will stick to isolated, finite molecules (not crystals)
DESCRIPTION
Will stick to isolated, finite molecules (not crystals). SYMMETRY OPERATION. Carry out some operation on a molecule (or other object) - e.g. rotation. If final configuration is INDISTINGUISHABLE from the initial one - then the operation is a SYMMETRY OPERATION for that object. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/1.jpg)
![Page 2: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/2.jpg)
MOLECULAR SYMMETRYKnow intuitively what "symmetry" means - how to make it quantitative?
Will stick to isolated, finite molecules (not crystals).
SYMMETRY OPERATION
Carry out some operation on a molecule (or otherobject) - e.g. rotation. If final configuration isINDISTINGUISHABLE from the initial one - then theoperation is a SYMMETRY OPERATION for thatobject.
N.B. “Indistinguishable” does not necessarily mean“identical”.
![Page 3: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/3.jpg)
e.g. for a square piece of card, rotate by 90º as shown below:
1 2
4 3
4 1
3 2
90o
rotation
i.e. the operation of rotating by 90o is a symmetry
operation for this object
Labels show final configuration is NOT identical tooriginal.
Further 90º rotations give other indistinguishable configurations - until after 4 (360º) the result isidentical.
![Page 4: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/4.jpg)
SYMMETRY OPERATIONS
Motions of molecule (rotations, reflections, inversions etc.- see below) which convert molecule into configuration indistinguishable from original.
SYMMETRY ELEMENTS
Each element is a LINE, PLANE or POINT about which the symmetry operation is performed. Example above - operation was rotation, element was a ROTATION AXIS. Other examples later.
![Page 5: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/5.jpg)
Notes(i) symmetry operations more fundamental, but elements often easier to spot.
(ii) some symmetry elements give rise to more than one operation - especially rotation - as above.
ROTATIONS - AXES OF SYMMETRY
Some examples for different types of molecule: e.g.
H2OO
(1)H H(2)
O
(2)H H(1)
rotate
180o
Line in molecular plane, bisecting HOH angle is a
rotation axis, giving indistinguishable configuration
on rotation by 180o.
![Page 6: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/6.jpg)
BF3By VSEPR - trigonal, planar, all bonds equal,
all angles 120o. Take as axis a line
perpendicular to molecular plane, passing
through B atom.
B
(1)F F(2)
F(3)
B
(2)F F(3)
F(1)
120o
axis perpendicularto plane
N.B. all rotations CLOCKWISE when viewed along -z direction.
(1)F B
F(2)
F(3)
z
view down here
![Page 7: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/7.jpg)
C3: Isle of Man Coat of Arms
![Page 8: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/8.jpg)
Where is the Isle of Man?
![Page 9: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/9.jpg)
Symbol for axes of symmetry
Cnwhere rotation about axis gives indistinguishable
configuration every (360/n)o (i.e. an n-fold axis)
Thus H2O has a C2 (two-fold) axis, BF3 a C3 (three-fold)
axis. One axis can give rise to >1 rotation, e.g. for BF3,
what if we rotate by 240o?
B
(1)F F(2)
F(3)
B
(3)F F(1)
F(2)
240o
Must differentiate between two operations.
Rotation by 120o described as C31,
rotation by 240o as C32.
![Page 10: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/10.jpg)
C3
Picture byMC Escher
![Page 11: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/11.jpg)
In general Cn axis (minimum angle of rotation
(360/n)o) gives operations Cnm, where both m and
n are integers.
When m = n we have a special case, which introduces a new type of symmetry operation.....
IDENTITY OPERATION
For H2O, C22 and for BF3 C3
3 both bring the molecule
to an IDENTICAL arrangement to initial one.
Rotation by 360o is exactly equivalent to rotation by 0o,
i.e. the operation of doing NOTHING to the molecule.
![Page 12: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/12.jpg)
The operation of "doing nothing" may appear trivial, but it must be included in describing the symmetry of any molecule (reasons later!).
It is called the IDENTITY OPERATION , with the symbol E.
