Boundary conditions, molecular dynamic simulations

Juffer, A.H., Berendsen, H.J.C. Dynamic surface boundary conditions A simple boundary model for molecular dynamics simulations. Mol. Phys. 79 (1993) 623-644. 

A. Briinger, C. L. Brooks, III, and M. Karpins. Stochastic boundary conditions for molecular dynamics simulations of ST2 water. Chem. Phys. Lett., 105 495-500, 1982. 

A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

The first molecular dynamics simulations of a lipid bilayer which used an explicit representation of all the molecules was performed by van der Ploeg and Berendsen in 1982 [van dei Ploeg and Berendsen 1982]. Their simulation contained 32 decanoate molecules arranged in two layers of sixteen molecules each. Periodic boundary conditions were employed and a xmited atom force potential was used to model the interactions. The head groups were restrained using a harmonic potential of the form ... 

Force field calculations often truncate the non bonded potential energy of a molecular system at some finite distance. Truncation (nonbonded cutoff) saves computing resources. Also, periodic boxes and boundary conditions require it. However, this approximation is too crude for some calculations. For example, a molecular dynamic simulation with an abruptly truncated potential produces anomalous and nonphysical behavior. One symptom is that the solute (for example, a protein) cools and the solvent (water) heats rapidly. The temperatures of system components then slowly converge until the system appears to be in equilibrium, but it is not. 

Often you need to add solvent molecules to a solute before running a molecular dynamics simulation (see also Solvation and Periodic Boundary Conditions on page 62). In HyperChem, choose Periodic Box on the Setup menu to enclose a solute in a periodic box filled appropriately with TIP3P models of water molecules. 

In a normal molecular dynamics simulation with repeating boundary conditions (i.e., periodic boundary condition), the volume is held fixed, whereas at constant pressure the volume of the system must fluemate. In some simulation cases, such as simulations dealing with membranes, it is more advantageous to use the constant-pressure MD than the regular MD. Various schemes for prescribing the pressure of a molecular dynamics simulation have also been proposed and applied [23,24,28,29]. In all of these approaches it is inevitable that the system box must change its volume. 

Further progress in understanding membrane instability and nonlocality requires development of microscopic theory and modeling. Analysis of membrane thickness fluctuations derived from molecular dynamics simulations can serve such a purpose. A possible difficulty with such analysis must be mentioned. In a natural environment isolated membranes assume a stressless state. However, MD modeling requires imposition of special boundary conditions corresponding to a stressed state of the membrane (see Refs. 84,87,112). This stress can interfere with the fluctuations of membrane shape and thickness, an effect that must be accounted for in analyzing data extracted from computer experiments. 

Nymand TM, Linse P (2000) Molecular dynamics simulations of polarizable water at different boundary conditions. J Chem Phys 112(14) 6386-6395... 

Equation (9.3) has been derived for one-dimensional diffusion and supported by molecular dynamics simulation in the three-dimensional case (Powles, 1985 Tsurumi and Takayasu, 1986 Rappaport, 1984). For the partially diffusion-controlled recombination reaction we again refer to Figure 9.1, where the inner (Collins-Kimball) boundary condition is now given as... 

Molecular dynamics simulations are capable of addressing the self-assembly process at a rudimentary, but often impressive, level. These calculations can be used to study the secondary structure (and some tertiary structure) of large complex molecules. Present computers and codes can handle massive calculations but cannot eliminate concerns that boundary conditions may affect the result. Eventually, continued improvements in computer hardware will provide this added capacity in serial computers development of parallel computer codes is likely to accomplish the goal more quickly. In addition, the development of realistic, time-efficient potentials will accelerate the useful application of dynamic simulation to the self-assembly process. In addition, principles are needed to guide the selec-... 

Tieleman, D. P. and Berendsen, H. J. C. (1996). Molecular dynamics simulations of a fully hydrated dipalmitoylphosphatidylcholine bilayer with different macroscopic boundary conditions and parameters, J. Chem. Phys., 105, 4871 —4880. 

From this, the velocities of particles flowing near the wall can be characterized. However, the absorption parameter a must be determined empirically. Sokhan et al. [48, 63] used this model in nonequilibrium molecular dynamics simulations to describe boundary conditions for fluid flow in carbon nanopores and nanotubes under Poiseuille flow. The authors found slip length of 3nm for the nanopores [48] and 4-8 nm for the nanotubes [63]. However, in the first case, a single factor [4] was used to model fluid-solid interactions, whereas in the second, a many-body potential was used, which, while it may be more accurate, is significantly more computationally intensive. 

The problem of linking atomic scale descriptions to continuum descriptions is also a nontrivial one. We will emphasize here that the problem cannot be solved by heroic extensions of the size of molecular dynamics simulations to millions of particles and that this is actually unnecessary. Here we will describe the use of atomic scale calculations for fixing boundary conditions for continuum descriptions in the context of the modeling of static structure (capacitance) and outer shell electron transfer. Though we believe that more can be done with these approaches, several kinds of electrochemical problems—for example, those associated with corrosion phenomena and both inorganic and biological polymers—will require approaches that take into account further intermediate mesoscopic scales. There is less progress to report here, and our discussion will be brief. 

In order to overcome the limitations of currently available empirical force field param-eterizations, we performed Car-Parrinello (CP) Molecular Dynamic simulations [36]. In the framework of DFT, the Car-Parrinello method is well recognized as a powerful tool to investigate the dynamical behaviour of chemical systems. This method is based on an extended Lagrangian MD scheme, where the potential energy surface is evaluated at the DFT level and both the electronic and nuclear degrees of freedom are propagated as dynamical variables. Moreover, the implementation of such MD scheme with localized basis sets for expanding the electronic wavefunctions has provided the chance to perform effective and reliable simulations of liquid systems with more accurate hybrid density functionals and nonperiodic boundary conditions [37]. Here we present the results of the CPMD/QM/PCM approach for the three nitroxide derivatives sketched above details on computational parameters can be found in specific papers [13]. 

E.G. Karpov et al A Green s function approach to deriving non-reflecting boundary conditions in molecular dynamics simulations. Int. J. Num. Meth. Eng 62, 1250-1262 (2005)... 

The molecular dynamics simulation was performed using the MOTECC suite of programs [54] in the context of a microcanonical statistical ensemble. The system considered is a cube, with periodic boundary conditions, which contains 343 water molecules. The molecular dynamic simulation of water performed at ambient conditions revealed good agreement with experimental measurements. The main contribution to the total potential energy comes from the two-body term, while the many-body polarisation term contribution amounts to 23% of the total potential energy. Some of the properties calculated during the simulation are reported in Table 3. 

As the last example we mention the study of Takemura and Kitao. They studied different models for molecular-mechanics simulations on water. To this end, they studied the dynamics of a ubiquitin molecule solvated in water. They performed molecular-dynamics simulations for a system with periodic boundary conditions. At first they considered pure water without the solute and studied boxes with 360, 720, 1080, and 2160 water molecules. It turned out that even for these fairly large systems, finite-size effects could be recognized. Thus, the translational diffusion constant was found to depend linearly on where V is the volume of the repeated unit. 

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