# Theoretical Approaches

Physical adsorption may now, in fact, be seen as a preamble to chemisorption in heterogeneous catalysis, that is, as a precursor state (see Section XVIII-4). Physical adsorption is not considered to involve chemical bond formation, however, and the current theoretical approaches deal mainly with the relatively long range electrostatic and van der Waals types of forces. The quantum mechanics of chemical bonding is thus largely missing although aspects of it appear in the treatment of physisorption on metal surfaces. Steele [8] provides an extensive review of molecular interactions in physical adsorption generally, and for the case of molecules adsorbed on the graphite basal plane in particular [95]. [c.634]

Because this problem is complex several avenues of attack have been devised in the last fifteen years. A combination of experimental developments (protein engineering, advances in x-ray and nuclear magnetic resonance (NMR), various time-resolved spectroscopies, single molecule manipulation methods) and theoretical approaches (use of statistical mechanics, different computational strategies, use of simple models) [5, 6 and 7] has led to a greater understanding of how polypeptide chains reach the native confonnation. [c.2642]

An excellent summary of theoretical approaches to VER, their significance and comparison to experiment. [c.3053]

The magnitude of a coupling constant decreases as the number of intervening bonds between the coupled nuclei increases and typically three bonds, or is the detectable limit. The case is of particular interest because the magnitude of these constants is dependent on the conformation angle defined by the three bonds (12). The use of equations and theoretical approaches to the calculation of coupling constants has been reviewed (13). In general, the value of is maximum when coupled species are trans to one another. Within particular classes of compounds trigonometric functions of the torsion angle such as the Karplus equation may be used to predict the angle from the magnitude of the J. [c.403]

Settling of Suspensions. As the concentration of the suspension iacreases, particles get closer together and iaterfere with each other. If the particles are not distributed uniformly, the overall effect is a net iacrease ia settling velocity because the return flow caused by volume displacement predominates ia particle-sparse regions. This is the weU-known effect of cluster formation which is significant only ia nearly monosized suspensions. For most practical widely dispersed suspensions, clusters do not survive long enough to affect the settling behavior and, as the return flow is more uniformly distributed, the settling rate steadily declines with increasing concentration. This phenomenon is referred to as hindered settling and can be theoretically approached from three premises (4) as a Stokes law correction by iatroduction of a multiplying factor by adopting effective fluid properties for the suspension different from those of the pure fluid and by determination of bed expansion using a modified Carman-Kozeny equation. These three approaches yield essentially identical results [c.317]

Numerous theoretical approaches have been used in predicting and describing the bonding and stmcture of metal carbonyls. The Sidgwick concept of effective atomic number, or the 18-electron rule, has been particularly useful in predicting formulas, and molecular orbital and ligand field calculations have provided additional insight to the more detailed features of bonding in metal carbonyls. [c.62]

Two theoretical approaches relating to the nominal fragment size achieved in dynamic fracture events have been discussed. The first is based on the inherently reasonable concept of existing fracture-producing flaws within the fragmenting body, where fragment size (or number) is necessarily correlated with the description of the flaw distribution. A second approach is based only on energy balance concepts, where no recourse to a pre-existing flaw distribution is made. Considering the diverse applications for which this latter approach provides reasonable fragment size predictions, energy balance ideas clearly play an important role in the fragmentation process. In outward appearance, these two theoretical descriptions do not seem compatible. [c.293]

Prior to the elucidation of the 3D structure of proteins via experimental methods, theoretical approaches made significant inroads toward understanding protein structure. One of the most significant contributions was made by Pauling and Corey [8] in 1951, when they predicted the existence of the main elements of secondary structure in proteins, the a-helix and (3-sheet. Their prediction was soon confirmed by Perutz [9], who made the first glimpse of the secondary structure at low resolution. This landmark work by Pauling and Corey marked the dawn of theoretical studies of biomolecules. It was followed by prediction of the allowed confonnations of amino acids, the basic building block of proteins, in 1963 by Ramachandran et al. [10]. This work, which was based on simple hard-sphere models, indicated the potential of computational approaches as tools for understanding the atomic details of biomolecules. Energy minimization algorithms with an explicit potential energy function followed readily to assist in the refinement of model strucmres of peptides by Scheraga [11] and of crystal structures of proteins by Levitt and Lifson [12]. [c.2]

