# Lycll, Charles

Within a few years of the development of STM as an imaging tool, it became clear that the instrument could also find application in the manipulation of individual or groups of atoms on a surface [M]- Perhaps the most dramatic image originated from Eigler and Schweizer [M], who manipulated single physisorbed atoms of xenon on a Ni(l 10) surface, held at liquid helium temperature ( figure B 1,19,14). The tip-Xe distance was reduced (liy raising the setpoint for the tunnelling current) until the tip-sample interaction became strong enough for the tip to be able to pick up the atom. After being moved to the desired location, the atom was removed by reversing the procedure. Using a similar experimental set-up, Crommie et al [M] have managed to shape the spatial distribution of electrons on an atomic scale, by building a ring of 48 iron adatoms (a quantum corral ) on a Cu(l 11) surface, which confines the surface-state electrons of the copper by virtue of the scattering effect of the Fe atoms ( figure B 1.19.15 ). STS measurements of the local densities of states for the confined electrons correspond to the expected values for a particle-m-a-box , where the box is round and two-dimensional. In a similar way, Yokoyama et al [ ] fonned a pair of long straight chains of Al on the Si (001)-c (4 X 2) surface to create well defined ID quantum wells. The electrons in the FT surface states can propagate only in the dimer-row direction of Si(001)-c (4 x 2) because of nearly flat dispersion in the perpendicular direction. The STM/STS measurements of the standing-wave patterns and their discrete energy levels could be interpreted according to the ID particle-in-a-box model . This teclmique shows considerable promise for the fiirther investigation of confined electrons and waveguides. There are numerous other means for moving atoms in surfaces, including voltage-pulsing teclmiques, which show promise as potential lithographic methods for silicon [68]. [c.1689]

Another important difference between the mean field treatment and the simulations or experiments are fluctuations of the local interfacial position. While the mean field treatment assumes a perfectly flat, planar interface right from the outset, the local interfacial position fluctuates in experiments and simulations. A typical snapshot of the local interface position, as obtained from a Monte Carlo simulation of a binary polymer blend is depicted in figure B3.6.2. On not too small length scales the local position of the interface is smooth and without bubbles or overhangs. The system configuration can be described by two ingredients the position n(r ) of the centre of the interface as a fimction of the lateral coordinates and the local stnicture described by profiles across the interface. The latter quantities depend only on the coordinate nonnal to the interface. In many applications the coupling between the long-wavelength fluctuations of the local interfacial position u and the intrinsic profile is neglected. In this case the intrinsic profiles describe the variation of quantities across an ideally planar interface. The apparent interfacial profile which is averaged over [c.2371]

A multitude of different variants of this model has been investigated using Monte Carlo simulations (see, for example [M])- The studies aim at correlating the phase behaviour with the molecular architecture and revealing the local structure of the aggregates. This type of model has also proven useful for studying rather complex structures (e.g., vesicles or pores in bilayers). [c.2377]

The hst which follows gives an outline of the properties of a Monte Carlo simulation used in the context of molecular modeling studies for sampling either multiple conformations of smaller, flexible stmctures or multiple local minima of larger macromolecules or polymers [c.166]

In a lattice model the protein is represented as a string of beads threaded on a lattice (often denoted as a self-avoiding walk on a lattice). Each residue is positioned on a different grid point, and specific nearest-neighbor interactions, which depend on the residues involved, are defined. Once the model is defined the folding process is simulated by local Monte Carlo moves that change the position of the beads on the lattice until the chain reaches its lowest energy configuration. In many studies a simple square [20] or a cubic grid was used [26-28], although more complex lattices have also been employed [29,72]. Figure 2 illustrates a simple polypeptide chain with 27 amino acids (27-mer) folded on a 3 X 3 X 3 cubic lattice. All in all there are on the order of lO conformations of a 27-mer chain on an infinite cubic lattice. Due to an overall attraction between the residues (primarily of hydrophobic nature), the native state of the model protein is col- [c.376]

Incorporation of stereogenic centers into cyclic structures produces special stereochemical circumstances. Except in the case of cyclopropane, the lowest-eneigy conformation of the tings is not planar. Most cyclohexane derivatives adopt a chair conformation. For example, the two conformers of cis-l,2-dimethylcyclohexane are both chiral. However, the two conformers are enantiomeric so the conformational change leads to racemization. Because the barrier to this conformational change is low (lOkcal/mol), the two enantiomers arc rapidly interconverted. [c.86]

From this short discussion, it is clear that atomistically detailed molecular dynamics or Monte Carlo simulations can provide a wealth of information on systems on a local molecular atomistic level. They can, in particular, address problems where small changes in chemical composition have a drastic effect. Since chemical detail is avoided in mesoscopic models, these can often capture such effects only indirectly. [c.493]

