Theories of Covalent Bonding

Valence Bond Theory

Valence bond theory is a model of covalent bonds in which atomic orbitals overlap. The bond formed when two orbitals overlap end to end is called a sigma bond (σ\sigma bond). The bond formed when two orbitals overlap side by side on the same plane is a pi bond (π\pi bond).
A covalent bond forms between two atoms with similar electronegativities. Electronegativity is the tendency of an atom to attract electrons toward itself while forming bonds. Forces of attraction between the opposite charges and forces of repulsion between the like charges cause the formation of a covalent bond. Atoms that form covalent bonds share valence electrons. A covalent bond occurs at a distance at which these forces balance each other. In other words a covalent bond is formed when two atoms' nuclei are close enough that the pull between their protons and electrons is balanced by the push between their proton-proton and electron-electron interactions. When these competing forces are balanced, the potential energy of the atoms is minimized, much like a spring's potential energy is minimized when it is in its relaxed state, neither stretched out nor compressed. Atoms in a covalent bond are at a distance where their energy is at a minimum. Pushing the atoms closer together or pulling them farther apart both require energy.
Energy is plotted as a function of the separation distance, rr, between two atoms and is compared to the bond length, rB{r_{\rm{B}}}. At very short intermolecular distances, when r<rBr\lt{{r}_{\rm{B}}}, the energy is extremely high. When the separation distance is equal to the bond length, r=rBr={r_{\rm{B}}}, the energy is at a minimum. If the energy is increased enough, the distance between the atoms becomes large enough that they are no longer bonded. The energy required to reach this state is the bond dissociation energy.
The energy required to break a covalent bond is called bond dissociation energy. Bond dissociation energy is related to the bond's potential energy. A bond with a low potential energy is relatively stable and requires more energy to break. A bond with high potential energy is relatively less stable and requires less energy to break. Bond dissociation energy is commonly expressed in kilojoules per mole.

According to the valence bond theory, the electrons in a covalent bond remain centralized around their original nuclei, and their atomic orbitals overlap. An orbital is a region in which an electron has a high probability of being located. Orbitals are described by the quantum number \ell. Different orbitals are called s, p, d, and f, which differ from each other by their shapes. For example, s orbitals are spherical, while p orbitals have a dumbbell shape.

According to the valence bond theory, the orbital shape plays an important role in bonding. Two orbitals can overlap end-to-end or side-by-side. The bond formed when two orbitals overlap end to end is called a sigma bond (σ\sigma bond). The bond formed when two orbitals overlap side by side on the same plane is a pi bond (π\pi bond).

The spherical s orbitals can participate in σ\sigma bonds with another s orbital or a p orbital. Dumbbell-shaped p orbitals can bond end to end, forming a σ\sigma bond with an s orbital or a p orbital. Also, p orbitals can bond side by side, forming a π\pi bond with another p orbital.
Sigma bonds can form between two s orbitals, two π\pi orbitals, or one s and one π\pi orbital. They form when orbitals approach one another end to end. In contrast, pi bonds form when orbitals approach each other side by side.