II. RELATIONSHIPS BETWEEN EXPERIMENTAL AND THEORETICAL APPROACHES TO STUDYING DRUG-RECEPTOR INTERACTIONS [c.352]

Eor further details of the history, experimental set-up, and theoretical approaches of LEED please refer to books by Pendry [2.241], van Hove and Tong [2.242], van Hove, Weinberg, and Chan [2.243], and Clarke [2.244]. This article relies extensively on these works. [c.72]

Other procedures for generating chains from polycyclic fused ring systems and for disconnecting fused rings which use simple graph theoretical approaches have been described.35 They make use of the dual of the molecular graph, i.e. the figure generated by drawing a line between the centers of each fused ring pair through the corresponding fusion bond.35 [c.41]

Sohnel, O., Chianese, A. and Jones, A.G., 1991. Theoretical approaches to the design of precipitation systems The present state of the art. Chemical Engineering Communications, 106, 151-175. [c.323]

Finally, in Sec. IV, two examples of the application of the Monte Carlo simulation to investigate the structure and thermodynamic properties of adlayers of an associating fluid are given. The results of simulations are compared with those from theoretical approaches. In conclusion, we discuss some methodological perspectives in the discussed area of research. [c.171]

Adsorption of hard sphere fluid mixtures in disordered hard sphere matrices has not been studied profoundly and the accuracy of the ROZ-type theory in the description of the structure and thermodynamics of simple mixtures is difficult to discuss. Adsorption of mixtures consisting of argon with ethane and methane in a matrix mimicking silica xerogel has been simulated by Kaminsky and Monson [42,43] in the framework of the Lennard-Jones model. A comparison with experimentally measured properties has also been performed. However, we are not aware of similar studies for simpler hard sphere mixtures, but the work from our laboratory has focused on a two-dimensional partly quenched model of hard discs [44]. That makes it impossible to judge the accuracy of theoretical approaches even for simple binary mixtures in disordered microporous media. [c.306]

Our main focus in this chapter has been on the applications of the replica Ornstein-Zernike equations designed by Given and Stell [17-19] for quenched-annealed systems. This theory has been shown to yield interesting results for adsorption of a hard sphere fluid mimicking colloidal suspension, for a system of multiple permeable membranes and for a hard sphere fluid in a matrix of chain molecules. Much room remains to explore even simple quenched-annealed models either in the framework of theoretical approaches or by computer simulation. [c.341]

Theoretical Approaches to the Kinetics of Adsorption, Desorption, and Reactions at Surfaces [c.439]

From the experimental results and theoretical approaches we learn that even the simplest interface investigated in electrochemistry is still a very complicated system. To describe the structure of this interface we have to tackle several difficulties. It is a many-component system. Between the components there are different kinds of interactions. Some of them have a long range while others are short ranged but very strong. In addition, if the solution side can be treated by using classical statistical mechanics the description of the metal side requires the use of quantum methods. The main feature of the experimental quantities, e.g., differential capacitance, is their nonlinear dependence on the polarization of the electrode. There are such sophisticated phenomena as ionic solvation and electrostriction invoked in the attempts of interpretation of this nonlinear behavior [2]. [c.801]

Our second goal is to introduce these simple phenomena in a statistical mechanical scheme such that the calculations keep a transparent significance at each step. Nowadays, the predictions of theoretical approaches depend on approximations of a high level of technicality in the domain of liquid state theory. These approximations seem to have a mathematical rather than [c.801]