Both Monte Carlo simulations of lattice models [49, and spring-bead models [M] have been employed to study interfaces in polymeric systems. The simulations yield msight mto tire local properties of the polymeric fluid. Unlike in the Landau-Ginzburg expansion, the notion of polymers is retained and the orientation of the extended molecules at the interface or the enrichment of end segments have been studied. Moreover, the simulations incorporate fluctuations, which are ignored in the mean field approximation. In the vicinity of the critical temperature composition fluctuations are important. The mean field treatment overestimates the critical pomt and tlie binodals are flatter in the simulations which exliibit 3D Ismg critical behaviour (P = 0.324) than in the mean field case (P = A). The importance of composition fluctuations can be gauged by the Ginzburg criterion [ ] The neglect of fluctuations is justified when the order parameter fluctuations in one [c.2371]

The objective of molecular mechanics is to generate static minimum-energy configurations at tire prescribed density, corresponding to tire local minima of tire total potential energy. Such energy minimizations are used in tire generation of realistic confonnations suitable as starting stmctures for molecular dynamics and Monte Carlo simulations. They also allow tire estimation of phase stability from tire calculation of chemical potential differences tliough a procedure called tliennodynamic integration [64]. [c.2537]

Molecular imprinting is a technique by which molecular recognition capabiHties are bestowed upon organic or inorganic polymeric systems through tempiating (174,188). The imprinting imparts stmctural information ("memory") of a particular molecule, by positioning the functional groups of the polymer (the local environment of the imprint molecule) in a specific geometric configuration that can then recognize the target (imprint) molecule. The polymeric materials are typically copolymers of methacrylates or vinylpyridines. Potential apphcations of imprinted polymers include catalysis, separations (eg, separation of chiral molecules), and chemical sensing (188). [c.207]

The polyamides are soluble in high strength sulfuric acid or in mixtures of hexamethylphosphoramide, /V, /V- dim ethyl acetam i de and LiCl. In the latter, compHcated relationships exist between solvent composition and the temperature at which the Hquid crystal phase forms. The polyamide solutions show an abmpt decrease in viscosity which is characteristic of mesophase formation when a critical volume fraction of polymer ( ) is exceeded. The viscosity may decrease, however, in the Hquid crystal phase if the molecular ordering allows the rod-shaped entities to gHde past one another more easily despite the higher concentration. The Hquid crystal phase is optically anisotropic and the texture is nematic. The nematic texture can be transformed to a chiral nematic texture by adding chiral species as a dopant or incorporating a chiral unit in the main chain as a copolymer (30). [c.202]

Simulated annealing can be easily implemented in both molecular dynamics and Monte Carlo simulations. In molecular dynamics, the temperature is controlled through coupling to a heat bath (Chapter 3) with simulated annealing, the temperature of the bath is decreasing gradually. In Monte Carlo the trial move is accepted or rejected according to a temperature-dependent probability of the Metropolis type [Eq. (1)]. In simulated annealing MC, the temperature used in the acceptance probability is gradually decreased. It should be noted that it is not necessary to anneal all the way to 0 K, because once the kinetic energy kT gets below the characteristic barrier height, a significant change cannot occur. Thus, many simulated annealing protocols cool to room temperature (or somewhat below) and are followed by a local minimization algorithm to remove the excess energy. Specific implementations vary in cooling schedules, initial temperatures, the possibility of repeated heating spikes, etc. A detailed account of the method can be found in Ref. 26. [c.83]

Inclusion of explicit solvent in calculations on DNA involved simulations in which the DNA was both held rigid and allowed to evolve along with the solvent molecules. Application of the former approach allowed for a better understanding of the solvation of DNA to be obtained. For example, the hydration of AT and polyA-polyT B-form tracts was studied via Monte Carlo calculations [11], and MD simulations were used to investigate differences in hydration of the B and Z forms of DNA [12]. Although these works contributed to the understanding of the solvation of oligonucleotides, the local conformational heterogeneity of DNA structure observed in crystal structures of DNA emphasized the need to include both the DNA and solvent as flexible degrees of freedom in the simulations. One of the earlier calculations on DNA with an explicit solvent representation was performed on a d(CGCGA) duplex in a sphere of water that included neutralizing counterions [13]. The structure resulting from this simulation was shown to be similar to the B form of DNA however, the total simulation time was only 114 ps, not long enough to allow for significant relaxation of the DNA, which has been more recently shown to require 1 ns or longer. Though limited, this work strongly indicated that MD simulations of DNA duplexes with an explicit solvent representation were both feasible and a useful method to better our understanding of DNA structure. [c.442]

