SYMMETRY IN SPECTROSCOPY

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• SYMMETRY IN SPECTROSCOPY
• In C343 we apply symmetry to molecules in order
  to predict their behavior when exposed to
  electromagnetic radiation (EMR)--which generates
  what we call a spectrum.
• By doing so, the interpretation and prediction of
  various spectra, especially 1H-NMR, becomes much
  simpler.
• Brief Introduction to Spectroscopy
• When organic compounds interact with
  electromagnetic radiation, the energy absorbed is
  dependent on the structural environment in each
  molecule.
• For example, different frequencies of infrared
  energy are absorbed by covalent bonds in
  different functional groups carbonyls differ
  from alcohols which differ from alkenes etc.

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• If all groups and structures on a molecule
  absorbed the same energy, spectroscopy would be
  useless as an analytical tool.
• If, on a molecule, two or more structures are
  found to be in identical structural environments
  or symmetrical to another group, they will absorb
  EMR energy at exactly the same frequency.
• Each time a molecule absorbs EM energy at a
  specific frequency, the instrument being used
  reports a single signal (or peak) on a spectrum.
• For example, in an infrared spectrum of the
  following molecule, we will observe distinct
  signals at different energies for the alkene, the
  alcohol and the carboxylic acid functionalities
  found on the structure.

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Infrared Spectrum of Salicylic Acid
Spectra from SDBS
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Symmetry in 1H-NMR

• Question Now looking at symmetry in 1H-NMR
  spectroscopy (a hydrogen-based spectroscopy) do
  the two groups of hydrogens (Has vs Hbs) absorb
  at the same energy to one another? the hydrogens
  on the carboxylic acid groups?
• Question Do the hydrogens on the methylene
  groups absorb at the same energy as the hydrogens
  on the acid?
• To fully answer these questions, we must apply
  very simple symmetry rules to the molecule.
• Rule 1 Groups on a molecule that are determined
  to be symmetry equivalent to one another behave
  spectroscopically equivalent to one another.
• In other words, if two or more identical features
  on a molecule can be shown also to be in
  identical structural environments--symmetry
  equivalent to one another --together they absorb
  energy at the same frequency and produce one
  signal together on a spectrum.

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• Question Are the methylene hydrogen atoms (Has
  vs. Hbs) symmetry equivalent to one another? The
  acid group hydrogen atoms?
• Answers Yes and Yes.
• Question How many signals (or peaks) do we
  expect from the methylene group hydrogen atoms?
  The acid group hydrogen atoms?
• Answers One and One.
• The methylene group hydrogens on this molecule
  are said to belong to the same equivalent group,
  and therefore according to rule 1 behave
  spectroscopically identically to one
  another--absorbing energy at the same frequency,
  one signal on a spectrum. A similar assertion
  can be made for the acid group hydrogen atoms.
• As human beings we easily perceive when objects
  are or are not symmetrical.
• The example above is pretty simple to analyze
  using symmetry, and we can easily assert that we
  have two sets (acid hydrogens and methylene
  hydrogens) of symmetry equivalent hydrogen atoms
  which will give only two different signals on a
  spectrum.

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• With more complex molecules, it might be
  difficult or impossible to see this symmetry,
  therefore we need a fool proof method for
  detecting its presence. Look at the following
  molecule
• Question Are the acid hydrogen atoms symmetry
  equivalent to one another now? Are the alkyl
  hydrogens (Ha vs. Hbs)?
• Answer No, the symmetry of this molecule has
  somehow been "broken" making the H atoms on the
  alkyl groups (and on the acid groups) to be in
  slightly different environments from one another.
• Question How many signals do we expect from the
  alkyl hydrogen atoms? The acid groups?
• Answer Three and two.
• Since none of the alkyl hydrogen atoms belong to
  the same symmetry equivalent set, each will
  absorb at a unique frequency and give a unique,
  individual signal on a spectrum (same with the
  acid hydrogen atoms).
• The energies at which they absorb might be very
  close to one another but, they will be different!

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• What set of formal rules can be applied to
  molecules in order to determine whether groups
  are symmetry equivalent or not?
• Let's return to our original molecule
• If I asked you to close your eyes, then if I
  rotated this molecule 180o about an axis in the
  plane of the board and through the central carbon
  of the molecule, and if I then had you re-open
  your eyes.
• Question Would you be able to detect that I
  rotated the molecule?
• Answer No.
• This axis is called a rotational axis of symmetry
  and is given the symbol C.
• Furthermore, since during the rotation, hydrogen
  atoms on the alkyl groups and acid groups
  transform into one another during rotation, they
  belong to the same symmetry equivalent set or
  group.

