Carbon molecular dynamic

Key Words —Carbon, molecular dynamics, torus, helix, graphitic forms. 

Figure C2.3.7. Snapshot of micelle of sodium octanoate obtained during molecular dynamics simulation. The darkest shading is for sodium counter-ions, the lightest shading is for oxygens and the medium shading is for carbon atoms. Reproduced by pennission from figure 2 of [36].

The full ab-initio molecular dynamics simulation revealed the insertion of ethylene into the Zr-C bond, leading to propyl formation. The dynamics simulations showed that this first step in ethylene polymerisation is extremely fast. Figure 2 shows the distance between the carbon atoms in ethylene and between an ethylene carbon and the methyl carbon, from which it follows that the insertion time is only about 170 fs. This observation suggests the absence of any significant barrier of activation at this stage of the polymerisation process, and for this catalyst. The absence or very small value of a barrier for insertion of ethylene into a bis-cyclopentadienyl titanocene or zirconocene has also been confirmed by static quantum simulations reported independently... 

Calculations of relative partition coefficients have been reported using the free energy perturbation method with the molecular dynamics and Monte Carlo simulation methods. For example, Essex, Reynolds and Richards calculated the difference in partition coefficients of methanol and ethanol partitioned between water and carbon tetrachloride with molecular dynamics sampling [Essex et al. 1989]. The results agreed remarkably well with experiment... 

Fiber R and M Karplus 1990. Enhanced Sampling in Molecular Dynamics Use of the Time-Dependent Hartree Approximation for a Simulation of Carbon Monoxide Diffusion through Myoglobin. Journal of the American Chemical Society 112 9161-9175. 

If the amount of the sample is sufficient, then the carbon skeleton is best traced out from the two-dimensional INADEQUATE experiment. If the absolute configuration of particular C atoms is needed, the empirical applications of diastereotopism and chiral shift reagents are useful (Section 2.4). Anisotropic and ring current effects supply information about conformation and aromaticity (Section 2.5), and pH effects can indicate the site of protonation (problem 24). Temperature-dependent NMR spectra and C spin-lattice relaxation times (Section 2.6) provide insight into molecular dynamics (problems 13 and 14). 

In 1985 Car and Parrinello invented a method [111-113] in which molecular dynamics (MD) methods are combined with first-principles computations such that the interatomic forces due to the electronic degrees of freedom are computed by density functional theory [114-116] and the statistical properties by the MD method. This method and related ab initio simulations have been successfully applied to carbon [117], silicon [118-120], copper [121], surface reconstruction [122-128], atomic clusters [129-133], molecular crystals [134], the epitaxial growth of metals [135-140], and many other systems for a review see Ref. 113. 

Force fields split naturally into two main classes all-atom force fields and united atom force fields. In the former, each atom in the system is represented explicitly by potential functions. In the latter, hydrogens attached to heavy atoms (such as carbon) are removed. In their place single united (or extended) atom potentials are used. In this type of force field a CH2 group would appear as a single spherical atom. United atom sites have the advantage of greatly reducing the number of interaction sites in the molecule, but in certain cases can seriously limit the accuracy of the force field. United atom force fields are most usually required for the most computationally expensive tasks, such as the simulation of bulk liquid crystal phases via molecular dynamics or Monte Carlo methods (see Sect. 5.1). 

FIG. 23 Surface pressure vs. area/molecule isotherms at 300 K from molecular dynamics simulations of Karaborni et al. (Refs. 362-365). All are for hydrocarbon chains with carboxylate-like head groups, (a) (filled squares) A 20-carbon chain, (b) (filled circles) A 16-carbon chain with a square simulation box the curve is shifted 5 A to the right, (c) (open squares) A 16-carbon chain with a nonsquare box with dimensions in the ratio xly = (3/4) to fit a hexagonal lattice the curve is shifted 5 A to the right. (Reproduced with permission from Ref. 365. Copyright 1993 American Chemical Society.)... 

The simulation of a first-order phase transition, especially one where the two phases have a significant difference in molecular area, can be difficult in the context of a molecular dynamics simulation some of the works already described are examples of this problem. In a molecular dynamics simulation it can be hard to see coexistence of phases, especially when the molecules are fairly complicated so that a relatively small system size is necessary. One approach to this problem, described by Siepmann et al. [369] to model the LE-G transition, is to perform Monte Carlo simulations in the Gibbs ensemble. In this approach, the two phases are simulated in two separate but coupled boxes. One of the possible MC moves is to move a molecule from one box to the other in this manner two coexisting phases may be simulated without an interface. Siepmann et al. used the chain and interface potentials described in the Karaborni et al. works [362-365] for a 15-carbon carboxylic acid (i.e. pen-tadecanoic acid) on water. They found reasonable coexistence conditions from their simulations, implying, among other things, the existence of a stable LE state in the Karaborni model, though the LE phase is substantially denser than that seen experimentally. The re-... 

Chang TM, Peterson KA, Dang LX (1995) Molecular-dynamics simulations of liquid, interface, and ionic solvation of polarizable carbon-tetrachloride. J Chem Phys 103(17) 7502-7513... 

Elber, R. Karplus, M., Enhanced sampling in molecular-dynamics - use of the time-dependent Hartree approximation for a simulation of carbon-monoxide diffusion through myoglobin, J. Am. Chem. Soc. 1990,112, 9161-9175... 

The CH cation 1, protonated methane, is the parent of hypercoordinated carbocations containing a five coordinated carbon atom. It is elusive in solution and has not been observed by NMR spectroscopy but gas-phase infrared investigations have shown its fluxional structure which has been proven by ab initio molecular dynamic simulation.18... 

Figure 1 (Plate 1). A molecular view of a small section of a flat lipid bilayer generated by molecular dynamics simulations. The bilayers are composed of l-stearoyl-2-docosa-hexaenoyl-5M-g]ycero-3-phosphatidylcholine lipids, i.e. the sn 1 chain is 18 C atoms long and the sn2 chain has 22 carbons, including six cis double bonds. The hydrophobic core is in the centre of the picture, and the hydrated head-group regions are both on top and bottom of the view graph. The head group is zwitterionic and no salt has been added. From [102], Reproduced by permission of the American Physical Society. Copyright (2003)...

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