Animations to Illustrate the Morphing of Atomic Orbitals into Hybrid Atomic Orbitals

Mark Ray and Kristin D. Krantzman, Department of Chemistry and Biochemistry

and

Jeff Wragg, Department of Physics and Astronomy

Atomic Orbitals of the Hydrogen Atom

Hybridization

sp hybrid orbitals

Animations of the morphing of s and p atomic orbitals into two sp hybrid atomic orbitals

Spherical polar coordinates

Animations in spherical polar coordinates

Formation of sp hybrids

Formation of sp2 hybrids

Formation of sp3 hybrids

• 1s
• 2s
• 2p

Here is the probability density for a 1s electron. Note that the electron density drops dramatically as you get close to the nucleus, although strictly speaking it is not zero except at a point at the very center.

The electron density associated with a 2s electron orbital is zero at the very center, rises to a small peak at about radius=1, then drops to zero again, and rises to a maximum at about 5.

A 2p orbital is shaped like a dumbell. It has an axis of rotational symmetry shown in green.

• Bonding arises from the overlap of atomic orbitals
• s, px, py and pz orbitals do not have the correct geometry to describe bonding in polyatomic molecules
• Create hybrid orbitals from s, px, py and pz orbitals that have the correct geometry

sp Hybrid Atomic Orbitals

• sp hybrid orbitals are formed by a linear combinations of a 2s and a 2p_x orbital:

sp = (1/2)^(1/2) (s + p_x)

• The s and p_x orbitals on the central atom are hybrized into the two sp orbitals.
• We can illustrate this process by showing how the s and the p orbital "morph" into the two sp orbitals.
• The p_x orbital incorporates more and more s character until it
• becomes a full sp hybrid orbital:

• The s orbital incorporates more and more p_x character until it
• becomes a full sp hybrid orbital:

• Here c is the constant the controls the degree of hybrid character and N is a normalization constant which depends on the value of c.
• As c increases from c = 0 to c=1.0, sp changes from a s orbital to an sp orbital pointing in the left direction.
• 
• As c increases from c = 0 to c=1.0, sp changes from a p_x orbital to an sp orbital pointing in the right direction.
• 

• We can show an animation that shows how each of the atomic orbitals "morphs" into the hybrid sp orbitals.
• At the start of the animation, c is equal to 0, and we have the unhybridized s and px orbitals.
• As c increases, the s orbital obtains more p_x character and the p_x orbital obtains more s character.
• At the end of the animation, c is equal to 1.0 and we have the two hybridized sp orbitals.
• The two sp orbitals have linear geometry and are 180 degrees apart.
• Click below to view animations:
• one s + one p ---> two sp hybrid orbitals

Spherical Polar Coordinates

• The wavefunction for the hydrogen atom is written as a product of three wavefunctions:
• Y(r,q,f) = R(r) Q(q) F(f)
• Plots of the square of the angular wavefunctions, [Q(q) F(f)]² in spherical polar coordinates produce pictures of the orbitals that are most familiar to chemists.
• The radial function, R(r), is not shown in these plots.

sp orbitals in spherical polar coordinates

When c=0, sp is a s orbital. When c=1, sp is a sp orbital.

• When c=0, sp is a s orbital. When c=1, sp is a sp orbital.
• 
• Click below to view animation in spherical polar coordinates:

As c increases from 0 to 1:

sp morphs from a s orbital to a sp hybrid

• one s + one p ---> two sp hybrid orbitals

sp² orbitals in spherical polar coordinates

When c=0, sp² is a s orbital. When c=1, sp² is a sp² orbital.

When c=0, sp² is a p_y orbital. When c=1, sp² is a sp² orbital.

As c increases from 0 to 1:

sp² morphs from a s orbital to a sp² hybrid

sp² morphs from a p_y orbital to a sp² hybrid

• sp² morphs from a p_x orbital to a sp² hybrid
• Click below to view animation in spherical polar coordinates:
• one s + two p ---> three sp2 hybrid orbitals

sp³ orbitals in spherical polar coordinates

• When c=0, sp³ is a s orbital. When c=1, sp³ is a sp³ orbital.
• 
• When c=0, sp³ is a p_x orbital. When c=1, sp³ is a sp³ orbital.
• 

When c=0, sp³ is a p_y orbital. When c=1, sp³ is a sp³ orbital.

As c increases from 0 to 1:

sp³ morphs from a s orbital to a sp³ hybrid

sp³ morphs from a p_x orbital to a sp³ hybrid

• sp³ morphs from a p_y orbital to a sp³ hybrid
• sp³ morphs from a p_z orbital to a sp³ hybrid
  
  Click below to view animation in spherical polar coordinates:
• one s + two p ---> four sp3 hybrid orbitals