Molecular dynamics numerical results

The complexity of polymeric systems make tire development of an analytical model to predict tlieir stmctural and dynamical properties difficult. Therefore, numerical computer simulations of polymers are widely used to bridge tire gap between tire tlieoretical concepts and the experimental results. Computer simulations can also help tire prediction of material properties and provide detailed insights into tire behaviour of polymer systems. A simulation is based on two elements a more or less detailed model of tire polymer and a related force field which allows tire calculation of tire energy and tire motion of tire system using molecular mechanisms, molecular dynamics, or Monte Carlo teclmiques 1631. 

In the next section we describe the basic models that have been used in simulations so far and summarize the Monte Carlo and molecular dynamics techniques that are used. Some principal results from the scaling analysis of EP are given in Sec. 3, and in Sec. 4 we focus on simulational results concerning various aspects of static properties the MWD of EP, the conformational properties of the chain molecules, and their behavior in constrained geometries. The fifth section concentrates on the specific properties of relaxation towards equilibrium in GM and LP as well as on the first numerical simulations of transport properties in such systems. The final section then concludes with summary and outlook on open problems. 

Presently, only the molecular dynamics approach suffers from a computational bottleneck [58-60]. This stems from the inclusion of thousands of solvent molecules in simulation. By using implicit solvation potentials, in which solvent degrees of freedom are averaged out, the computational problem is eliminated. It is presently an open question whether a potential without explicit solvent can approximate the true potential sufficiently well to qualify as a sound protein folding theory [61]. A toy model study claims that it cannot [62], but like many other negative results, it is of relatively little use as it is based on numerous assumptions, none of which are true in all-atom representations. 

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. 

Following earlier workby Warshel, Halley and Hautman"" and Curtiss etal presented an approximate numerical scheme to calculate the nonadiabatic electron transfer rate under the above conditions. The method is based on solving Eq. (18) to the lowest order in the coupling F by treating the elements Hj and as known functions of time obtained from the molecular dynamics trajectories. The result for the probability of the system making a transition to the final state at time t, given that it was in the initial state at time fo. is given by... 

The inconsistencies arising from the formulation of quantum-classical mechanics based on eq.(7) are at the origin of important complications within numerical implementations of the resulting quantum-classical molecular dynamics. 

The approach has been tested by controlling nuclear wavepacket motion in a two-dimensional model system [23], The relative simplicity of the system makes it possible to compare the semiclassical results with exact quantum ones. Numerical applications to the control of HCN-CNH isomerization [24] demonstrates that the new semiclassical formulation of optimal control theory provides an effective and powerful tool for controlling molecular dynamics with many degrees of freedom. 

Very striking results on the interactions of molecules with a catalyst have been recently reported in zeolite catalysis because of the well ordered structure of these materials it is worth mentioning the subjects of zeolite design [10] and of acidic properties of metallosilicates [11]. In other areas where polycrystallinic or even amorphous materials arc applied, highly interesting results are now numerously emerging (such as hydrocarbon oxidation on vanadium-based catalysts [12] location of transition metal cations on Si(100) [13] CO molecules on MgO surfaces [14] CH4 and O2 interaction with sodium- and zinc-doped CaO surfaces [15] CO and NO on heavy metal surfaces [16]). An illustration of the computerized visualization of molecular dynamics of Pd clusters on MgO(lOO) and on a three-dimensional trajectory of Ar in Na mordenitc, is the recent publication of Miura et al. [17]. 

At room temperature, these molecules occupy well-defined locations in their respective crystal lattices. However, they tumble freely and isotropically (equally in all directions) in place at their lattice positions. As a result, their solid phase NMR spectra show features highly reminiscent of liquids. We will see an illustration of this point shortly. Other molecules may reorient anisotropically (as in solid benzene). Polymer segmental motions in the melt may cause rapid reorientation about the chain axis but only relatively slow reorientation of the chain axes themselves. Large molecular aggregates in solution (such as surfactant micelles or protein complexes or nucleic acids) may appear to have solidlike spectra if their tumbling rates are sufficiently slow. There are numerous other instances in which our macroscopic motions of solid and liquid may be at odds with the molecular dynamics. Nuclear magnetic resonance is one of the foremost ways of investigating these situations. 

It should be mentionned that the result of q-dependent chain orientation in shear was also found by nonequilibrium molecular dynamics (NEMD) simulations by Kroger et al [32], The increasing power of computational techniques will surely result in increased accuracy and usefulness of this type of numerical simulation. 

---