# 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

Figure 1: s-orbitals are spherical shells at a specific distance from the nucleus

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

Figure 2: The p-orbital has a positive phase and negative phase on either side of a nucleus.

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.

Figure 3: P-subshells consist of three orbitals of equal energy

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 p 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, Figure 4.

Figure 4: Mixing s and p orbitals produces a hybrid spn orbital

When a spherical s orbital adds to a bi-modal  p orbital, a two lobed spn orbital results. The positive phase of the bi-modal p orbital adds to the s orbital and enlarges. The negative phase of the p orbital subtracts from the all positive s orbital. The result is a two lobed spn  hybrid orbital.

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

Figure 5: The combination of s and p orbital forms an s,p hybrid orbital

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 p orbital lowers the overall energy of the sum of the s orbital and the p orbital energy would have if they were not hybridized.

### sp3 Hybridization

When three p orbitals mix with one s orbital, four new orbitals form, Figure 6. The addition of each p orbital to a single s orbital produces a set of four sp3 orbitals.

Figure 6: formation of four sp3 hybridized orbitals from three p orbitals and one s orbital

Each one of the sp3 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 s orbital?

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 sp3 hybridized orbital.

Figure 7: A tetrahedral sp3 hybridized orbital is composed of one s orbital and three p orbitals

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.

### sp2 Hybridization

Figure 8: The sp2 orbital is formed from one s orbital and two p orbitals. The non-hybridized p orbital is 90º to to the plane the trigonal planar sp2 hybridized orbitals

Similar logic applies when two p orbitals and one s orbital combine to make an sp2 hybridized orbital, Figure 8.

In this case, the sp2 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 p 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 sp2 trigonal planar orbitals.

### sp Hybridization

Figure 9: one s orbital and one p orbital combine to make an sp hybridized orbital. The two non-hybridized p orbitals sit at a 90 degree angle to the sp hybridized orbital and one another.

The final case occurs when one s orbital and one p orbital combine together to make an sp orbital, 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 sp hybridized orbital. They are also perpendicular to each other.

## Polyhedral ModelsPolyhedral Models

Introduction to Polyhedral Models     An alternative to represent ionic compounds is to use polyhedral models. When we can see the way in which three=dimensional shapes represent the individual