Hybridization of Atomic Orbitals I

s and p orbitals overlapping to form covalent bonds cannot yield the various molecular shapes in the VSEPR model. Valence bond theory helps to explain this molecular geometry through the hybridization, or mixing, of atomic orbitals. 

Some atomic orbitals involved in bonding recombine to form new orbitals whose shapes are a hybrid of the originals. The initial number of atomic orbitals and the number of hybrid orbitals generated is always the same. 

Beryllium fluoride is a linear molecule. The beryllium atom has two valence electrons found in its 2s orbital in the ground state.  

The s orbital mixes with one of the empty p orbitals to create orbitals that contain unpaired electrons available for bonding. This leaves two unhybridized p orbitals and produces two sp hybrid orbitals, named for the original atomic orbitals.

The hybrid orbitals have a different shape from their constituent atomic orbitals with one lobe that is significantly larger than the other. Thus, the electron probability density is highly concentrated in a directional lobe, which leads to a more effective overlap with the orbitals of other atoms. For clarity, these orbitals are often shown without the minor lobes. 

The half-filled hybrid orbitals undergo end-to-end overlap with orbitals from the fluorine atoms to form two identical covalent bonds, which are also known as sigma (σ) bonds.  Therefore, beryllium fluoride exhibits sp hybridization, is linear, and has a 180° bond angle.

The trigonal planar geometry boron trihydride can be explained by sp² hybridization. Boron has one 2s and three 2p valence orbitals and three valence electrons. 

Three of these orbitals, one s, and two p orbitals, mix to produce a set of three sp² orbitals, each containing one unpaired electron, and one 2p orbital remains unhybridized. 

Each of these overlap with a 1s orbital from a hydrogen atom to form three sigma bonds.

A molecule with sp² hybridization has a trigonal planar geometry with 120° bond angles.  

sp³ hybrid orbitals form the tetrahedral shape of a methane molecule. The carbon atom has four valence electrons. The mixing of the 2s and three 2p orbitals generates four equivalent sp³ hybrid orbitals that each can hold one unpaired electron. 

The hybrid orbitals obtained through sp³ hybridization overlap with the 1s orbitals of the hydrogen atoms to produce a methane molecule that has tetrahedral geometry and 109.5° bond angles.