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Topics

• Introduction• Molecular Structure and Bonding• Molecular Symmetry• Coordination Complexes• Electronic Spectra of Complexes• Reactions of Metal Complexes• Organometallic Chemistry

Symmetry

• Powerful mathematical tool for understanding structures and properties

• Use symmetry to help us with:– Detecting optical activity and dipole

moments– Forming MO’s– Predicting and understanding spectroscopy

of inorganic compounds• Infrared, Raman and UV-visible

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Symmetry and Your Text(s)

• Symmetry tools and language– Sec 4.1-4.4 (Atkins)

3.1-3.6, 4.4 (Housecroft)– Flow chart p.122 (Atkins)

p.81 (Housecoft)• Bonding Theory

– Sec 4.5-4.7 (Atkins)– Box 4.1, sec 4.5-4.7 (Housecroft)

Symmetry and the Exam

• Recognize symmetry elements• Identify the important elements present in a

molecule• Assign the point group of an object or

molecule• Read a character table

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Symmetry Elements

• A symmetry element is present if the operation is performed and the object is indistinguishable from its original state

Do nothingIdentityE

Rotation as Cn followed by reflection in perpendicular mirror plane

Improper rotation axisSn

Inversion through the center of the object

Center of inversioni

Reflection through a planemirror planeσ

rotate by 360°/nn-fold rotationCn

OperationNameElement

Center of Inversion: I

• Inverts all atoms through the centre of the object

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Inversion vs Rotation (C2)

Mirror Planes: σ

• Reflection of object through a mirror plane• Objects in the plane are reflected onto

themselves, objects on either side of the plane are reflected to the other side

• Three types– σh : Horizontal, perpendicular to principal axis– σv : Vertical, parallel to principal axis– σd : Dihedral, same plane as σv related by half a

rotation of the principal axis

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Dihedral vs. Vertical

• Typically σd and σv are related by rotation of 180/n

• Labelling:– Exception: when n=2, label is σv’ not σd

• Rule of Thumb: dihedral planes pass through fewer atoms (i.e. is dihedral to the angle of the bonds)

• Rotate 360/n followed by reflection in mirror plane perpendicular to axis of rotation

• All planar molecules have an Sn

Improper Rotation Axis: Sn

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Special Cases: S1 and S2

• S1= σh and S2 = i

Comparing Symmetry

• Compare NH3 and BF3

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Point Groups

• collections of symmetry elements are summarized into Point Groups– these are groups as strictly defined by

mathematical group theory • short form method for identifying all of the

symmetry elements present in a molecule

CO

Mo

CO

OC CO

COOCOh 8C3, 6C2, 6C4, i,

3C2, 6S4, 8S6, 3σh, 6σd

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Identifying Molecular Symmetry

• Requires knowing molecular geometry– First draw a Lewis structure– Use VSEPR to predict molecular geometry– Use VSEPR geometry to identify symmetry

elements present– Classify molecule according to its point group

Lewis Structures

1. Count valence electrons available, include net charges.

2. Write skeleton structure, drawing bonds between atoms using up two valence electrons for each bond.

3. Distribute remaining electrons to most electronegative species first to fill electron shells.

4. Satisfy unfilled octets where possible by drawing multiple bonds

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Resonance Structure and Formal Charge

• Resonance allows for non-integer bond order and delocalized electron distribution

• Formal Charge– Predicts which of multiple possible structures are

more favourable

electronsunsharedelectronsbondedgroupFC 21# −−=

VSEPR

• Relies on the electron distribution around the central atom– Bonded pairs

• Typically ignore bond order (1,2 etc)• Ignore what atom it is bound to• Occupy less volume than lone pair

– Lone pairs (on the central atom)• Bulkier than bonds• Have largest impact on molecular geometry

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Examples

• trans-CrCl4O2

• PCl5

Character Tables

• Character tables are “tell-all” manuals of symmetry, tabulated in your text

• Using group theory, lists of behaviour under the symmetry elements in a point group are tabulated, these are called “irreducible representations” and they are said to “span” the group– Therefore, a portion of a molecule can be

described by some linear combination of these irreducible representations.

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Reading the Character Tables

Character values:1 means no change-1 means change of sign2, 0 sum of multicomponent behaviour

(x2-y2,xy)(x,y), (Rx,Ry)0-12E

Rz-111A2

x2+y2+z2z111A1

3σv2C3EC3v

Mulliken Labels

• A,B,E,T – indicating degeneracy• A vs B : symmetric or antisymmetric wrt highest order

rotation axis• 1,2 : symmetric or antisymmetric wrt C2 axis or σv

• g,u : symmetric or antisymmetric wrt i• ‘,” : symmetric or antisymmetric wrt σv

• MO are labeled with the Mulliken labels using lower case to differentiate them from irreducible representations

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D3h Character Table

(x2-y2, xy)(x,y)0-120-12E’

-1-1-1111A1”

x2+y2, z2111111A1’

Rz-111-111A2’

(zx, yz)-2

-1

σh

1

-1

2S3

2

1

E

-1

1

2C3

0

-1

3C2

(Rx, Ry)0E”

Z1A2”

3σvD3h

Basis Functions

• Shows how standard components transform (are described by which irreducible representation)

• x,y,z :corresponds to the behaviour of the px, py, pz orbitals

• x2+y2+z2 : behaviour of an s orbital• xy, xz, yz, z2, x2: behaviour of respective d orbitals

• Ri : behaviour of Rotation around axis i

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Degeneracy

• When two basis functions are shown in parenthesis these objects transform together and are degenerate– eg. (x,y)

• They cannot be considered individually and must be treated as a pair

Applications of Symmetry

• Chirality– means non-superimposable on its mirror image– presence of Sn, mirror plane or i all rule out

chirality• Dipole moment (polarity)

– a permanent dipole cannot exist if i is present– dipole moment cannot be perpendicular to any

mirror plane or Cn

• IR/Raman Spectroscopy• Constructing MO’s

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Constructing MO’s

• typical structure of inorganic compounds involves a central atom with some arrangement of surrounding atoms attached to it (ligands)

• Build Symmetry Adapted Linear Combinations of Atomic Orbitals (SALC’s) out of groups of atomic orbitals (from the ligands)– Shown in Appendix 4 of Shriver and Atkins

• Combine SALC’s with orbitals on the central atom– Recall that only orbitals of the same symmetry can be

combined

• We use symmetry to assign and build orbitals and combinations of orbitals to make complete MO’s

Identifying the MO Components

• it is helpful to determine in advance how many MO’s of each type and what their symmetry should be

• use vectors to represent bonds– use vectors between the atoms for the sigma orbitals– use vectors perpendicular to the sigma orbitals for the pi

orbitals• determine how these vectors transform under the

symmetry of the molecule• determine the irreducible representations which

combine to produce this behaviour• these irreducible representations are the MO labels• now all we have to do is figure out what orbital

combinations they are formed from ....

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Identifying Symmetry Adapted Orbitals

Steps:1. Identify the point group2. Arrange the group of ligand orbitals,

determine their transformation under the symmetry operations of the point group.

3. Assign a symmetry label to the group orbital.4. Match the labeled group orbitals with atomic

orbitals on the central atom.

Energy Levels of MO’s

• Can be roughly estimated by – energies of atomic orbitals– degree of overlap

• Determine computationally

• Recall that our biggest concern is understanding possible interactions and populating existing MOELD’s

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Conclusions

SymmetryIdentifying symmetry elementsAssigning point groupsReading character tables

transformsbasis functions

Constructing MO’s