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The Lennard-Jones potential (also referred to as the L-J potential, 6-12 potential, or 12-6 potential) is a mathematically simple model that approximates the interaction between a pair of neutral atoms or molecules. A form of this interatomic potential was first proposed in 1924 by John Lennard-Jones.〔.〕 The most common expressions of the L-J potential are : : where ''ε'' is the depth of the potential well, ''σ'' is the finite distance at which the inter-particle potential is zero, ''r'' is the distance between the particles, and ''r''m is the distance at which the potential reaches its minimum. At ''r''m, the potential function has the value −ε. The distances are related as ''r''m = 21/6σ ≈ 1.122σ. These parameters can be fitted to reproduce experimental data or accurate quantum chemistry calculations. Due to its computational simplicity, the Lennard-Jones potential is used extensively in computer simulations even though more accurate potentials exist. ==Explanation== The ''r''−12 term, which is the repulsive term, describes Pauli repulsion at short ranges due to overlapping electron orbitals and the ''r''−6 term, which is the attractive long-range term, describes attraction at long ranges (van der Waals force, or dispersion force). Differentiating the L-J potential with respect to 'r' gives an expression for the net inter-molecular force between 2 molecules. This inter-molecular force may be attractive or repulsive, depending on the value of 'r'. When 'r' is very small, the 2 molecules repel each other. Whereas the functional form of the attractive term has a clear physical justification, the repulsive term has no theoretical justification. It is used because it approximates the Pauli repulsion well, and is more convenient due to the relative computational efficiency of calculating ''r''12 as the square of ''r''6. The Lennard-Jones (12,6) potential can be further approximated by the (exp-6) potential later proposed by R. A. Buckingham, in which the repulsive part is exponential:〔Peter Atkins and Julio de Paula, "Atkins' Physical Chemistry" (8th edn, W. H. Freeman), p.637〕 : The L-J potential is a relatively good approximation and due to its simplicity is often used to describe the properties of gases, and to model dispersion and overlap interactions in molecular models. It is particularly accurate for noble gas atoms and is a good approximation at long and short distances for neutral atoms and molecules. The lowest energy arrangement of an infinite number of atoms described by a Lennard-Jones potential is a hexagonal close-packing. On raising temperature, the lowest free energy arrangement becomes cubic close packing and then liquid. Under pressure the lowest energy structure switches between cubic and hexagonal close packing.〔.〕 Real materials include BCC structures as well.〔Calculation of the Lennard-Jones n–m potential energy parameters for metals. Shu Zhen,G. J. Davies. physica status solidi (a)Volume 78, Issue 2, pages 595–605, 16 August 1983〕 Other more recent methods, such as the Stockmayer potential, describe the interaction of molecules more accurately. Quantum chemistry methods, Møller–Plesset perturbation theory, coupled cluster method or full configuration interaction can give extremely accurate results, but require large computational cost. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lennard-Jones potential」の詳細全文を読む スポンサード リンク
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