MCSS technique

Finally, we mention two methods for de novo library design. Caflisch [127] applied the MCSS technique generating fragment placements which are subsequently connected. The DREAM++ software [128] combines tools for fragment placement and selection. The selection process is done such that only a small set of well characterized organic reactions are needed to create the library. 

A major drawback of MD and MC techniques is that they calculate average properties. The free energy and entropy fiinctions caimot be expressed as simple averages of fimctions of the state point y. They are directly coimected to the logaritlun of the partition fiinction, and our methods do not give us the partition fiinction itself Nonetheless, calculating free energies is important, especially when we wish to detennine the relative thenuodynamic stability of different phases. How can we approach this problem ... 

Monte Carlo (MC) techniques for molecular simulations have a long and rich history, and have been used to a great extent in studying the chemical physics of polymers. The majority of molecular modeling studies today do not involve the use of MC methods however, the sampling capabiUty provided by MC methods has gained some popularity among computational chemists as a result of various studies (95—97). Relevant concepts of MC are summarized herein. 

There are basically two different computer simulation techniques known as molecular dynamics (MD) and Monte Carlo (MC) simulation. In MD molecular trajectories are computed by solving an equation of motion for equilibrium or nonequilibrium situations. Since the MD time scale is a physical one, this method permits investigations of time-dependent phenomena like, for example, transport processes [25,61-63]. In MC, on the other hand, trajectories are generated by a (biased) random walk in configuration space and, therefore, do not per se permit investigations of processes on a physical time scale (with the dynamics of spin lattices as an exception [64]). However, MC has the advantage that it can easily be applied to virtually all statistical-physical ensembles, which is of particular interest in the context of this chapter. On account of limitations of space and because excellent texts exist for the MD method [25,61-63,65], the present discussion will be restricted to the MC technique with particular emphasis on mixed stress-strain ensembles. 

By far the most common methods of studying aqueous interfaces by simulations are the Metropolis Monte Carlo (MC) technique and the classical molecular dynamics (MD) techniques. They will not be described here in detail, because several excellent textbooks and proceedings volumes (e.g., [2-8]) on the subject are available. In brief, the stochastic MC technique generates microscopic configurations of the system in the canonical (NYT) ensemble the deterministic MD method solves Newton s equations of motion and generates a time-correlated sequence of configurations in the microcanonical (NVE) ensemble. Structural and thermodynamic properties are accessible by both methods the MD method provides additional information about the microscopic dynamics of the system. 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

Most liquid phase molecular simulations with explicit atomic polarizabilities are performed with MD rather than MC techniques. This is due to the fact that, despite its general computational simplicity, MC with explicit polarization [173, 174] requires that Eq. (9-21) be solved every MC step, when even one molecule in the system is moved, and the number of configurations in an average Monte Carlo computation is orders of magnitude greater than in a MD simulation. For nonpolarizable, pairwise-additive models, MC methods can be efficient because only the... 

One can apply the MC technique to the same molecular model, as explored in MD. One can use the same box and the same molecules that experience exactly the same potentials, and therefore the results are equally exact for equilibrium membranes. However, MC examples of this type are very rare. One of the reasons for this is that there is no commercial package available in which an MC strategy is combined with sufficient chemistry know-how and tuned force fields. Unlike the MD approach, where the phase-space trajectory is fixed by the equations of motion of the molecules, the optimal walkthrough phase space in an MC run may depend strongly on the system characteristics. In particular, for densely packed layers, it may be very inefficient to withdraw a molecule randomly and to let it reappear somewhere else in... 

With the Monte Carlo technique, a very large number of membrane problems have been worked on. We have insufficient space to review all the data available. However, the formation of pores is of relevance for permeation. The formation of perforations in a polymeric bilayer has been studied by Muller by using Monte Carlo simulation [67] within the bond fluctuation model. In this particular MC technique, realistic moves are incorporated, such that the number of MC steps can be linked to a simulated time. 

Coarse-grained polymer models neglect the chemical detail of a specific polymer chain and include only excluded volume and topology (chain connectivity) as the properties determining universal behavior of polymers. They can be formulated for the continuum (off-lattice) as well as for a lattice. For all coarse-grained models, the repeat unit or monomer unit represents a section of a chemically realistic chain. MD techniques are employed to study dynamics with off-lattice models, whereas MC techniques are used for the lattice models and for efficient equilibration of the continuum models.36 2 A tutorial on coarse-grained modeling can be found in this book series.43... 

