Numerical calculations using the hyper-molecular dynamics simulation method Original Research Article

Hyper-molecular dynamics (H-MD) is a new simulation method developed to increase the time scale over which a molecular dynamics 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. A bias potential which gives a substantial ‘boost’ can be defined as a function of 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. In order to obtain a numerical approximation for these quantities without the diagonalization of the Hessian matrix, numerical minimization methods have been proposed. The performance of a hyper-molecular dynamics simulation depends on the accuracy and speed of such minimization methods. Here we present a numerical approximation for the H-MD simulation method and prove the mathematical expressions required for that approach. The speed of a H-MD simulation increases by a factor of up to 3 compared to previous derivations with improved accuracy. Some numerical examples are calculated and compared in order to assess the applicability of the method.