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.

What are atomic orbitals?

What are atomic orbitals?

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

What are atomic orbitals?

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

• Atomic orbitals are 3-D surfaces.

Shapes of Atomic Orbitals

• s orbitals are spherical surfaces

Shapes of Atomic Orbitals

• s orbitals are spherical surfaces

• p orbitals are two-lobed surfaces

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.

s

px

py

pz

s

px

py

pz

The p orbitals liealong the x, y, and zaxes.

All are centered at the origin.

Here are all four of the atomic orbitals relativeto each other.

Adding Equations

• Equations can be added or subtracted.

Adding Equations

• Equations can be added or subtracted.

• The result is a new equation.

Let’s add some (relatively) simple equations. . .

Y = sin x

Two sine waves. . .

sin x + sin x

Adding the equations results in a functionwith twice the amplitude.

sin x - sin x

Subtracting a sine wave results in a functionwith zero amplitude.

sin x - sin x

Subtracting a sine wave results in a functionwith zero amplitude.

We’re not limited to adding or subtracting just two equations . . .

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

Here’s a bunch o’ sine functions . . .

Remember that atomic orbitals are also mathematical equations, just a tad more

complicated . . .

s

px

py

pz

1

2

1

2

3 ( )cos

1

2

3 ( )cos ( )sin

1

2

3 ( )sin ( )sin

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.

n AO’s n HO’s

S

P

P

P

n AO’s n HO’s

2 sp hybridsS

P

P

P

n AO’s n HO’s

2 sp hybridsS

P

P

P

s + p

s - p

n AO’s n HO’s

3 sp2 hybridsS

P

P

P

n AO’s n HO’s

3 sp2 hybridsS

P

P

P

s + p + ps + p - ps - p - p

n AO’s n HO’s

4 sp3 hybrids

S

P

P

P

n AO’s n HO’s

4 sp3 hybrids

S

P

P

P

s + p + p + ps + p + p - ps + p - p - ps - p - p - p

Phases of Orbitals

“s+p”

sp hybrid

“s-p”

“s+p”

sp hybrid

sp hybrid

LET’S HYBRIDIZE!

Let’s add the s orbitalto one of the p orbitals.

s + p

s + p

s + p

s + p

s + p

s + p

One sp hybrid orbital.

Now let’s subtract s from p.

p - s

p - s

p - s

p - s

p - s

p - s

Another sp hybrid orbital.

p + s

p - s

sp hybrid

sp hybrid

sp hybrid

sp hybridWhere are theunhybridized

p orbitals?

The unhybridized orbitals arestill there.

pz

py

sp

sp