The book is divided into 18 chapters written by different experts on various aspects. In many areas of contemporary science, one is confronted with the problem of theoretical descriptions of adsorption on solids. This problem is discussed in the first part of the volume. The majority of interfacial systems may be considered as fluids in confinement. Therefore, the first chapter is devoted to the behavior of confined soft condensed matter. Because quantum mechanics is a paradigm for microscopic physics, quantum effects in adsorption at surfaces are considered (Chapter 2). The theory of simple and chemically reacting nonuniform fluids is discussed in Chapters 3 and 4. In Chapters 5 and 6, the current state of theory of adsorption on energetically and geometrically heterogeneous surfaces, and in random porous media, is presented. Recent molecular computer-simulation studies of water and aqueous electrolyte solutions in confined geometries are reviewed in Chapter 7. In Chapter 8, the Monte Carlo simulation of surface chemical reactions is discussed within a broad context of integrated studies combining the efforts of different disciplines. Theoretical approaches to the kinetic of adsorption, desorption, and reactions on surfaces are reviewed in Chapter 9. [c.944]

The existing books cover the simple, rather than the advanced, theoretical approaches to interfacial systems. This volume should fill this gap in the literature. It is the purpose of this volume to serve as a comprehensive reference source on theory and simulations of various interfacial systems. Furthermore, it shows the power of statistical thermodynamics that offers a [c.958]

The phenomenon of BLEVE is discussed in this chapter. BLEVE is an acronym for boiling liquid, expanding vapor explosion. As indicated in Chapter 2, most BLEVEs are accompanied by fireball radiation, fragmentation, and blast effects. This chapter treats each of these effects separately. First, some general information is given. Next, effects are treated in the following order radiation, fragmentation, and blast. Experimental investigations, theoretical approaches, and prediction methods are given for each effect. [c.156]

Applying Statistical or Theoretical Approaches [c.311]

Various theoretical approaches that have been used so far have indicated the difficulties associated with these problems and have shown that the magnetic behavior of small ferromagnetic clusters is the outcome of a very dehcate interplay among various factors such as the kind of atoms (filling of the d-band), size of the cluster, bond lengths and coordination numbers, as well as the symmetry of the cluster. Each of these factors represent an independent variable of the total energy of the cluster and in the search for the true ground state of the cluster it is necessary to minimize its total energy with respect to a simultaneous variations of all these variables. Thus, the quantitative description of the properties of the magnetic clusters is a very difficult computational problem. As a consequence, while the ah initio calculations " are restricted to very small clusters, (n < 7), the results reported for larger clusters (n > 7) involve total energy optimizations that use severe constraints in one or more of the independent parameters of the system . Among the constraints employed to expedite the calculations the most severe is the one restricting its geometry (symmetry). Furthermore, model approximations, (e.g., the neglect of the s — d interactions in a tight-binding description) seem to introduce significant errors. [c.262]

Figure 16 illustrates wastage on the thick side of an eccentric tube and the wall thickness plot that would result. When wastage is located at this position, the life of the tube may theoretically be extended because material loss is subtracted from the thickest part of the tube. This type of wastage is identified by sharp dips located in the positive half cycle of the thickness plots. Figure 17 is an expanded plot showing wastage located on the thick side of an eccentric tube. On this tube the eccentricity grows from 0,75 mm to 1,50 mm as the scan advances away from the tube sheet. The wastage profile meanwhile develops as the approaches the tube sheet. The maximum wastage of 1,14 mm (30 mm probe travel) is severe enough to drop below the minimum wall thickness of the eccentricity. On occasion significant wastage can remain hidden within an eccentric tube until it emerges below the eccentric minimum. [c.1039]

Nucleation in a cloud chamber is an important experimental tool to understand nucleation processes. Such nucleation by ions can arise in atmospheric physics theoretical analysis has been made [62, 63] and there are interesting differences in the nucleating ability of positive and negative ions [64]. In water vapor, it appears that the full heat of solvation of an ion is approached after only 5-10 water molecules have associated with [c.337]

In the final section, we will survey the different theoretical approaches for the treatment of adsorbed molecules on surfaces, taking the chemisorption on transition metal surfaces, a particularly difficult to treat yet extremely relevant surface problem [1], as an example. Wliile solid state approaches such as DFT are often used, hybrid methods are also advantageous. Of particular importance in this area is the idea of embedding, where a small cluster of surface atoms around the adsorbate is treated with more care than the surroundmg region. The advantages and disadvantages of the approaches are discussed. [c.2202]

