Explicit Time Integration Algorithm for Fully Flexible Cell Molecular Dynamics


Article Preview

Fully flexible cell with Nose-Poincare method preserves Hamiltonian in structure, so the extended Hamiltonian is preserved in the real time domain. In the previous development of Nose- Poincare method for NVT, NPT, and NT ensemble unit cell simulations, implicit algorithm such as generalized leapfrog integration scheme was used. The formulation and numerical implementatio n of the implicit formula is much more complicated because it includes nonlinear iteration procedur e. Furthermore, it is not easy to show time reversibility in implicit formula. Thus for these reasons, it is necessary to develop explicit formula in MD unit cell simulation. We develop fully flexible explicit Nσ T ensemble MD simulation algorithm. It guarantees the preservation of extended Hamil tonian in real time domain and time reversibility. The numerical implementation is easy and relative ly simple since it does not require iteration process. It is established by using the splitting time integ ration. It separates flexible cell Hamiltonian into several terms corresponding to each Hamiltonian part, so the simple and completely explicit recursion formula was obtained. Unit cell tension, shear test for bulk material tension and shear tests are performed to demonstrate the validity and performance of the present explicit molecular dynamics scheme formulated through the spitting method. We compare the results of the explicit splitting time integration scheme with those of the implicit generalized leapfrog time integration scheme. The proposed explicit NT unit cell simulati on method should serve as a powerful tool in the prediction of the material behavior.



Key Engineering Materials (Volumes 326-328)

Edited by:

Soon-Bok Lee and Yun-Jae Kim




S. D. Park and M. H. Cho, "Explicit Time Integration Algorithm for Fully Flexible Cell Molecular Dynamics", Key Engineering Materials, Vols. 326-328, pp. 337-340, 2006

Online since:

December 2006




[1] E. Hernanderz : J. Chem. phys., Vol115, No. 22, pp.10282-10290(2001).

[2] I. Souza and J. L. Martins : Phys. Rev. B, Vol. 55, pp.8733-8742(1997).

[3] S. D. Bond, B. J. Leimkuhler, and B. B. Laird, J. Comput. Phys. Vol. 151, pp.114-134(1999).

[4] Robert I. McLachlan and G. Reinout W. Quispel, Acta Numerica(2002) , pp.341-434.

DOI: https://doi.org/10.1017/cbo9780511550140.005

[5] Goldstein and Poole and Safko, Classical Mechanics third edition, Addison Wesley, p.341434. (2002).

[6] S. Nosé, Jounal of the Physical Society of Japan., Vol. 70, No. 1, January, 2001 pp.75-77(2000).

[7] W.J. Chang, T.H. Fang, J. Phys. Chem. Solids, Vol. 64, pp.1279-1283.

[8] A.B. Lebedev, Y.A. Burenkov, A.E. Romanov, V.I. Kopylov, V.P. Filonenko, V.G. Gryaznov, Mater. Sci. Engng A, Vol. 203, pp.165-170(1995).

DOI: https://doi.org/10.1016/0921-5093(95)09868-2