Mie potential

The potential curve of the Mie potential in reduced units, for different values of the repulsive exponent ( n ), all depicted curves use the attractive exponent m = 6 . The black curve corresponds to the Lennard-Jones potential.
The potential curve of the Mie potential in reduced units, for different values of the repulsive exponent (), all depicted curves use the attractive exponent . The black curve corresponds to the Lennard-Jones potential.

The Mie potential is an interaction potential describing the interactions between particles on the atomic level. It is mostly used for describing intermolecular interactions, but at times also for modeling intramolecular interaction, i.e. bonds.

The Mie potential is named after the German physicist Gustav Mie;[1] yet the history of intermolecular potentials is more complicated.[2][3][4] The Mie potential is the generalized case of the Lennard-Jones (LJ) potential, which is perhaps the most widely used pair potential.[5][6]

The Mie potential is a function of , the distance between two particles, and is written as[7]

with

.

The Lennard-Jones potential corresponds to the special case where and in Eq. (1). In Eq. (1), is the dispersion energy, and indicates the distance at which , which is sometimes called the "collision radius." The parameter is generally indicative of the size of the particles involved in the collision. The parameters and characterize the shape of the potential: describes the character of the repulsion and describes the character of the attraction.

The attractive exponent is physically justified by the London dispersion force,[4] whereas no justification for a certain value for the repulsive exponent is known. The repulsive steepness parameter has a significant influence on the modeling of thermodynamic derivative properties, e.g. the compressibility and the speed of sound. Therefore, the Mie potential is a more flexible intermolecular potential than the simpler Lennard-Jones potential.

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.

  1. ^ Mie, Gustav (1903). "Zur kinetischen Theorie der einatomigen Körper". Annalen der Physik (in German). 316 (8): 657–697. Bibcode:1903AnP...316..657M. doi:10.1002/andp.19033160802.
  2. ^ Fischer, Johann; Wendland, Martin (October 2023). "On the history of key empirical intermolecular potentials". Fluid Phase Equilibria. 573: 113876. doi:10.1016/j.fluid.2023.113876. ISSN 0378-3812.
  3. ^ Lenhard, Johannes; Stephan, Simon; Hasse, Hans (February 2024). "A child of prediction. On the History, Ontology, and Computation of the Lennard-Jonesium". Studies in History and Philosophy of Science. 103: 105–113. doi:10.1016/j.shpsa.2023.11.007. ISSN 0039-3681. S2CID 266440296.
  4. ^ a b Lafitte, Thomas; Apostolakou, Anastasia; Avendaño, Carlos; Galindo, Amparo; Adjiman, Claire S.; Müller, Erich A.; Jackson, George (2013-10-21). "Accurate statistical associating fluid theory for chain molecules formed from Mie segments". The Journal of Chemical Physics. 139 (15): 154504. Bibcode:2013JChPh.139o4504L. doi:10.1063/1.4819786. hdl:10044/1/12859. ISSN 0021-9606. PMID 24160524.
  5. ^ Stephan, Simon; Staubach, Jens; Hasse, Hans (November 2020). "Review and comparison of equations of state for the Lennard-Jones fluid". Fluid Phase Equilibria. 523: 112772. doi:10.1016/j.fluid.2020.112772. S2CID 224844789.
  6. ^ Stephan, Simon; Thol, Monika; Vrabec, Jadran; Hasse, Hans (2019-10-28). "Thermophysical Properties of the Lennard-Jones Fluid: Database and Data Assessment". Journal of Chemical Information and Modeling. 59 (10): 4248–4265. doi:10.1021/acs.jcim.9b00620. ISSN 1549-9596. PMID 31609113. S2CID 204545481.
  7. ^ J., Stone, A. (2013). The theory of intermolecular forces. Oxford Univ. Press. ISBN 978-0-19-175141-7. OCLC 915959704.{{cite book}}: CS1 maint: multiple names: authors list (link)