Because multiple scattering dominates the electron diffraction process at low energies, there is no easy way of determining the surface directly such as the Patterson function in X-ray crystallography. Instead, I-V curves must be calculated for a large number of model geometries and compared with experimental I-V curves. Their agreement is then quantified by the means of a reliability factor (R factor). There are several ways of defining such R factors [2.243] with Pendrys R factor, Rp, being the most common [2.260]. By convention, Rp is 0 when the agreement is perfect, 1 for uncorrelated sets of I-V curves, and 2 for completely anti-correlated curves (each maximum of one curve coincides with a minimum of the other). Usually, automated search procedures, which modify the model geometries to be tested according to the R factor values achieved by the preceding geometries, are used to find a R factor minimum within the set of geometrical data to be optimized. The search strategies are either conventional downhill-oriented algorithms (simplex method, Powell s method, Marquard s algorithm [2.261]), which usually find only the nearest local minimum, or stochastic Monte-Carlo methods (simulated annealing [2.261], genetic algorithm [2.262]) which, in principle, always find the global minimum. A set of experimental and theoretical I-V curves for benzene on Ru(OOOl) [2.263], depicted in Pig. 2.49, shows a typical degree of agreement achieved in a structure optimization for organic molecules. [c.79]

The diffraction space of the MWCNT is thus formed by the loci generated by rotation about the tube axis, of the "features" of the local diffraction space of a volume element (Fig. 8). The resulting diffraction space consists of sharp circles in the plane through the origin perpendicular to the tube axis, described by the sharp 00./ nodes. The streaked nodes hereby generate "coronae which are limited inwards by sharp circles with radii gho.o (or 5hh.o) planes perpendicular to the tube axis and which fade gradually outwards (Fig. 8). In chiral tubes each streaked node generates a separate corona whereas in a chiral tube two mirror symmetrically related nodes generate a single corona. According to this model the diffraction pattern, which in ED is a planar section through the origin of diffraction space, has 2mm planar symmetry. This model accounts correctly for the geometrical behaviour on tilting, however taking intensities into account the 2mm symmetry is sometimes broken in experimental images. The following model explains why this is so. [c.19]

FIG. 1 Total local density p(z) for bulk density p = 0.821 and e /k T = 4.25. The solid line is for PYl theory, the dashed line is for HNCl approximation and the points denote the Monte Carlo simulation results. (Reprinted from S. Sokolowski, D. Henderson, A. Trokhymchuk, O. Pizio. Density profiles of associating fluid near a hard wall PY/EMSA and HNC/EMSA singlet theory, Physica A, 220, 22-32. (1995), with permission from Elsevier Science.) [c.181]

A different approach to the simulation of oscillations, namely the HS model, has very recently been proposed by Gelten et al. [15]. Here the grid consists of unit cells with two kind of site, H and S , which indicate the surface phase, hexagonal and (1 x 1), respectively. A site of the (1 x 1) phase has four neighbors whereas a site of the hexagonal type has only three neighbors. A species adsorbs and desorbs from both phases whereas B2 can only dissociatively adsorb on neighboring unit cells of the (1x1) type. Reaction events (Eq. (3)) occur between different species in adjacent sites. Plausible rules for reversible phase transformation between H and S phases are also stated (for more details see Ref. 15). The model is simulated by applying the dynamic Monte Carlo approach, so that parameters such as the rates of desorption, diffusion, etc., are taken from experimental data. The model exhibits self-sustained oscillations within temperature and pressure ranges compatible with experimental observations, as shown in Fig. 14 [15]. The sharp peak in the power spectra of the oscillations indicates that they are almost monochromatic . However, an interesting finding is that the amplitude of the oscillations depends on the grid size, as, e.g., in the ZGB model with local reconstruction of the surface [72]. It is also interesting [c.412]

J. J. Luque, F. Jimenez-Morales, M. C. Lemos. Monte Carlo simulation of a surface reaction model with local interaction. J Chem Phys 96 8535-8538, 1992. [c.433]

These methods starts from a given geometry, which typically is a (local) minimum, and new configurations are generated by adding a random kick to one or more atoms. In Monte Carlo (MC) methods the new geometry is accepted as a starting point for the next perturbing step if it is lower in energy than the current. Otherwise the Boltzmann factor g-Afi/Ztsf calculated and compared to a random number between 0 and 1. If is less than this number the new geometry is accepted, otherwise the next step is taken from the old geometry. This generates a sequence of configurations from which geometries may be selected for subsequent minimization. In order to have a reasonable acceptance ratio, however, the step size must be fairly small. [c.341]

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**Lycll, Charles**:

**[c.426] [c.840] [c.1714] [c.2220] [c.2368] [c.468] [c.114] [c.287] [c.287] [c.60] [c.174] [c.192] [c.230] [c.391] [c.496] [c.640] [c.916] [c.311] [c.46] [c.129] [c.287]**

Macmillan encyclopedia of energy Volumes 1,2,3 (2001) -- [ c.732 ]