Large-Scale Normal Mode Analysis and Molecular Dynamics Simulations

Donald W. Noid1, Bobby G. Sumpter1, Robert E. Tuzun2, Chao Yang3, Bryan C. Hathorn1

1Computer Science and Mathematics Division, Computational Chemical Sciences Group, ORNL
2Department of Computational Science, State University of New York at Brockport
3National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory

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Enumerating the normal modes of molecular-based materials is often crucial for the determination of thermodynamic properties, vibrational spectra, and possible reaction mechanisms. The reason for this is that once the spectral information has been obtained it is a relatively simple task to link to observations from experimentally accessible macroscopic properties. In the past, normal coordinate analysis has been generally limited to relatively small systems (ie ~1000 atoms). Recently we have introduced a new method for obtaining a complete set of frequencies, thereby determining the vibrational density of states spectrum for large macromolecular systems. This method effectively eliminates the plague of negative eigenvalues that are typical of traditional eigen-based methods by using a time averaged Hessian matrix. Extensions of this method using sparse matrix techniques and Sylvester’s theorem has allowed for the rapid calculation of heat capacities and other thermodynamic information as well as for examining the vibrational structure of several large polymer particle systems and nanotechnology applications. We have also been able to characterize the scaling of low frequency modes as a function of polymer particle size and to analyze the eigenvectors and the structure of the vibrational spectra of these systems.


  • B. Hathorn, D. W. Noid, B.G. Sumpter, C. Yang, W.A. Goddard, "Normal Modes and Multibody Modes in Structure Soft Matter Systems", Dekker Encylopedia of Nanoscience and Nanotechnology (2004).
  • B. C. Hathorn, B. G. Sumpter, D. W. Noid, R. E. Tuzun, and C. Yang, Polymer 44, 3761 (2003).
  • R. E. Tuzun, D. W. Noid, B. G. Sumpter, and C Yang, Macromol. Theory and Simulation 11, 711 (2002).
  • B. C. Hathorn, B. G. Sumpter, and D. W. Noid, J. Phys. Chem. A 106, 9174 (2002).
  • C. Yang, P. Radhavan, L. Arrowood, D. W. Noid, B. G. Sumpter, and R. E. Tuzun, Int. J. High Perform. Comput. Appl. 15, 409 (2002).
  • C. Yang, D. W. Noid., B. G. Sumpter, D. C. Sorensen, R. E. Tuzun, Macromol. Theory Simul. (2001).
  • K. Fukui, D.W. Noid, B.G. Sumpter, C. Yang and R. Tuzun, J. Phys. Chem B 104 , 526-531 (2000)
  • C. Yang, B. Peyton, D. W. Noid., B. G. Sumpter, R. E. Tuzun, SIAM J. Sci. Comp. (2000).
  • Kazuhiko Fukui, Bobby G. Sumpter, Chao Yang, Donald W. Noid, Robert E. Tuzun Comput. Theor. Polym. Sci. 9, 428-432 (2000).
  • Kazuhiko Fukui, Bobby G. Sumpter, Chao Yang, Donald W. Noid, Robert E. Tuzun Polymer Science: B. Polymer Physics 38, 1812-1823 (2000).
  • Chao Yang, Kazuhiko Fukui, Bobby G. Sumpter, Donald W. Noid, and Robert E. Tuzun Macromol. Theory and Simul. 9, 428-432 (2000).
  • K. Fukui, D. W. Noid, B. G. Sumpter, C. Yang and R. Tuzun, J. Phys. Chem B 104, 526-531 (2000).
  • D. W. Noid, K. Fukui, B. G. Sumpter, C. Yang and R. Tuzun, Chem. Phys. Lett 316 , 285-296 (2000)
  • For more information contact:

    Bobby Sumpter


    Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy

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