Molecular orbital theory
Overcoming the shortcomings of
the valence bond
Learning objectives
 Describe basic principles of MO theory
 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
Molecular wavefunction ΨA + ΨB
Joint density is (ΨA + ΨB)2 = ΨA2 + ΨB2 +
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
 Antibonding orbital:
subtractive combination of
atomic orbitals
 In antibonding orbital there
is no density between the
atoms
 The antibonding orbitals
are at higher energy
MO energy level diagrams:
H2 exists but He2 does not
 In H2 two electrons are
paired in the bonding σ
MO, and the antibonding
σ* MO is vacant.
 Total number of bonds = 1
 Configuration (σ1s)2
 In He2 four electrons are
paired, two in the bonding
and two in the antibonding
σ*
 Total number of bonds = 0
 Configuration (σ1s)2(σ*1s)2
Bond order
Bond order = ½(no. bonding electrons – no.
antibonding electrons)
 Bond order 1 = single bond
 Bond order 2 = double bond
 Bond order 3 = triple bond
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 are lower in energy
than the 2p orbitals. The σ2s
and σ*2s orbitals are lower than
the 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)
2s - 2p interactions affect energy
levels
 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: σ2p < π2p
 Case B: σ2p > π2p
Filling the orbitals: the second row
diatomics
 B2, C2, and N2 are case B
 O2, F2 and Ne2 are case A
 Note bond order from MO theory matches what we
obtain from Lewis dot diagrams
MO theory and magnetism
 Paramagnetism: substance is attracted by a magnetic field
 Diamagnetism: substance is repelled by a magnetic field
 Paramagnetic effect is much greater than diamagnetic effect
 Diamagnetic substances have no unpaired electrons
 Paramagnetic substances have unpaired electrons
Magnetic properties of O2 expose
limitations of Lewis
 MO theory gives two degenerate π and π* orbitals
 In O2, Hund’s rule states that these are singly
occupied
 O2 is paramagnetic
O
O
Correlate magnetic properties with
MO diagram
Heteronuclear molecules and NO
 NO contains 11 electrons implies high reactivity
 Two possible Lewis structures
0
N
0
O
-1
N
+
1
O
 Lewis structure favours unpaired electron on N
 Experimental bond order appears greater than 2
MO description of NO
 AOs of more electronegative
atom are lower in energy
 The bonding orbitals have more
of the more electronegative
atom character
 The antibonding orbitals have
more of the less electronegative
atom character
 MO diagram shows bond order
2.5 consistent with experiment
 Unpaired electron is in π* orbital
which is more N-like (consistent
with Lewis dot structure