Molecular dynamics approach limitations

CWG van Gelder, EJJ Leusen, JAM Leunissen, JH Noordik. A molecular dynamics approach for the generation of complete protein structures from limited coordinate data. Proteins 18 174-185, 1994. 

The most fruitful of the three approaches, and the one likely to grow most in the future, is the molecular dynamics approach (Section 2.3.2). Here, a limited system of ions and molecules is considered and the Newtonian mechanics of the movement of... 

However, the drawback of ab initio calculations is that they usually refer to the athermal limit (T = 0 K), so that pressure but not temperature effects are included in the simulation. Although in principle the ab initio molecular dynamics approach[13] is able to overcome this limitation, at the present state of the art no temperature-dependent quantum-meehanieal simulations are feasible yet for mineral systems. Thus thermal properties have to be dealt with by methods based on empirical interatomic potential functions, containing parameters to be fitted to experimental quan-tities[14,15, 16]. The computational scheme applied here to carbonates is that based on the quasi-harmonic approximation for representing the atomic motion[17]. 

Molecular dynamics simulations are limited largely by the speed and storage constraints of available computers. Hence, usually simulations are done on systems containing 100-1000 particles although calculations involving 10 particles have also been performed [11]. Hence, molecular dynamics approach has the following limitations ... 

The CLS methodology uses an FE description to model the continuum, classical MD to simulate the evolution of the mesoscopic regime, and a TB molecular dynamics approach to include quantum effects in the overall treatment. The FE description is at the linear elastic level because its use is limited to regions where the atoms are only slightly perturbed from equilibrium. The classical molecular dynamics makes use of semiempirical potentials such as the Stillinger-Weber (SW) potential for Si. Lastly, the tight-binding method was chosen instead of other, more accurate, quantum descriptions because of its computational speed. 

Sect. 2.3.2, these long time scales can range from fj,s to hours. These time scales are clearly beyond the reach of any classical or quantum molecular dynamics approach. Several methods have been proposed over the years to overcome this difficulty. Here we limit our discussion to a couple of them, since they are by far the most successful and widely applied ones in the field of disordered materials and condensed phases. 

A brief overview of energy calculations and molecular dynamics approaches currently used to model the dynamics of atomic or molecular clusters has been presented. The discussion has been limited to methods in which the nuclear dynamics are classical. Much effort is currently devoted to the field of quantum dynamics, but such an approach is still limited to systems composed of a few nuclei and a small number of electrons. 

This is the most sophisticated (and computationally demanding) approach and involves the explicit determination of the electronic wavefunctions for both the solvent and solute. At present serious approximations relating to the size of samples studied and/or the liquid structure, and/or the electronic wavefunctions are necessary. A very successful scheme is the local-density-functional molecular-dynamics approach of Car and Parrinello that treats the electronic wave functions and liquid structure in a rigorous and sophisticated manner but is at present limited to sample sizes of the order of 32 molecules per unit cell to represent liquid water, for example. Clusters at low temperatures are well suited to supermolecular approaches as they are intrinsically small in size and could be characterized on the basis of a relatively small number of cluster geometries. Often, however, liquids are approximated by low temperature clusters in supermolecular calculations with the aim of qualitatively describing the processes involved in a particular solvation process. Alternatively, semiempirical or empirical electronic structure methods can be used in supermolecular calculations, allowing for more realistic sample sizes and solvent structures. Care must be taken, however, to ensure that the method chosen is capable of adequately describing the intermolecular interactions. 

The method of molecular dynamics (MD), described earlier in this book, is a powerful approach for simulating the dynamics and predicting the rates of chemical reactions. In the MD approach most commonly used, the potential of interaction is specified between atoms participating in the reaction, and the time evolution of their positions is obtained by solving Hamilton s equations for the classical motions of the nuclei. Because MD simulations of etching reactions must include a significant number of atoms from the substrate as well as the gaseous etchant species, the calculations become computationally intensive, and the time scale of the simulation is limited to the... 

A variety of techniques have been introduced to increase the time step in molecular dynamics simulations in an attempt to surmount the strict time step limits in MD simulations so that long time scale simulations can be routinely undertaken. One such technique is to solve the equations of motion in the internal degree of freedom, so that bond stretching and angle bending can be treated as rigid. This technique is discussed in Chapter 6 of this book. Herein, a brief overview is presented of two approaches, constrained dynamics and multiple time step dynamics. 

In literature, some researchers regarded that the continuum mechanic ceases to be valid to describe the lubrication behavior when clearance decreases down to such a limit. Reasons cited for the inadequacy of continuum methods applied to the lubrication confined between two solid walls in relative motion are that the problem is so complex that any theoretical approach is doomed to failure, and that the film is so thin, being inherently of molecular scale, that modeling the material as a continuum ceases to be valid. Due to the molecular orientation, the lubricant has an underlying microstructure. They turned to molecular dynamic simulation for help, from which macroscopic flow equations are drawn. This is also validated through molecular dynamic simulation by Hu et al. [6,7] and Mark et al. [8]. To date, experimental research had "got a little too far forward on its skis however, theoretical approaches have not had such rosy prospects as the experimental ones have. Theoretical modeling of the lubrication features associated with TFL is then urgently necessary. 

Enzyme reactions, like all chemical events, are dynamic. Information coming to us from experiments is not dynamic even though the intervals of time separating observations may be quite small. In addition, much information is denied to us because of technological limitations in the detection of chemical changes. Our models would be improved if we could observe and record all concentrations at very small intervals of time. One approach to this information lies in the creation of a model in which we know all of the concentrations at any time and know something of the structural attributes of each ingredient. A class of models based on computer simulations, such as molecular dynamics, Monte Carlo simulations, and cellular automata, offer such a possibility. 

The advantages of the simple approach outlined above are the limited number of water molecules needed in the simulation and the well-defined water structure. The major drawback is that, owing to the periodicity, this water structure fits best on a (111) or (lll)-like surface, e.g., (211). There are at least two other approximations to model the water interaction. One is to include a large number of water molecules and apply molecular dynamics to determine a structure for the water and include this water arrangement in the simulations [Filhol and Neurock, 2006]. The drawbacks of this approach are the computational time required and the results sensitivity to the water structure. 

Hpp describes the primary system by a quantum-chemical method. The choice is dictated by the system size and the purpose of the calculation. Two approaches of using a finite computer budget are found If an expensive ab-initio or density functional method is used the number of configurations that can be afforded is limited. Hence, the computationally intensive Hamiltonians are mostly used in geometry optimization (molecular mechanics) problems (see, e. g., [66]). The second approach is to use cheaper and less accurate semi-empirical methods. This is the only choice when many conformations are to be evaluated, i. e., when molecular dynamics or Monte Carlo calculations with meaningful statistical sampling are to be performed. The drawback of semi-empirical methods is that they may be inaccurate to the extent that they produce qualitatively incorrect results, so that their applicability to a given problem has to be established first [67]. 

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