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Quaternion Dynamics for Dynamical Simulations in Computational Nanotechnology

Karl Sohlberg*, Robert E. Tuzun, Bobby G. Sumpter, and Donald W. Noid

Oak Ridge National Laboratory

This is an abstract for a poster to be presented at the Fifth Foresight Conference on Molecular Nanotechnology.

While previous computational models of nano-systems have almost exclusively employed fully atomistic classical molecular dynamics simulations, by analogy to macroscopic systems, it can be intuited that the dynamical performance of nano-machines will be governed predominantly by the gross movements of their components and not by the details of the motion of the individual atoms. This observation suggests that accurate predictions about the performance of nano-systems can be achieved through the use of the rigid body approximation. Furthermore, fully atomistic classical molecular dynamics simulations can exhibit excessive vibrational motion which results from pooling of the quantum zero-point vibrational energy into low frequency modes, a process not quantum mechanically allowed. The rigid body approximation evades the zero point energy problem.

One complication which arises with the use of the rigid body approximation is that the orientation of each body must be specified as well as its position. The conventional Euler angles for specifying orientation are inappropriate for use in numerical simulations because they become singular for certain orientations of the body. An elegant solution to this problem is found in the use of quaternion parameters. We will discuss the use of the quaternion parameters in nanotechnology simulations and present example applications.

Related work: gopher.CCS.ORNL.GOV/vizlab/animations.html

*Corresponding Address:
Karl Sohlberg, Oak Ridge National Laboratory, Chemical and Analytical Sciences Division, 4500N MS6197, Oak Ridge, TN 37831-6197, ph: 423-576-4974, fax: 423-576-5235, email:
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