo/h ? Bo
?o radiofrequency for typical magnetic fields ?o
? Bo, can vary either
magnet
NMR Spectrometer
Intensity
Fix ?o (400 MHz) and vary Bo Bo for
transition depends on nucleus
sample
RF Generator Detector
Bo
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Chemistry So far everything derived is for
bare nucleus In molecules, nuclei surrounded
by electrons For diamagnetic molecules, e-s
create magnetic field in opposite direction to
applied external field and proportional to
it at nucleus j -sjBo So magnetic field
at nucleus is Bj Bo(1- sj) sj depends on
e- distribution about nucleus j which depends
upon chemical bonding This is the
chemical shift!!!
E
Splitting due to Bj
So transition is now ?o ?Bj ?Bo(j)(1 -
sj) or Bo(j) ?o/(1 sj)?
Bo(z)
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Bo
Bo
Bo
low resolution
CH3OH
Bo
high resolution
Bo
B
Intensity
B(j)
Bo(1-sj)
Bo
Bo
Bo
OH
CH3
Bo(r) Bo(j) Bo(r)
Bo)
d
Bo
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Bo
Bo
Bo(H)
Bo
Bo(D)
8
CH3OH is left as a homework problem Note for
intensities OH mI ?1/2 What about CH3?? 3
equivalent protons, so spins combine
MI SimI(i) of
ways ??? 3/2
1 ???, ???, ??? 1/2
3 ???, ???, ???
-1/2 3 ???
-3/2 1
CH3OH
1/2 -1/2
1/2 -1/2 3/2 -3/2
OH
CH3