The Molecular Dynamics Method

Both the Monte Carlo and the molecular dynamics methods (see Section III-2B) have been used to obtain theoretical density-versus-depth profiles for a hypothetical liquid-vapor interface. Rice and co-workers (see Refs. 72 and 121) have found that density along the normal to the surface tends to be a... 

Both molecular dynamics studies and femtosecond laser spectroscopy results show that molecules with a sufficient amount of energy to react often vibrate until the nuclei follow a path that leads to the reaction coordinate. Dynamical calculations, called trajectory calculations, are an application of the molecular dynamics method that can be performed at semiempirical or ah initio levels of theory. See Chapter 19 for further details. 

The molecular dynamics method is useful for calculating the time-dependent properties of an isolated molecule. However, more often, one is interested in the properties of a molecule that is interacting with other molecules. With HyperChem, you can add solvent molecules to the simulation explicitly, but the addition of many solvent molecules will make the simulation much slower. A faster solution is to simulate the motion of the molecule of interest using Langevin dynamics. 

The simulations to investigate electro-osmosis were carried out using the molecular dynamics method of Murad and Powles [22] described earher. For nonionic polar fluids the solvent molecule was modeled as a rigid homo-nuclear diatomic with charges q and —q on the two active LJ sites. The solute molecules were modeled as spherical LJ particles [26], as were the molecules that constituted the single molecular layer membrane. The effect of uniform external fields with directions either perpendicular to the membrane or along the diagonal direction (i.e. Ex = Ey = E ) was monitored. The simulation system is shown in Fig. 2. The density profiles, mean squared displacement, and movement of the solvent molecules across the membrane were examined, with and without an external held, to establish whether electro-osmosis can take place in polar systems. The results clearly estab-hshed that electro-osmosis can indeed take place in such solutions. 

D. J. Tildesley, The Molecular Dynamics Method, Kluwer Academic Publishers, Boston, 1998, 23-47. 

A theoretical treatment of the effect caused by the competition between the sine-like angular-dependent component of the adsorption potential and dipole lateral interaction demonstrated that the values 6 are the same in the ground state and at the phase transition temperature.81 Study of the structure and dynamics for the CO monolayer adsorbed on the NaCl(lOO) surface using the molecular dynamics method has also led to the inference that angles 0j are practically equalized in a wide temperature range.82 That is why the following consideration of orientational structures and excitations in a system of adsorbed molecules will imply, for the sake of simplicity, the constant value of the inclination angle ty =0(see Fig. 2.14) which is due to the adsorption potential u pj,q>j). 

The study of liquids near solid surfaces using microscopic (atomistic-based) descriptions of liquid molecules is relatively new. Given a potential energy function for the interaction between liquid molecules and between the liquid molecules and the solid surface, the integral equation for the liquid density profile and the liquid molecules orientation can be solved approximately, or the molecular dynamics method can be used to calculate these and many other structural and dynamic properties. In applying these methods to water near a metal surface, care must be taken to include additional features that are unique to this system (see later discussion). 

In order to study the behavior of ions at the water/metal interface using the molecular dynamics method, the potential energy functions for the interaction between the ions and the water and between the ions and the metal surface must be specified. 

Following the early studies on the pure interface, chemical and electrochemical processes at the interface between two immiscible liquids have been studied using the molecular dynamics method. The most important processes for electrochemical research involve charge transfer reactions. Molecular dynamics computer simulations have been used to study the rate and the mechanism of ion transfer across the water/1,2-dichloroethane interface and of ion transfer across a simple model of a liquid/liquid interface, where a direct comparison of the rate with the prediction of simple diffusion models has been made. ° ° Charge transfer of several types has also been studied, including the calculations of free energy curves for electron transfer reactions at a model liquid/liquid... 

The molecular dynamics method is based on the time evolution of the path (p (t), for each particle to feel the attractions and repulsions from all other particles, following Newton s law of motion. The simplest case is a dilute gas following the hard sphere force field, where there is no interaction between molecules except during brief moments of collision. The particles move in straight lines at constant velocities, until collisions take place. For a more advanced model, the force fields between two particles may follow the Lennard-Jones 6-12 potential, or any other potential, which exerts forces between molecules even between collisions. 

Lantelme, R, Turq, R, Quentrec, B., and Lewis, J.W.E., Application of the molecular dynamics method to a liquid system with long range forces (Molten NaCl), Mol. Phys., 28,1537-1549, 1974. 

The molecular dynamics method uses similar boundary conditions and employs one of the following approximations to solve the problem of an assembly of molecules contained in a box and whose motions are governed by the laws of classical dynamics. 

We wish to end this section by saying that now it is possible to perform molecular dynamics simulations on the fly without precomputing the potential energy surface. This idea was introduced by Carr and Parrinello344-345, and is known as the Carr-Parrinello dynamics. In this approach the nuclear motions are treated classically within the molecular dynamics method, but the energy and force are precomputed for each configuration of the nuclei with a suitable version of... 

