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In quantum mechanics, hybridization is a concept used to explain the bonding properties of atoms in molecules. It provides a way to describe the arrangement of atomic orbitals and the formation of molecular orbitals. Hybridization is particularly useful in understanding the geometry and bonding in molecules that cannot be explained solely by using the atomic orbitals of the isolated atoms.

The process of hybridization involves combining atomic orbitals to form hybrid orbitals that are more suitable for bonding. The most common types of hybridization are sp, sp², and sp³ hybridization, which are associated with linear, trigonal planar, and tetrahedral geometries, respectively. Let's focus on sp³ hybridization as an example.

Consider the case of carbon in methane (CH₄). Carbon has four valence electrons, occupying the 2s and 2p orbitals. In methane, carbon forms four covalent bonds by sharing electrons with four hydrogen atoms. However, if we were to consider the isolated carbon atom, it would have two unpaired electrons in separate p orbitals, which are not ideal for forming four bonds.

To explain the bonding in methane, we invoke sp³ hybridization. In this process, the carbon's 2s orbital and three of its 2p orbitals (2px, 2py, 2pz) combine to form four new hybrid orbitals called sp³ orbitals. These hybrid orbitals have a different shape and energy compared to the original atomic orbitals. In the case of methane, the four sp³ orbitals arrange themselves in a tetrahedral geometry around the carbon atom.

Each of the four sp³ hybrid orbitals then overlaps with a hydrogen 1s orbital, forming four C-H sigma bonds. The electrons from each hydrogen atom pair up with the electrons in the sp³ hybrid orbitals to complete the octet around the carbon atom.

Hybridization provides a more accurate description of the bonding and geometry in molecules than considering only the atomic orbitals of the isolated atoms. It allows us to rationalize the observed molecular structures and properties based on the hybridized orbitals and their overlap with other atomic orbitals in the molecule.

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