Dear Arvind,

The potential φ can be a classical analytical formula, ranging from a very simple

sum of two-body terms, such as the Lennard-Jones potential, which models vdW interactions, to many-body potentials for modeling metals and semiconductors, such as the Tersoff potential[31]. Invoking the Born-Oppenheimer approximation, which allows one to separate Schr¨odinger’s equation into ionic and electronic components, and further choosing to treat the ions classically due to their large mass relative to the electrons, φ may then be of an explicitly quantum nature. In this case, the electronic Schr¨odinger’s  equation may be solved with various degrees of accuracy, and the resulting charge density and electronic band structure may be used to determine the potential energy of the full system and, if needed, the forces on the ions.

For more details, please see attached chapter.

Hoping this will be helpful,

Rafik