Molecular orbital theory

Overcoming the shortcomings of

the valence bond

Learning objectives

Describe basic principles of MO theory

Describe differences between Valence Bond

and MO theories

Write MO diagrams for some simple

diatomic molecules

Explain optical and magnetic properties of

O2 using MO theory

Shortcomings of valence bond

The orbitals still maintain atomic identity

Bonds are limited to two atoms

Cannot accommodate the concept of

delocalized electrons – bonds covering

more than two atoms

Problems with magnetic and spectroscopic

properties

Molecular orbital theory:

wavefunctions revisited

The wave function describes the path of the electron – ΨA (has no real physical meaning)

Wave functions have phase – indicated by “+” and “-”

Approach of atoms causes overlap of orbitals + adds to + (constructive

interference)

+ subtracts from – (destructive interference)

Wavefunctions and electron density

Ψ describes the electron path

Ψ2 describes the electron density

Orbital ΨA and ΨB overlap to form bond

Molecular wavefunction (ΨA + ΨB)

Joint density is (ΨA + ΨB)2 = ΨA2 + ΨB

2 + 2ΨAΨB

In molecular orbital the density is greater between

the nuclei by an amount 2ΨAΨB

Molecular orbital theory: bonding

and antibonding

Bonding orbital: additive

combination of atomic

orbitals σ

Antibonding orbital:

subtractive combination of

atomic orbitals σ*

Linear combination of atomic orbitals

Valence Bond theory

Hybrid orbitals made using weighted average of

different ao’s on the same atom

Hybrid orbital confined to that atom

Molecular Orbital theory (LCAO)

Weighted average of different ao’s on all atoms

of molecule

Resulting mo involves all atoms of molecule

Formation of molecular orbitals

Bonding orbital

More electron density

between nuclei

More electrostatic attraction

Bonding MO at lower energy

Antibonding orbital

No density between atoms

Lower electrostatic attraction

Antibonding MO at higher

energy

Bond order

Bond order 1 = single bond (1/2 x 2)

Bond order 2 = double bond (1/2 x 4)

Bond order 3 = triple bond (1/2 x 6)

1 { bonding elecs - antibonding elecs}2

BO

Summary of important concepts in MO

MO’s are formed by linear combination of AO’s

Two AO’s combine to give two MO’s: one is higher in energy, one is lower

Orbital filling follows aufbau principle: lowest energy orbitals first

Maximum occupancy of MO is two (spin-paired)

Hund’s rule: degenerate orbitals are singly occupied before pairing

Bond order is one half times (number of electrons in bonding MO’s minus number of electrons in anti-bonding MO’s)

On the existence of molecules:

MO energy level diagrams H2 (2 electrons) in bonding σ MO; antibonding σ* MO is

vacant.

Total number of bonds = (+1 – 0) = 1

Configuration (σ1s)2

He2 (4 electrons): two in bonding σ, two in antibonding σ*

Total number of bonds = (+ 1 – 1) = 0

Configuration (σ1s)2(σ*1s)

2

Second row elements

Li2 contains 6 electrons

Bonding σ orbitals between 1s and 2s

Antibonding σ* orbitals between 1s and 2s

Occupied: σ1s,σ2s, and σ*1s

Bond order = 2 – 1 = 1

Does Be2 exist?

Formation of π orbitals in MO

Defining the

internuclear axis as z

Overlap of the pz

orbitals produces σ

bond

Overlap of px and py

orbitals produces π

bonds

General energy level diagram for

second-row homonuclear diatomics Assumes no interaction

between the 2s and 2p orbitals 2s orbitals lower in energy

than 2p orbitals

σ2s and σ*2s orbitals lower than σ2p orbital

Overlap of the 2pz is greater than that of the 2px or 2py so σ2p is lower than the π2p orbital

The π2p and π*2p are degenerate (2 orbitals with the same energy)

Consequences of interaction

between 2s and 2p The 2s and 2p orbitals

do interact

σ2s and σ2p orbitals move further apart in energy

Strength of interaction changes with atomic number Case A NO interaction:

σ2p < π2p

Case B STRONG interaction:

σ2p > π2p

Second row diatomics: interaction

decreases across period

B2, C2, and N2 are case B (strong interaction)

O2, F2 and Ne2 are case A (weak interaction)

Bond order from MO theory matches bond order

from Lewis dot diagrams perfectly

Magnetism and electrons

Paramagnetism: attracted by a magnetic field

Diamagnetism: repelled by a magnetic field Paramagnetic effect is much greater than diamagnetic effect

Electrons have magnetic moments

Diamagnetic substances have no unpaired electrons

Paramagnetic substances have unpaired electrons

Magnetism of O2 and the limitations

of Lewis

O2 is paramagnetic (YouTube)

O2 must contain unpaired electrons

Lewis dot diagram shows simple lone pairs

Lewis predicts diamagnetism

Another shortcoming of Lewis dot structures

O O

Lewis dot

structure

MO theory to the rescue MO theory gives two degenerate π and π* orbitals

Hund’s rule states that these are singly occupied

O2 is paramagnetic

If the σ* was below the π* what is the situation?

Correlate magnetic properties with

MO diagram

Heteronuclear molecules and NO

NO contains 11 electrons implies high

reactivity

Lewis structure favours unpaired electron on

N

Experimental bond order appears greater

than 2

+1 -1

N O

0 0

N O

MO description of NO

AOs of more electronegative atom lower in energy (O more electronegative than N)

Bonding orbitals have more of more electronegative atom character (O)

Antibonding orbitals have more of less electronegative atom character (N)

MO diagram shows bond order 2.5 consistent with experiment

Unpaired electron in π* orbital is more N-like (consistent with Lewis dot structure)

0 0

N O