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Variational approach for minimizing Lennard-Jones energies

Peterson, Carsten LU ; Sommelius, Ola LU and Söderberg, Bo LU (1996) In Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 53(2). p.1725-1731
Abstract

A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, rotors, and consists of the iterative solution of a set of deterministic equations with an annealing in temperature. The singular short-distance behavior of the Lennard-Jones potential is adiabatically switched on in order to obtain stable convergence. As testbeds for the approach two distinct ensembles of molecules are used, characterized by a roughly dense-packed or a more elongated ground state. For the latter, problems are generated from natural frequencies of occurrence of amino acids and phenomenologically... (More)

A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, rotors, and consists of the iterative solution of a set of deterministic equations with an annealing in temperature. The singular short-distance behavior of the Lennard-Jones potential is adiabatically switched on in order to obtain stable convergence. As testbeds for the approach two distinct ensembles of molecules are used, characterized by a roughly dense-packed or a more elongated ground state. For the latter, problems are generated from natural frequencies of occurrence of amino acids and phenomenologically determined potential parameters; they seem to represent less disorder than was previously assumed in synthetic protein studies. For the dense-packed problems in particular, the variational algorithm clearly outperforms a gradient descent method in terms of minimal energies. Although it cannot compete with a careful simulating annealing algorithm, the variational approach requires only a tiny fraction of the computer time. Issues and results when applying the method to polyelectrolytes at a finite temperature are also briefly discussed.

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published
in
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
volume
53
issue
2
pages
7 pages
publisher
American Physical Society
external identifiers
  • scopus:5344252329
ISSN
1063-651X
language
English
LU publication?
yes
id
a31f2287-63a3-4c32-b5f6-b1dcda9e9046
date added to LUP
2016-10-03 19:17:06
date last changed
2017-11-16 11:08:17
@article{a31f2287-63a3-4c32-b5f6-b1dcda9e9046,
  abstract     = {<p>A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, rotors, and consists of the iterative solution of a set of deterministic equations with an annealing in temperature. The singular short-distance behavior of the Lennard-Jones potential is adiabatically switched on in order to obtain stable convergence. As testbeds for the approach two distinct ensembles of molecules are used, characterized by a roughly dense-packed or a more elongated ground state. For the latter, problems are generated from natural frequencies of occurrence of amino acids and phenomenologically determined potential parameters; they seem to represent less disorder than was previously assumed in synthetic protein studies. For the dense-packed problems in particular, the variational algorithm clearly outperforms a gradient descent method in terms of minimal energies. Although it cannot compete with a careful simulating annealing algorithm, the variational approach requires only a tiny fraction of the computer time. Issues and results when applying the method to polyelectrolytes at a finite temperature are also briefly discussed.</p>},
  author       = {Peterson, Carsten and Sommelius, Ola and Söderberg, Bo},
  issn         = {1063-651X},
  language     = {eng},
  number       = {2},
  pages        = {1725--1731},
  publisher    = {American Physical Society},
  series       = {Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
  title        = {Variational approach for minimizing Lennard-Jones energies},
  volume       = {53},
  year         = {1996},
}