Transcript Molecular Orbital Theory - Parkway C-2

Molecular Orbital Theory
Bonding Models:
Lewis Structures and VSEPR
Accuracy
Valence Bond (VB) or
Localized Electron (LE) Theory
Molecular Orbital (MO) Theory
Ease of use
Molecular Orbital Theory


Molecular Orbital Theory
For homonuclear diatomic molecules (O2,N2,Cl2,etc) the molecular
orbitals (MOs) can be approximated as linear combinations of atomic
orbitals.
Ψbonding orbital = ΨMO =
[Ψ1 + Ψ2]
Ψantibonding orbital = ΨMO* =
[Ψ1 - Ψ2]*
Ψ = wave function of
the electrons combining
Molecular Orbital Theory
A molecular orbital is formed from interactions between two atomic orbitals
that merge when two atoms attempt to share electrons, which then may or
may not be occupied by the electron(s) from the atoms. These new molecular
orbitals result from orbital overlap occurring during an attempt to bond. MO
Theory doesn’t treat the electrons as belonging to specific bonds, but as
being spread out over the whole new molecule that has been formed. MO
theory treats electrons as if they are delocalized, or spread out over the entire
molecule, now orbiting in a new orbital created by two electrons merging in
their wave functions.
Molecular orbitals form when:
• the symmetries of the atomic orbitals are compatible with each other,
• the region of overlap between the two atomic orbitals is significant, and
• the atomic orbitals are relatively close in energy to each other
Molecular Orbital Theory
The number of molecular orbitals (MOs) that can be
formed must equal the number of atomic orbitals of the
combining atoms
A-B*
A
A-B
B
In MO theory we
construct the orbital
interaction diagram
first and then put in
the electrons
according to the
aufbau principle
Molecular Orbital Theory
Bond order = ½ [(number of bonding electrons) – (number of
antibonding electrons)]
While the bond order cannot be measured directly, we can
make correlations between the bond order and bond distances,
bond dissociation energies, and bond stability
Species
Bond order
Bond
distance
Bond
dissociation
enthalpy
H 2+
0.5
105 pm
255 kJ/mol
H2
1.0
74 pm
458 kJ/mol
Molecular Orbital Theory – Homonuclear
Diatomics
We eventually want to use molecular orbital theory to explain the
bonding in polyatomic molecules and ions such as: H2O, CO2,
NH3, BF3, CH4, NO3-, and B2H6.
To do this we are going to have to look at the symmetry of
different sized atomic orbitals that are overlapping.
Before we consider these molecules, where a detailed look at
symmetry is important, we will start with molecules in which
symmetry is more straightforward – homonuclear diatomic
molecules such as H2, O2, and F2 – as the orbitals on each atom
are identical
Molecular Orbital Theory – H2
Molecular Orbital Theory – H2
Molecular Orbital Theory – H2
Molecular Orbital Theory – H2+
Molecular Orbital Theory – He2+
Molecular Orbital Theory – He2
Molecular Orbital Theory – Li2
Li2
 (1s)2  *(1s)2  (2s)2
Bond order = ½ [(4) – (2)] = 1.0
Molecular Orbital Theory – Be2
Be2
 (1s)2 *(1s)2  (2s)2 *(2s)2
Bond order = ½ [(4) – (4)] =
0.0
Be
Be2
Be
This is evidence for an extremely
unstable Be2 species with a bond
energy of only 10 kJ mol-1
Molecular Orbital Theory – valence 2s and 2p
The pz orbitals, can
interact with each
other along the bond
axis to form a 
bonding molecular
orbital, g(2pz), and a
 antibonding
molecular orbital,
u*(2pz).
Molecular Orbital Theory - pz orbitals for s
bonding
Molecular Orbital Theory – valence 2s and 2p
The p orbitals, px and
py, which are
perpendicular to the
bond axis, can
overlap in a sideways
manner to form p
bonds. The overlap
in the p bonds is
smaller than the
direct overlap in the
 bonds.
The bonding MO is
pu, while the
antibonding MO is
pg*.
Molecular Orbital Theory – px orbitals for p
bonding
Molecular Orbital Theory – X2 diatomics, such
as F2, O2
Molecular Orbital Theory – O2
Why is O2 paramagnetic,
even though its electron
configuration from localized
electron bonding theory
shows otherwise?
Molecular Orbital Theory - F2
Molecular Orbital Theory - energy exceptions
- Notice that the 2p and the
p2p orbitals are flipped why is this?
Molecular Orbital Theory - energy exceptions
Molecular Orbital Theory - energy exceptions
Diatomic
Bond distance
(pm)
Bond dissocation
energy (kJ/mol)
Bond
order
Magnetic
properties
Li2
267
110
1
diamagnetic
Be2
(245)
(10)
0
B2
159
297
1
paramagnetic
C2
124
607
2
diamagnetic
N2
110
945
3
diamagnetic
O2
121
498
2
paramagnetic
F2
141
159
1
diamagnetic
Molecular Orbital Theory – Heteronuclear
diatomics
With homonuclear diatomic molecules such as H2 and O2, the
atomic orbitals of the same label, such 2s – 2s and 2pz - 2pz,
were symmetry matched and the resulting MOs from their
interactions had equal contributions from the atomic orbitals on
each atom.
With heteronuclear diatomic molecules, such as HF and CO, the
set of orbitals available from each atom might be different and
the energies of the orbitals are going to be different.
How do these atomic orbital symmetry and energy
considerations affect the appearance of the molecular orbital
energy diagram?
Molecular Orbital Theory – XY molecules
The overlap of
these two orbitals
would be
nonbonding, as
they are not
symmetry
compatible
The overlap of
these two orbitals
would be
nonbonding, as
they are not
symmetry
compatible
The overlap of
these two orbitals
would be bonding,
as they are
symmetry
compatible
Molecular Orbital Theory – XY molecules
When the energies of the atomic orbitals that are interacting
(allowed by symmetry) are different, the resulting MOs have
different contributions from each atomic orbital, according to the
energy difference (DE) between the atomic orbitals. The ψ* MO
has more “X” character, while the ψ MO has more “Y” character.
Molecular Orbital Theory - HF
The H atom has only one
orbital with an electron in
it, the 1s orbital. Which
F atomic orbital is it
going to interact with?
In terms of symmetry, it
could interact with the 2s
or the 2pz atomic orbitals
on F. In terms of energy,
the F 2pz orbital is closer
in energy to the H 1s
orbital than is the F 2s
orbital
Molecular Orbital Theory - HF
The H 1s orbital
interacts with the F
2pz orbital to form a 
and a * orbital, with
each contributing one
electron to fill the 
orbital and form a H-F
bond.
2s2
The remaining
orbitals on F have no
orbitals on H to
interact with and form
filled nonbonding (n)
orbitals at the same
energy as the F
atomic orbitals
Molecular Orbital Theory - CO
The Lewis structure and valence bond theory suggest to us that CO
has a triple bond, with one lone pair of electrons on the oxygen atom
and one lone pair of electrons on the carbon atom:
C
O
It is important to note that:
• Zeff(O) > Zeff(C)
• the energy of the O 2s atomic orbital is lower than that of the C 2s atomic
orbital
• the 2p level in O is at a lower energy than that in C
• the 2s-2p energy separation in O is greater than that in C
Molecular Orbital Theory - CO
2p*
2p
2s*
2s
2s2 2s2 p2p4 2p2
Molecular Orbital Theory - CO
(doubly degenerate)
(doubly degenerate)
http://www.wellesley.edu/Chemistry/chem120/mo2.html