Can classical equations simulate quantum‐mechanical behavior? a molecular dynamics investigation of a diatomic molecule with a morse potential

Tamar Schlick, Charles S. Peskin

Research output: Contribution to journalArticle

Abstract

In a recent paper, we presented a new computational method for molecular dynamics which uses the Backward‐Euler scheme to solve the classical Langevin dynamics equations. Parameters for the simulation include a target temperature T, a time step Δt, and a cutoff frequency ωc. We showed for a harmonic oscillator system that the cutoff frequency can be set as ωc = kT/h in order to mimic quantum‐mechanical behavior. We now continue this investigation for a nonlinear case: a diatomic molecule governed by a Morse bond potential. Since approximate quantum‐mechanical energy levels are explicitly known for this model, a comparison of energies can be made with molecular dynamics results. By performing dynamics runs for a wide range of temperatures and calculating mean energies, we find a very good agreement between these energies and quantum mechanical predictions. Vibrational excitation begins at temperatures around 800 K, and for higher temperatures both energy curves (molecular dynamics and quantum mechanics) approach the classical prediction of 7/2kT energy per molecule. Future investigations will focus on more general nonlinear potential functions employed in force fields of nucleic acids and proteins.

Original languageEnglish (US)
Pages (from-to)1141-1163
Number of pages23
JournalCommunications on Pure and Applied Mathematics
Volume42
Issue number8
DOIs
StatePublished - 1989

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Morse potential
Morse Potential
Molecular Dynamics
Molecular dynamics
Molecules
Cutoff frequency
Energy
Temperature
Quantum theory
Nucleic acids
Langevin Dynamics
Computational methods
Electron energy levels
Prediction
Langevin Equation
Force Field
Potential Function
Energy Levels
Dynamic Equation
Harmonic Oscillator

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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