# Orbital Hybridization

Orbital hybridization controls the local geometry around an atom. More than any other factor, the hybridization state of electron orbitals is responsible for the shape of molecules.

Solitary atoms undergo orbital hybridization under the influence of interactions with other atoms. This allows orbitals with different energies and different shapes to mix together to form new orbitals.

## The *s*-orbital

* S*-orbitals are spherical and occupy a region of space at a fixed distance from the nucleus of an atom. The area resembles a layer or shell. You can compare it to a layer of an onion.

Electrons are constrained to follow a roughly circular orbit. The electron is shown as an arrow to depict the fact it is in constant motion and actually has no fixed position, **Figure 1**.

## The **p**-orbital

**p**

* P*-orbitals have two portions which possess and opposite sign to their wave function.

In addition, these opposite phases form a roughly two lobe set of spheres on opposite sides of an atomic nucleus. This pair of lobes do not have any electron density near the nucleus, **Figure 2**.

This is where electrons show they have a wave nature. It makes no sense for an object to occupy two sides of a sphere while not being in the middle. Yet that makes perfect sense for a wave.

More over, students often make the mistake of thinking a ‘plus’ side and a ‘minus’ side mean an electron occupies one side of a * p*-orbital and not the other. An electron or pair of electrons occupy both sides of the lobe equally. At the same time, they never pass through the center in order to travel from one side to the other side.

Together, there are a set of three * p*-orbitals in each subshell where they occur. The orbitals correspond to the three possible orientations: the

**x**,

**y**, and

**z**axes,

**Figure 3**.

Each* p*-orbital which composes the p-subshell results from a spherical orbital when it is cut in half. The fact that there are three of them comes from the three possible ways to slice a three-dimensional sphere into two parts: one along each axis.

## The *d*-orbital

The * d*-orbitals form a set of five orbitals. They are more complicated, and they will receive their own treatment elsewhere when the subject of transition metals is taken up.

## Mixing Orbitals

The* s* and

*orbitals mix under the influence of encountering other atoms. This happens when an element with available*

**p***orbitals recast themselves to prepare to form chemical bonds,*

**p****Figure 4**.

When a spherical* s* orbital adds to a bi-modal

*orbital, a two lobed*

**p***orbital results. The positive phase of the bi-modal*

**sp**^{n}*orbital adds to the*

**p***orbital and enlarges. The negative phase of the*

**s***orbital subtracts from the all positive*

**p***orbital. The result is a two lobed*

**s***hybrid orbital.*

**sp**^{n}

Notice the nucleus of the atom is now inside the enlarged lobe.

Why does this happen? Because s and p orbital mixing lowers the over all energy of the sum of the electrons.

**Figure 5** shows the addition of and * s* orbital to a

*orbital lowers the overall energy of the sum of the*

**p***orbital and the*

**s***orbital energy would have if they were not hybridized.*

**p**

### sp^{3} Hybridization

When three * p* orbitals mix with one

*orbital, four new orbitals form,*

**s****Figure 6**. The addition of each

*orbital to a single*

**p***orbital produces a set of four*

**s***orbitals.*

**sp**^{3}

Each one of the * sp^{3}* orbitals adopts an orientation which points towards the corner of a tetrahedron. That allows maximum distance between each orbital which can contain a negatively charged electron.

What does this look like when you look at how three * p* orbitals interact with a single

*orbital?*

**s**

It comes together like in **Figure 7**. The s orbital raises its energy while three p orbitals lower their energy when the four orbitals together form the ** sp^{3}** hybridized orbital.

The individual lobes of the orbitals point away from each other in order to minimize electron-electron repulsion. This leaves an overall tetrahedral geometry around the central nucleus.

The negative phase of each individual orbital is physically blocked from sight by the larger positive lobes.

### sp^{2 }Hybridization

Similar logic applies when two p orbitals and one s orbital combine to make an * sp^{2} *hybridized orbital,

**Figure 8**.

In this case, the* sp^{2} *hybrid orbital has three lobes. They maximize the angle between themselves. This produces a trigonal planar geometry.

Hybridization raises the energy of the * s* orbital and lowers the energy of two of the three

*orbitals. In addition, one of the*

**p***orbitals does not hybridize and remains at the same energy. The unchanged*

**p***orbital takes a perpendicular orientation to the three*

**p***trigonal planar orbitals.*

**sp**^{2}### sp Hybridization

The final case occurs when one * s* orbital and one

*orbital combine together to make an*

**p***orbital,*

**sp****Figure 9**.These two orbitals adopt a linear geometry. This way they minimize the interaction of their two lobes.

Two **p** orbitals do not mix with with the * s* orbital. This leaves the non-hybridized

**p**orbitals perpendicular to the

*hybridized orbital. They are also perpendicular to each other.*

**sp**