Numerical implementation of the hyper-molecular dynamics method with examples applied to diffusion

  • Sanz-Navarro C
  • Smith R
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Abstract

Hyper-molecular dynamics (H-MD) is a powerful simulation method developed to increase the time-scale over which a molecular dynamics (MD) simulation can be carried out. Adding a bias potential to the interatomic potential, the simulated time can be boosted by a factor dependent upon the temperature of the system. Such a bias potential may be defined as a function of two parameters: the lowest eigenvalue of the Hessian matrix of the total interatomic potential with respect to the atom co-ordinates and the projection of the gradient of the potential onto the eigenvector. Two minimisation methods have been proposed in the literature in order to obtain a numerical approximation of such parameters without the diagonalisation of the Hessian matrix. The performance of a H-MD simulation depends on the accuracy and speed of such minimisation methods. We have found that only one minimisation is necessary to calculate numerically the bias force. The speed of a H-MD simulation increases by a factor ∼3 and improves the accuracy of the numerical approximation. We show examples where H-MD can be applied obtaining high boosts of between 102and 5 × 105in the simulated time, thus extending time-scale of the simulation from nanoseconds to milliseconds. © 2001 Elsevier Science B.V.

Author-supplied keywords

  • Bias potential
  • Diffusion processes
  • Hyper-molecular dynamics
  • Long time-scales
  • Rate of escape

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Authors

  • C. F. Sanz-Navarro

  • Roger Smith

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