1. 9.4 Covalent Bonding and Orbital Overlap
The sharing of electrons in forming covalent bonds can only occur when orbitals on the two atoms overlap.
In the example for H2, below, as the 1s orbitals overlap, electron density is increased between the nuclei. Because the electrons in the overlap region are simultaneously attracted to both nuclei, they hold the atoms together by forming a covalent bond.
Orbital overlap applies to other atoms as well, as when the 1s orbital of H overlaps with the 3p orbital of chlorine to form HCl; or when two 3p orbitals on Cl atoms overlap to form the Cl2 molecule.

2. There is an optimum distance between bonded nuclei in any covalent bond.
As shown below, the potential energy of the system changes as two H atoms approach (on the left) to form H2.
Increased overlap brings the electrons and nuclei closer together while simultaneously decreasing electron-electron repulsion.
However, if atoms get too close, the internuclear repulsion greatly raises the energy.
The internuclear distance at the minimum of the PE curve corresponds to the observed bond length of Å (the equilibrium bond distance).
The energy at this point corresponds to the energy change for the formation of the H-H bond (see Table 8.4).

3. 9.5 Hybrid Orbitals
The idea of orbital overlap does not easily extend to polyatomic molecules.
Valence-bond theory must explain both the formation of electron-pair bonds and the observed geometries.
To explain observed geometries the atomic orbitals are described as mixing to form hybrid orbitals in a process called hybridization.
The shapes of the hybrid orbitals are different from the shapes of the original atomic orbitals.

4. sp Hybrid Orbitals
Consider the example of BeF2 which has the Lewis structure
This is a linear molecule with two bonds of equal length.
But how can valence-bond theory explain this structure and its geometry?
The electron configuration of F (1s2 2s2 2p5) shows an unpaired electron in the 2p orbital.
This electron can be paired with an unpaired electron from the Be atom to form a covalent bond.

5. However, the ground-state orbital diagram for Be shows no singly-occupied orbitals. It would be unable to form a bond with fluorine.
But if Be absorbs a small amount of energy it can promote an electron from the 2s to the 2p orbital and form two bonds.
The two bonds, however, would not be identical since one would be formed from the Be 2s orbital and one from the Be 2p orbital.
The promotion of an electron allows two Be—F bonds to form but doesn’t explain the structure.

6. The problem is solved by “mixing” the 2s orbital and one 2p orbital to generate two new orbitals, as shown.
The sp orbitals are higher in energy than the 1s orbital but lower than the 2p.
The electrons in the sp hybrid orbitals can now form two-electron bonds with the two fluorine atoms. (Note that no extra orbitals have been created.)
Original Be orbitals
Hybrid Be sp orbitals

7. These two equivalent sp hybrid orbitals have two lobes like a p orbital, but one of the lobes is larger.
The larger lobes can be better directed at other atoms better than unhybridized atomic orbitals.
Hence, they can overlap more strongly with the orbitals of other atoms

8. The two degenerate (i.e., they have the same amount of energy) orbitals would align themselves 180 from each other.
This is consistent with the observed geometry of beryllium compounds: linear.
The observed bonds of equal length would not be possible if Be were unhybridized.

9. sp2 and sp3 Hybrid Orbitals
Other orbital combinations can be mixed to produce hybrid orbitals to support other geometries.
An sp2 geometry is seen in BF3, for example, which produces three equivalent hybrid orbits that point in different directions.
Hybridization in boron:
The three sp2 hybrid orbitals lie in the same plane 120o apart from one another, leading to the trigonal-planar geometry of BF3.

10. One s orbital and two p orbitals hybridize to form three equivalent (degenerate) sp2 hybrid orbitals.
The large lobes point to the corners of an equilateral triangle.

11. Carbon can form up to four bonds with other elements.
Its electron configuration is 1s2 2s2 2p2.
It hybridizes four orbitals to produce four equivalent sp3 hybridized orbitals.

12. sp3 hybridization supports tetrahedral molecular geometry.
Each lobe points to a different corner of a tetrahedron.
The bonding in CH4 is described as the overlap of four equivalent sp3 hybrid orbitals on C with the 1s orbitals of four H atoms to form four equivalent bonds.

13. Hybridization and nonbonding electrons
sp3 hybridization can describe bonding in atoms containing nonbonding pairs of electrons.
In water, for example, the electron-domain around the central O atom is approximately tetrahedral.
Two of the hybrid orbitals contain nonbonding pairs of electrons, while the other two forms bonds with H atoms.

14. Hybridization Involving d Orbitals
For geometries involving expanded octets on the central atom, we must use d orbitals in our hybrids.
Mixing one s orbital, three p orbitals, and one d orbital leads to five sp3d hybrid orbitals.
The formation of five sp3d hybrid orbitals is seen in P in PF5:

15. The five equivalent sp3d orbitals support the trigonal bipyramidal molecular geometry.
The six equivalent sp3d2 orbitals support the octahedral molecular geometry.

16. Summary
Once you know the electron-domain geometry, you know the hybridization state of the atom.