CH160 (Coordination Chemistry – APD) Tutorial 2
1. Sketch or describe all of the associated symmetry elements detailed for the following:
(a) The tetrahedral complex [Co(Cl)4]- (symmetry operations: E, C3, C2, S4 and d).
(b) The square planar complex [Pt(Cl)4]2- (symmetry operations: E, C4, C2, i, S4, σh, σv, σd).
(a)
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(b)
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E is the identity operation i.e. nothing is done to the molecule
C3 axis coincident with each metal-ligand bond ( N.B. rotation anticlockwise is different to
clockwise as they result in different operations)
C2 axes bisects each LML angle. Drawing the tetrahedron in a cube means each axis goes
through the centre of opposite faces of the cube. There are 3 mutually perpendicular to
each other.
The S4 axes are coincident with the C2 axes (clockwise and anticlockwise rotations are not
identical) – they have seen these in lectures.
Each d mirror plane contains a C3 rotation axis. The plane
also contains two M-L bonds. The planes are ‘dihedral’
because they bisect an angle made by two C2 axes. For the
‘tetrahedron in a cube’, each mirror plane cuts diagonally
across a face (shaded bit in picture). There is one mirror
plane per face of the cube so 6 in total.
E is the identity operation i.e. nothing is done to the molecule
C4 axis through what would be the axial bonds ( N.B. rotation anticlockwise is different to
clockwise as they result in different operations)
C2 axes (there are 3 types). One type is along the Cl-Pt-Cl bond, another bisects each LML
angle and the third is coincident with the C4 axis.
i is at the Pt atom
The S4 axes are coincident with the C4 axes (clockwise and anticlockwise rotations are not
identical).
h, v and d mirror planes are along the plane of the bonds (h), in the plane of the Cl-PtCl bonds and C4 axis (v) and in the plane of the remaining C2 axis (bisects each LML
angle) and the C4 axis.
2. Identify all of the symmetry operations for the following complexes and assign the point group.
NOTE: ignore ligand symmetry when assigning point groups etc. students should only think about
each ligand as a point
(a) HCN
(b) CO2
(c) [VO(acac)2] (where acac is 2,4-pentane dione and the O is axial) (classic square based
pyramid)
(d) PCl5 (this will be a trigonal bipyramid)
(e) PClF4 (with Cl equatorial)
(f) fac-[CrCl3(OH2)3]
(g) mer-[CrCl3(OH2)3]
(h) trans-[CrCl2(OH2)4]
(i) cis-[CrCl2(OH2)4]
(j) Mo(CO)6
Symmetry operations – and elements
E – identity
C∞ - along bonds
v – through the middle of the molecule along the HCN axis
Point Group
C∞v
b)
E – identity
C∞ - along bonds
C2 – through C (there are ∞ of them!)
i – at C
v – through the middle of the molecule along the HCN axis
D∞v
c)
E - identity
C2 – down V-O bond
v – through plane including V-O bond and bisecting acac ligands
v’ – perpendicular to the other v
C2v
d)
E - identity
C3 – through axial Cl-P-Cl bonds
C2 – 3x perpendicular to C3 through one side and one face
S3 - same as C3 axis (different as atoms end up in different places)
h – perpendicular to C3
v – 3x plane includes one side and bisects opposite face
D3h
e)
E - identity
C2 – along P-Cl bond
v – 2x through plane including Cl, P and F
C2v
a)
f)
E - identity
C3 – between axial and equatorial atoms (note clockwise and anti clockwise
are different)
v – 3x through plane including Cl, Cr and OH2
C3v
g)
E - identity
C2 – down Cl-Cr-O bond
v – through plane including Cr, 3x Cl and 1x OH2
v’ – through plane including Cr, 1x Cl and 3x OH2
C2v
h)
E - identity
C4 – along Cl-Cr-Cl bond (goes both ways)
C2, C2’, C2’’ – same as C4 and 2x perpendicular to C4 along OH2-Cr-OH2
bonds as well as 2x bisecting OH2-Cr-OH2 bonds
i – at Cr
S4 - same as C4 axis (different as atoms end up in different places)
h – perpendicular to C4
v – 2x includes both Cl-Cr bonds and 2x OH2-Cr bonds
d – 2x includes both Cl-Cr bonds and bisects 2x OH2-Cr-OH2 bonds
D4h
i)
E - identity
C2 – down bisecting Cl-Cr-Cl bond and through Cr
v – plane including Cr, 2x Cl and 2x OH2
v’ –plane including C2 axis, Cr and 2x OH2
C2v
j)
E - identity
C3 – between axial and equatorial atoms (note clockwise and anti clockwise
are different)
C4 – Along each L-M-L bond
C2 – same as C4 (3x) and bisecting LML each angle (6x)
i – at Mo
S4 – 3x same as C4 axis (different as atoms end up in different places)
S6 – 4x same as C3 axis (different as atoms end up in different places)
h – perpendicular to each C4 axis
d – bisecting equatorial LML angle and through axial L-M-L bond (6x)
Oh
Point group tree from Shriver and Atkins: