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.
Sanz-Navarro, C. F., & Smith, R. (2001). Numerical implementation of the hyper-molecular dynamics method with examples applied to diffusion. In Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms (Vol. 180, pp. 130–138). https://doi.org/10.1016/S0168-583X(01)00407-4