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Concept
Interatomic potential
Summary
Interatomic potentials are mathematical functions to calculate 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 computational chemistry, computational physics and computational materials science to explain and predict materials properties. Examples of quantitative properties and qualitative phenomena that are explored with interatomic potentials include lattice parameters, surface energies, interfacial energies, adsorption, cohesion, thermal expansion, and elastic and plastic material behavior, as well as chemical reactions.
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 potential of the system can
be written as
Here is the one-body term, the two-body term, the
three body term, the number of atoms in the system,
the position of atom , etc. , and are indices
that loop over atom positions.
Note that in case the pair potential is given per atom pair, in the two-body
term the potential should be multiplied by 1/2 as otherwise each bond is counted
twice, and similarly the three-body term by 1/6. Alternatively,
the summation of the pair term can be restricted to cases
and similarly for the three-body term , if
the potential form is such that it is symmetric with respect to exchange
of the and indices (this may not be the case for potentials
for multielemental systems).
The one-body term is only meaningful if the atoms are in an external
field (e.g. an electric field). In the absence of external fields,
the potential should not depend on the absolute position of
atoms, but only on the relative positions. This means
that the functional form can be rewritten as a function
of interatomic distances
and angles between the bonds
(vectors to neighbours) .
Official source
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