United atom models

In a united atomforce field the van der Waals centre of the united atom is usually associated v ilh the position of the heavy (i.e. non-hydrogen) atom. Thus, for a united CH3 or CH2 group the vem der Waals centre would be located at the carbon atom. It would be more accurate to associate the van der Waals centre with a position that was offset slightly from the carbon position, in order to reflect the presence of the hydrogen atoms. Toxvaerd has developed such a model that gives superior performance for alkemes than do the simple united atom models, particularly for simulations at high pressures [Toxvaerd 1990]. In... 

All the complete sets mentioned here are referred to a certain origin and, in an atomic application, this point may conveniently be chosen to coincide with the nucleus. In a molecular problem, this problem is more difficult one may use a single complete set as in the united atom model, or one may introduce a complete set at every nucleus or at certain suitably chosen points ( floatingpoint wave functions). If more than one complete set is intro-... 

Uniform positive background, 255 United atom model, 276 Univariant, equilibrium, 19, 23 system, 91... 

Fig. 5.5. Illustration of the coarse-graining procedure for a united atom chain. The chain is a segment of PE at 509 K from molecular dynamics simulations with the united atom model [Eqs. (5.7)—(5.11)]. One coarse-grained bond represents the end-to-end distance of n = 5 consecutive united atom bonds. From [32]...

PE, the united atom model. We considered a sufficiently long PE chain made up of 5000 united atoms under periodic conditions in each direction. The initial amorphous sample prepared at 600 K was quenched to 100 K and drawn up to 400%. The sample was then quickly heated to various crystallization temperatures, and the molecular processes of fiber formation were monitored in situ via the real-space image and its Fourier transform, the structure function S3d([Pg.79]

Attempts were made to include all hydrogen atoms explicitly in the simulations. This computationally demanding explicit-atom model shows (Fig. 1) that the crystal symmetry is orthorhombic, in agreement with the well-known experimental result for polyethylene single crystals, instead of the hexagonal symmetry seen in united-atom model simulations. 

However, the essential mechanisms of lamellar formation and growth are found to be the same in both the united-atom and explicit-atom models. Only the united-atom model simulation results are therefore discussed in Sect. 3. 

The wall-PRISM equation has been implemented for a number of hard-chain models including freely jointed [94] and semiflexible [96] tangent hard-sphere chains, freely rotating fused-hard-sphere chains [97], and united atom models of alkanes, isotactic polypropylene, polyisobutylene, and polydimethyl siloxane [95]. In all implementations to date, to my knowledge, the theory has been used exclusively for the stmcture of hard-sphere chains at smooth structureless hard walls. 

For the united atom models of realistic polymers the wall PRISM theory predicts interesting structure near the surface [95]. For example, the side chains are found preferentially in the immediate vicinity of the surface and shield the backbone from the surface. This behavior is expected from entropic considerations. Computer simulations of these systems would be of considerable interest. 

When we think of simulations involving bead-spring models, all scatterers can be assigned the same scattering lengths [that are absorbed into arbitrary units for S(q )], and for united atom models like the one used for PB, we can consider scattering from the united atoms in the same way. This simplifies the scattering functions of Eqs. [59] and [60] to be... 

Fig. 3.9 Dynamic structure factor for a 100 monomer PE chain in the melt at 509 K vs. scaled time for the experiment (symbols), the united atom model (full curves) and the explicit atom model (dashed curves). (Reprinted with permission from [52]. Copyright 1998 American Institute of Physics)...

The configuration-bias Monte Carlo (CB-MC) technique (112) has also been extensively applied to characterize the sorption of alkanes, principally in silicalite (111, 156, 168-171) but also in other zeolites (172-174). Smit and Siepmann (111, 168) presented a thorough study of the energetics, location, and conformations of alkanes from n-butane to n-dodecane in silicalite at room temperature. A loading of infinite dilution was simulated, based on a united-atom model of the alkanes and a zeolite simulation box of 16 unit cells. Potential parameters were very similar to those used in the MD study of June et al. (85). As expected, the static properties (heat of adsorption, Henry s law coefficient) determined from the CB-MC simulations are therefore in close agreement with the values of June et al. The... 

In this section, some ideas developed by Haag [100], Gorte [101,104], and others [98,99,102] employing the slit [105], cylindrical [106], and spherical pore models [107] to develop a model for the description of the channels and cavities of zeolites and other nanoporous acid catalysts [97] and the united-atom model to describe the n-alkanes of m carbons are described [108],... 

Applying the united-atom model for an n-alkane, the total average potential for the different geometries of the catalyst pore systems is given by [97]... 

Kini RM, Evans HJ (1992) Comparison of protein models minimized by the all-atom and united atom models in the amber force field, J Biomol Structure and Dynamics, 10 265-279... 

Over the last years, the basic concepts embedded within the SCRF formalism have undergone some significant improvements, and there are several commonly used variants on this idea. To exemplify the different methods and how their results differ, one recent work from this group [52] considered the sensitivity of results to the particular variant chosen. Due to its dependence upon only the dipole moment of the solute, the older approach is referred to herein as the dipole variant. The dipole method is also crude in the sense that the solute is placed in a spherical cavity within the solute medium, not a very realistic shape in most cases. The polarizable continuum method (PCM) [53,54,55] embeds the solute in a cavity that more accurately mimics the shape of the molecule, created by a series of overlapping spheres. The reaction field is represented by an apparent surface charge approach. The standard PCM approach utilizes an integral equation formulation (IEF) [56,57], A variant of this method is the conductor-polarized continuum model (CPCM) [58] wherein the apparent charges distributed on the cavity surface are such that the total electrostatic potential cancels on the surface. The self-consistent isodensity PCM procedure [59] determines the cavity self-consistently from an isodensity surface. The UAHF (United Atom model for Hartree-Fock/6-31 G ) definition [60] was used for the construction of the solute cavity. 

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