where F i is a so-called embedding function (not to be confused with the force F → → i ) that is a function of the sum of the so-called electron density ρ ρ ( r i j ) . V 2 is a pair potential that usually is purely repulsive. In the original formulation the electron density function ρ ρ ( r i j ) was obtained from true atomic electron densities, and the embedding function was motivated from density-functional theory as the energy needed to 'embed' an atom into the electron density. . However, many other potentials used for metals share the same functional form but motivate the terms differently, e.g. based on tight-binding theory or other motivations .