This chapter concentrates on describing molecular simulation methods which have a counectiou with the statistical mechanical description of condensed matter, and hence relate to theoretical approaches to understanding phenomena such as phase equilibria, rare events, and quantum mechanical effects. [c.2239]

The dominant theoretical approaches to study molecular processes break the problem down into separate parts, the first being the determination of one or more potential energy surfaces. This involves electronic structure calculations for a large number of nuclear geometties and interpolation techniques [6-8] to provide as accurate as possible a functional form of each PES. Electronic structure methods and algorithms have been developed into efficient codes such as Gaussian [9], and ACES II [10], which can be used with minimal knowledge of electronic structure theory. These and many other codes have made computational chemistry a working tool for the bench chemist on an equal footing with various spectroscopic methods. [c.222]

In this chapter, we give a review of results of ab initio treatments of the R-T effect and spin-orbit coupling in hiatomic and tetraatomic molecules. We have tried to present a comprehensive up to date literature survey and to compare various approaches with one another. Our prime goal was to present the development of ideas that finally resulted in those methods that aie nowadays widely used to produce numerical results serving to interpret and to predict features of concrete moleculai systems. A consequence of these restrictions is that we only mentioned those model treatments in which the main goal is rather to explain qualitative aspects of the vibronic coupling than to consider pai ticulai molecules, and the effective Hamiltonian approaches that do not rely on ab initio computations we did not even mention several alternative theoretical approaches [168,169] not directly on the main stream we followed in this study. We have tried to document that the handling of the R-T effect by means of modem ab initio techniques not only offers reliable interpretation of experimental findings but also has reached the level of numerical accuracy so that it can compete with high-resolution spechoscopy. [c.532]

Abstract. Protein-ligand interactions control a majority of cellular processes and are the basis of many drug therapies. First, this paper summarizes experimental approaches used to characterize the interactions between proteins and small molecules equilibrium measurement of binding constant and standard free energy (jf binding and the dynamic approach of ligand extraction via atomic force microscopy. Next, the paper reviews ideas about the origin of different component terms that contribute to the the stability of protein-ligand complexes. Then, theoretical approaches to studying protein-small molecule interactions are addressed, including forced extraction of ligand and perturbation methods for calculating potentials of mean force and free energies for molecular transformation. Last, these approaches are illustrated with several recent studies from our laboratory (1) binding of water in cavities inside proteins, (2) calculation of binding free energy from first principles by a new application of molecular transformation, and (3) extraction of a small ligand (xenon) from a hydrophobic cavity in mutant T4-lysozyme L99A. [c.129]

Experimental methods such as X-ray ciystallography, electron diffraction, 2D NMR, IR, or microwave spectroscopy observe a molecule under certain physical and chemical conditions, c.g., in the solid state or in solution. Theoretical approaches rely on numerical calculations and empirical approaches of various levels of sophistication depending on the method applied in order to predict or to generate a 3D molecular model. Therefore, the deployment of machine.s and computers ha.s a long tradition in this field of chemoinformatics, automatic 3D stmeture generation. The term automatic 3D struc ture generators" describes computer programs which arc capable of automatically predicting, without any intervention by the user, a 3D molecular model starting from the constitution and the stereochemical information of a molecule under consideration (sec Figure 2-93, Clearly there is a need for these methods, as demonstrated by the misbalancc between the approximately 270000 compounds with an c.xpcrimcntalJy determined 3D structure and the number about 25 million) of known compound.s. [c.95]

The input to a minimisation program consists of a set of initial coordinates for the system. The initial coordinates may come from a variety of sources. They may be obtained from an experimental technique, such as X-ray crystallography or NMR. In other cases a theoretical method is employed, such as a conformational search algorithm. A combination of experimenfal and theoretical approaches may also be used. For example, to study the behaviour of a protein in water one may take an X-ray structure of the protein and immerse it in a solvent bath, where the coordinates of the solvent molecules have been obtained from a Monte Carlo or molecular dynamics simulation. [c.275]

