Mie potential

The Mie potential is an interaction potential describing the interactions between particles on the atomic level.

The Mie potential is named after the German physicist Gustav Mie;[1] yet the history of intermolecular potentials is more complicated.

The Lennard-Jones potential corresponds to the special case where

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

is physically justified by the London dispersion force,[4] whereas no justification for a certain value for the repulsive exponent is known.

has a significant influence on the modeling of thermodynamic derivative properties, e.g. the compressibility and the speed of sound.

The Mie potential is used today in many force fields in molecular modeling.

Typically, the attractive exponent is chosen to be

, whereas the repulsive exponent is used as an adjustable parameter during the model fitting.

As for the Lennard-Jonesium, where a theoretical substance exists that is defined by particles interacting by the Lennard-Jones potential, a substance class of Mie substances exists that are defined as single site spherical particles interacting by a given Mie potential.

Since an infinite number of Mie potentials exist (using different n, m parameters), equally many Mie substances exist, as opposed to Lennard-Jonesium, which is uniquely defined.

For practical applications in molecular modelling, the Mie substances are mostly relevant for modelling small molecules, e.g. noble gases, and for coarse grain modelling, where larger molecules, or even a collection of molecules, are simplified in their structure and described by a single Mie particle.

However, more complex molecules, such as long-chained alkanes, have successfully been modelled as homogeneous chains of Mie particles.

[8] As such, the Mie potential is useful for modelling far more complex systems than those whose behaviour is accurately captured by "free" Mie particles.

Thermophysical properties of both the Mie fluid, and chain molecules built from Mie particles have been the subject of numerous papers in recent years.

Investigated properties include virial coefficients[9] and interfacial,[10] vapor-liquid equilibrium,[11][12][13][14] and transport properties.

[15] Based on such studies the relation between the shape of the interaction potential (described by n and m) and the thermophysical properties has been elucidated.

Also, many theoretical (analytical) models have been developed for describing thermophysical properties of Mie substances and chain molecules formed from Mie particles, such as several thermodynamic equations of state[8][16][17] and models for transport properties.

) can yield similar phase behaviour,[19] and that this degeneracy is captured by the parameter

[19] Due to its flexibility, the Mie potential is a popular choice for modelling real fluids in force fields.

It is used as an interaction potential many molecular models today.

Several (reliable) united atom transferable force fields are based on the Mie potential, such as that developed by Potoff and co-workers.

[20][21][22] The Mie potential has also been used for coarse-grain modeling.

There, the molecular models have only the parameters of the Mie potential itself.