the determination of point groups of molecules only one rotational axis = c 2 two σ v but no σ h...
TRANSCRIPT
The determination of point groups of molecules
only one rotationalaxis = C2
two σv but no σh mirror planes means
point group is C2v
The point group of the water molecule is C2v
Naming point groups:The name of the point group has information about the symmetry elements present. The letter is the rotational group and the subscript number after the letter indicates the order
of the principal rotational axis (e.g. 3-fold or 4 fold etc.):
C3 C3v D4d D4h
A ‘C’ indicates only one rotational axis
A ‘D’ indicates an n-foldprincipal rotation axisplus n 2-fold axes at right angles to it
3-fold rotational has σv but 4-fold d = no ‘h’ indicates
axis no σh mirror principal σh mirror a σh mirror planes in a C group axis plane plane
A subscript ‘h’ means that there is a σh mirror plane at right angles to the n-fold principal axis:
Naming point groups (contd.):
D4h
C4 principal axis
σh
C3 principal axis
σv
A subscript ‘d’ (or v for C groups) means there is no σh mirrorplane, but only n σv mirror planes containing the principal Cn axis.
only oneof the three
σv planes
is shown
D3d
Naming platonic solids:
Platonic solids: T = tetrahedral = 4 three-fold axes O = octahedral = 3 four-fold axes I = icosahedral = 6 five-fold axes
Td Oh Ih
C60
‘bucky-ball’or ‘Fullerene’
Flow chart for determining point groups.
The point group of the carbon dioxide molecule
We start at the top of theflow-chart, and can see thatthe CO2 molecule is linear, and has a center of inversion
(i) so it is D∞h. Note the C∞
principal rotation axis.
i
C∞
D∞h
Other linear molecules:
HC≡N HI C≡O
N2 O2 F2 H2
D∞h
C∞v
i i
The top row of linear molecules all have a center ofinversion (i) and so are D∞h.
The bottom row have noi and so are C∞v
All have a C∞
axis
The Platonic solids:
Td Oh Ih C60
‘buckyball’
tetrahedron octahedron icosahedron
The Cs point group:
Cs
σ
chloro-difluoro-iodo-methane
I
FCl
C
F
Most land animals have bilateral symmetry, and belong to the Cs point group:
Mirror planes (σ)Cs Cs
The C1 point group:
Molecules that have no symmetry elements at all except the trivial one where they are rotated through 360º and remain unchanged, belong to the C1 point group. In other
words, they have an axis of 360º/360º = 1-fold, so have a
C1 axis. Examples are:
Bromo-chloro-fluoro-iodo- chloro-iodo-amine methane
I
Br
F
ClC
I
Cl
H
N
C1C1
The division into Cn and Dn point groups:
After we have decided thatthere is aprincipal rotat-ional axis, wecome to thered box. If thereare n C2 axesat right anglesto the principalaxis, we have aDn point group,If not, it is a Cn
point group.
Dn
Cn
The Cn point groups:
The Cn point groups all have only a single rotational
axis, which can theoretically be very high e.g. C5 in the complex [IF6O]- below. They are further divided
into Cn, Cnv, and Cnh point
groups. The Cn point groups have no other symmetry elements, the Cnv point groups have also n mirror planes containing the Cn rotational
axis, while the Cnh point
groups also have a σh mirror plane at right angles to the
principal rotational axis.
C5
iodine
[IF6O]-
O
F
F
The point group of the water molecule
We start at the top of theflow-chart, and can see thatthe water molecule is notlinear, and is not tetrahedral (Td),
octahedral (Oh), or icosahedral,
(Ih) so we proceed down the chart
C2 Yes, there is a principal Cn axis,
so we proceed down the chart, butin answer to the next question, thereare no further C2 axes at right anglesto the principal axis, which is the onlyaxis, so we proceed down the chart
The point group of the water molecule is C2v
there is no σh plane
at right angles tothe C2 axis, but
there are two σv
planes containingthe C2 axis.