Jhh spin-coupling results in first-order coupling figures that are easy to interpret. Only the long-range couplings of protons a- to nitrogen are uncertain because of their broad signals. Besides the already mentioned systematic studies concerning signal assignments, where the coupling constants are usually given, three studies are particularly devoted to the determination of homonuclear couplings Bojesen et al. (113), Jacobsen, et al. (252), and Bildsoe and Schaumburg (251). There is a Jhh coupling of approximately 3.2 Hz between H(4) and H(5), a Jhh coupling of approximately 2 Hz between H(2) and H(5), and a very low Jhh coupling of 0.4 to 0.5 Hz between H(2) and H(4). This last coupling does not usually appear because of the signal broadening due to the nitrogen atom, but could be revealed by certain solvents (235) or by nitrogen decoupling (255). Some attempts to calculate these couplings based on results of theoretical approaches have been performed using the method of finite perturbations or that of state summation (256). The results have not been very convincing (251, 252). Only in the case of Jhh in fluorinated derivatives of thiazole (253) was it possible to obtain, by CNDO calculations, Jfh coupling constants in reasonable agreement with the experimental values (251). [c.76]

Phosphoms-31 [7723-14-0] also is readily accessible for nmr because of its spin of 1/2, 100% natural abundance, magnetogyric ratio of 10.8, 600-ppm chemical shift window, and moderate relaxation times. Early P studies were done in CW mode (24,25). The availabiUty of ft instmmentation led to improved sensitivity such that analysis of millimolar solutions in standard 5-mm tubes has become routine. Technically, the primary difficulty Hes in achieving satisfactory digital resolution using this large chemical shift window. Both the large chemical shift Hterature and theoretical approaches to the P chemical shift are discussed elsewhere (26). The occurrence of phosphoms in cell membrane phosphoHpids and in nucleotides has led to its use as a reporter on stmcture and dynamics in en2yme complexes, cell membranes, and nucleic acids as well as organophosphorous compounds (27). In nucleic acid studies the P chemical shift is considered to report on both local conformation and sequence. The assignments of specific resonances to individual nucleotides usually involves HETCOR-type studies of P—correlations similar to studies of multidimensional nmr (28). Among the more [c.405]

Other theoretical approaches which have not been discussed here may have merit and, in several cases, are being actively pursued. Dynamic geometric statistical methods, which include active crack processes such as growing and intersecting cracks and interacting stress relief waves, may go a step beyond strictly static geometric methods (Mott, 1947 Gilbert, 1967 Grady, 1981a, b Grady and Kipp, 1985). Again however, this is a study which is most easily implemented in one dimension and can be expected to increase in complexity when extended to two and three dimensions. [c.311]

The molecular and liquid properties of water have been subjects of intensive research in the field of molecular science. Most theoretical approaches, including molecular simulation and integral equation methods, have relied on the effective potential, which was determined empirically or semiempirically with the aid of ab initio MO calculations for isolated molecules. The potential parameters so determined from the ab initio MO in vacuum should have been readjusted so as to reproduce experimental observables in solutions. An obvious problem in such a way of determining molecular parameters is that it requires the reevaluation of the parameters whenever the thermodynamic conditions such as temperature and pressure are changed, because the effective potentials are state properties. [c.422]

Judging from our present knowledge, such a description is far from the whole story. The article of Benderskii and Goldanskii [1992] addressed mostly the vast amount of experimental data accumulated thus far. On the other hand, the major applications of QTST involved gas-phase chemical reactions, where quantum effects were not dominant. All this implies that there is a gap between the possibilities offered by modern quantum theory and the problems of low-temperature chemistry, which apparently are the natural arena for testing this theory. This prompted us to propose a new look at this field, and to consistently describe the theoretical approaches which are adequate even at T = 0. [c.7]