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• The actual process of rotating the molecule is
  called a symmetry operation.
• As the H atoms on the alkyl groups (or the acid
  groups) exactly change their positions, they are
  said to exactly transform into one another.
• Rule 2 Groups on a molecule that transform
  exactly into one another during a symmetry
  operation are symmetry equivalent to one another
  and therefore absorb energy at the same
  frequency. So, they belong to the same
  equivalent set and give one signal (or peak) on a
  spectrum.

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• Question Are the two hydrogen atoms on either
  alkyl group symmetry equivalent to one another?
  (Ha vs Ha or Hb vs Hb)
• To show that the two hydrogen atoms on each alkyl
  group are indeed equivalent, we utilize a second,
  different symmetry element found on the molecule.
• Can you find it? It's called an internal plane of
  symmetry or a mirror plane and is given the
  symbol ?.

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• With a reflective plane of symmetry, one half of
  the molecule is completely and exactly reflected
  (transformed) into the second half of the
  molecule. The two halves of the molecule are
  mirror images of one another separated by the
  internal mirror or plane of symmetry. This
  molecule has two of them.
• Note above that each group on the right half of
  the molecule is exactly reflected (transformed)
  into each group on the left half of the molecule.
• The presence of this plane of symmetry along with
  the axis of rotation, shows that the alkyl
  hydrogen atoms are all equivalent to one another.

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• Lets return to our molecule which we found to be
  non-symmetrical
• Question Do any of the hydrogen atoms in this
  structure belong to the same, symmetry equivalent
  set?
• To answer this question, you simply have to
  identify any symmetry elements which might
  present that cause groups to transform into one
  another (something we just did with another
  molecule).
• Question Are there any legitimate symmetry
  elements on this molecule?
• Answer No
• There is no symmetry element nor any symmetry
  operation that can be performed on this molecule
  to transform any of the atoms in the structure.
• Therefore all five of the hydrogen atoms belong
  to five separate sets and thus give five distinct
  signals on a 1H-NMR spectrum.
• Rule 3 In order to show that any two or more
  groups on a molecule are symmetrically
  equivalent, only one symmetry element--that
  exactly transforms the groups-- needs to be found
  on the molecule!

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• Question How many unique, symmetry equivalent
  sets of hydrogen atoms are on the following
  molecule? How many different signals will they
  generate?
• Again, to answer the question, you must first
  identify any symmetry elements present and check
  to see which hydrogen atoms--if any--exactly
  transform into one another during a symmetry
  operation.
• Question Is there a symmetry axis of rotation?
• Answer No.
• Question Is there a plane of symmetry?
• Answer No.
• Question How many different signals are expected
  from hydrogen atoms?
• Answer Six.
• Note The less symmetry found on a molecule, the
  greater the number of different signals will be
  found on its spectrum. Conversely, if a
  complicated molecule has very few hydrogen
  signals but lots of hydrogen atoms, it indicates
  the presence of a high degree of symmetry.

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• Question Are the hydrogen atoms on the methyl
  group in the following molecule symmetry
  equivalent to one another?
• Methyl groups illustrate another important aspect
  of symmetry.
• Occasionally one or more portions of a molecule
  exhibit what's referred to as localized or local
  symmetry as opposed to global symmetry (what
  we've seen up to this point). Local symmetry
  applies to just a small portion of a molecule.
• By virtue of their structures, most methyl groups
  have free rotation about the CC bonds connecting
  them to larger molecules. This CC bond is
  coincident to a local symmetry axis of rotation,
  C3, which renders all three hydrogen atoms
  symmetrically equivalent to one another

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• Question How many different equivalent sets of
  hydrogen atoms are found on the following
  molecule?
• Answer Three.
• Notice that because of a local axis of rotation,
  all three methyl groups are equivalent and hence
  all nine methyl hydrogen atoms are equivalent and
  form one set.
• The two hydrogen atoms on the methylene
  carbon(CH2) are equivalent and form a second
  different set, while the aldehyde hydrogen forms
  a third set.

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• In 1H-NMR spectroscopy, when looking for
  symmetrical hydrogen groups, it will typically be
  much simpler than the previous examples. How
  many equivalent hydrogen sets exist on each
  molecule below?
• Why does the 1st compound not work as easily?

See 1H-NMR below
See 1H-NMR below
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1 peak 2 equivalent hydrogen sets
3 peaks 3 unique hydrogen sets
Spectra from SDBS
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• Determine the number of different equivalent sets
  of hydrogen atoms on each of the following. In
  addition, determine the number of hydrogen atoms
  in each set and identify as many symmetry
  elements as possible.