Solution space, structure

In the context of studies on the coordination of organotin(IV) moieties by thiolic S and heterocyclic N atoms, diorganotin(IV) complexes of 2-mercapto-pyridine, R2Sn(SPy)2 and R2SnCl(SPy), have been characterized in the solid state and in solution. The structure of the latter complex (R = Ph) was determined by XRD (Figure 17). The crystal is monoclinic in the space... 

The vertical reactor simulations reported In this paper typically Involved 14,000 unknowns and took 25 CPU seconds per Newton Iteration on a Cray-2. The tracing of a complete family of solutions for one parameter (e.g. susceptor temperature) cost approximately 25 CPU minutes. The latter number underscores the advantage of using supercomputers to understand the structure of the solution space for physical problems which often Involve many parameters. 

The large size of the solution space for combinatorial optimization problems forces us to represent it implicitly. The branch-and-bound algorithm encodes the entire solution space in a root node, which is successively expanded into branching nodes. Each of these nodes represents a subset of the original solution space specialized to contain some particular element of the problem structure. 

Having formally defined the branching structure, we must now make explicit the mechanisms by which we can eliminate subsets of the solution space from further consideration. Ibaraki (1978) has stated three major mechanisms for controlling the evolution of the branch-and-bound search algorithms, by eliminating potential solution through... 

An important extension of lipid-solute interaction components [20] to membrane partitioning is provided by solute molecular structure. Spacing between polar and nonpolar regions (Fig. 8) within a solute molecule may result in significant distortion of the KpDm product across the membrane polar headgroup/lipid core interface [21], Such interactions may be responsible for deviations from projected transport predictions based on simple partitioning theory translating to deviations from predicted absorption kinetics [1],... 

Keywords Powder diffraction Molecular solids Organic crystals Crystal structure Direct space Structure solution Structure determination... 

Validation Before Direct-Space Structure Solution. 147... 

Aspects of validation prior to direct-space structure solution are focused on (1) establishing the correct representation of molecular geometry to be used in the direct-space structure solution calculation and (2) establishing independent evidence for the correct number of molecules in the asymmetric unit. 

Fig. 10.1 (Continued), (b) Distribution of local optima in solution space for a basic amino acid dope (30% Arg, 30% Lys, 40% His). Due to die structure of die genetic code, a perfect soludon of fracdons of nucleotides for die given example does not exist. Instead, several islands of different suboptimal solutions are found. Seven local optima, marked by different colors (see die color version on die CD diat accompanies diis book), can be identified. Note diat die SOM uses toroidal boundaries, i.e., die left-most and right-most points lie close togedier, as do die top and bottom points.

Multiple Objective Decision Analysis (MODA) designs the most preferred alternative within a (usually continuous) solution space using a mathematical programming structure to optimize the level of a set of quantifiable objectives. 

Figure 3.17 Comparison between experiment (dashed curve) and calculations combining the polarizable continuum model for solute electronic structure and continuum dielectric theory of solvation dynamics in water. SRF(t) stands for S(t) in our notation. The calculations are for a cavity based on a space-filling model of Cl53, while the experiments are for C343. The two sets of theoretical results correspond to using water e(o>) from simulation (full curve) of SPC/E water and from a fit to experimental data (dash-dotted curve). (Reprinted from F. Ingrosso, A. Tani andJ. Tomasi, J. Mol. Liq., 1117, 85-92. Copyright (2005), with permission from Elsevier).

In order to correlate the solid state and solution phase structures, molecular modelling using the exciton matrix method was used to predict the CD spectrum of 1 from its crystal structure and was compared to the CD spectrum obtained in CHC13 solutions [23]. The matrix parameters for NDI were created using the Franck-Condon data derived from complete-active space self-consistent fields (CASSCF) calculations, combined with multi-configurational second-order perturbation theory (CASPT2). 

FIGURE 3 Depiction of the heuristic search procedure which employs spectral information to reduce the solution space of structures to one or several solutions. 

The same situation obtains when the solution space is formed by candidate structures generated from any preliminary known information, e.g., an empirical formula. With any increase in the number of atoms in... 

Our efforts have been directed toward the development of a new strategy for the construction of a CASE system that incorporates both treatments of the uncertainty inherent in the inverse problem. The uncertainties arise from the combinatorial explosion and the fuzzy character of the spectral information. It is clear that the process of structure elucidation must start from preliminary information considered more or less certain. This information is necessary to constrain the number of candidate structures within the solution space otherwise, this number will be infinite. In more general terms, each piece of information may serve as a constraint on the number of possible candidate structures. It is very... 

Times are currently very exciting in the field of NMR research. From initial research into the proton nucleus of solutions, the science has developed over the past 50 years to the stage where the space structure of proteins is now being analysed. 

The solution NMR structure determination strongly relies on NOE, because inter-atomic distances can be predicted by it. Spatially adjacent hydrogen atoms are coupled by dipole-dipole through space magnetization transfers, and cause the distance-dependent NOE. The dependency is approximated by a rigid two-spin system hypothesis stating that the intensity of the NOE is correlated with r 6 (crude first-order approximation), where r is the distance... 

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