Symmetry and MolecularOrbitals (I)

Simple Bonding Modelhttp://chiuserv.ac.nctu.edu.tw/~htchiu/Chemistry/Fall-2005/Chemical-Bonds.htm

Lewis StructuresOctet RuleResonanceFormal ChargeOxidation NumberHypervalence

Resonance and Formal Charge

A0

A+1

VSEPR Some Molecules

VSEPR Some Molecules

VSEPR Model

Bond LengthBond Strength

Less Repulsion More Repulsion

Why Sharing Electron FormsCovalent Bond?

Without Electrons, Internuclei Repulsion Forces PushesNuclei Apart.

Sharing Electrons (in some area around the nuclei)Generates Attractive Force to Bind Nucleus Together.

Why Sharing Electron Forms Anti-Bond?

In Some Area, Sharing Electrons Generates RepulsiveForce.

Bonding and AntibondingRegion Around The Nuclei has Binding (bonding) andAntibinding (antibonding) Zones.

Spherical Boundary Surface of s and pOrbitals

Spherical BoundarySurface of dOrbitals

Spherical Boundary Surface of fOrbitals

Valence Bond Theory•VB Theory is a quantum mechanical model

describes the distribution of electrons in bonds.Developed from Lewis theory and the VSEPR model.

•Usually provides bonding picture with localized view.

•Simple VB theory cannot explain bonding inpolyatomic molecules. The concept of Hybridizationis developed to explain different geometry variations.Describes molecular geometry easier.

•Using Delocalization and Resonance to explainextended distribution of electrons over many atoms ina substance.

Valence Bond Theory

s p

p p

N2

Square of a Wavefunction isProbability Density

Constructive and DestructiveInterference

Hybridization•Linear Combination of Atomic Orbitals of an Atom

forms a new set of orbitals.•Hybridization divides the electron density distribution

of an atom into new areas.

• (sp)A = (1/2)1/2((s) + (p))

• (sp)B = (1/2)1/2((s) - (p))

• (sp2)A = (1/3)1/2(s) + (2/3)1/2(px)

• (sp2)B = (1/3)1/2(s) - (1/6)1/2(px) + (1/2)1/2(py)

• (sp2)C = (1/3)1/2(s) - (1/6)1/2(px) - (1/2)1/2(py)

• (sp3)A = (1/2)((s) + (px) + (py) + (pz))

• (sp3)B = (1/2)((s) + (px) - (py) - (pz))

• (sp3)C = (1/2)((s) - (px) + (py) - (pz))

• (sp3)D = (1/2)((s) - (px) - (py) + (pz))

Hybridization sp

Hybridization sp

+ -

Hybridization sp2

Hybridization sp2

Hybridization sp2 + p

Hybridization sp3

Hybridization sp3

Hybridization H2O Bonds

Hybridization C2H2 Bonds

Molecular Orbital Theory

•Electrons occupy orbitals that spread through the entiremolecule.

•Providing bonding pictures with non-localized view.•Deals with entire area surrounding a molecule.

•Hyperchem Litehttp://www.hyper.com/sales/electronic/electronic-lite.htm

•CACAO98 (Beta Version)http://www.chembio.uoguelph.ca/oakley/310/cacao/cacao.htm

Rules of Molecular Orbitals

Rules for forming bonding and antibonding MOsnumber of total molecular orbitals = number of total atomic orbitalsatomic orbitals have the right symmetryatomic orbitals overlap wellatomic orbitals have similar energy

Rules for filling electrons are the same for MOs and AOs.start filling from the lowest energy orbitalfollows Pauli exclusion principle and Hund's rule

Provides molecular energy informationExplains magnetic behaviorCan provide molecular structural explanation, but moredifficult to comprehend than VB theory

Bonding Molecular Orbitals

Bonding Molecular Orbitals

Constructive InterferenceSymmetric: i

Antibonding MolecularOrbitals

Antibonding Molecular Orbitals

Destructive Interference

Anti-symmetric: i

Molecular Orbital Energy Level Diagram•Better Overlap => Higher E•Bond Order = ½(# of B.O. e - - # of A.O. e -)•Diamagnetic: all e- paired•Paramagnetic: with e- unpaired

EE

0

½

1

½

B.O.

-He2

PH2-

DH2

PH2+

MagneticProperty

Overlap of MOs

Wrong symmetry

Right symmetryBad OverlapGood Overlap

Wrong symmetry

+

+

+

+

+

+

+

+

++

-

-

-

MO Symmetrybond: no nodal plane passing through internuclear axisbond: 1 nodal plane passing through internuclear axisbond: 2 nodal planes passing through internuclear axis

+ +

+ +

+ +

+ +

-

++

+-

-

--

-- -

P Orbitals

P Orbitals

MO Symmetry

B.MO

A.MO

g: geradeu: ungerade

+ +

+ +

+

+ +-

- -

-

-

MO Energies of Period 2 M2 Molecules

Energy Levels ofMany ElectronAtoms in PeriodicTable

M2 MO Energy Level Diagrams

Higher Zeff2s 2p more separated2s e- closer to nuclei2s MOs more like 2s AOss-s overlap not effective

2s and 2pz in same spacebetween nucleiGreater 1 u –2 g repulsion2s 2pz MOs same symmetryMore mixing

1g

1u

1g

1u

1g

1g

O2 –F2 Li2 –N2

MO of Period 2 M2 Molecules

LUMOLowestUnoccupiedMolecularOrbital

HOMOHighestOccupiedMolecularOrbital

DPDDPDDMagnet.

1232101B.O.

PhotoelectronSpectroscopy

•Ek = h–I

measured known calculated E(MO)

UV photoelectron Spectrum of N2

Heteronuclear Diatomic Molecules

•A more electronegative•B less electronegative

+

+

+ +

+ -

CO MO Energy Level Diagram

2

1

3

2

1u

1g

1g

CO MO Energy Level Diagram

2

1

3

2

CO MO Energy Level Diagram

2

1

3

2

ICl MO Energy Level Diagram

1g

1u

1g

HF MO Energy Level Diagram

AMO

NBMO

BMO

H+ F-

H :F:::

Bond Order, Strength and Length

Bond Strength and Length

O-O

N-NC-N,C-O

C-C