In general n rotations about a Cn axis are equivalent to the identity, and we can write:
Cnn = E
Including E we see that every rotation axis of symmetry, Cn, generates n operations:
Cn1, Cn
2, Cn3,.......Cn
n-1, Cnn (= E)
![Page 13: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/13.jpg)
MORE ROTATION AXES
xenon tetrafluoride, XeF4C4
Xe(4)F
F(1)
F(3)
F(2) Xe(3)F
F(4)
F(2)
F(1)90o
cyclopentadienide ion, C5H5–
C
C C
C
C
H(1)
H(2)
H(3)(4)H
(5)H
C5
C
C C
C
C
H(5)
H(1)
H(2)(3)H
(4)H.
72o
![Page 14: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/14.jpg)
![Page 15: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/15.jpg)
benzene, C6H6
C
CC
C
CC
H(1)
H(2)
H(3)
H(4)
(5)H
(6)H
C6
C
CC
C
CC
H(6)
H(1)
H(2)
H(3)
(4)H
(5)H
60o.
Examples also known of C7 and C8 axes.
Some additional points about symmetry axes:
![Page 16: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/16.jpg)
![Page 17: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/17.jpg)
![Page 18: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/18.jpg)
![Page 19: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/19.jpg)
![Page 20: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/20.jpg)
![Page 21: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/21.jpg)
![Page 22: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/22.jpg)
If a C2n axis (i.e. even order) present, then Cn must also be present:
C4
Xe(4)F
F(1)
F(3)
F(2) Xe(3)F
F(4)
F(2)
Xe(2)F
F(1)
F(3)
F(1)
F(4)
90o
i.e. C41
180oi.e. C4
2
( C21)
Therefore there must be a C2 axis coincident with C4, and the operations generated by C4 can be written:
C41, C4
2 (C21), C4
3, C44 (E)
Similarly, a C6 axis is accompanied by C3 and C2, and the operations generated by C6 are:
C61, C6
2 (C31), C6
3 (C21), C6
4 (C32), C6
5, C66 (E)
![Page 23: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/23.jpg)
Molecules can possess several distinct axes, e.g. BF3:
C3
F
B
F F
C2
C2
C2
Three C2 axes, one along each B-F bond, perpendicular to C3
![Page 24: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/24.jpg)
Reflection
![Page 25: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/25.jpg)
REFLECTIONS / PLANES OF SYMMETRY
e.g H2O
(1)H H(2)
O
z
y
x(2)H H(1)
O
(xz)
(v)
reflect
in (xz)
Reflect each half of the molecule through the plane shown gives an indistinguishable form, so reflection in that plane is a symmetry operation for H2O, and the plane is a PLANE OF SYMMETRY.
![Page 26: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/26.jpg)
Mirror Plane
![Page 27: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/27.jpg)
Operation = reflection
Element = plane of symmetrysymbol
Greek letter ‘sigma’
Several different types of symmetry plane -different orientations with respect to symmetry axes.
By convention - highest order rotation axis drawn VERTICAL.
Therefore any plane containing this axis is a VERTICAL PLANE, v.
e.g. H2O plane above (often also called (xz))
Can be >1 vertical plane, e.g. for H2O there is also:
![Page 28: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/28.jpg)
C2
σvσv’
![Page 29: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/29.jpg)
H(2)
O
(1)H
z
y
x
(yz) - reflection leaves all atoms unshifted, therefore symmetry plane
This is also a vertical
plane, but symmetrically
different from other, could
be labelled v'.
Any symmetry plane PERPENDICULAR to main axis is a
HORIZONTAL PLANE, h. e.g. for XeF4:
C4
XeF
F F
F
Plane of molecule (perp. to C4) is a
symmetry plane, i.e. h)
![Page 30: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/30.jpg)
Some molecules possess additional planes, as well as v and h,
which need a separate label. e.g. XeF4
F Xe F
F
F
v
v
d
d
Four "vertical"
planes - but two
different from
others.Those along
bonds called v, but
those bisecting
bonds d - i.e.
DIHEDRAL PLANES
Usually, but not always, v and d
differentiated in same way.
