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Scholars Day 2008, Wednesday, April 9

Normal Coordinate Analysis

Normal coordinate analysis (NCA) determines vibrational frequencies and corresponding motions about equilibrium from eigenvalues and corresponding eigenvectors of a second derivative (Hessian) matrix. And NCA is an important tool in studying the structure, dynamics, and physical properties of polymer systems. Also, trajectory averaging is a recently developed method for eliminating negative eigenvalues in systems with tens of thousands of atoms. Noid, Tuzun et al have found that performing molecular dynamics simulations and constructing trajectory averaged Hessian matrices eliminates the appearance of imaginary frequencies for NCA of polymer systems with up to 36,000 atoms. In this study, several single and nested carbon nanotubes, as well as polymer “droplets” and crystals, are modeled and analyzed by trajectory averaged NCA, and the extent of annealing required for accurate results is mapped out for these systems. Computation of thermodynamic properties (from frequencies) is found to require annealing down to about 1K mean temperature, whereas dynamical properties (which require individual eigenvectors) require more annealing. In either case, significant effort is required for the annealing stage than for single configuration NCA. In addition, for the purpose of saving storage space, it is desirable to eliminate the smallest magnitude Hessian matrix elements. Elimination of the lowest 5% of the matrix elements does not appreciably affect vibrational frequencies or cause significant mode mixing. These results are consistent with a simple perturbation theory analysis.

Presenter: Daniel Omowole (Undergraduate Student)
Topic: Computational Science
Location: 101 Edwards
Time: 9 am (Session I)