Computer-simulated molecular dynamics

If we wish to know the number of (VpV)-collisions that actually take place in this small time interval, we need to know exactly where each particle is located and then follow the motion of all the particles from time tto time t+ bt. In fact, this is what is done in computer simulated molecular dynamics. We wish to avoid this exact specification of the particle trajectories, and instead carry out a plausible argument for the computation of r To do this, Boltzmann made the following assumption, called the Stosszahlansatz, which we encountered already in the calculation of the mean free path ... 

One way to test and compare these various statistical approaches is by computer simulation. Molecular dynamics (MD) simulations are based on the classical equations of motion to be solved for a limited number of molecules. From such simulations information about equilibrium properties as well as the dynamics of the system are obtained. In order to test theories based on primitive models for the solvent, Monte Carlo simulations are more appropriate. In Monte... 

The principal advantage of the time correlation function method is that it provides a new set of microscopic functions for a fluid, the time correlation functions, which can be studied directly by experimental observations of the fluidt or by computer-simulated molecular dynamics. The time correlation functions depend even more sensitively on the microscopic properties of the fluid molecules than the transport coefficients, which are expressed as time integrals of the correlation functions. Thus, a further test of kinetic theory has been found it must not only lead to expressions for the transport coefficients for dilute and dense gases that are in agreement with experiment, but also describe the dependence of the time correlation functions on both time and the density of the gas. One of the principal successes of kinetic theory is that it provides a quantitatively correct description of the short- and long-time... 

Fig. 19. A plot of T// as a function of density for hard-sphere molecules. Here 17 is the actual viscosity as determined by computer-simulated molecular dynamics, 17 the Enskog theory value of the viscosity at the same density, Vq the volume of the system of spheres at close packing, and V the actual volume of the system. The computer data on which this curve is based are good to about 5%. [From B. J. Alder, D. M. Gass, and T. E. Wainwright, J. Chem. Phys. 53, 3813 (1970).]...

As we discussed earlier, the generalized Boltzmann equation leads to a density expansion of the transport coefficients of a dense gas. However, general expressions for transport coefficients of a fluid that are not in the form of an expansion can be derived by another technique, the time correlation function method. This approach has provided a general framework by means of which one can make detailed comparisons between theoretical results, the results of computer-simulated molecular dynamics,and experimental results. ... 

Conducting experiments for material characterization of the nanocomposites is a very time consuming, expensive and difficult. Many researchers are now concentrating on developing both analytical and computational simulations. Molecular dynamics (MD) simulations are widely being used in modeling and... 

A comparison of the radial distribution function of a Lennard-Jones 6-12 fluid calculated from the Percus-Yevick equation (solid circles) with computer simulation (molecular dynamics) results (open circles). The reduced... 

Keywords Computer simulation, Molecular dynamics, Canonical ensemble. Thermostat algorithm... 

Hilbers P A J and Esselink K 1993 Parallel computing and molecular dynamics simulations Computer Simulation In Chemloal Physios /o 397 NATO ASI Series Ced M P Allen and D J Tlldesley (Dordrecht Kluwer) pp 473-95... 

Although, the notion of molecular dynamics was known in the early turn of the century, the first conscious effort in the use of computer for molecular dynamics simulation was made by Alder and Wainright, who in their paper [1] reported the application of molecular dynamics to realistic particle systems. Using hard spheres potential and fastest computers at the time, they were able to simulate systems of 32 to 108 atoms in 10 to 30 hours. Since the work of Alder and Wainright, interests in MD have increased tremendously, see... 

P. A. J Hilbers and K. Esselink, Parallel computing and molecular dynamics simulations , Computer Simulations in Chemical Physics, Proc. of the NATO advanced study institute on new perspectives in computer simulations in chemical physics, 473-95, 1993. 

Sometimes the theoretical or computational approach to description of molecular structure, properties, and reactivity cannot be based on deterministic equations that can be solved by analytical or computational methods. The properties of a molecule or assembly of molecules may be known or describable only in a statistical sense. Molecules and assemblies of molecules exist in distributions of configuration, composition, momentum, and energy. Sometimes, this statistical character is best captured and studied by computer experiments molecular dynamics, Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. Interaction potentials based on quantum mechanics, classical particle mechanics, continuum mechanics, or empiricism are specified and the evolution of the system is then followed in time by simulation of motions resulting from these direct... 

