Symmetry and Molecular Orbitals (I)

Simple Bonding Model http://chiuserv.ac.nctu.edu.tw/~htchiu/chemistry/fall-2005/chemical-bonds.htm Lewis Structures Octet Rule Resonance Formal Charge Oxidation Number Hypervalence

Resonance and Formal Charge A 0 A +1

VSEPR Some Molecules

VSEPR Model Less Repulsion More Repulsion Bond Length Bond Strength

Why Sharing Electron Forms Covalent Bond? Without Electrons, Internuclei Repulsion Forces Pushes Nuclei 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 Repulsive Force.

Bonding and Antibonding Region Around The Nuclei has Binding (bonding) and Antibinding (antibonding) Zones.

Spherical Boundary Surface of s and p Orbitals

Spherical Boundary Surface of d Orbitals

Spherical Boundary Surface of f Orbitals

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 in polyatomic molecules. The concept of Hybridization is developed to explain different geometry variations. Describes molecular geometry easier. Using Delocalization and Resonance to explain extended distribution of electrons over many atoms in a substance.

Valence Bond Theory N 2 s p p p

Square of a Wavefunction is Probability Density

Constructive and Destructive Interference

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)) (sp 2 )A = (1/3) 1/2 (s) + (2/3) 1/2 (px) (sp 2 )B = (1/3) 1/2 (s) - (1/6) 1/2 (px) + (1/2) 1/2 (py) (sp 2 )C = (1/3) 1/2 (s) - (1/6) 1/2 (px) - (1/2) 1/2 (py) (sp 3 )A = (1/2)( (s) + (px) + (py) + (pz)) (sp 3 )B = (1/2)( (s) + (px) - (py) - (pz)) (sp 3 )C = (1/2)( (s) - (px) + (py) - (pz)) (sp 3 )D = (1/2)( (s) - (px) - (py) + (pz))

Hybridization sp

Hybridization sp + -

Hybridization sp2

Hybridization sp 2 + p

Hybridization sp3

Hybridization H 2 O Bonds

Hybridization C 2 H 2 Bonds

Molecular Orbital Theory Electrons occupy orbitals that spread through the entire molecule. Providing bonding pictures with non-localized view. Deals with entire area surrounding a molecule. Hyperchem Lite http://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 MOs number of total molecular orbitals = number of total atomic orbitals atomic orbitals have the right symmetry atomic orbitals overlap well atomic orbitals have similar energy Rules for filling electrons are the same for MOs and AOs. start filling from the lowest energy orbital follows Pauli exclusion principle and Hund's rule Provides molecular energy information Explains magnetic behavior Can provide molecular structural explanation, but more difficult to comprehend than VB theory

Bonding Molecular Orbitals

Bonding Molecular Orbitals Constructive Interference Symmetric: i

Antibonding Molecular Orbitals

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 B.O. Magnetic Property E E H + 2 H 2 ½ 1 P D H 2 - ½ P He 2 0 -

Overlap of MOs + + + + - Wrong symmetry + + - Right symmetry Bad Overlap Good Overlap Wrong symmetry + + + + -

MO Symmetry bond: no nodal plane passing through internuclear axis bond: 1 nodal plane passing through internuclear axis bond: 2 nodal planes passing through internuclear axis + + + + + - + + - + - - - + + - - - +

P Orbitals

MO Symmetry g: gerade u: ungerade + + B.MO + + - - + - A.MO - + + -

MO Energies of Period 2 M 2 Molecules

Energy Levels of Many Electron Atoms in Periodic Table

M 2 MO Energy Level Diagrams O 2 F 2 Li 2 N 2 1 g 1 g 1 u 1 u 1 g Higher Z eff 2s 2p more separated 2s e - closer to nuclei 2s MOs more like 2s AOs s-s overlap not effective 1 g 2s and 2p z in same space between nuclei Greater 1 u 2 g repulsion 2s 2p z MOs same symmetry More mixing

MO of Period 2 M 2 Molecules B.O. 1 0 1 2 3 2 1 Magnet. D D P D D P D LUMO Lowest Unoccupied Molecular Orbital HOMO Highest Occupied Molecular Orbital

Photoelectron Spectroscopy E k = 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 1 g 2 1 u 3 1 1 g 2

CO MO Energy Level Diagram 2 3 1 2

ICl MO Energy Level Diagram 1 g 1 u 1 g

HF MO Energy Level Diagram H + F - AMO H :F: : : NBMO BMO

Bond Order, Strength and Length

Bond Strength and Length C-C N-N C-N,C-O O-O