DOI QR코드

DOI QR Code

A Splitting Time Integrator for Fully Flexible Cell Molecular Dynamics

분할 적분 기법을 적용한 N-sigma-T 분자동역학 전산모사

  • 박시동 (서울대학교 기계항공공학부) ;
  • 조맹효 (서울대학교 기계항공공학부)
  • Published : 2007.08.01

Abstract

Fully flexible cell preserves Hamiltonian in structure so that the symplectic time integrator is applicable to the equations of motion. In the direct formulation of fully flexible cell N-Sigma-T ensemble, a generalized leapfrog time integration (GLF) is applicable for fully flexible cell simulation, but the equations of motion by GLF has structure of implicit algorithm. In this paper, the time integration formula is derived for the fully flexible cell molecular dynamics simulation by using the splitting time integration. It separates flexible cell Hamiltonian into terms corresponding to each of Hamiltonian term. Thus the simple and completely explicit recursion formula was obtained. We compare the performance and the result of present splitting time integration with those of the implicit generalized leapfrog time integration.

Keywords

References

  1. Hernandez, E., 2001, 'Metric-Tensor Flexible-Cell Algorithm for Isothernal-Isobaric Molecular Dynamics Simulation,' J. Chem. phys., Vol. 115, No. 22,pp.10282-10290 https://doi.org/10.1063/1.1416867
  2. Souza, I. and Martins, J. L., 1997, 'Metric Tensor as the Dynamical Variable for Variable-Cell-Shape Molecular Dynamics,' Phys. Rev. B, Vol. 55, pp. 8733-8742 https://doi.org/10.1103/PhysRevB.55.8733
  3. Bond, S. D., Leimkuhler, B. J. and Laird, B. B., 1999, 'The Nose-Poincare Method for Constant Temperature Molecular Dynamics,' J. Comput. Phys., Vol. 151, pp. 114-134 https://doi.org/10.1006/jcph.1998.6171
  4. Choi, K. and Cho, M., 2006, 'Fully Flexible Unit Cell Simulation with Recursive Thermostat Chains,' J. Chem. Phys., Vol. 125, pp. 184105 https://doi.org/10.1063/1.2354159
  5. Nose, S., 2000, 'An Improved Symplectic Integrator for Nose-Poincare Thermostat,' Journal of the Physical Society of Japan., Vol. 70, No.1, pp. 75-77 https://doi.org/10.1143/JPSJ.70.75
  6. Park, S. and Cho, S., 2004, 'Molecular Dynamics Simulation of Adhesive Friction of Silicon Aspertity,' Transactions of KSME A, Vol. 28, No.5, pp.547-553 https://doi.org/10.3795/KSME-A.2004.28.5.547
  7. Park, S, 2003, 'Applications of Molecular Dynamics Simulation,' Journal of the KSME, Vol.43, No.3, pp.49-57
  8. McLachlan, R. I. and Quispel, G. R. W., 2002, 'Splitting methods,' Acta Numerica , pp. 341-434
  9. Goldstein, Poole and Safko, 2002, Classical Mechanics, Addison Wesley, pp. 341-434
  10. Nose, S., 1984, 'A Unified Formulation of the Constant Temperature Molecular-Dynamics Methods,' J. Chem. Phys., Vol. 81, pp. 410-440 https://doi.org/10.1063/1.447334
  11. Nose, S., 2002, 'A Molecular-Dynamics Method for Simulations in the Canonical Ensemble,' Mol. Phys., Vol. 10, No.1, pp. 191-198
  12. Hoover, W. G., 1985, 'Canonical Dynamics: Equilibrium Phase-Space Distributions,' Phys. Rev. A, Vol. 31, pp. 1695-1697 https://doi.org/10.1103/PhysRevA.31.1695
  13. Meyers, M. A. and Chawla, K. K., 1999, 'Mechanical Behavior of Materials,' Prentice Hall, p. 87
  14. Shen, T.D., Koch, C.C., Tsui, T.Y. and Pharr, G.M., 1995, 'On the Elastic Moduli of Nanocrystalline Fe, Cu, Ni, and Cu Ni Alloys Prepared by Mechanical Milling/Alloying,' J. Mater. Res., Vol. 10, p.2892 https://doi.org/10.1557/JMR.1995.2892
  15. Frenkel, D. and Srnit, B., 1996, Understanding Molecular Simulation, Academic Press