The fifth section provides a brief description of multicanonical techniques and their use and applicability in MC simulations. We touch upon the benefits that MC techniques provide in sampling ensembles other than the canonical ensemble for biomacromolecular systems. 

In 1977, Jochum et aZ.12,14 developed the multiple ion counting (MC) technique using an old spark source mass spectrometer with 20 separate channeltrons 1.8 mm wide for simultaneous electrical ion detection. The sensitivity was increased by a factor of 20 compared to SSMS with ion detection using a photoplate and the precision of the analytical results was improved. 

Quantitative depth profiling using polyatomic MCs+ and MCs2+ ions instead of atomic ions M= ions is well established in surface analysis using SIMS. The MCs+ technique, which reduces matrix effects significantly, was proposed by Gao in 1988.100 The formation of MCs+ has been explained by the recombination of sputtered neutral atoms (M) with... 

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... 

The efficiency of the CB-MC technique has been used by Maginn et al. (769), who considered the low-occupancy thermodynamics of sorption of alkanes as long as C25 in silicalite. The locations of such long molecules are no longer correctly predicted by considering the end-to-end vector and the chain midpoint. To overcome this problem, a coarse-graining technique was used to describe both the adsorbate and the zeolite, allowing for accurate microscopic characterization. 

Once the potential is chosen, Monte Carlo (MC) and molecular dynamics (MD) simulations form important tools for calculating phase equilibria [176]. With one notable exception [51], only MC techniques were employed. Methodological developments in MC techniques were addressed in a previous volume of this series [177], so that we summarize here only some aspects important for the treatment of ionic fluids. 

The overview in this section is intended to only provide a brief background for discussion of MD and MC techniques as applied to thermodynamic results. For the reader interested in MD or MC details, Table 5.11 includes a list of standard references. The LD technique, which was originally applied for low temperature solids, will not be considered in this brief overview (see the standard reference in Table 5.11). Kinetic results for molecular simulations are in Chapter 3. 

Except the kinetic equations, now various numerical techniques are used to study the dynamics of surfaces and gas-solid interface processes. The cellular automata and MC techniques are briefly discussed. Both techniques can be directly connected with the lattice-gas model, as they operate with discrete distribution of the molecules. Using the distribution functions in a kinetic theory a priori assumes the existence of the total distribution function for molecules of the whole system, while all numerical methods have to generate this function during computations. A success of such generation defines an accuracy of simulations. Also, the well-known molecular dynamics technique is used for interface study. Nevertheless this topic is omitted from our consideration as it requires an analysis of a physical background for construction of the transition probabilities. This analysis is connected with an oscillation dynamics of all species in the system that is absent in the discussed kinetic equations (Section 3). 

An interpretation of the results for catalytic reaction kinetics on active supported nanoparticles on the scale down to 10nm has been obtained by the MC technique [285]. The technique allows the peculiarities of the reaction performance on the nanometer scale, including the inherent heterogeneity of metal crystallites as well as spontaneous and adsorbate-induced changes of the shape and degree of dispersion of supported catalysts. 

The main goal of simulation methods is to obtain information on the spatial and temporal behavior of a complex system (a material), that is, on its structure and evolution. Simulation methods are subdivided into atomistic and phenomenological methods. Atomistic methods directly consider the evolution of the system of interest at the atomic level with regard to the microscopic structure of the substance. These methods include classical and quantum MD and various modifications of the MC technique. Phenomenological methods are based on macroscopic equations in which the atomistic nature of the material is not directly taken into account. Within the multiscale approach, both groups of methods mutually complement each other, which permits the physicochemical system under study to be described most comprehensively. 

To represent the molecular structure with reasonable accuracy as well as to reduce computational time, the coarse-grained, bead-spring model [Fig. 1.28(b)] was employed to approximate a PFPE molecule. This simplifies the detailed atomistic information while preserving the essence of the molecular internal structure [167]. The off-lattice MC technique with the bead-spring model was used to examine nanoscale PFPE lubricant film structures and stability with internal degrees of freedom [168],... 

With the use of the MCs+ technique to reduce matrix effects in SIMS, Gao et al measured the composition of InxGai.xN alloys and confirmed the validity of this technique with the RBS method [12], It was shown that the SIMS-MCs+ method can provide very accurate measurements of composition on complex structures and devices [13],... 

In 1977, Jochum et developed the multiple ion counting (MC) technique using an old... 

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