Abstract
It is shown that the Parrinello–Rahman Lagrangian is obtained by assuming that (i) the cell inertia tensor is spherical and constant in time, and that (ii) the cell fluctuation motions are irrotational. A slightly different Lagrangian is suggested, arrived at by dropping the sphericity assumption in (i). A related metadynamics is also proposed, based on replacing by (ii) the various no-cell-rotation assumptions that are customarily used. Finally, a zero-temperature, scale-bridging relation is proposed between the intermolecular potential and the macroscopic stored-energy mapping.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Andersen, H.C.: Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 72, 2384–2393 (1980)
Behler, J., Martonák, R., Donadio, D., Parrinello, M.: Metadynamics simulations of the high-pressure phases of silicon employing a high-dimensional neural network potential. Phys. Rev. Lett. 100, 185501-1/4 (2008)
E, W., Ming, P.: Cauchy–Born rule and the stability of crystalline solids: Static problems. Arch. Ration. Mech. Anal. 183, 241–297 (2007)
Ensing, B., DeVivo, M., Liu, Z., Moore, P., Klein, M.: Metadynamics as a tool for exploring free energy landscapes of chemical reactions. Acc. Chem. Res. 39, 73–81 (2006)
Ericksen, J.L.: On the Cauchy–Born rule. Math. Mech. Solids 13, 199–220 (2008)
Fried, E., Gurtin, M.E.: Continuum theory of thermally induced phase transition based on an order parameter. Physica D 68, 326–343 (1993)
Gurtin, M.E.: Generalized Ginzburg–Landau and Cahn–Hilliard equations based on a microforce balance. Physica D 92, 178–192 (1996)
Laio, A., Parrinello, M.: Escaping free-energy minima. Proc. Natl. Acad. Sci. USA 99, 12562–12566 (2002)
Martonák, R., Donadio, D., Oganov, A.R., Parrinello, M.: Crystal structure transformations in SiO2 from classical and ab initio metadynamics. Nat. Mater. 5, 623–626 (2006)
Martonák, R., Laio, A., Parrinello, M.: Predicting crystal structures: The Parrinello-Rahman method revisited. Phys. Rev. Lett. 90(7), 075503(4) (2003)
Parrinello, M., Rahman, A.: Crystal structure and pair potentials: A molecular-dynamics study. Phys. Rev. Lett. 45, 1196–1199 (1980)
Parrinello, M., Rahman, A.: Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys. 52, 7182–7190 (1981)
Parrinello, M., Rahman, A.: Strain fluctuations and elastic constants. J. Chem. Phys. 76, 2662–2666 (1982)
Podio-Guidugli, P.: Models of phase segregation and diffusion of atomic species on a lattice. Ric. Mat. 55, 105–118 (2006)
Zanzotto, G.: On the material symmetry group of elastic crystals and the Born rule. Arch. Ration. Mech. Anal. 121, 1–36 (1992)
Zanzotto, G.: The Cauchy–Born hypothesis, nonlinear elasticity and mechanical twinning of crystals. Acta Cryst. A 52, 839–849 (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Podio-Guidugli, P. On (Andersen–)Parrinello–Rahman Molecular Dynamics, the Related Metadynamics, and the Use of the Cauchy–Born Rule. J Elast 100, 145–153 (2010). https://doi.org/10.1007/s10659-010-9250-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10659-010-9250-0