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Chem 332.3 Fall 2005
Instructor:
Lab Manager:
Course Web Site:
Course Text:
Lecture Hours:
Laboratory Hours:
Molecular Symmetry
Inorganic Chemistry II
Why is symmetry important?
Dr. Stephen Foley, Office: Thorv 255
Tel: 966-2960; email: [email protected]
Dr. Pia Wennek, Office: SG 32
Tel: 966-1628; e-mail: [email protected]
http://www.usask.ca/chemistry/courses/332/
C. E. Housecraft and A. G. Sharpe, Inorganic Chemistry, 2nd Ed. 2005, Pearson/Prentice Hall.
Mon, Weds, and Fri: 11:30-12:20 in Thorv 125
Mon, Tues: 1.30-5.30 in SG 215
Method of Evaluation:
Final Exam (3 hour):
Mid-term Exam:
Assignments (including oral presentation):
Laboratory:
- Symmetry is important for all kind of spectroscopy!
- Usage of symmetry simplifies theoretical calculations
- Many properties are symmetry related
50%
15%
10%
25%
Course Description: An introduction to transition metal chemistry including coordination geometry and stereochemistry, ligand field theory,
spectroscopic, magnetic and thermodynamic properties of inorganic compounds, organometallic chemistry and homogeneous catalysis. The
laboratory work includes experiments on the preparation and characterization of transition metal compounds.
Topics to be covered (Chapter references are to Housecraft et al.):
Molecular Symmetry (Chapter 3)
Coordination Chemistry
Molecular structure and bonding (Chapters 1, 20)
d-block metal complexes (Chapters 19, 20)
Electronic spectra of complexes (Chapter 20)
NMR spectroscopy in inorganic chemistry (Chapter 2)
Descriptive Chemistry of the Transition Metal Elements (Chapters 21-22)
Organometallic Chemistry of the d-block (Chapter 23)
Types of ligands. Bonding. Electron counting. Reaction mechanisms.
Catalysis (Chapter 26 )
General Principles. Homogeneous catalysis.
Symmetry element
Symmetry operation
Application of a symmetry operation must not alter the
molecule or its properties.
A symmetry operation (SO) is a movement of a body
such that, after the movement has been carried out,
every point of the body is coincident with an equivalent
point (“before and after are the same”).
Effect of a SO is to take the body into an equivalent
configuration.
Each symmetry operation is related to a symmetry
element.
A symmetry element (SE) is a geometrical entity (a
line, a plane, a point) with respect to which one or
more SOs may be carried out.
SO: Proper rotation by 2π/n or 360°/n
Symbol
1
SE: Axis of rotation Cn
- the molecule appears unchanged after a rotation by 360°/n.
Identity
E
n-Fold symmetry axis
Rotation by 2π/n
Cn
Mirror plane
Reflection
σ
Center of inversion
Inversion
i
n-Fold symmetry axis
of improper rotation
Rotation by 2π/n
Sn
principal rotation axis
- in cases in which more than one rotational axis is present, the one of highest order
followed by
reflection
perpendicular to
rotation axis
Note that E is a special case of Cn, and that i and σ are special cases of Sn:
E = C1, S1 = σ, S2 = i.
2
4
SO: Reflection
SE: Mirror planes σ
- reflection of all atoms through a plane passing through the molecule.
C6
σv vertical plane
- plane that contains the principal axis
σd dihedral plane
- plane that contains the principal axis
and bisect the angle formed between adjacent
C2 axes.
*
σh horizontal plane
- plane perpendicular to the principal axis
5
1
2
SO: Inversion
SE: Center of inversion i
- if it is possible to move in a straight line from every atom of a molecule through a
single point to an identical atom at the same distance on the other side of the
center, the molecule has a center of inversion.
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SO: Improper rotation by 2π/n
SE: n-Fold symmetry axis Sn
- the combination of a rotation by 360°/n followed by reflection across a plane
perpendicular to the rotation axis.
S4
S1 = σ
S2 = i
15
SO: Identity
- the identity operation is denoted by E.