At a meeting at Battelle Memorial Institute in Ohio in 1967, Kaufman demonstrated some approximate calculations of binary phase diagrams using an ideal solution model, but met opposition particularly from solid-state physicists who preferred to use first-principles calculations of electronic band structures instead of thermodynamic inputs. For some years, this became the key battle between competing approaches. At about this time, Kaufman began exchanging letters with William Hume-Rothery concerning the best way to represent thermodynamic equilibria. Thereupon, Hume-Rothery, in his capacity as editor of Progress in Materials Science, invited Kaufman to write a review about lattice stabilities of phases, which appeared (Kaufman 1969) shortly after Hume-Rothery s death in 1968. Shortly before his death, Hume-Rothery had written to Kaufman to say that he was not unsympathetic to any theory which promises reasonably accurate calculations of phase boundaries, and saves the immense amount of work which their experimental determination involves , but that he was still sceptical about Kaufman s approach. This extract comes from a full account of the history of CALPHAD in Chapter 2 of a recent book (Saunders and Miodownik 1998). In his short overview, Kaufman took great trouble to counter Hume-Rothery s reservations, and he also gave a fair account of the competing band-theoretical approaches. The imperative need to account for the competition in stability between alternative phases, actual and potential, was central to Kaufman s case. [c.483]

Problems of the theoretical descripti i of nonequilibrium statistical systems are important for various areas of physics. For equilibrium systems, such a description is given by the Gibbs distribution and statistical thermodynamics, but for states far from equilibrium there are no analogous standard apjrroaches available. The elaboration of suitable approaches is of particular interest for configurational alloy kinetics, the evolution of the atomic distribution in nonequilibrium alloys. The raicrostructure and macroscopic properties of such alloys, e.g. strength and plasticity, depend crucially on their thermal and mechanical history, for example, on the particular kinetic path of the phase transformation. A number of theoretical approaches have been proposed in that field, e.g. . However, these approaches either treat the uniform alloy case which excludes from consideration most applications of interest, or use various unclear approximations, such as the extrapolation of the linear Onsager equation for weakly nonequilibrium states to the nonlinear region of states far from equilibrium , which can result in significant errors . [c.101]

Soft mode refers to a mode of lattice vibration with the eigenvector corresponding to the statie atomie displaeements whieh result in the transformed phase and for whieh the frequeney, co —> 0 as the temperature is lowered towards the transformation temperature, Tm. The softening may take plaee at the zone eentre, in whieh case there is a decrease in the eorresponding elastie modulus, or at a wave vector close to a reciprocal space lattiee vector for the new phase. The origin of the soft-mode behaviour is well understood in terms of the renormalization of the mode ffequeneies due to anharmonie effects. A less well understood feature of the soft-mode transition is the development of an elastic component in the phonon scattering, the so-called central peak , which diverges as Tm is approached. Two theoretical approaches have been proposed one dynamieal and linked with the anharmonie behaviour, the other arising from the statie distortion of the lattiee due to defect-indueed strain fields. [c.333]

Detemiination of a PES from spectroscopic data generally requires fitting a parameterized surface to the observed energy levels together with theoretical and other experimental data. This is a difficult process because it is not easy to devise realistic fimctional representations of a PES with parameters that are not strongly correlated, and because calculation of the vibrational and rotational energy levels from a PES is not straightforward and is an area of current research. The fomier issue will be discussed further in section Al.5.5.3. The approaches available for the latter currently include numerical integration of a truncated set of close-coupled equations, methods based on the discrete variable representation and diffusion Monte Carlo teclmiqiies [28]. Some early and fine examples of potential energy surfaces detemiined in this maimer include the H2-rare gas surfaces of LeRoy and coworkers [97, 98 and 99], and the hydrogen halide-rare gas potential energy surfaces of Hutson [100. 101 and 102]. More recent work is reviewed by van der Avoird et aJ [103]. [c.201]

See pages that mention the term

**Theoretical Approaches**:

**[c.2237] [c.606] [c.187] [c.93] [c.647] [c.760] [c.252] [c.35]**

See chapters in:

** Chemical kinetics the study of reaction rates in solution
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