Molecular dynamics modeling method

In MD modeling, the molecular adsorption concept is used to interpret the Pt-C interactions during the fabrication processes. The Pt complexes are mostly attached to the hydrophilic sites on the carbon particles, viz. carbonyl or hydroxyl groups (Hao et ah, 2003). The adsorption is based on both the physical and chemical adsorptions. Many efforts have been done on the MD simulations of Pt nano-particles adsorbed on carbon with or without ionomers (Balbuena et ah, 2005 Chen and Chan, 2005 Huang and Balbuena, 2002 Lamas and Balbuena, 2003 2006). The Pt-Pt interactions are modeled with the many-body Sutton-Chen (SC) potential (Rafii-Tabar et al, 2006), whereas a Lennard-Jones (LJ) potential is used to describe the Pt-C interactions. The SC potential for Pt-Pt and Pt-C interactions provides a reasonable description of the properties for small Pt clusters. The diffusion of platinum nano-particles on graphite has also been investigated, with diffusion coefficients in the order of 10 cm s (Morrow and Striolo, 2007). 

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Bala, P., Grochowsky, R, Lesyng, B., McCammon, J.A. Quantum-classical molecular dynamics. Models and applications. In Quantum mechanical simulation methods for studying biological systems, D. Bicout and M. Field, eds. Springer, Berlin (1996) 119-156. 

P. Bala, P. Grochowski, B. Lesyng, and J. A. McCammon Quantum-classical molecular dynamics. Models and applications. In Quantum Mechanical Simulation Methods for Studying Biological Systems (M. Fields, ed.). Les Houches, France (1995)... 

Abstract. The overall Hamiltonian structure of the Quantum-Classical Molecular Dynamics model makes - analogously to classical molecular dynamics - symplectic integration schemes the methods of choice for long-term simulations. This has already been demonstrated by the symplectic PICKABACK method [19]. However, this method requires a relatively small step-size due to the high-frequency quantum modes. Therefore, following related ideas from classical molecular dynamics, we investigate symplectic multiple-time-stepping methods and indicate various possibilities to overcome the step-size limitation of PICKABACK. 

Some authors have described the time evolution of the system by more general methods than time-dependent perturbation theory. For example, War-shel and co-workers have attempted to calculate the evolution of the function /(r, Q, t) defined by Eq. (3) by a semi-classical method [44, 96] the probability for the system to occupy state v]/, is obtained by considering the fluctuations of the energy gap between and 11, which are induced by the trajectories of all the atoms of the system. These trajectories are generated through molecular dynamics models based on classical equations of motion. This method was in particular applied to simulate the kinetics of the primary electron transfer process in the bacterial reaction center [97]. Mikkelsen and Ratner have recently proposed a very different approach to the electron transfer problem, in which the time evolution of the system is described by a time-dependent statistical density operator [98, 99]. 

An overview of the approaches that have been taken to linking different theoretical and computational modeling descriptions is also provided in Fig. 2 The first principles (QC) descriptions are based on the Schrodinger equation and the Bom Oppenheimer approximation as realized in most chemical applications by density functional [14] or Hartree-Fock [15] methods. Molecular dynamics (MD) methods [16], based on classical Newtonian me-... 

Aiming to describe any kind of time-dependent phenomena, it would be highly desirable to couple the standard molecular dynamics (MD) methods, both classical and ab initio, with the implicit solvent model. This can be achieved either by solving the... 

For the past several years we have been developing and applying quantum dynamics (QD) and quantum-classical molecular dynamics (QCMD) methods, which are based on the explicitly time-dependent Schroedinger equation. For an overview of the models and simulation results see e.g.4 and the references cited... 

Figure 3-2. Molecular Mechanics (MM) and Molecular Dynamics (MD) methods. In coarse-grained models, groups of nuclei (atoms) are replaced by larger objects...

Bala P, Grochowski P, Lesyng B, McCammon JA (1995) Quantum Classical Molecular Dynamics. Models and Applications. In Field M (ed) Quantum Mechanical Simulation Methods for Studying Biological Systems. Les Houches Physics School Series, Springer Verlag and Les Houches Editions de Physique, 119-156... 

In the light of the previous discussion it is quite apparent that a detailed mathematical simulation of the combined chemical reaction and transport processes, which occur in microporous catalysts, would be highly desirable to support the exploration of the crucial parameters determining conversion and selectivity. Moreover, from the treatment of the basic types of catalyst selectivity in multiple reactions given in Section 6.2.6, it is clear that an analytical solution to this problem, if at all possible, will presumably not favor a convenient and efficient treatment of real world problems. This is because of the various assumptions and restrictions which usually have to be introduced in order to achive a complete or even an approximate solution. Hence, numerical methods are required. Concerning these, one basically has to distinguish between three fundamentally different types, namely molecular-dynamic models, stochastic models, and continuous models. 

Transport coefficients of molecular model systems can be calculated by two methods [8] Equilibrium Green-Kubo (GK) methods where one evaluates the GK-relation for the transport coefficient in question by performing an equilibrium molecular dynamics (EMD) simulation and Nonequilibrium molecular dynamics (NEMD) methods. In the latter case one couples the system to a fictitious mechanical field. The algebraical expression for the field is chosen in such a way that the currents driven by the field are the same as the currents driven by real Navier-Stokes forces such as temperature gradients, chemical potential gradients or velocity gradients. By applying linear response theory one can prove that the zero field limit of the ratio of the current and the field is equal to the transport coefficient in question. 

Perhaps one of the greatest successes of the molecular dynamics (MD) method is its ability both to predict macroscopically observable properties of systems, such as thermodynamic quantities, structural properties, and time correlation functions, and to allow modeling of the microscopic motions of individual atoms. From modeling, one can infer detailed mechanisms of structural transformations, diffusion processes, and even chemical reactions (using, for example, the method of ab initio molecular dynamics).Such information is extremely difficult, if not impossible, to obtain experimentally, especially when detailed behavior of a local defect is sought. The variety of different experimental conditions that can be mimicked in an MD simulation, such as... 

The structure of DNA is quite well preserved throughout nature. It is the double helix. There are small differences, the so-called fine structure of DNA, which are modeled in the computer with methods like energy minimization and molecular dynamics. These methods are also used for modeling other biomolecules, notably, proteins. Therefore modeling the structure of DNA is not covered in this book. 

Molecular dynamic simulation methods, in addition to being essential for interpreting NMR data at the atomic level, also augment experimental studies in a number of other ways [101] modeling techniques can (i) yield structural information where experimental data has not yet been acquired, (ii) expand on experimental data through simulations that yield dynamic trajectories whose analysis provides unique information on lesion mobility, and (iii) provide thermodynamic insights by ensemble analysis using statistical mechanical methods. Furthermore, reaction mechanisms can now be determined with some confidence by combined quantum mechanical and molecular mechanical methods [104, 105],... 

The possibility of a fluid-to-solid transition in the hard-sphere model was first predicted by Kirkwood and his co-workers [17-19]. This prediction was part of the stimulus for the celebrated studies of hard spheres by Alder and Wainwright [20] at the Lawrence-Livermore National Laboratory using the molecular dynamics (MD) method and by Wood and Jacobson [21] at the... 

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