Computer simulation is being used increasingly in diverse areas of science in the past few years. It has also emerged to become one of the powerful means for investigating condensed matter (/). The principal tools employed in computer simulation are the Monte Carlo and the molecular dynamics methods. In these methods, properties of a collection of particles, usually between 30 and 1000 in number, interacting via a potential />(r) are obtained numerically. Reliable estimates of equilibrium and transport properties as well as microscopic properties can be obtained from such calculations. 

In this article, we shall discuss studies of phase changes in solids carried out by the application of the generalized Monte Carlo and the molecular dynamics methods. This topic is of particular significance because of the recent modifications of the method to include both variation in size and shape of the simulation cell. What is especially gratifying is that we are now able to make meaningful predictions of phase transitions in real solids by employing reliable pair potentials. Besides phase transitions of molecular solids, we shall examine phase transi-... 

There are many excellent reviews on the standard molecular dynamics method dealing with calculations in the microcanonical ensemble as well as on the Monte Carlo method involving calculations in the canonical, isothermal isobaric, and grand canonical ensemble (< ). In the present article, we shall limit ourselves exclusively to those developments that have taken place since the work of Andersen (4). In the molecular dynamics method, the developments are the constant-pressure, constant-temperature, constant-temperature-constant-pressure, variable shape simulation cell MD, and isostress calculations in the Monte Carlo method, it is the variable shape simulation cell calculation. 

The problems being addressed in recent work carried out in various laboratories include the fundamental nature of the solute-water intermolecular forces, the aqueous hydration of biological molecules, the effect of solvent on biomolecular conformational equilibria, the effect of biomolecule - water interactions on the dynamics of the waters of hydration, and the effect of desolvation on biomolecular association 17]. The advent of present generation computers have allowed the study of the structure and statistical thermodynamics of the solute in these systems at new levels of rigor. Two methods of computer simulation have been used to achieve this fundamental level of inquiry, the Monte Carlo and the molecular dynamics methods. 

The molecular dynamics method has been applied recently to do an extensive study of solvent interactions in a solution of an alanine dipeptide in water[l7b,c]. The effect of solute proximity on dynamic behavior of the solvent, the range of influence of the solvent, the nature of the solvent in the neighborhood of various functional groups in the peptide, as well as the effects of solvent on the peptide dynamics were investigated in these works. 

The first structure of human renin was obtained from prorenin produced by expression of its cDNA in transfected mammalian cells. Prorenin was cleaved in the laboratory to renin using the protease trypsin. Because the carbohydrates in renin are not required for bioactivity, oligosaccharides were removed enzymatically. This process facilitates crystallization in some cases and also removes the contribution of the heterogeneous sugar chains to the diffraction pattern. The structure was determined without the use of heavy-atom derivatives, by application of molecular replacement techniques based on the atomic coordinates of porcine pepsinogen as the model. The molecular dynamic method of refinement was used extensively to arrive at a 2.5 A resolution structure. However, some of the loop regions were not well resolved in this structure (Sielecki et al, 1989 Sail et al, 1990). 

The molecular dynamic methods can also be very useful in the study of the molecular motions in polymer chains with bulky side groups. 

There are some alternative methods for locating the dividing surface r2 can be experimentally measured at the liquid-vapor interface by using radioactive tracer methods or it may also be determined using ellipsometry so that the thickness of an adsorbed film is calculated from the ellipticity produced in light reflected from the film covered surface. On the other hand, the theoretical calculation of r2 is also possible using Monte Carlo and the molecular dynamics methods. 

Consider the causal model of explanation. Is notthe molecular dynamics simulation of a molecule a classic example of a simulation of a causal process, and is not the causal model of explanation, hence, a perfect candidate to describe these simulations as explanations To address the first question, I consider the two conceptions of causality discussed above to see if either serves to capture the molecular dynamics method as picturing a causal process. Keep in mind that usually when asking whether a process is causal one cannot look at the process itself, but must rely on a model that simulates it. This is not simply a practical necessity in our example, for instance, it... 

The two major methods for the simulations are the Monte Carlo method (so named for its use of random number generation) and the molecular dynamics method. The Monte Carlo method, as applied to problems of chemistry, was first described by N. Metropolis and his co-workers at the Los Alamos... 

A different technique used for exploring conformational space is the molecular dynamics method. While it is effective for searching local conformational space, it requires remarkably more computer time than the other methods for global search problems. ... 

The molecular dynamics methods that we have discussed in this chapter, and the examples that have been used to illustrate them, fall into the category of atomistic simulations, in that all of the actual atoms (or at least the non-hydrogen atoms) in the core system are represented explicitly. Atomistic simulations can provide very detailed information about the behaviour of the system, but as we have discussed this typically limits a simulation to the nanosecond timescale. Many processes of interest occur over a longer timescale. In the case of processes which occur on a macroscopic timescale (i.e. of the order of seconds) then rather simple models may often be applicable. Between these two extremes are phenomena that occur on an intermediate scale (of the order of microseconds). This is the realm of the mesoscale Dissipative particle dynamics (DPD) is particularly useful in this region, examples include complex fluids such as surfactants and polymer melts. 

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