- it leaves the whole molecule unchanged.
- every molecule has at least this operation.
- it is included for mathematical completeness.
Point group
17
symmetry element
shape
examples
C1
E
SiBrClFI
C2
E, C2
H2O2
Cs
E, σ
NHF2
C2v
E, C2, σv, σv
H2O, SO2Cl2
NH3, PCl3, POCl3
C3v
E, C3, 3 σv
C∞v
E, C∞, ∞σv
CO, HCl, OCS
D2h
E, C2(x, y, z), σ(xy,yz,zx), i
N2O4, B2H6
D3h
E, C3, 3 C2, 3 σv, σh, S3
BF3, PCl5
D4h
E, C4, 2 C2’, 2 C2’’, i, S4, σh, 2 σv, 2 σd
XeF4, trans-MA4B2
D∞h
E, C∞, ∞C2, ∞σv, i, S ∞
H2, CO2, C2H2
Td
E, 4 C3, 3 C2, 6 σd, 3 S4
CH4, SiCl4
Oh
E, 3 C4, 4 C3, 6 C2, i, 4 S6, 3 S4, 3 σh, 6 σd
SF6
18
3
The Point Groups of Molecules
Determination of the point group of a molecule: method 1
1. Locate the principal axis of symmetry , this determines the index n.
2. Locate secondary axes C2, C3, C4, or C5 at an angle to the principal axis.
This determines the primary symbol C, D, T, O or I.
none →C, nC2 →Dn, 4 C3 and C2 →T, 3 C4 and C2, C3 →O, 6 C5 and C2, C3 →I.
3. Identify the mirror planes and their positions with respect to the principal axis.
This determines the index h, v or d.
or method 2 : Use the decision tree.
Point group
Number of SOs
Cn
n
Cnv, Cnh, Dn
2xn
groups of n-folded rotation axis: Cn, Cnv, Cnh
Dnd,Dnh
2x2xn
dihedral groups: Dn, Dnh, Dnd
Td
24
Oh
48
Ih
120
groups of low symmetry: C1, Cs, Ci
groups with very high symmetry: Td, Oh, Ih
22
Decision tree for identifying a molecular point group
Applications of Symmetry
Polar molecules
A polar molecule is a molecule with a permanent dipole moment.
Dipole moment: µ = δ x d (unit = debye (D)).
Certain symmetry elements rule out a permanent electric dipole moment in molecules:
A molecule cannot be polar if it has a center of inversion.
A molecule cannot have an electric dipole moment perpendicular to any mirror plane.
A molecule cannot have an electric dipole moment perpendicular to any axis of rotation.
Symmetry forbidden:
(with respect to possible dipole moments)
Ci
Sn
Cnh (Cn + σh)
Dn (Cn + n C2)
Dnh (Cn +n C2 + σh)
Dnd (Cn + n C2)
Td (4 C3 + 3 C2)
Oh (i, C4 + 4 C2, and σh)
Ih (i, C5 + 5 C2, and σh)
Symmetry allowed:
C1
Cs
Cn
Cnv
24
4
Applications of symmetry
Chiral molecules
A chiral molecule is a molecule that cannot superimposed on its own mirror image.
Chiral molecules are optically active (they can rotate the plane of polarized light).
In organic chemistry chirality is based upon
asymmetric carbon atoms
(nonsuperimposable mirror image).
Inorganic molecules may be optically active based on asymmetric atoms (N, P, or S),
but most compounds are chiral because of the overall molecular symmetry.
Chiral
Achiral (identifying symmetry element)
C1 (asymmetric)
Cn (dissymmetric)
Dn (dissymmetric)
Cs
Ci
Dnh
Dnd
Sn
Td
Oh
Ih
Cnv
Cnh
(plane of symmetry)
(center of symmetry)
(plane of symmetry)
(plane of symmetry)
(improper axis)
(plane of symmetry)
(center and plane of symmetry)
(center and plane of symmetry)
(plane of symmetry)
(center and plane of symmetry)
A molecule is not chiral if
it possesses an improper rotation axis Sn
(recall that S1 = σ and S2 = i)
25
26
5
IR Spectroscopy
IR Spectroscopy
(Excitation of molecular vibrations by infrared radiation).
