Morse potential

Morse potential
Lawrence Livermore National Laboratory · Public domain · source
Name	Morse potential
Type	Potential energy function
Introduced	1929
Introduced by	Philip M. Morse

Morse potential is an empirical interatomic potential function introduced to model diatomic bond energies and vibrational spectra. It provides an analytic approximation to the potential energy curve of a pair of atoms, capturing anharmonicity and bond dissociation behavior that is absent in the simple harmonic oscillator. The function has played a central role in spectroscopic analysis, molecular dynamics, and quantum chemistry, influencing methods used at institutions such as Harvard University, Massachusetts Institute of Technology, and Bell Labs.

History and development

The Morse potential was proposed in 1929 by Philip M. Morse as part of efforts to explain molecular vibrational spectra following experimental results from groups including Frederick A. Lindemann and theoretical advances by Erwin Schrödinger and Paul Dirac. Early adoption came from spectroscopists working with data from laboratories such as Bell Labs and universities like University of Cambridge and University of Chicago, linking the model to empirical work by Gerhard Herzberg and Molecular Spectroscopy research at National Institute of Standards and Technology. Subsequent developments drew on mathematical physics contributions from figures including John von Neumann and Max Born and were applied in computational projects at Los Alamos National Laboratory and Lawrence Berkeley National Laboratory.

The model influenced later interatomic potentials such as those developed by researchers at Argonne National Laboratory and in force field programs originating from groups at Columbia University and Stanford University. Experimental validations used spectrometers at institutions like Imperial College London and University of Oxford, and comparisons were made with ab initio calculations from groups led by John Pople and Martin Head-Gordon.

Mathematical form and properties

The Morse potential is given by an analytic expression featuring parameters relating to bond energy and length, developed within the mathematical framework used by Albert Einstein and Paul Ehrenfest. Its functional form was motivated by phenomenology observed in experiments performed by laboratories such as Rutherford Appleton Laboratory and Cavendish Laboratory. The potential includes an exponential decay term reflecting dissociation, a depth parameter comparable to dissociation energies tabulated by IUPAC committees and spectroscopic compendia compiled by NIST.

Key properties derive from parameter choices often obtained from fits to spectroscopic transitions measured by groups associated with Royal Society fellowships and national laboratories like Sandia National Laboratories and Oak Ridge National Laboratory. The Morse form allows closed-form expressions for vibrational spacing analogous to work by Viktor F. Weisskopf and Hendrik Lorentz on oscillator models, and it connects to semiclassical approximations developed in the tradition of Arnold Sommerfeld and Ludwig Boltzmann.

Quantum mechanical treatment

Exact solutions of the one-dimensional Schrödinger equation with the Morse potential were obtained in the mathematical physics lineage including contributions by Eugene Wigner and later pedagogical expositions at Princeton University. Bound state eigenvalues and eigenfunctions are expressible via special functions used by researchers such as E. T. Whittaker and G. N. Watson and parallel methods applied in scattering theory at CERN and Max Planck Institute for Physics. The spectrum displays anharmonic level spacing that matches high-resolution results from experimental groups at Max Planck Institute for Chemical Physics of Solids and Weizmann Institute of Science.

Transition probabilities and vibrational wavefunctions computed with the Morse potential have been used in analyses by teams at Bell Labs and IBM Research and are compared against ab initio spectra calculated by groups led by Walter Kohn and Linus Pauling. Semiclassical quantization methods by Gutzwiller and coherent state techniques developed by Roy Glauber provide approximate connections between classical trajectories and quantum states for this potential.

Applications in chemistry and physics

The Morse potential is used widely in molecular vibration studies at facilities like Brookhaven National Laboratory and in force fields developed at University of California, Berkeley and California Institute of Technology. It underpins models of bond breaking in reaction dynamics studied by research groups including those at Argonne National Laboratory and Yale University. Applications extend to solid-state modeling in projects at National Renewable Energy Laboratory and to surface science probed at SLAC National Accelerator Laboratory.

In spectroscopy, the potential informs interpretation of infrared and Raman data gathered at centers such as Max Planck Institute for Biophysical Chemistry and Scripps Research, and in atmospheric chemistry experiments undertaken at NOAA. The Morse form also appears in pedagogical contexts at University of Illinois Urbana-Champaign and in textbooks authored by scholars affiliated with Oxford University Press and Cambridge University Press.

Computational methods and parameterization

Parameterization strategies for the Morse potential have been developed in computational chemistry traditions emanating from groups led by John Pople and Martin Head-Gordon, using fitting protocols established at Gaussian, Inc. and other software houses. Parameters (equilibrium distance, well depth, range parameter) are obtained by fits to spectroscopic datasets curated by NIST and computational benchmarks produced by consortia including The Materials Project and MolSSI.

Numerical implementations appear in molecular dynamics packages developed at Sandia National Laboratories and in quantum chemistry codes from teams at University of California, Berkeley and Harvard University. Advanced parameter sets are derived using methods from density functional theory popularized by Walter Kohn and coupled-cluster theories developed by Hendrik J. Monkhorst and collaborators at Argonne National Laboratory.

Category:Interatomic potentials