Lennard-Jones potential
Model of intermolecular interactions / From Wikipedia, the free encyclopedia
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In computational chemistry, molecular physics, and physical chemistry the Lennard-Jones potential (also termed the LJ potential or 12-6 potential; named for John Lennard-Jones) is an intermolecular pair potential. Out of all the intermolecular potentials, the Lennard-Jones potential is probably the one that has been the most extensively studied.[1][2] It is considered an archetype model for simple yet realistic intermolecular interactions.
The Lennard-Jones potential models soft repulsive and attractive (van der Waals) interactions. Hence, the Lennard-Jones potential describes electronically neutral atoms or molecules.[3][4][5] The commonly used expression for the Lennard-Jones potential is
where r is the distance between two interacting particles, ε is the depth of the potential well (usually referred to as 'dispersion energy'), and σ is the distance at which the particle-particle potential energy V is zero (often referred to as 'size of the particle'). The Lennard-Jones potential has its minimum at a distance of where the potential energy has the value
The Lennard-Jones potential is a simplified model that yet describes the essential features of interactions between simple atoms and molecules: Two interacting particles repel each other at very close distance, attract each other at moderate distance, and do not interact at infinite distance, as shown in Figure 1. The Lennard-Jones potential is a pair potential, i.e. no three- or multi-body interactions are covered by the potential.
Statistical mechanics[6] and computer simulations[7][8] can be used to study the Lennard-Jones potential and to obtain thermophysical properties of the 'Lennard-Jones substance'. The Lennard-Jones substance is often referred to as 'Lennard-Jonesium,'[2] suggesting that it is viewed as a (fictive) chemical element.[9] Moreover, its energy and length parameters can be adjusted to fit many different real substances. Both the Lennard-Jones potential and, accordingly, the Lennard-Jones substance are simplified yet realistic models, such as they accurately capture essential physical principles like the presence of a critical and a triple point, condensation and freezing. Due in part to its mathematical simplicity, the Lennard-Jones potential has been extensively used in studies on matter since the early days of computer simulation.[10][11][12][13] The Lennard-Jones potential is probably still the most frequently studied model potential.[14][9]
The Lennard-Jones potential is usually the standard choice for the development of theories for matter (especially soft-matter) as well as for the development and testing of computational methods and algorithms. Upon adjusting the model parameters ε and σ to real substance properties, the Lennard-Jones potential can be used to describe simple substance (like noble gases) with good accuracy. Furthermore, the Lennard-Jones potential is often used as a building block in molecular models (a.k.a. force fields) for more complex substances.[15][16][17][18][19]