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?

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 pxpx pypy pzpz

s pxpx pypy pzpz The p orbitals lie along the x, y, and z axes. All are centered at the origin.

Here are all four of the atomic orbitals relative to 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 function with twice the amplitude.

sin x - sin x Subtracting a sine wave results in a function with zero amplitude.

sin x - sin x Subtracting a sine wave results in a function with 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 pxpx pypy pzpz

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

2 sp hybrids S P P P

n AO’s n HO’s 2 sp hybrids S P P P s + p s - p

n AO’s n HO’s 3 sp 2 hybrids S P P P

n AO’s n HO’s 3 sp 2 hybrids S P P P s + p + p s + p - p s - p - p

n AO’s n HO’s 4 sp 3 hybrids S P P P

n AO’s n HO’s 4 sp 3 hybrids S P P P s + p + p + p s + p + p - p s + p - p - p s - p - p - p

Phases of Orbitals

“s+p” sp hybrid

“s-p” “s+p” sp hybrid

LET’S HYBRIDIZE!

Let’s add the s orbital to one of the p orbitals.

s + p

One sp hybrid orbital.

Now let’s subtract s from p.

p - s

Another sp hybrid orbital.

p + s p - s

sp hybrid

Where are the unhybridized p orbitals?

The unhybridized orbitals are still there.

pzpz pypy sp