According to Brønsted-Lowry theory, only a species containing at least one hydrogen atom has the potential to act as an acid in a reaction. Lewis theory is an attempt to extend the concept of acidity beyond species containing hydrogen. According to Lewis theory, in a reaction, a species that accepts a pair of electrons to form a new covalent bond is an acid, and a species that contribute s a pair of electrons toward a new covalent bond is a base.
In this reaction, BF3 accepts a pair of electrons from F ¯ to form a new covalent bond and, therefore, acts as an acid; F ¯ contributes a pair of electrons toward a new covalent bond with BF3 and, therefore, acts as a base.
In a reaction a species that acts as an acid according to Lewis theory is called a Lewis acid and a species that acts as a base a Lewis base.