Number of independent motions of an N atomic molecule is 3N.
Number of vibrational modes of a molecule is
3N-6 (or 3N-5 if linear) = number of the normal modes.
Wavenumber: ν = cm-1 region: 4000-40 cm-1
stretching
bending
stretching
32
IR Spectroscopy
The four normal modes for CO2.
A vibration is infrared active, when there is a change of
the dipole moment.
Therefore the symmetric stretching mode is IR inactive.
Information from the symmetry of normal modes
square-planar complexes
Both have bands in the Pd-Cl stretching region between 200-400 cm-1.
33
6
Coordination Chemistry
Coordination Compound
Coordination Chemistry
MLn
Central metal atom M surrounded by a set of ligands L. n is the number of ligands
and corresponds to the coordination number n of the center atom.
Combination of a Lewis acid (center metal atom) and a Lewis base (ligand).
Chapter 19 (Housecroft)
Ligand
May be charged or uncharged, and may consist of one
or more atoms.
Donor atom
The atom in the ligand which forms the bond to the
centre atom.
Metal atom or ion, which is the Lewis acid. .
Acceptor atom
Examples:
[Co(NH3)6]Cl3
Ni(CO)4
[PtCl4]2-
Trichlorohexaamminecobalt(III)
Tetracarbonylnickel
Tetrachloroplatinate(II)
42
7
Coordination Chemistry
Organometallic Chemistry
One class of coordination compounds which involves metal carbon bonds.
Bioinorganic Chemistry
Coordination compounds which are present in living organism.
Alfred Werner (Swiss chemist 1866-1919)
Nobel prize in chemistry 1913
"in recognition of his work on the linkage of atoms in
molecules by which he has thrown new light on earlier
investigations and opened up new fields of research
especially in inorganic chemistry"
First Nobel prize in inorganic chemistry.
43
d-orbitals
8
Coordination Chemistry
The problem:
4 coordination compounds of cobalt (III) chloride with ammonia has been
discovered and named according to their colours:
CoCl3·6NH3
CoCl3·5NH3
CoCl3·4NH3
CoCl3·4NH3
Addition of
CoCl3·6NH3
CoCl3·5NH3
CoCl3·4NH3
yellow
purple
green
violet
Luteo complex
Purpureo complex
praseo complex
violeo complex
Ag+:
+ excess Ag+ →
+ excess Ag+ →
+ excess Ag+ →
3AgCl (s)
2AgCl (s)
1AgCl (s)
Werner’s conclusion:
Compound Co(NH3)5Cl3 is derived from compound Co(NH3)6Cl3 by loss of
one ammonia. With this loss a change in function of one chloride ion occurs (one
chlorine no longer acts as an ion).
Werner’s formulation of the compounds:
[Co(NH3)6]Cl3, [Co(NH3)5Cl]Cl2, [Co(NH3)4Cl2]Cl,
Difference in the conductivity.
50
Coordination Chemistry
Coordination Chemistry
Werner assigned the correct geometric structure to many coordination compounds
long before any direct methods were able to determine structures.
(like X-ray diffraction, nuclear magnetic resonance)
He used patterns of reactions and isomerism.
Example: The structure of [Co(NH3)6]3+
Geometrical isomerism in six-coordination
[MX4Y2]
His postulation: Symmetrical arrangement of the ammonia molecules around the
center cobalt atom.
The numbers of isomers found was equal to that expected for an octahedral
complex.
[MX3Y3]
51
mer (for meridional)
fac for facial
52
9
Coordination Chemistry
Central metal atom could have coordination numbers from 2 to 12.
Three factors determine the coordination number of a complex:
1. The size of the central atom or ion.
2. The steric interactions between the ligands.
3. Electronic interactions.
Higher coordination numbers in the complexes of atoms and ions in
period 5 and 6.
