Programs in Physics & Physical Chemistry
|[Licence| Download | New Version Template] aecw_v1_1.tar.gz(4213 Kbytes)|
|Manuscript Title: An improved version of the Green's function molecular dynamics method|
|Authors: Ling Ti Kong, Colin Denniston, Martin H. Müser|
|Program title: FixGFC/FixGFMD v1.12|
|Catalogue identifier: AECW_v1_1|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 182(2011)540|
|Programming language: C++.|
|Operating system: Linux.|
|Has the code been vectorised or parallelized?: Yes. Code has been parallelized using MPI directives.|
|RAM: Depends on the problem|
|Keywords: elastic stiffness coefficients, elastic Green's function, molecular dynamics simulation.|
External routines: LAMMPS (http://lammps.sandia.gov/), MPI (http://www.mcs.anl.gov/research/projects/mpi/), FFT (http://www.fftw.org/)
Does the new version supersede the previous version?: Yes
Nature of problem:
Green's function molecular dynamics (GFMD) is a coarse-graining method that enables one to investigate the full elastic response of an interface between a semi-infinite solid and a contact while taking only the surface atoms in the solid into consideration. The effect of long-range elastic deformations on the surface atoms from the semi-infinite solid is replaced by effective elastic interactions, thus reducing the problem from three dimensions to two dimensions without compromising the physical essence of the problem.
See "Nature of problem".
Reasons for new version:
The basic theory underlying the new version is essentially the same as the previous one, while the special treatment to reduce the finite size effect on effective elastic coefficients at the Γ point is now realized in a physically meaningful manner. Finite size effects are an important issue in molecular dynamics simulations, particularly for GFMD, they result in a violation of the acoustic sum rule (ASR) for the effective elastic coefficients measured at the Γ-point (ΦΓ). In the previous implementation, the effective elastic coefficients measured at the Γ point were altered by setting their eigenvalues corresponding to the acoustic modes to zero. This scheme was found to work well for simple Bravais lattices as long as only atoms within the last layer were treated as Green's function atoms. However, it failed to function as expected in all other cases. We therefore adopt a new algorithm to enforce the ASR for ΦΓ, which is implemented in this revision.
Summary of revisions:
Assuming the lattice under study consists of surface unit cells with n basis atoms labeled by k =1, 2, ..., n. When all atoms in the lattice are moved by the same amount, i.e., the crystal is rigidly translated, the force on any atom must be zero. This is known as the translational invariance, leading to the so-called acoustic sum rule:
Σk′ Φkα,k′β(Γ) = 0
where Φkα,k′β(Γ) is the kα,k′β component of the effective elastic coefficients at the Γ-point; we will denote it as ΦΓ hereafter. α and β enumerate the Cartesian directions. In addition, ΦΓ should be Hermitian (Or symmetric, since at the Γ point, the imaginary part of ΦΓ is zero.) because of the commutative nature of the force constants:
ΦΓkα,k′β = ΦΓk′β,kα
These two properties are expected for ΦΓ, yet the ASR is not satisfied during the measurement (done by FixGFC) because of the finite size effect. A scheme is therefore needed to enforce ASR on ΦΓ afterwards, while the symmetric nature of ΦΓ should also be enforced.
We list below the detailed scheme adopted to enforce ASR implemented in the improved version of GFMD together with some other revisions to the code after the previous release.
By adopting the new method to enforce the acoustic sum rule, the restriction that atoms in the Green's function slab must be in the same layer is lifted, while it is still necessary to ensure that the mean equilibrium positions of atoms in the Green's function slab satisfies the Born-von Karman boundary condition. In addition, only deformations within the harmonic regime are produced in the slab during Green's function molecular dynamics simulations.
The new version is not compatible with the previous one: the contents in the binary file are different and therefore the effective elastic coefficients measured by the previous version of FixGFC cannot be used by the current version of FixGFMD.
FixGFC varies from minutes to days, like a typical molecular dynamics simulation, depending on the system size, the number of processors used, and the complexity of the force field. FixGFMD varies from seconds to hours, depending on the system size and the number of processors used.
|||L. T. Kong, G. Bartels, C. Campañá, C. Denniston, M.H. Müser Implementation of Green's function molecular dynamics: An extension to LAMMPS, Computer Physics Communications 180(6)(2009) 1004-1010|
|||C. Campañá, M.H. Müser, Practical Green's function approach to the simulation of elastic semi-infinite solids, Physical Review B (Condensed Matter and Materials Physics) 74(7)(2006) 075420.|
|||L. T. Kong, Phonon dispersion measured directly from molecular dynamics simulations, submitted to Computer Physics Communications,(2010).|
|||S. J. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comp. Phys. 117(1995) 1-19|
|||S.J.Plimpton, R.Pollock, M.Stevens, Particle-mesh Ewald and RRESPA for parallel molecular dynamics simulation, in: Proc of the Eighth SIAM Conference on Parallel Processing for Scientific Computing, Minneapolis, MN, 1997.|
|||Large-scale Atomic/Molecular Massively Parallel Simulator, LAMMPS, available at: http://lammps.sandia.gov.|
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