Neutral atoms and molecules are subject to two distinct forces in the limit of large distance and short distance: an attractive force at long ranges (van der Waals force, or dispersion force) and a repulsive force at short ranges (the result of overlapping electron orbitals, referred to as Pauli repulsion from Pauli exclusion principle). The Lennard-Jones potential (also referred to as the L-J potential, 6-12 potential or, less commonly, 12-6 potential) is a simple mathematical model that represents this behavior. It was proposed in 1931 by John Lennard-Jones of Bristol University.^[1] The title given to this article is incorrect due to technical limitations. ... The electron is a fundamental subatomic particle that carries a negative electric charge. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925, which states that no two identical fermions may occupy the same quantum state simultaneously. ... John Edward Lennard-Jones (October 27, 1894 - November 1, 1954) was a mathematician who held a chair of theoretical physics at Bristol University, and then a chair of theoretical science at Cambridge University. ... The University of Bristol was founded in 1876 as the University College, Bristol. ...

Lennard-Jones potential for argon dimer

The L-J potential is of the form Image File history File links Download high resolution version (1500x1050, 46 KB) Summary Description: Interaction energy of argon dimer. ... Image File history File links Download high resolution version (1500x1050, 46 KB) Summary Description: Interaction energy of argon dimer. ...

where ε is the depth of the potential well and σ is the (finite) distance at which the potential is zero. The function is also often written as

where r_min = 2^1/6σ is the distance at the minimum of the potential.

These parameters can be fitted to reproduce experimental data or deduced from results of accurate quantum chemistry calculations. The term describes repulsion and the term describes attraction. The force function is the negative of the gradient of the above potential: In statistics, regression analysis is used to model relationships between variables and determine the magnitude of those relationships. ... Linus Pauling, as a pioneer of the valence bond theory, is one of the first quantum chemists. ...

The L-J potential is approximate. The form of the repulsion term has no theoretical justification; the repulsion force should depend exponentially on the distance, but the repulsion term of the L-J formula is more convenient due to the ease and efficiency of computing r¹² as the square of r⁶. The attractive long-range potential, however, is derived from dispersion interactions. The L-J potential is a relatively good approximation and due to its simplicity 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. On the graph, Lennard-Jones potential for argon dimer is shown. Small deviation from the accurate empirical potential due to incorrect long range part of the repulsion term can be seen. The exponential function is one of the most important functions in mathematics. ... The title given to this article is incorrect due to technical limitations. ... For the musical band, see Noble Gas (band) The noble gases are the chemical elements in group 18 (old-style Group 0) of the periodic table. ... General Name, Symbol, Number argon, Ar, 18 Chemical series noble gases Group, Period, Block 18, 3, p Appearance colorless Atomic mass 39. ... Sucrose, or common table sugar, is composed of glucose and fructose. ...

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.^[2] Close-packing of spheres refers to arranging an infinite lattice of spheres so that they take up the greatest possible fraction of an infinite 3-dimensional space. ... The free energy is a measure of the amount of mechanical (or other) work that can be extracted from a system, and is helpful in engineering applications. ... Close-packing of spheres is the arranging of an infinite lattice of spheres so that they take up the greatest possible fraction of an infinite 3-dimensional space. ...

Other more recent methods, such as the Stockmayer equation and the so-called multi equation, 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. Walter Hugo Stockmayer (7 April 1914, Rutherford, New Jersey - 9 May 2004, Norwich, Vermont) was an internationally known chemist and university teacher. ... Linus Pauling, as a pioneer of the valence bond theory, is one of the first quantum chemists. ... Møller-Plesset perturbation theory is an implementation of perturbation theory in quantum chemistry, which provides a method for adding excitations to the Hartree-Fock wavefunction and therefore including the effect of electron correlation. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Full configuration interaction (or full CI) is a linear variational approach which provides numerically exact solutions (within the given one-particle basis set) to the electronic Schrödinger equation. ... In computer science, efficiency is used to describe several desirable properties of an algorithm or other construct, besides clean design, functionality, etc. ...

See also

• Embedded atom model
• Morse potential
• Force field (chemistry)

To meet Wikipedias quality standards, this article or section may require cleanup. ... The Morse potential (blue) and harmonic oscillator potential (green). ... It has been suggested that this article or section be merged with force field (physics). ...

References

1. ^ Lennard-Jones, J. E. Cohesion. Proceedings of the Physical Society 1931, 43, 461-482.
2. ^ Baron, T. H. K., Domb, C. On the Cubic and Hexagonal Close-Packed Lattices. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 1955, 227, 447-465.