s 117 Lecture 102011-molecular orbital lecture
Transcript of s 117 Lecture 102011-molecular orbital lecture
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The wavefunctions add and subtract to
result in the wavefunction experienced bythe molecule. This is the basis of thecovalent bond
The electrons occupy the same orbital and
have opposite spins.
This new orbital that the bonding electronsoccupy is called a molecular orbital
Molecular orbital theory
Reconsider H2
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Adding (and subtracting) wavefunctions
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The wavefunctions overlap to form acovalent bond
The electrons occupy the same orbital andhave opposite spins.
This new orbital that the bonding electronsoccupy is called a molecular orbital
The resultant molecular orbital, which theelectrons occupy can be thought of as beingobtained from the addition of the 2, 1s
orbitals
This last statement is the key idea that wewill use to build the concept of molecular
orbital theory
I want to re-stress what happened for H2
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Molecular orbitals: How exactly do the Hydrogen 1s orbital
waves interfere to screen the nuclear Coulomb repulsion?
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Think particle-in-a-box again to understand
qualitatively the molecular orbital shapes here
(From constructive
interference of waves)
(From destructive
interference of waves)
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Molecular bonding and anti-bonding
orbitals
Molecular orbitals, add and subtract to give
new orbitals that can be occupied by theelectrons belonging to the molecule
Obtained from adding the 2,
1s orbitals. Probability is high
between the atoms. Hencecalled bonding
Obtained from subtracting the2, 1s orbitals. Probability is
low (actually zero) between
the atoms. Hence called anti-
bonding
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Hence, when two hydrogen atoms get close to each
other, within bonding distance, the 1s orbitalsinteract, to form these new molecular orbitals.
We have two electrons and the two electrons occupy
the lowest energy level that they possibly can occupyand here that is the 1s or bonding 1s orbital.
The shape of this new orbital was seen in the previousslide.
Bond Order =
Number of covalent chemical
bonds =
[ # bonding electrons # anti-bonding electrons ]
For H2
, Bond Order=
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Molecular Orbital Diagrams
1s*
H1s H1s
Putting electrons intoantibonding orbitals
weakens bonds.
Putting electrons intobonding orbitals
strengthens bonds.1s
Bond order is a measure of the number of chemical bonds
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He He
1s
*
1s*
H2
BO=1
H2
BO=1/2
+H2
BO=1/2
He2
BO=0
He2
BO=1/2
+
This is observable.
1s
1s
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That was the case for H2 and He2. How aboutelements from the second period?
Well, these elements have 2s orbitals which shouldinteract much the same was as the 1s orbitals we sawin the previous slide.
But these elements also have 2p orbitals.
Example, two oxygen atoms that get close to form O2have all these 2p orbitals that can interact!!
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Obtained from adding the 2,
2px orbitals. Probability is
high between the atoms.
Hence called bonding
Obtained from subtracting the2, 2px orbitals. Probability is
low (actually zero) between
the atoms. Hence called anti-
bonding
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Obtained from adding the 2,
2pz orbitals. Probability is
high between the atoms.
Hence called bonding
Obtained from subtracting the
2, 2pz orbitals. Probability is
low (actually zero) between
the atoms. Hence called anti-
bonding
But now, notice that that this bonding orbitaldoes not quite have a maximum probability
between the two atoms !!!
It is for this reason, that we call this a bond.
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*
Li 12s Li 12s
2s
2s
1s*
Li11s Li11s
L12 BO = 1
L12 exists (stable)
1s
Be2sBe2s
2s*
2s
1s*
Be1s Be1s
Be2 BO = 0
Be2 is only weakly
stable
1s
But we only need to include valence electrons while calculating BO
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2p*
2p
LUMO
HOMO
C2
BO=2
N2
BO=3
2 unpaired spins
B2
BO=1
HOMO= highest occupied molecular orbital
LUMO= lowest unoccupied molecular orbital
2s
2p*
2p
2p*
2p
2s*
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Now we are in a position to put everything
together
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So why is O2paramagnetic (have unpaired electrons)?
Lewis Dot Structure of O2
All electrons are paired Hence O2 should be diamagnetic
Since it has no unpaired electrons
But experimentally: O2 is
paramagnetic (has unpaired
electrons)
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Heteronuclear Diatomics
Two different atoms with atomic orbitals at different energies.
Atoms with higher nuclear charge draw their electrons closer to the nucleus
and have lower energy atomic orbitals.
Example: NO Bond Order = 2
Single
unpaired
electron NO
is reactive!
N2p
O2p2p
2p*
2p*
2p
2s*
2s
O is more electronegative than N so
its atomic orbitals are lower in energy.
N2s
O2s
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Delocalized Bonding and Resonance Structures
O3 Lewis Structures
OO OO OO
+ ++ + +
+
+
+
++
nodes
anti-bonding
non-bonding
bonding
delocalized molecularorbital
Note the qualitative similarity between the MO states
and the particle in a box states
This qualitative similarity is the reason we used PIB tounderstand resonance earlier
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Summary of Molecular Orbital Theory
The s, p, d, f orbitals are solutions to the Schrodingers equation for a single atom
(the hydrogen atom).
When we form a molecule, we combine these atomic orbitals to form orbitals of
the molecule, i.e., the molecular orbitals.
These molecular orbitals are in fact, solutions to the Schrodingers equation
when you consider the molecule.
We did not solve the Schrodingers equation, instead we used a different way to
obtain molecular orbitals, by combining (adding and subtracting) atomic
orbitals.
This worked, because orbitals are made from waves and waves interfere,
they can be added and subtracted.
Adding the orbitals of each atom, gave us a more stable orbital for the molecule
and we called it a bonding molecular orbital.
Subtracting the orbitals of each atom, gave us a less stable orbital for the molecule
and we called this an anti-bonding molecular orbital.
MO theory teaches you about resonance