Concerning quantum chemical computations, we have used the MOLE-COLE program [18a], for HF and MP2 type computations. The Molecular Dynamics simulations with analytical force fields have been performed with the DINAMICA program [18b], The MOLECOLE-DFT program [18c] has been used for both the DFT energy minimization and for the DFT-Molecular Dynamics. 

The computer simulation of dynamic evolution in a molecular system rests on a few, rather simple principles and basic procedures that can be summarized as follows [57] ... 

Interestingly, in the experiments devoted solely to computational chemistry, molecular dynamics calculations had the highest representation (96-98). The method was used in simulations of simple liquids, (96), in simulations of chemical reactions (97), and in studies of molecular clusters (98). One experiment was devoted to the use of Monte Carlo methods to distinguish between first and second-order kinetic rate laws (99). One experiment used DFT theory to study two isomerization reactions (100). 

The method presented in this chapter serves as a link between molecular properties (e.g., cavities and their occupants as measured by diffraction and spectroscopy) and macroscopic properties (e.g., pressure, temperature, and density as measured by pressure guages, thermocouples, etc.) As such Section 5.3 includes a brief overview of molecular simulation [molecular dynamics (MD) and Monte Carlo (MC)] methods which enable calculation of macroscopic properties from microscopic parameters. Chapter 2 indicated some results of such methods for structural properties. In Section 5.3 molecular simulation is shown to predict qualitative trends (and in a few cases quantitative trends) in thermodynamic properties. Quantitative simulation of kinetic phenomena such as nucleation, while tenable in principle, is prevented by the capacity and speed of current computers however, trends may be observed. 

An example drawn from Deitrick s work (Fig. 2) shows the chemical potential and the pressure of a Lennard-Jones fluid computed from molecular dynamics. The variance about the computed mean values is indicated in the figure by the small dots in the circles, which serve only to locate the dots. A test of the thermodynamic goodness of the molecular dynamics result is to compute the chemical potential from the simulated pressure by integrating the Gibbs-Duhem equation. The results of the test are also shown in Fig. 2. The point of the example is that accurate and affordable molecular simulations of thermodynamic, dynamic, and transport behavior of dense fluids can now be done. Currently, one can simulate realistic water, electrolytic solutions, and small polyatomic molecular fluids. Even some of the properties of micellar solutions and liquid crystals can be captured by idealized models [4, 5]. 

As part of their efforts to employ parallel computers for molecular dynamics simulations, Schulten and co-workers generated a series of MD benchmarks based on their own program on a wide range of machines, including an Apple Macintosh II, a Silicon Graphics 320 VGX, a 32K-processor Conneaion Machine CM-200, a 60-node INMOS Transputer system, and a network of Sun workstations (using Linda).2 8 j e benchmarks demonstrated that the program runs very efficiently on many platforms (e.g., at sevenfold Cray 2 processor speed on the CM-200 and at Cray 2 processor speed on the Transputer system). 

Figure 2 compares the distribution after the impact, computed from molecular dynamics simulations, to the Maocwell-Boltzmann functional form. In Sec. 4, we discuss the reasons why the initially directed energy is so rapidly thermalized. 

D. Fincham and D. M. Heyes, Recent Advances in Molecular Dynamics Computer Simulation, in Dynamical Processes in Condensed Matter, M. W. Evans, ed., vol. LXIII of Adv. Chem. Phys., John Wiley Sons, New York, London, Sydney, 1985, 493-575. 

The protein folding problem - the ability to predict a protein fold from its sequence - is one of the major prizes in computational chemistry. Molecular dynamics simulations of solvated proteins is currently not a feasible approach to this problem. However, Duan and Kollman have shown that a 1 ps simulation on a small hydrated protein, here the 36 residue villin headpiece, is now possible using a massively parallel super computer.33 The native protein is estimated to fold in about 10-100 ps and so the simulation can only be used to study the early stages of protein folding. Nevertheless, starting from an extended structure the authors were able to observe hydrophobic collapse and secondary structure formation (helix 2 was well formed, helices 1 and 3 were partially formed and the loop connecting helices 1 and 2 was also partially... 

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