Bonds can fall between one of two extremescompletely nonpolar or completely polar. A completely nonpolar bond occurs when the electronegativities are identical and therefore possess a difference of zero. A completely polar bond is more correctly called an ionic bond, and occurs when the difference between electronegativities is large enough that one atom actually takes an electron from the other. The terms "polar" and "nonpolar" are usually applied to covalent bonds, that is, bonds where the polarity is not complete. To determine the polarity of a covalent bond using numerical means, the difference between the electronegativity of the atoms is used.
Bond polarity is typically divided into three groups that are loosely based on the difference in electronegativity between the two bonded atoms. According to the Pauling scale:
* Nonpolar bonds generally occur when the difference in electronegativity between the two atoms is less than 0.5
* Polar bonds generally occur when the difference in electronegativity between the two atoms is roughly between 0.5 and 2.0
* Ionic bonds generally occur when the difference in electronegativity between the two atoms is greater than 2.0
Pauling based this classification scheme on the partial ionic character of a bond, which is an approximate function of the difference in electronegativity between the two bonded atoms. He estimated that a difference of 1.7 corresponds to 50% ionic character, so that a greater difference corresponds to a bond which is predominantly ionic.
As a quantum-mechanical description, Pauling proposed that the wave function for a polar molecule AB is a linear combination of wave functions for covalent and ionic molecules: ψ = aψ(A:B) + bψ(AB). The amount of covalent and ionic character depends on the values of the squared coefficients a and b.