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Lennard-Jones potential

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Lennard-Jones potential
NameJohn Edward Lennard-Jones
Birth date1894
Death date1954
NationalityBritish
FieldTheoretical chemistry
Known forInteratomic potentials

Lennard-Jones potential The Lennard-Jones potential is a mathematical model used to describe intermolecular interactions in neutral atoms and nonpolar molecules. It was introduced in the early 20th century and has become foundational in molecular physics, physical chemistry, and computational materials science. The model informs studies ranging from gas-phase collisions to condensed-matter simulations employed by researchers in institutions such as Cambridge University, Imperial College London, Massachusetts Institute of Technology, California Institute of Technology, and Max Planck Society.

Introduction

The potential was proposed by John Edward Lennard-Jones and quickly influenced work by scientists at Royal Society, University of Oxford, University of Manchester, Harvard University, and Princeton University. It provided a simple analytic form that captured both attractive dispersion interactions discussed by Hendrik Lorentz and Friedrich London and short-range repulsion associated with electron overlap analyzed in studies at Bell Laboratories and Los Alamos National Laboratory. The model underpins many force fields developed at University of California, Berkeley and used in projects connected to National Institutes of Health, European Molecular Biology Laboratory, and Lawrence Livermore National Laboratory.

Mathematical Formulation

The canonical expression combines a r^-12 repulsive term and a r^-6 attractive term, with depth and distance parameters often denoted ε and σ. Derivations relate the r^-6 term to London dispersion forces originally explored by Heike Kamerlingh Onnes and Walther Nernst and the short-range behavior to Pauli exclusion principles discussed in work by Paul Dirac and Wolfgang Pauli. The model is frequently presented alongside alternative analytic forms such as Buckingham and Morse potentials used by groups at Argonne National Laboratory and Oak Ridge National Laboratory.

Physical Interpretation and Properties

Physically, the attractive component approximates induced dipole–induced dipole interactions characterized in treatments by Maxwell and James Clerk Maxwell’s successors, while the repulsive component represents electron cloud overlap with roots in quantum mechanical analyses by Erwin Schrödinger and Werner Heisenberg. The potential predicts equilibrium separation and cohesive energy values that compare with experimental measurements from techniques developed at CERN, Brookhaven National Laboratory, Stanford Linear Accelerator Center, and synchrotron facilities such as Diamond Light Source. It also yields analytic expressions for virial coefficients used in thermodynamic studies conducted at National Physical Laboratory and NIST.

Parameterization and Variants

Parameters ε and σ are fit to reproduce experimental observables or high-level calculations from methods like Hartree–Fock, configuration interaction, and coupled-cluster used by groups at ETH Zurich, École Normale Supérieure, Yale University, and Tsinghua University. Variants include shifted, truncated, and smoothing forms used in molecular mechanics packages developed at Schrödinger (company), OpenEye Scientific Software, and Molecular Sciences Software Institute. Other generalized forms such as the 12-6-4 potential, Buckingham potential, and modified Lennard-Jones parametrizations have been proposed in collaborations involving University of Tokyo, Seoul National University, University of Toronto, and University of Sydney.

Applications in Molecular Simulations

The potential is integral to classical molecular dynamics and Monte Carlo simulations implemented in software from Lawrence Berkeley National Laboratory, University of Illinois Urbana-Champaign, and commercial suites at Accelrys. It is used to model noble gases in studies by researchers affiliated with Argonne National Laboratory, to describe van der Waals contacts in protein-ligand simulations at Scripps Research Institute and Columbia University, and to explore surface phenomena investigated at IBM Research and Hitachi. Large-scale simulations leveraging the potential run on platforms such as Oak Ridge Leadership Computing Facility, Blue Gene installations at IBM, and national supercomputing centers like NERSC and PRACE facilities.

Limitations and Extensions

Limitations include the absence of explicit electrostatics and polarization, prompting extensions that couple Lennard-Jones-like terms with polarizable models, Drude oscillators, and explicitly correlated quantum approaches developed at Los Alamos National Laboratory, Riken, Swiss Federal Institute of Technology (EPFL), and Johns Hopkins University. For metals and covalent materials, embedded-atom methods and reactive force fields such as ReaxFF and Tersoff—used by teams at Sandia National Laboratories, Oak Ridge National Laboratory, and Toyota Central R&D Labs—offer improved accuracy. Multiscale coupling schemes incorporating density functional theory from groups at Flatiron Institute and Lawrence Livermore National Laboratory address shortcomings for chemically reactive systems.

Computational Implementation and Efficiency

Efficient evaluation in molecular simulations uses neighbor lists, cell lists, and cutoff schemes implemented in engines like GROMACS, LAMMPS, NAMD, and AMBER developed at European Molecular Biology Laboratory, Scripps Research Institute, University of Illinois, and University of California, San Diego. Long-range correction techniques and particle-mesh algorithms developed at Princeton Plasma Physics Laboratory and Rutgers University mitigate truncation artifacts. Performance optimizations for GPUs and exascale architectures have been pursued in collaborations involving NVIDIA, Intel, Cray Research, and national labs including Oak Ridge National Laboratory.

Category:Interatomic potentials