Hybrid orbitals . . .

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Hybrid orbitals . . .

• Used to describe the shapes of molecules.
• Used to describe properties of various types of
  bonds holding atoms together.
• Used to discuss how molecules react.
• Used to make predictions about reactions.

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What are atomic orbitals?
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What are atomic orbitals?

• Atomic orbitals are equations that describe the
  probability of finding electrons in an atom.

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What are atomic orbitals?

• Atomic orbitals are equations that describe the
  probability of finding electrons in an atom.
• Atomic orbitals are 3-D surfaces.

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Shapes of Atomic Orbitals

• s orbitals are spherical surfaces

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Shapes of Atomic Orbitals

• s orbitals are spherical surfaces
• p orbitals are two-lobed surfaces

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There are three p orbitals and one s orbital.

• The p orbitals are orthogonal to each other.
• The spherical s orbital is centered at the origin.

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s
px
py
pz
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s
px
The p orbitals lie along the x, y, and
z axes. All are centered at the origin.
py
pz
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Here are all four of the atomic orbitals
relative to each other.
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Adding Equations

• Equations can be added or subtracted.

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Adding Equations

• Equations can be added or subtracted.
• The result is a new equation.

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Lets add some (relatively) simple equations. . .
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Two sine waves. . .
Y sin x
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sin x sin x
Adding the equations results in a function with
twice the amplitude.
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sin x - sin x
Subtracting a sine wave results in a
function with zero amplitude.
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sin x - sin x
Subtracting a sine wave results in a
function with zero amplitude.
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Were not limited to adding or subtracting just
two equations . . .
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Heres a bunch o sine functions . . .
y sin x
y (1/3) sin 3x
y (1/5) sin 5x
y (1/7) sin 7x
y (1/9) sin 9x
y (1/11) sin 11x
y (1/13) sin 13x
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Remember that atomic orbitals are also
mathematical equations, just a tad more
complicated . . .
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s
px
py
pz
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Hybridization of atomic orbitals

• Hybridization is the combining of atomic orbitals
  to create new orbitals
• The number of hybrid orbitals depends on how many
  atomic orbitals
• one adds together.

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n AOs n HOs
S
P
P
P
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n AOs n HOs
S

• 2 sp hybrids

P
P
P
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n AOs n HOs
S
s p

• 2 sp hybrids

P
s - p
P
P
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n AOs n HOs
S

• 3 sp2 hybrids

P
P
P
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n AOs n HOs
S
s p p s p - p s - p - p

• 3 sp2 hybrids

P
P
P
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n AOs n HOs
S
P

• 4 sp3 hybrids

P
P
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n AOs n HOs
S
s p p p s p p - p s p - p - p s - p -
p - p
P

• 4 sp3 hybrids

P
P
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Phases of Orbitals
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sp hybrid
sp
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sp hybrid
sp
s-p
sp hybrid
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LETS HYBRIDIZE!
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Lets add the s orbitalto one of the p orbitals.
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s p
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s p
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s p
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s p
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s p
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s p
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One sp hybrid orbital.
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Now lets subtract s from p.
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p - s
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p - s
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p - s
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p - s
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p - s
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p - s
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Another sp hybrid orbital.
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p s
p - s
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sp hybrid
sp hybrid
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Where are the unhybridized p orbitals?
sp hybrid
sp hybrid
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The unhybridized orbitals are still there.
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sp
pz
py
sp
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