NMR Theory

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NMR Theory

• There are 2 variables in NMR an applied magnetic
  field B0, and the frequency (? ) of radiation
  required for resonance, measured in MHz.

http//vam.anest.ufl.edu/forensic/nmr.html
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Effect of B0 on resonance frequency

• NMR spectrometers are designated according to the
  frequency required to make protons resonate. The
  modern standard is 300 MHz. However,
  manufacturers are actively pursuing stronger
  magnets. 900 MHz is currently as high as it gets.

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Schematic of an NMR
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Resonance Frequency

• Different nuclei resonate at greatly different ?
  on a 300 MHz instrument (1H 300 MHz) 13C
  resonates at 75 MHz.
• The same type of nucleus also absorbs at slightly
  different ?, depending on its chemical
  environment.
• Exact frequency of resonance chemical shift
• The strength of the magnetic field actually felt
  by a nucleus (Beff) determines its resonance
  frequency.
• Electron clouds shield the nucleus from the
  magnet
• Circulation of electrons in p orbitals can
  generate local magnetic fields that influence
  Beff
• Modern NMR spectrometers use a constant magnetic
  field strength B0, and pulse a broad range of
  frequencies to bring about the resonance of all
  nuclei at the same time.

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Chemical Shift

• Peaks on NMR spectrum resonances .
• Chemical shift is measured in ppm
• ppm ? in Hz relative to ref peak/instrument ?
  in MHz.
• Protons absorb between 0-10 ppm. C-13 nuclei
  absorb between 0-250 ppm.
• Reference peak 0 ppm (CH)4Si
  tetramethylsilane (TMS). TMS is an inert compound
  that gives a single peak at higher frequency than
  most typical NMR peaks.

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Electronic Shielding
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Shielding in Spectrum
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1H NMR Interpretation

1. Number of Resonances
2. Chemical Shifts
3. Integrations
4. Splitting Patterns
5. Exchangeable Protons

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Number of Resonances
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Stereochemistry

• Watch out when you have rings and/or double
  bonds! To determine equivalent protons in
  cycloalkanes and alkenes, always draw all bonds
  to hydrogen.

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Number of Signals in a Cyclic Compound

• Proton equivalency in cycloalkanes can be
  determined similarly.

Types of NMR relationships 1. chemically
equivalent 2. coincidentally equivalent 3.
non-equivalent, enantiotopic 4. non-equivalent,
diastereopic 5. non-equivalent. Use substitution
criterion to decide.
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Chemical Shift - Local Diamagnetic Shielding
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Induced Anisotropic Shielding - Benzene

• In a magnetic field, the six ? electrons in a
  benzene ring circulate around the ring creating a
  ring current.
• The magnetic field induced by these moving
  electrons reinforces the applied magnetic field
  in the vicinity of the protons.
• The protons feel a stronger magnetic field and
  thus are deshielded. A higher frequency is needed
  for resonance.

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Induced Anisotropic Shielding - Alkenes

• In a magnetic field, the loosely held ? electrons
  circulate creating a magnetic field that
  reinforces the applied field in the vicinity of
  the protons.
• Since the protons now feel a stronger magnetic
  field, they require a higher frequency for
  resonance. Thus the protons are deshielded and
  the absorption is downfield.

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Induced Anisotropic Shielding - Alkyne

• In a magnetic field, the ? electrons of a
  carbon-carbon triple bond are induced to
  circulate, but in this case the induced magnetic
  field opposes the applied magnetic field (B0).
• Thus, the proton feels a weaker magnetic field,
  so a lower frequency is needed for resonance. The
  nucleus is shielded and the absorption is upfield.

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Summary of pi electron effects
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Characteristic Shifts
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Integrations

• The integration of each resonance is proportional
  to the number of absorbing protons.
• The integral ratios tell us the ratios of the
  protons causing the peak.
• Strategy - find a peak that you can assign
  unambiguously and set its integral at the
  appropriate number of Hs.

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Splitting Patterns

• Consider the spectrum below

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Theory of spin-spin splitting

• Spin-spin splitting occurs only between
  nonequivalent protons on the same carbon or
  adjacent carbons.

Let us consider how the doublet due to the CH2
group on BrCH2CHBr2 occurs
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Triplet
Let us now consider how a triplet arises

• When placed in an applied magnetic field (B0),
  the adjacent protons Ha and Hb can each be
  aligned with (?) or against (?) B0.
• Thus, the absorbing proton feels three slightly
  different magnetic fieldsone slightly larger
  than B0, one slightly smaller than B0, and one
  the same strength at B0.

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Triplet
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Peak ratios in a multiplet.

• Doublet The two spin states of the proton
  causing splitting are nearly equally populated
  (because the energy difference is so small).
  Therefore a doublet is has a peak ratio of 11.
• Triplet - Because there are two different ways
  to align one proton with B0, and one proton
  against B0that is, ?a?b and ?a?bthe middle peak
  of the triplet is twice as intense as the two
  outer peaks, making the ratio of the areas under
  the three peaks 121.
• Higher use Pascals triangle

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Multiplet names
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Rules for predicting splitting patterns

1. Equivalent protons do not split each others
   signals.
2. A set of n nonequivalent protons splits the
   signal of a nearby proton into n 1 peaks.
3. Splitting is observed for nonequivalent protons
   on the same carbon or adjacent carbons.

If Ha and Hb are not equivalent, splitting is
observed when
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Nuclear Magnetic Resonance Spectroscopy
1H NMRSpin-Spin Splitting
Whenever two (or three) different sets of
adjacent protons are equivalent to each other,
use the n 1 rule to determine the splitting
pattern.