Molecular Dynamic Modeling

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. 

Approximation Properties and Limits of the Quantum-Classical Molecular Dynamics Model... 

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)... 

Bornemann, F. A., Schiitte, Ch. On the Singular Limit of the Quantum-Classical Molecular Dynamics Model. Preprint SC 97-07 (1997) Konrad-Zuse-Zentrum Berlin. SIAM J. Appl. Math, (submitted)... 

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. 

F.A. Bornemann and Ch. Schiitte. On the singular limit of the quantum-classical molecular dynamics model. Preprint SC 97-07, ZIB Berlin, 1997. Submitted to SIAM J. Appl. Math. 

The MYD analysis assumes that the atoms do not move as a result of the interaetion potential. The eonsequenees of this assumption have recently been examined by Quesnel and coworkers [50-55], who used molecular dynamic modeling techniques to simulate the adhesion and release of 2-dimensional particles from 2-D substrates. Specifically, both the Quesnel and MYD models assume that the atoms in the different materials interact via a Lennard-Jones potential

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In their initial stndies, Pallant and Tinker (2004) found that after learning with the molecular dynamic models, 8th and 11th grade students were able to relate the difference in the state of matter to the motion and the arrangement of particles. They also used atomic or molecular interactions to describe or explain what they observed at the macroscopic level. Additionally, students interview responses included fewer misconceptions, and they were able to transfer their understanding of phases of matter to new contexts. Therefore, Pallant and Tinker (2004) concluded that MW and its guided exploration activities could help students develop robust mental models of the states of matter and reason about atomic and molecular interactions at the submicro level. 

Pallant, A., Tinker, R. F. (2004). Reasoning with atomic-scale molecular dynamic models. Journal of Science Education and Technology, 75(1), 51-66. 

Halley JW, Rustad JR, Rahman A (1993) A polarizable, dissociating molecular-dynamics model for liquid water. J Chem Phys 98(5) 4110-4119... 

Yamamoto, T. Molecular Dynamics Modeling of the Crystal-Melt Interfaces and the Growth of Chain Folded Lamellae. Vol. 191, pp. 37-85. 

As pointed out by Warshel and co-workers, the derivation of the important relation (14) is based on the assumption of non-saturation of the dielectric medium, which does not necessarily applies in the case of a macromolecule in solution [43]. These authors have shown that the validity of relation (14) could be directly tested by simulating the dipole motions through molecular dynamics models [43, 44, 45]. Detailed numerical calculations were carried out for the selfexchange reaction of cytochrome c [43], and for the electron transfer between two benzene-like molecules in water [45]. A similar approach was recently developed for the system (Fe " ", Fe ) in aqueous solution [46]. From these calculations, it was concluded that relation (14) applies provided that X is evaluated from a microscopic model. 

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]. 

Many more such curves were measured in subsequent years, some of which were reported by Abragam (17). When Abragam s work was published it was already quite clear that the dispersion curves could become a valid tool for the study of molecular dynamics, thus laying down the foundation for variable field NMR relaxometry. In principle, the dispersion curves are potentially powerful tools to discriminate between various molecular dynamics models. 

Fig. 2. Radial distribution functions compared between ab initio molecular dynamics (CPMD) and the parameterized molecular dynamics model (MD). Multiple traces for the CPMD calculations represent repeated molecular dynamics calculations.

Figure 9.9 Calculated atom jumps in the core of a E5 symmetric (001) tilt boundary in b.c.c. Fe. A pair-potential-molecular-dynamics model was employed. For purposes of clarity, the scales used in the figure are [130] [310] [001] = 1 1 5. All jumps occurred in the fast-diffusing core region. Along the bottom, a vacancy was inserted at B, and subsequently executed the series of jumps shown. The trajectory was essentially parallel to the tilt axis. Near the center of the figure, an atom in a B site jumped into an interstitial site at I. At the top an atom jumped between B, I and B sites. From Balluffi et al. [14],...

Our calculations of the activation free energy barrier for the cuprous-cupric electron transfer were not precise enough to permit a very accurate estimate of the absolute value of the exchange current for comparison with experiment. In principle, a determination of the absolute rate from the activation energy requires a calculation of the relevant correlation function [82] when the ion is in the transition region within the molecular dynamics model. We have not carried out such a calculation, but can obtain some information about the amplitude by comparing experiments with the transition state theory expression [84]... 

Xu, X., Kalinichev, A. G., and Kirkpatrick, R. J. (2006). 133Cs and 35C1 NMR spectroscopy and molecular dynamics modeling of Cs+ and CL complexation with natural organic matter. 

Zheng, G., Me, S., Elstner, M., Morokuma, K. (2004), Quantum Chemical Molecular Dynamics Model Study of Fullerene Formation from Open-Ended Carbon Nanotubes, J. Phys. Chem. A 108, 3182-3194. 

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