Atomistic simulation boundary conditions

A polymer coil does not only possess a structure on the atomistic scale of a few A, corresponding to the length of covalent bonds and interatomic distances characteristic of macromolecules are coils that more or less, obey Gaussian statistics and have a diameter of the order of hundreds of A (Fig. 1.2) [17]. Structures of intermediate length scales also occur e. g., characterized by the persistence length. For a simulation of a polymer melt, one should consider a box that contains many such chains that interpenetrate each other, i. e., a box with a linear dimension of several hundred A or more, in order to ensure that no artefacts occur attributable to the finite size of the simulation box or the periodic boundary conditions at the surfaces of the box. This ne-... 

Atomistic computer simulations are a statistical mechanical tool to sample configurations from the phase space of the physical system of interest. The system is uniquely treated by specifying the interactions between the particles (which are usually described as being pointlike), the masses of all the particles, and the boundary conditions. The interactions are calculated either on-the-fly by an electronic structure calculation (see Section 2.2.3) or from potential functions, which have been parametrized before the simulation by fitting to the results of electronic structure calculations or a set of experimental data. In the first case, one frequently speaks of AIMD (see Section 2.2.3), although the motion of the nuclei is still treated classically. 

Equation 1.3 represents a system of usually several thousand coupled differential equations of second order. It can be solved only numerically in small time steps At via finite-difference methods [16]. There always the situation at t + At is calculated from the situation at t. Considering the very fast oscillations of covalent bonds, At must not be longer than about 1 fs to avoid numerical breakdown connected with problems with energy conservation. This condition imposes a limit of the typical maximum simulation time that for the above-mentioned system sizes is of the order of several ns. The limited possible size of atomistic polymer packing models (cf. above) together with this simulation time limitation also set certain limits for the structures and processes that can be reasonably simulated. Furthermore, the limited model size demands the application of periodic boundary conditions to avoid extreme surface effects. 

One-way, top-down interfaces. These involve a one-way transfer of information from a higher level of modelling to a lower level. Examples include using a CG model to reconstruct an atomistic model of a protein, or using a continuum model to provide the boundary conditions for an atomistic simulation. 

Oliver PM, Watson GW, Kelsey ET, Parker SC (1997) Atomistic simulation of the surface structure of the Ti02 polymorphs ratile and anatase. J Mater Chem 7 563-568 Penn RL, Banfield JF, Kerrick DM (1999) TEM investigation of Lewiston, Idaho, fibrolite microstructure and grain boundary energetics. Am Mineral 84 152-159 Peiyea EJ, Kittrick JA (1988) Relative solubility of corandum, gibbsite, boehmite, and diaspore at standard state conditions. Clays Clay Minerals 36 391-396... 

All of our atomistic simulations were performed using standard Grand Canonical Monte Carlo (GCMC) and Equilibrium Molecular Dynamics (EMD) simulation methods. The RASPA [15] code was employed. Electrostatic energies were calculated using Ewald summation [16, 17] with a relative error of 10 . A 12 A van der Waals cutoff was used for the short-range interactions. Periodic boundary conditions were employed. 

In the case where the membrane is deformed, the deformation profiles can be compared to a variety of theories [16,17,27, 33, 245-247]. Both in coarse-grained [30,234] and atomistic [248] simulations, it was reported that membrane thickness profiles as a function of the distance to the protein are not strictly monotonic, but exhibit a weakly oscillatory behavior. This feature is not compatible with membrane models that predict an exponential decay [16,17,27], but it is nicely captured by the coupled elastic monolayer models discussed earlier [22, 28, 30]. Coarsegrained simulations of the Lenz model showed that the coupled monolayer models describe the profile data at a quantitative level, with almost no fit parameters except the boundary conditions [30, 244]. 

Atomistic MD simulations use the laws of classical physics and therefore can only approximate full quantum-mechanical reality. The most straightforward type of MD simulation tracks the motion of a fixed number N of atoms, constrained to move inside a fixed volume V. Because any today computer can operate only with a drastically smaller number of particles than in a real maaoscopic system, where N is 10, for emulating a large sample of matter, all the particles are placed in a box - a basic cell - which usually is a cube with a specified edge L To eliminate the influence of surface effects, one can use periodic boundary conditions in which the basic cell is surrounded by identical translated images. Any particle is free to ctoss the box boundary, and when this happens, an identical particle enters the box from the opposite side, with the same velocity vector. One can picture a periodic system either as extending infinitely far in all directions, or as a finite system in which opposite sides are artificially coupled together (see Box 5). 

At each macroscopic time step, MD calculations, constrained by the local macrostate of the system, are used to compute the missing data needed in the numerical solution of the PDEs. These data are obtained as time averages of microscopic variables after the MD simulation has equilibrated. The physical requirement to minimize/eliminate wave reflection at the boundary between the atomistic and the continuum treatment is achieved via well-chosen boundary conditions for the MD simulational cell. ... 

Simple Flexible Boundary Conditions for the Atomistic Simulation of Dislocation Core Structure and Motion. 

A, 77,231 (1998). Green s Function Boundary Conditions in Two-Dimensional and Three-Dimensional Atomistic Simulations of Dislocations. 

The simulation of molecular crystals can be addressed with atomistic MD, fully accounting for finite temperature and anharmonic effects. Here, a typical simulation is set up by considering a sample built as an 1 x m x n replica of the unit cell (superceU) with 3D periodic boundary conditions applied. The dynamics below the melting point is in most cases hmited to intramolecular vibrations, and oscillations of molecular positions and orientations around their equilibrium values. From the point of view of the supramolecular organization these simulations may not add further information to that of the equilibrium crystal strucmre, but they can be very useful for other purposes. The simulation of crystal supercells in the NpT ensemble, in which the simulation box is free to rearrange under the effect of molecular forces, can be used to benchmark the FF employed [2,119, 127]. The explicit verification that the FF is able to maintain (within a tolerance of a few percent) the crystal cell parameters measured at the same temperature and pressure than in experiments is a necessary test of the acctuacy of the model potential. 

The key property that makes phase change materials attractive for applications in nonvolatile memories is the fast crystallization which allows for a full crystallization in PCM devices on the time scale of 10-100 ns. The fact that both nucleation rate and crystal growth velocity are very large has stimulated direct simulations of the crystallization process by DFT-MD [13-16]. Simulations with up to 180-atom cell and periodic boundary conditions shed light on the atomistic mechanism of formation of the crystalline nucleus and on the role of four-membered rings as seeding structures for nucleation [13-16]. 

The availability of CG models for phospholipids has made it possible to observe the self-assembly of Langmuir monolayers of phospholipids [31], bilayers of nonionic surfactants [38], and finally of phospholipids [41], all beginning from initial conditions where lipid or surfactant molecules are completely dissolved in water. Figure 2 shows the self-assembly of a DPMC/water system into a multilamellar stack [41], modeled in periodic boundary conditions by a unit cell of about 20 nm edge. The simulation time required to observe self-assembly (100 ns) is much shorter than that suggested for equivalent simulations at fully atomistic detail. This illustrates the ability of CG models to greatly accelerate many diffusion-limited processes, such as self-assembly. 

Previously, the flexible GFBC method of Rao et al. [51,52] for dynamically updating the boundary conditions used in atomistic simulations was implemented for MGPT potentials and applied to study Ta dislocation properties at ambient... 

Fig. 2. Schematic representation of the domain decomposition scheme used to implement flexible Green s function boundary conditions in our GFBC/MGPT atomistic simulation code for dislocation calculations, (a) The three main computational regions separated into a layered

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