s 117 lecture 102011-molecular orbital lecture

7/30/2019 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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2px orbitals. Probability is

high between the atoms.

Hence called bonding

Obtained from subtracting the2, 2px orbitals. Probability is



bonding


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2pz orbitals. Probability is

high between the atoms.

Hence called bonding

Obtained from subtracting the

2, 2pz orbitals. Probability is



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

s 117 lecture 102011-molecular orbital lecture

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