Higher coordination numbers on the left side of a row of the d-block.
Especially when the metal ion has only few d electrons, so that it can
accept more electrons from Lewis bases.
e.g. [Mo(CN)8]4- octacyanomolybdate(IV)
Low coordination numbers with bulky ligands.
Lower coordination numbers are found on the right side of the d-block.
Especially when the metal ion has a high number of d electrons.
e.g. [PtCl4]2tetrachloroplatinate(IV)
57
Coordination Chemistry
Coordination Chemistry
Ligands
Ligands
monodentate ligands - one point of attachment to the metal atom
The ligand ethylendiamintetraacetato can attach the
metal at six points and can form five five-membered
rings.
complexometric titration of Ca2+or Zn2+
Br-, Cl-, OH- H2O, NH3, CO,
polydentate ligands - more than one point of attachment
(CH3COCHCOCH3)- (acac), H2NCH2CH2NH2 (en) , C2O42- (ox)
Bite angle
L-M-L angle in the chelate
a bidentate ligand with a small bite angle can
result in distortions from standard structures.
ambidentate ligands - different potential donor atoms
NO2-, SCNchelating ligand - polydentate ligands can produce a chelate, a complex in
which the ligand forms a ring that includes the metal atom.
five- and six-membered chelate rings are especially stable.
59
acetylacetonato
distortion from octahedral to
trigonal-prismatic
60
10
Coordination Chemistry
Coordination Chemistry
Optical isomers
Chirality and optical isomerism in six-coordination
chiral – not superimposable on its own mirror image
enantiomers – two mirror-image isomers
View along a three-folded rotation axis
to determine the handedness of the helix
formed by the ligands.
trans-[CoCl2(en)2]
enantiomers of cis-[CoCl2(en)2]
Remember the criterion for chirality is the absence of an axis of improper
rotation, which includes the absence of a mirror plane σ = S1 and the absence
of an inversion center i = S2.
right-hand
screw
left-hand
screw
61
62
Chelate Effect
The chelate effect or chelation is one of the most important ligand effects
in transition metal coordination chemistry. Since most metal-ligand
bonds are relatively weak compared to C-C bonds, M-L bonds can often
be broken rather easily, leading to dissociation of the ligand from the
metal. Consider the two metal ligand complexes shown below:
L
M
“eta-x” was originally developed to indicate how many carbons of a π-system
were coordinated to a metal center. Hapticity is another word used to
describe the bonding mode of a ligand to a metal center.
L
L
M
ηx
+
L
L
L
L
M
L
M
µx
“mu-x” is the nomenclature used to indicate the presence
of a bridging ligand between two or more metal centers.
The x refers to the number of metal centers being bridged
by the ligand. Usually most authors omit x = 2 and just use
µ to indicate that the ligand is bridging the simplest case of
two metals.
Hund’s Rule
¾Rule to fill electrons into p,d,f orbitals containing more than one sublevel of
the same energy.
¾filling p, d, f orbitals: Put electrons into separate orbitals of the subshell with
parallel spins before pairing electrons.
¾The existence of unpaired electrons can be tested for since each acts like a
tiny electromagnet.
¾Paramagnetic - attracted to magnetic field. Indicates the presence of
unpaired electrons.
¾Diamagnetic - pushed out of a magnetic field. Indicates that all electrons are
paired.
11
Molecular Structure
And Bonding
Chapter 4
67
Bonding of Coordination Compounds
Valence Bond Theory of Complexes
1930 developed by Linus Pauling and J.C.Slater
Covalent approach: the bonded atoms share an electron pair.
The two electrons come from the same atom, the ligand L.
Metal atom or ion is acting as a Lewis acid
Ligand is acting as a Lewis base
Use of hybridization of metal s, p, and d valence orbitals
This model makes it possible:
- to predict composition and stability
- to interpret the structure and magnetic properties of the complexes
This model cannot explain the colours of complexes
(spectroscopic properties).
69
12
13
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