Examples of Molecular Dynamics Simulations

Example Brady investigated classical dynamics of a-d-glucose in water.In this simulation, 207 water molecules surrounded one a-d-glucose. The system was in a cubic box with periodic boundary conditions. During the simulation, several hydroxyl group transitions occurred. These transitions are normally unlikely with an in vacuo simulation. 

You can detect hydroxyl group transitions by plotting dihedral angles versus time over the course of the simulation. This is the distance history. Brady investigated the distance history of water 19. Brady, J.W. Molecular dynamics simulations of a-d-glucose in aqueous solution. 

---

In the following section, we will discuss some examples of molecular dynamics simulations of surfactants at liquid interfaces and in aqueous solution. 

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. 

The field of electrochemical ion transfer reactions (EITRs) is relatively recent compared with that of electron transfer reactions, and the application of molecular dynamics simulations to study this phenomenon dates from the 1990s. The simulations may shed light on various aspects of the EITR. One of the key questions on this problem is if EITR can be interpreted in the same grounds as those employed to understand electron transfer reactions (ETRs). Eor example, let us consider the electrochemical oxidation reaction of iodine ... 

This equation means that when there is a free energy difference of a few fcs T the probability P( ) is reduced considerably, that is, those conformations with large A( ) are sampled very rarely. This is a very important observation in terms of numerical efficiency. At the transition region for example, the free energy is maximum and typically very few sample points are obtained during the course of molecular dynamics simulation. In turn this results in very large statistical errors. Those errors can only be reduced by increasing the simulation time, sometimes beyond what is practically feasible. 

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. 

Experimental as well as theoretical methods have been widely employed to study such phenomena as solubility, the conformational structures, size change, and so on. Although these methods have been very successful, however, for example the experimental methods cannot reveal the detailed solvation structures to describe the interaction between solvent and polymer. Either theoretical methods are also not completely atomistic or they assume a certain molecular behavior. Molecular simulation methods, on the other hand, can produce most atomistic information about the solvation process. In this section we will mostly focus on the application of molecular dynamics simulation technique to understand solvation process in polymers. 

The above formula for Z, the NPT partition function, was first reported by Guggenheim [74], who wrote the expression down by analogy rather than based on a detailed derivation. While this form of the partition function is thought to be broadly valid and is widely applied (for example in molecular dynamics simulation [6]), it introduces the conceptual difficulty that the meaning of the discrete volumes Vi is not clear. Discrete energy states arise naturally from quantum statistics. Yet it is not necessarily obvious what discrete volumes to sum over in Equation (12.50). In fact for most applications it makes sense to replace the discrete sum with a continuous volume integral. Yet doing so results in a partition function that has units of volume, which is inappropriate for a partition function that formally should be unitless. 

The multiple time step propagation scheme is expected to be useful whenever a mixed quantum-classical molecular simulation is performed where only a few degrees of freedom are necessarily described within quantum mechanics and the force calculations in the classical subsystem is the time-limiting step. These conditions hold, for example, in molecular dynamics simulations of electron-and/or proton-transfer processes in the complex photosynthetic centre or in liquid phase. Furthermore, since the RPS is time-reversible, it is possible to calculate quantum reaction rates by propagating mixed quantum-classical trajectories located on the transition state back and forward in time. This opens a wide range of applications. 

See, for example, M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 1987) D. C. Rapaport, The Art of Molecular Dynamics Simulation, 2nd edn (Cambridge University Press, Cambridge, 2004) Daan Frenkel and B. Smit, Understanding Molecular Simulation, 2nd edn (Academic Press, San Diego, CA, 2002) J. M. Haile, Molecular Dynamics Simulation Elementary Methods ( Wiley, New York, 1997). 

Given the complexity and diversity of the problems involved a wide range of computational methods is needed. We will limit our discussion to the case of molecular dynamics simulations and quantum chemistry methods. Specific examples will be used to illustrate the benefit of various approaches for particular problems. 

To conclude this section we note that large molecular systems other than proteins have been the subject of hybrid QM/MM studies. Two such examples involve molecular dynamics simulations of surfaces using AMl/MM and PM3/MM potentials. In one the absorption of acetylene on a silicon surface was investigated [95] and in the other diamond surface reconstructions [96]. 

In recent work, much of which is reviewed elsewhere in this volume, surface areas of metal fluorides, for example as measured by the BET method, can be increased markedly if the synthetic method leads to aggregates of very small (sometimes called nanoscopic) particles. Such solids will exhibit properties that are very different from the conventionally prepared analogues, for example a molecular dynamics simulation of cubic nanoparticles of a-AIp3 indicated the presence of structural motifs that are found also in the metastable... 

Molecular-dynamics calculations provide valuable insight into the evolution with time of defect structures created in the collision caiscade. Consider, for example, the molecular-dynamics simulations of low-energy displacement cascades in the Bll-ordered compound CuTi (Figure 7) by Zhu et al, (1992). Figure 8 shows the number of Frenkel pairs produced by a Cu primary knock-on atom (PKA) as a function of recoil energy at the end of the collisional phase (0.2 p ) and at the end of the cooling phase (2.5 ps). The number of Frenkd... 

A continuum description becomes increasingly inaccurate as distances from the interface become comparable to the size of a solute molecule. Another crude concept used in simple continuum models of interfaces for calculating adsorption free energy and electronic spectra involves the use of an effective interfacial dielectric constant. For example, the reduced orientational freedom of interfacial water molecules and their reduced density result in a smaller effective dielectric constant than in the bulk. This is consistent with assigning the water liquid/vapor a polarity value similar to that of CCI4. Finally, we mention that a molecular theory of a local dielectric constant, which reproduces interfacial electric fields, can be developed with the aid of molecular dynamics simulation as described by Shiratori and Morita. ... 

---