Two final points about planes of symmetry:
(i) if no Cn axis, plane just called ;
(ii) unlike rotations, only ONE operation per plane. A second reflection returns you to original state, i.e. ()() = 2 = E
![Page 31: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/31.jpg)
![Page 32: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/32.jpg)
![Page 33: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/33.jpg)
![Page 34: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/34.jpg)
![Page 35: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/35.jpg)
INVERSION : CENTRES OF SYMMETRY
z
y
x
z
y
x
inversion
.(x, y, z)
.(-x, -y, -z)
The origin, (0, 0, 0) is the centre of inversion. If the coordinates of every point are changed from (x,y,z) to (-x, -y, -z), and the resulting arrangement is indistinguishable from original - the INVERSION is a symmetry operation, and the molecule possesses a CENTRE OF SYMMETRY (INVERSION) (i.e. CENTROSYMMETRIC)
Involves BOTH rotation AND reflection.OPERATION : INVERSIONELEMENT : a POINT - CENTRE OF SYMMETRY or INVERSION CENTRE.
Best described in terms of cartesian axes:
![Page 36: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/36.jpg)
![Page 37: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/37.jpg)
Centre of inversion
![Page 38: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/38.jpg)
Centre of inversion?
![Page 39: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/39.jpg)
e.g. trans-N2F2
(1)N N(2)
(1)F
F(2)
(2)N N(1)
(2)F
F(1)
inversion.
centre of symmetry
In practice, inversion involves taking every atom to the centre - and out the same distance in the same direction on the other side.
Symbol - same for operation (inversion) and element (centre): iAnother example: XeF4
(4)F Xe F(2)
F(3)
F(1)
(2)F Xe F(4)
F(1)
F(3)
i
Xe atom is centre of symmetry
![Page 40: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/40.jpg)
Position of P given by x,y,z
![Page 41: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/41.jpg)
As for reflections, the presence of a centre of symmetry only generates one new operation, since carrying out inversion twice returns everything back to start.
(x, y, z)i
(-x, -y, -z)i
(x, y, z) i.e. (i)(i) = i2 = E
Inversion is a COMPOSITE operation, with both rotation and reflection
components. Consider a rotation by 180o about the z axis:
(-x, -y, z)(x, y, z)Follow this by reflection in the xy plane
(-x, -y, z) (-x, -y, -z)
i.e. net result is same as inversion
![Page 42: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/42.jpg)
BUT individual components need not be symmetry operations themselves.............
e.g. staggered conformation of CHClBr-CHClBr
H
ClBr
C C
H
ClBr
.
centre
Inversion at centre gives indistinguishable configuration.
The components, of
rotation by 180o or
reflection in a plane
perpendicular to the axis,
do not.
If, however, a molecule does possess a C2 axis and a h
(perpendicular) plane as symmetry operations, then
inversion (i) must also be a symmetry operation.
![Page 43: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/43.jpg)
IMPROPER ROTATIONS :ROTATION-REFLECTION AXES
Operation: clockwise rotation (viewed along -z direction) followed by reflection in a plane perpendicular to that axis.
Element: rotation-reflection axis (sometimes known as "alternating axis of symmetry")
As for inversion - components need not be themselves symmetry operations for the molecule.
![Page 44: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/44.jpg)
e.g. a regular tetrahedral molecule, such as CH4
H
C
H
H HH
C
H
H H
H
C
H
H H
rotate
90oreflect
four-fold rotation reflectionS4
1
Symbols: rotation-reflection axis Sn (element)
rotation-reflection Snm
(operations)
where rotation is through (360/n)o
![Page 45: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/45.jpg)
S4 axis requires presence of coincident C2 axis
If Cn and h are both present individually - there must
also be an Sn axis :
e.g. BF3 - trigonal planar
F B
F
F
C3, S3 h in plane of molecule.
C31 + h individually,
therefore S31 must also be a
symmetry operation
Other Sn examples: IF7, pentagonal bipyramid, has C5
and h, therefore S5 also.
Ethane in staggered conformation
S6C
H
HH
C
H
HH
i.e. rotate by 60o and
reflect in perp. plane.
Note NO C6, h
separately.
