Mie potential

The Mie potential is an intermolecular pair potential, i.e. it describes the interactions between particles on the atomic level. The Mie potential is one of the most simple, yet most powerful pair potentials, and describes both repulsive and dispersive (attractive) interactions of atoms and molecules. The Mie potential is attributed to the German physicist Gustave Mie.[1]

The Mie potential is written as[2]

${\displaystyle V_{\mathrm {Mie} }(r)=C\,\varepsilon \left[\left({\frac {\sigma }{r}}\right)^{n}-\left({\frac {\sigma }{r}}\right)^{m}\right],~~~~~~(1)}$

with

${\displaystyle C={\frac {n}{n-m}}\left({\frac {n}{m}}\right)^{\frac {m}{n-m}}}$ .

In Eq. (1), ${\displaystyle r}$ is the distance between two particles, ${\displaystyle \varepsilon }$ is the dispersion energy, and ${\displaystyle \sigma }$ indicates the distance at which ${\displaystyle V=0}$, which is sometimes called the "collision radius." The parameter ${\textstyle \sigma }$ is generally indicative of the size of the particles involved in the collision. The parameters ${\textstyle n}$ and ${\textstyle m}$ characterize the shape of the potential: ${\textstyle n}$ describes the character of the repulsion and ${\textstyle m}$ describes the character of the attraction.

The Mie potential is the generalized case of the Lennard-Jones (LJ) potential, which is perhaps the single most widely used pair potential.[3][4] Hence, the LJ potential has ${\textstyle n=12}$ and ${\textstyle m=6}$ in Eq. (1). The attractive exponent ${\textstyle m=6}$ is physically justified by the London dispersion force,[5] whereas no justification for a certain value for the repulsive exponent is known. The repulsive steepness parameter ${\textstyle n}$ has a significant influence on the modelling of thermodynamic derivative properties, e.g. the compressibility and the speed of sound. 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 in molecular modeling. Typically, the attractive exponent is chosen to be ${\textstyle m=6}$, 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 frequently studied in the past decades, e.g. its virial coefficients,[6] interfacial[7] and vapor-liquid equilibrium[8][9] properties.