Energy and Force Concepts in Chemical Bonding

The concepts of energy and force are the two familiar concepts in chemistry that are used to explain almost every phenomenon or process in chemistry. While the concept of energy is represented by virial theorem, the concept of force is given by the Hellmann–Feynman (H-F) theorem of electrostatic forces. The H-F theorem is a highly useful tool for developing qualitative chemical models based on firm quantum mechanical foundations and is also open to quantitative extension. Both these theorems have been derived in this chapter from quantum mechanical principles and discussed with examples. Virial theorem has been used to explain bond formation in diatomic molecules. H-F theorem has been used to calculate intramolecular forces in molecules and to gather information about their electronic structure and equilibrium geometries. Forces in a diatomic molecule have been used to get a physical picture of chemical bond in terms of the binding, antibinding, and nonbinding regions. A comparison has been made between the virial, H-F force, and Bader concepts of molecular binding.