![Page 46: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/46.jpg)
C2H6
![Page 47: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/47.jpg)
Note sequence of symmetry operations generated by S3 axis:
S31, S3
2 (C32), S3
3 (h), S34 (C3
1), S35, S3
6 (E)
Also note : no reference to "S2" because this is i
(rotation by 180o + reflect in perp. plane)
Summary of symmetry elements and operations:
Symmetry element Symmetry operation(s)
– E (identity)
Cn (rotation axis) Cn1.....Cn
n-1 (rotation about axis)
(reflection plane) (reflection in plane)
i (centre of symm.) i (inversion at centre)
Sn (rot./reflection axis)Sn1...Sn
n-1 (n even) (rot./reflection about axis)
Sn1...Sn
2n-1 (n odd)
![Page 48: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/48.jpg)
POINT GROUPS
A collection of symmetry operations all of which pass through a single point
A point group for a molecule is a quantitative measure of the symmetry of that molecule
![Page 49: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/49.jpg)
ASSIGNMENT OF MOLECULES TO POINT GROUPS
STEP 1 : LOOK FOR AN AXIS OF SYMMETRY
If one is found - go to STEP 2
If not: look for
(a) plane of symmetry - if one is found, molecule
belongs to point group Cs
Assignment of molecules to point
groups
Step 1: Is there an axis of
symmetry?
Step 2: Are there C2
axes perpendicul
ar to Cn?
Are there n vertical
planes of symmetry?
Is there a horizontal plane of
symmetry?
Are there n vertical planes of symmetry?
Is there a plane of symmetr
y?
Is there a centre of symmetr
y?
Molecule inpoint group
Cs
Molecule inpoint group Cj
No symmetry except E:
point group C1
Molecule belongs to point group Dnh
Molecule inpoint group Dnd
Molecule inpoint group Cnh
Molecule inpoint group Cnv
Step 3: There are nC2's
perpendicular to Cn
Is there a horizontal plane of
symmetry?
N
N
N
N
N
N
Y
Y
YY
Y
YY
Y
![Page 50: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/50.jpg)
e.g. SOCl2S
O ClCl
.. No axis, but plane containing S, O, bisecting ClSCl angle, is a symmetry plane. Hence Cs point group.
If no plane is found, look for
(b) centre of symmetry - if one is found, molecule belongs to point group Ci.
e.g. CHClBrCHClBr (staggered conformation):
CC
H
ClBr H
ClBr No axis, no planes, but
mid-point of C-C bond is centre of symmetry. Therefore Ci point group.
No axes, plane or centre, therefore
(c) no symmetry except E : point group C1(so called because E = C1,
rotation through 360o)e.g. CHFClBr H
C
FCl
Br
No symmetry except E, therefore point group C1.
![Page 51: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/51.jpg)
STEP 2 : LOOK FOR C2 AXES PERPENDICULAR TO Cn
If found, go to STEP 3. If not, look for
(a) a HORIZONTAL PLANE OF SYMMETRY, if found - point group is Cnh
(Cn = highest order axis)
e.g. trans-N2F2:
F
N
N
F.
Highest order axis is C2
(perp. to plane, through
mid-pt. of N=N bond).
No C2 axes perp. to this, but
molecular plane is plane of
symmetry (perp. to C2, i.e.
h). Point group C2h.
If there is no horizontal plane, look for
(b) n VERTICAL PLANES OF SYMMETRY. If found, molecule belongs to point
group Cnv
![Page 52: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/52.jpg)
Many examples, e.g. H2O
H
O
HC2
C2 axis as shown. No other C2's, no
h, but two sv's, one in plane, one
perp. to plane, bisecting HOH angle.
Point group C2v
PCl3
P
ClCl
Cl
C3
C3 highest order axis
No C2's perp. to C3
No h, but
3 v's, each contains P, one Cl
Therefore C3v
BrF5 By VSEPR, square pyramidal
Br
F
F F
F
F
C4
Highest order axis : C4
No C2's perp. to C4
No h, but
4 vertical planes.
