Hyper-molecular dynamics was a powerful simulation method developed to increase the time-scale over which a molecular dynamics simulation could be carried out. Adding a bias potential to the interatomic potential, the simulated time could 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 were 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 hyper-molecular dynamics simulation depended on the accuracy and speed of such minimisation methods. It was found that only one minimisation was necessary to calculate numerically the bias force. The speed of a hyper-molecular dynamics simulation increased by a factor ∼3 and improves the accuracy of the numerical approximation. Examples were given where hyper-molecular dynamics could be applied obtaining high boosts of between 102 and 5 x 105 in the simulated time, thus extending time-scale of the simulation from nanoseconds to milliseconds.

Numerical Implementation of the Hyper-Molecular Dynamics Method with Examples Applied to Diffusion. Sanz-Navarro, C.F., Smith, R.: Nuclear Instruments and Methods in Physics Research B, 2001, 180[1-4], 130-8