The Mie potential is an intermolecular

pair potential In physics, a pair potential is a function that describes the potential energy of two interacting objects solely as a function of the distance between them. Examples of pair potentials include the Coulomb's law in electrodynamics, Newton's law of ...

, i.e. it describes the interactions between particles at the atomic level. The model is attributed to the German physicist Gustave Mie. The Mie potential is the generalized case of the Lennard-Jones (LJ) potential, which is perhaps the single most widely used pair potential. The Mie potential

V(r)

is a function of

r

, the distance between two particles, and is written as

V(r) = C \, \varepsilon \left \left(\frac \right)^-  \left( \frac\right)^m \right,~~~~~~ (1)

with

C = \frac \left( \frac\right)^

. The Lennard-Jones potential corresponds to the special case where

n=12

and

m=6

in Eq. (1). In Eq. (1),

\varepsilon

is the dispersion energy, and

\sigma

indicates the distance at which

V = 0

, which is sometimes called the "collision radius." The parameter

\sigma

is generally indicative of the size of the particles involved in the collision. The parameters

n

and

m

characterize the shape of the potential:

n

describes the character of the repulsion and

m

describes the character of the attraction. The attractive exponent

m=6

is physically justified by the

London dispersion force London dispersion forces (LDF, also known as dispersion forces, London forces, instantaneous dipole–induced dipole forces, fluctuating induced dipole bonds or loosely as van der Waals forces) are a type of intermolecular force acting between at ...

, whereas no justification for a certain value for the repulsive exponent is known. The repulsive steepness parameter

n

has a significant influence on the modelling of thermodynamic derivative properties, e.g. the

compressibility In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a fl ...

and the

speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as w ...

. Therefore, the Mie potential is a more flexible and better generalized intermolecular potential than the simpler Lennard-Jones potential. The Mie potential is used today in state-of-the-art

force fields Force field may refer to: Science * Force field (chemistry), a set of parameter and equations for use in molecular mechanics simulations * Force field (physics), a vector field indicating the forces exerted by one object on another * Force field ( ...

molecular modeling Molecular modelling encompasses all methods, theoretical and computational, used to model or mimic the behaviour of molecules. The methods are used in the fields of computational chemistry, drug design, computational biology and materials scien ...

. Typically, the attractive exponent is chosen to be

m=6

, whereas the repulsive exponent is used as an adjustable parameter during the model fitting. Thermophysical properties of systems modeled with the Mie potential have been the subject of numerous papers in recent years, including

virial coefficient Virial coefficients B_i appear as coefficients in the virial expansion of the pressure of a many-particle system in powers of the density, providing systematic corrections to the ideal gas law. They are characteristic of the interaction potential ...

s and interfacial and vapor-liquid equilibrium properties.

References

{{Reflist Thermodynamics Intermolecular forces Computational chemistry Quantum mechanical potentials