Interatomic potential

Interatomic potentials are mathematical functions for calculating the potential energy of a system of atoms with given positions in space. Interatomic potentials are widely used as the physical basis of molecular mechanics and molecular dynamics simulations in chemistry, molecular physics and materials physics, sometimes in connection with such effects as cohesion, thermal expansion and elastic properties of materials.

Interatomic potentials can be written as a series expansion of functional terms that depend on the position of one, two, three, etc. atoms at a time. Then the total energy of the system V can be written as

Here ${\displaystyle \textstyle V_{1}}$ is the one-body term, ${\displaystyle \textstyle V_{2}}$ the two-body term, ${\displaystyle \textstyle V_{3}}$ the three body term, ${\displaystyle \textstyle N}$ the number of atoms in the system, ${\displaystyle {\vec {r}}_{i}}$ the position of atom i, etc. i, j and k are indices that loop over atom positions.

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