Therefore C4v
![Page 53: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/53.jpg)
N.B. of 4 vertical planes, two are v's, two d's
F Br F
F
F
v
d
d
v
(looking down C4 axis)
If no planes at all, could have
(c) no other symmetry elements: point group Cn , or
(d) an S2n axis coincident with Cn: point group S2n
![Page 54: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/54.jpg)
STEP 3 If there are nC2's perp. to Cn, look for:
(a) horizontal plane of symmetry. If present, point group is Dnh
e.g. ethene (ethylene), C2H4
C
C
H H
H H
C2
C2C2
Highest order axis C2 - along C=C bond
Two additional C2's as shown.
h in plane defined by the
last two C2's
Point group D2h
BF3
F B
F
F
C3
C2
C2
C2
Planar trigonal molecule by VSEPR
Main axis C3
3 C2's perp. to C3
h - plane of molecule
Point group D3h
![Page 55: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/55.jpg)
Ripening C2H4
![Page 56: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/56.jpg)
XeF4 Square planar by VSEPR
XeF
F F
F
C4
C2'C2"
C2"
C2'Main axis C4
4 C2's perp. to C4 (2 along XeF bonds (C2'), 2 bisecting, (C2"))
h - plane of molecule
Point group D4h
If no h, look for:
(b) n vertical planes of symmetry (v/d).
If these are present, molecule belongs to point
group Dnd
![Page 57: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/57.jpg)
e.g. allene, H2C=C=CH2.
CC
H
H
C
H
H C2 (main axis)
Looking down C=C=C bond
H
C
H
HH
C2'
C2'
Main axis C2 - along C=C=C
Two C2's as shown
Two vertical planes (d) - each containing one CH2 unit
Point group D2d
A few molecules do not appear to fit into this general scheme..........
![Page 58: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/58.jpg)
H2CCCH2
H2CCCH2
![Page 59: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/59.jpg)
Assignment of molecules to point
groups
Step 1: Is there an axis of
symmetry?
Step 2: Are there C2
axes perpendicul
ar to Cn?
Are there n vertical
planes of symmetry?
Is there a horizontal plane of
symmetry?
Are there n vertical planes of symmetry?
Is there a plane of symmetr
y?
Is there a centre of symmetr
y?
Molecule inpoint group
Cs
Molecule inpoint group Cj
No symmetry except E:
point group C1
Molecule belongs to point group Dnh
Molecule inpoint group Dnd
Molecule inpoint group Cnh
Molecule inpoint group Cnv
Step 3: There are nC2's
perpendicular to Cn
Is there a horizontal plane of
symmetry?
N
N
N
N
N
N
Y
Y
YY
Y
YY
Y
![Page 60: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/60.jpg)
LINEAR MOLECULES
Molecular axis is C - rotation by any arbitrary angle
(360/)o, so infinite number of rotations. Also any plane
containing axis is symmetry plane, so infinite number of
planes of symmetry.
Divide linear molecules into two groups:
Do in fact fit into scheme - but they have an infinite number of symmetry operations.
(i) No centre of symmetry, e.g.: H C N C
No C2's perp. to main axis, but v's containing
main axis: point group Cv
![Page 61: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/61.jpg)
HCN Zyklon - B
![Page 62: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/62.jpg)
HCN in Space - Titan
![Page 63: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/63.jpg)
(ii) Centre of symmetry, e.g.:
C2
O C O
C2
C
hi.e. C + C2's + h
Point group Dh
A few geometries have several, equivalent, highest order axes. Two geometries most important:
Highly symmetrical molecules
![Page 64: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/64.jpg)
Regular tetrahedron
e.g. Cl
Si
ClCl
Cl
4 C3 axes (one along each bond)
3 C2 axes (bisecting pairs of bonds)
3 S4 axes (coincident with C2's)
6 d's (each containing Si and 2
Cl's) Point group: Td
Regular octahedron
e.g.
SF
F F
F
F
F
3C4's (along F-S-F axes)also 4 C3's. 6 C2's, several planes, S4, S6 axes, and a centre of symmetry (at S atom) Point group Oh
These molecules can be identified without going through the usual steps.
Note: many of the more symmetrical molecules possess many more symmetry operations than are needed to assign the point group.
![Page 65: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/65.jpg)
SiCl4
![Page 66: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/66.jpg)
SiF4
![Page 67: Will stick to isolated, finite molecules (not crystals)](https://reader036.vdocuments.net/reader036/viewer/2022062314/56812bf4550346895d906b14/html5/thumbnails/67.jpg)