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5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Molecular Spectroscopy
January 29, 2008Molecular Groups, Projection Diagrams, and PointGroups
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Element Operation Example
E, the identity Does nothing All objects posses E
Cn, n-fold rotation
Rotate object by 2/n about the n-fold axis.The axis with the highest n is called the principleaxis.
For n>2 the sense is importantCn+ - clockwise
rotationCn
--counterclockwise rotation
H2O posses a C2 axisNH
3posses a C
3axis
Benzene posses a C2, C3, C6, and two sets ofthree C
2axes perpendicular to the C
6axis
, reflection plane Reflects through the plane Three types
v, vertical plane Plane containing the principle axis
H2O
h, horizontal plane Plane perpendicular to the principle axis Benzene
d, dihedral plane
Vertical plane which bisects two C2
axes perpendicular
to the principal axis
Benzene
i, inversion center
Sends each atom through the origin along a straight
line so that x-x, y-y, and z-z
H2
CO2
BenzeneSF
6
Sn, n-fold improper rotation axis Rotate object by 2/n, then reflects through plane
perpendicular to the axis of rotation
CH4
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Lets take the ECLIPSED conformation of ethane
One three-fold axis coincident with the C-C bond
Three two-fold axes perpendicular to the C-C bond and intersecting its midpoint
Three reflection planes, each containing the C-C bond and a pair of C-H bonds
One reflection plane perpendicular to the C-C bond and bisecting it
NO CENTER OF INVERSION IS PRESENT
One three-fold improperaxis coincident with the C-C bond
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Lets take the STAGGERED conformation of ethane
One three fold axis coincident with the C-C bond
Three two-fold axes perpendicular to the C-C bond and intersecting its midpoint
Three reflection planes, each containing the C-C bond and a pair of C-H bond
No reflection plane perpendicular to the C-C bondwe lost it!
One point of inversion at the midpoint of the C-C bondwe gained it!
One six-fold improper axis coincident with the C-C bondchanged its order!
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Stereographic Projections
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Lets consider the symmetry elements of the C2v point group and
the resulting symmetry operations
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Still considering the symmetry elements of the C2v point group
and the resulting symmetry operations
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Lets compare our results with the C2v character table
C2v
E C2
v
v'
E E C2
v
v'
C2
C2
E v'
v
v v v' E C2
v'
v'
v
C2
E
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Lets try this with another point group and build the character table
C2h E C2 h i
E
C2
h
i
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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This gives us the following for the Character Table
C2h E C2 h i
E
i
C2
h
h C2
i
E
Complete the rest as we have done and hand it in on Tuesday
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Point Groups
Symmetry operations may be organized into groups that obey the four properties
of mathematical groupsnamely
1. There exists an identity operator that commutes with all other members
2. The product of any two members must also be a member3. Multiplication is associative
4. The existence of an inverse for each member
It will be possible to assign ANY molecule to one of these so-called Point Groups So named because the symmetry operation leaves one point
unchanged
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Point Groups
Point Group C1Trivial group with contains all molecules having no symmetry
There is no center of inversion, plane of reflection, improper axis of
rotation, etc.
The molecule HNClF (below) is such a molecule
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Point Groups
Point Group CsOnly molecules which have to them a plane of reflection as a symmetry
element
Formyl Chloride belongs to this point group
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Point Groups
Point Group Ci
Molecules whose sole symmetry element is an inversion center
As an example take the rotamer of 1,2-dichloro-1,2-diflouroethane in
which the fluorine atoms are off-set to one another
The only operations generated by this inversion are i and i2=Ethis is a
group of order 2 and is designated Ci
Important to note that i is the same as an S2 axis
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Point Groups
Point Group CnMolecules with only an n-fold axis of rotation
Boric acid with the hydrogen atoms lying above the BO3 plane is an
example
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Point Groups
Point Group CnvMolecules with an n-fold Cn axis of rotation and n vertical mirror planes
which are colinear with the Cn axis
Water belongs to such a point groupthe C2V
Note that if you find a Cn axis and one v plane then you are
gauranteed to find n v planes
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Point Groups
Point Group CnhThis point group is generated by a Cn axis of rotation AND a horizontal
mirror plane, h, which is perpendicularto the Cn axis
Trans-butadiene (trans-1,3-butene) is an example of the C2h point
group
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Point Groups
Point Group DnThis point group is generated by a Cn axis of rotation and a C2 axis which
is perpendicularto the Cn axisno mirror planes
Tris(ethylenediamine)cobalt(III) posses idealized D3 symmetry
Build this molecule and convince yourself that this in indeed the case!!
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Point Groups
Point Group DndThis point group is generated by a Cn axis of rotation and a C2 axis which
is perpendicularto the Cn axis and a dihedral mirror plane, dThe dihedral plane is colinear with the principal axis and bisects the
perpendicular C2 axisCrystals of Cs2CuCl4 have a squashed tetrahedral D2d structure
5/28/2018 .Moleculary Symmetry, Projection Diagrams, And Point Groups
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Point Goups
Point Group DnhThis point group is generated by a Cn axis of rotation and n C2 axis which
is perpendicularto the Cn axis and a horizontal mirror plane which is by
definition perpendicularto the principal axis of rotation
Benzene is the classic example, possesing D6h symmetry
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Point Goups
Point Groups SnThese point groups are generated by an Sn axis.
For example, the spirononanetetraflourospirononane belongs to the
S4 point group and only elements generated by S4
S4S4
2 = C2S4
3
S44 = E
The S2 point group is just Ci since S2 = i
When n is odd the point groups are just the same as the Cnh point groups
and so are designated as such
As a direct result, only S4, S6, and S8, have a separate existence
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Special Point Goups
Tetrahedral molecules belong to the point group Td
Octahedral molecules belong to the point group Oh
Molecules with icosahedral (20 triangular faces) or dodecahedral (12 pentagonal
faces) belong to the point group Ih
Atomswhich have spherical symmetry, belong to the point group Kh
The point group Th, which may be obtained by adding to Td as set of h planes,
which contain pairs of C2 axisas opposed to the d planes which contain one C2axis and bisect another pair, giving Td)