C2 C2C2
σv σv
Other Cnv molecules:
C2v
C3v
C4v
ammoniawater
σv
σv
σv
Vanadyl tetrafluoride (VOF4)
V
Some more C2v molecules:
σv
σv
σvσv
σvσv
C2 C2C2
Phosphorus iodo- sulfur tetra- carbonyltetrafluoride (PF4I) fluoride (SF4) chloride (COCl2)
CSP
These have a Cn axis as their only symmetry element. They
generally resemble propellers which have the front and back different. Important examples are (hydrogens omitted for clarity):
The Cn point groups:
C3C3
C3 C3
C3
C3 triphenyl phosphineviewed down C3 axis
Cobalt(III)tris-glycinateviewed down C3 axis
triphenyl phosphineviewed from the side
Cobalt(III)tris-glycinateviewed from the side
The Dnh point groups:
C2 σh
four C2
axes atrt. anglesto C4 axis
C2C2
C2
C4 principal axis
mirror planeat rt. anglesto C4 axis
D4h
Examples of molecules belonging to Dnh point
groups:
D2h D3h D3h D3h
D4h D4h D5h D5h
C2 C3C3 C3
C4
C4C5 C5
C6
principal axisC2 C2
C2C6C2
σvσv
Benzene, an example of the D6h point group:
σh
C6
principal axis
C6
principal axis
D6h
The Dn point groups:
C2
C2
C2 principal axis
D2
these have a principal
n-fold axis, and n2-fold axes at rightangles to it, but nomirror planes.
[Cu(en)2]2+ complex with H-atomsomitted for clarity. (en = ethylene diamine)
CuN
NC
Some further views of the symmetry elements of [Cu(en)2]2+, point group D2 :
C2
[Cu(en)2]2+ complex with H-atomsomitted for clarity. (en = ethylene diamine)
C2
C2
C2
C2
C2
C2 principal
axis
C2 principal axis
C2 principal
axis
C2 principal
axis
C2C2
D2
C2
C2
C2
C3 principal axis
Some views of the symmetry elements of [Co(en)3]3+, point group D3.
C3
principal axis
C2
axis
view down the C3 axisof [Co(en)3]3+ showing
the three C2 axes.
D3
view down one of the three C2 axes of [Co(en)3]3+
at right angles to C3
Other examples of the D3 point group
[Co(oxalate)3]3- [Co(bipyridyl)3]3+
C2 C2
C2
C2
C2
C2C3
principal axis
D3D3
Some cobalt(III) complexes belonging to the D3 point group:
NH2
Co
NH2
H2NH2N
H2N NH2
Co
N
N
N
N
N
N
CoO
O
O
O
O
O
CH3
H3C
H3C
CH3
CH3
CH3
3+ 3+
tris(ethylenediamine) tris(2,2’-bipyridyl) tris(acetylacetonato)cobalt(III) cation cobalt(III) cation cobalt(III)
D3
C2 C2C2
Comparison of C3 and D3 tris(chelates)
NH2
Co
NH2
H2NH2N
H2N NH2
O
Co
NH2
H2NH2N
O O
3+O
O
O
D3 C3C2
no C2 axis at
this point
tris(ethylenediamine)cobalt(III) tris(glycinato)cobalt(III)
Molecules belonging to the Dnd point groups
These have mirror planes parallel to the principal axis, but not at right angles to it.
C3 axisC5 axis
Staggered form of ethane Staggered form of ferrocene
σv planescontain theprincipalaxis
D3d D5d
The D4d point group:
C2 C2
C2 C2
C4
principal axis
C4 principal axis
C2
σv
σv
σv
σv
C4
principal axis [ZrF8]4-
Square antiprism
As predicted by VSEPR, the [ZrF8]4- anion has a square anti-prismaticstructure. At left is seen the C4 principal axis. It has four C2 axes atright angles to it, so it has D4 symmetry. One C2 axis is shown side-on
(center). There are four σv mirror planes (right), but no mirror plane at
right angles to C4, so the point group does not rate an h, and is D4d.
D4d
[K(18-crown-6)]+, an example of a D3d
point group:
The complex cation [K(18-crown-6)]+ above is an important structure that
has D3d symmetry. It has a C3 principal axis with 3 C2 axes at right
angles to it, as well as three σv mirror planes that contain the C3 axis,
but no σh mirror plane (because it’s not flat, as seen at center), so is D3d.
D3d
σv
σv
K+
C3
principal axis C3 principal axis
σv
C2 C2
C2
C2
C2
C2
Some Point groups