Coding Considerations for Standalone Molecular Dynamics Simulations of Atomistic Structures

The laws of Newtonian mechanics allow ab-initio
molecular dynamics to model and simulate particle trajectories in
material science by defining a differentiable potential function. This
paper discusses some considerations for the coding of ab-initio
programs for simulation on a standalone computer and illustrates
the approach by C language codes in the context of embedded
metallic atoms in the face-centred cubic structure. The algorithms use
velocity-time integration to determine particle parameter evolution
for up to several thousands of particles in a thermodynamical
ensemble. Such functions are reusable and can be placed in a
redistributable header library file. While there are both commercial
and free packages available, their heuristic nature prevents dissection.
In addition, developing own codes has the obvious advantage of
teaching techniques applicable to new problems.




References:
[1] Mendelev MI, Han S, Srolovitz DJ, Ackland GJ, Sun DY, Asta M.
Development of new interatomic potentials appropriate for crystalline
and liquid iron, Philosophical Magazine, 83:35 (2003), 3977-3994, DOI:
10.1080/14786430310001613264
[2] Sutton AP, Chen J. Long-range Finnis-Sinclair potentials. Philosophical
Magazine Letters, 1990 Vol. 61 (3), 139-156.
[3] Das A, Ghosh MM. MD simulation-based study on the melting
and thermal expansion behaviours of nanoparticles under heat
load. Computational Materials Science 101 (2015) 88-95. doi:
10.1016/j.commatsci.2015.01.008
[4] van der Walt C, Terblans JJ, Swart HC. Molecular dynamics study
of the temperature dependence and surface orientation dependence
of the calculated vacancy formation energies of Al, Ni, Cu, Pd,
Ag, and Pt. Computational Materials Science 83 (2014) 7077. doi:
10.1016/j.commatsci.2013.10.039
[5] Abraham MJ, Murtolad T, Roland Schulz R, Palla S, JSmith JC, Hessa
B, Lindahl E. GROMACS: High performance molecular simulations
through multi-level parallelism from laptops to supercomputers.
SoftwareX (2015). doi: 10.1016/j.softx.2015.06.001
[6] Smirnov BM. Energetics of clusters with a face centered-cubic structure.
Zh. Eksp. Teor. Fiz. 107 (1995), 2080-2091
[7] Terblans JJ. Calculating the bulk vacancy formation energy (Ev) for a
Schottky defect in a perfect Cu(111), Cu(100) and a Cu(110) single
crystal. Surf. Interface Anal. 2002; 33: 767770 doi: 10.1002/sia.1451
[8] Mattsson TR, Mattsson AE. Calculating the vacancy formation energy
in metals: Pt, Pd, and Mo. Physical Review B 66 (2002) 214110.
[9] Sebastian IS, Aldazabal J, Capdevila C, Garcia-Mateo C. Diffusion
simulation of CrFe bcc systems at atomic level using a random walk
algorithm. p hys. stat. sol. (a) 205, No. 6, 13371342 (2008). doi:
10.1002/pssa.200778124
[10] Jian-Min Z, Fei M, Ke-Wei, X. Calculation of the surface energy of
fcc metals with modified embedded-atom method. Vol. 13 (7) 2004.
1009-1963/2004/13(07)/1082-09
[11] Griebel M, Knapek S, Zumbusch G, in Barth TJ et al.(Eds.), Numerical
Simulation in Molecular Dynamics, in: Texts in Computational Science
and Engineering 5, Springer, Berlin, 2007, ISBN 978-3-540-68094-9
[12] Car R, Parrinello M, Unified Approach for Molecular Dynamics and
Density Functional Theory, Phys. Rev. Lett, 55(22), 1985, 2471-2474.
[13] Car R, Parrinello M, The Unified Approach for Molecular Dynamics
and Density Functional Theory, in Simple Molecular Systems at Very
High Density, vol. 186 of NATO ASI Series , series B, Physics, P.P.
Loubeyre and N. Boccara (Eds.) (Plenum Press, NY), 1989, 455-476.
[14] Remler DK, Madden PA, Molecular dynamics without effective
potentials via the Car-Parrinello approach, Mol. Phys., 70(6) 1990,
921-966.
[15] Tuckerman ME. Ab initio molecular dynamics: basic concepts, current
trends and novel applications. J. Phys.: Condens. Matter 14 (2002)
R1297R1355 Online at stacks.iop.org/JPhysCM/14/R1297
[16] Finnis MW, Sinclair JE, Philos. Mag. A 50 (1984) 45.
[17] Daw MS, Foiles SM, Baskes MI, Mater. Sci. Rep. 9 (1993) 251.
[18] Daw MS, Baskes MI, Phys. Rev. B 29 (1984) 6443.
[19] Todd BD, Lynden-Bell RM. Surface and bulk properties of
metals modelled with Sutton-Chen potentials. Surface Science 281,
1993,191-206.
[20] Chamati H, Papanicolaou NI, Mishin Y, Papaconstantopoulos DA.
Embedded-atom potential for Fe and its application to self-diffusion on
Fe (100). Surface Science; 2006, 1-11. doi:10.1016/j.susc.2006.02.10 [21] Mishin Y, in: Yip S (Ed.), Handbook of Materials Modeling, Springer,
The Netherlands, 2005, p. 459.
[22] Doye JPK, Wales DJ. Global minima for transition metal clusters
described by the Sutton-Chen potentials. New J. Chem. 1998, 733-744.
[23] Swope W, Andersen H, Berens P, Wilson K. A computer simulation
method for the calculation of equilibrium constants for the formation of
physical clusters of molecules: Application to small water clusters, J.
Chem. Phys., 76 (1982), pp. 637649.
[24] Landau L, Lifschitz E. Mechanics, Course of Theoretical Physics, Vol.
1, Pergamon Press, Oxford, 1976.
[25] Hockney, R. The potential calculation and some applications, Methods
Comp. Phys., 9 (1970), pp. 136211.
[26] Verlet L. Computer experiments on classical fluids. I. Thermodynamical
properties of Lennard-Jones molecules, Phys. Rev., 159 (1967), pp.
98103.
[27] Chandler D. Introduction to modern statistical mechanics, Oxford
University Press, New York, 1987.