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?
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