Molecular dynamics is effective for nano-scale phenomenon analysis. There are two major computational steps associated with computer simulation of dynamics of molecular conformation and they are the calculation of the interatomic forces and the formation and solution of the equations of motion. Currently, these two computational steps are treated separately, but in this paper an O(N) (order N) procedure is presented for an integration between these computational steps. For computational costs associated with calculating the interatomic forces, an internal coordinate method (ICM) approach is used for determining potentials due to both the bonding and non-bonding interactions. Thus, the potential gradients can be expressed as a combination of the potential in absolute and relative coordinates. For computational costs associated with the formation and solution of the equations of motion for the system, a constraint method that is used in computational multibody dynamics is utilized. This frees some degrees of freedom so that Kane’s method can be applied for the recursive formation and solution of equations of motion for the atomistic molecular system. Because the inclusion of lightly excited high frequency degrees of freedom, such as inter-atomic oscillations and rotation about double bonds would force the use of very small integration step sizes, holonomic constraints are introduced to freeze these “uninteresting” degrees of freedom. By introducing these hard constraints the time scale can be appropriately sized for to provide a less computationally intensive dynamic simulation of molecular conformation. The algorithm developed improves computational speed significantly when compared with any traditional O(N3) procedure.

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