Mie potential

The Mie potential is an intermolecular pair potential, i.e. it describes the interactions between particles at the atomic level.

The model is attributed to the German physicist Gustav Mie.[1] The Mie potential is the generalized case of the Lennard-Jones (LJ) potential, which is perhaps the single most widely used pair potential.[2][3]

The Mie potential ${\displaystyle V(r)}$ is a function of ${\displaystyle r}$, the distance between two particles, and is written as[4]

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

with

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

The Lennard-Jones potential corresponds to the special case where ${\textstyle n=12}$ and ${\textstyle m=6}$ in Eq. (1). In Eq. (1), ${\displaystyle \varepsilon }$ 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 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 the subject of numerous papers in recent years, including virial coefficients[6] and interfacial[7] and vapor-liquid equilibrium[8][9][10] properties.