Transcript Document

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.
alcohol
carboxylic acid
O
OH
HO
alkene
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Infrared Spectrum of Salicylic Acid
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Spectra from SDBS
Symmetry in 1H-NMR
Question: Now looking at symmetry in 1H-NMR spectroscopy (a hydrogen-based
spectroscopy) do the two groups of hydrogens (Ha’s vs Hb’s) 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 (Ha’s vs. Hb’s) 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. Hb’s)?
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
O Cl Cl
O
groups are symmetry equivalent or not?
Let's return to our original molecule
HO
OH
H
H H
H
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.
O
Cl
Cl
O
HO
OH
H H
H H
180o
symmetrical molecule
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.
Cl Cl
O
Cl Cl
O
O
O
HO
HO
OH
HH
HH
OH
HH
HH
the second plane of symmetry
is the plane of the paper
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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Let’s return to our molecule which we found to be non-symmetrical:
O
Cl Cl
HO
O
OH
Br H
H H
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?
O
OH
H
O
O
HO
OH
O
H Br
H Cl
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?
O
O
CH3
H
CH2
CH2
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 C—C
bonds connecting them to larger molecules. This C—C bond is coincident to a
local symmetry axis of rotation, C3, which renders all three hydrogen atoms
symmetrically equivalent to one another:
H
O
O
H
CH2
C
CH2
H
A C3 axis of rotaion.
H
Each rotation being 120o
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Question: How many different equivalent sets of hydrogen atoms are found on the
following molecule?
CH3
O
C
H
C
H
H
CH3
A C3 axis of rotaion.
Each rotation being 120o
CH3
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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3 peaks = 3 unique hydrogen sets
1 peak = 2 equivalent hydrogen sets
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Spectra from SDBS
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.
O
O
OCH3
O
1.
CH2
2.
CH2
CH2
Cl
OH
OCH3
H3C
glutaric anhydride
CH2
3.
H3C
CH2
CH2
3-chloro-1-propanol
2,2-dimethoxpropane
H
HO
O
4.
H
NO2
5.
HO
H
6.
Br
OH
H
H
6-bromohexanoic acid
H
H
H
3-nitrophenol
7.
8.
fluorene
NO2
CH2
CH3
O
O
O
C
C
CH2
4-nitrophenol
CH2
O
diethylmalonate
CH3
9.
CH2
CH3
O
O
C
C
O
C
Br
CH2
O
H
dethylbromomalonate
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CH3