Theoretical Concepts

It is especially timely to review the subject of exciton effects because, with the advent of the X-ray structural model of the Rhodopseudomonas viridis RC [9-12], it is becoming apparent that analyses of exciton effects exhibit a dichotomy. On the one hand there are analyses based on incomplete structural information, on the other there are those based on X-ray structural models. The former generally seem theoretically straightforward and consistent with all experimental data, while the latter tend to be theoretically involuted and inconsistent with at least some of the data. Because the underlying interactions are quite important in photosynthesis, it is worthwhile exploring this situation and trying to understand what underlies it. In Section 2 basic theoretical concepts are briefly summarized. Exciton analyses based on partial structural information are discussed in Sections 3 and 4, and those based on X-ray models are considered in Sections 5-7. 

The resonance interactions that give rise to the exciton effects in spectra are interactions among the electronic transition moments of closely juxtaposed pigment 

TABLE 1 Formulas for calculating exciton stick spectra  

For Chi and BChl, only the lowest 4 (neutral) excited states are considered. These are labelled, in order of ascending energy [27], Qy, 0,, B, and By. 

F can he suppressed hy the high site symmetry of the central atom In many perovskite-like structures of the ABO3 type the lone pair of the B-cat-ion leads not to a structural distortion. In CsPbF3 under ambient conditions no lone-pair activity observed [27], but upon cooling a phase transition is observed that leads to less symmetrical surrounding of Pb by fluoride [28]. 

Lighter elements show a stronger tendency to develop a stereochemically active lone pair than their heavier homologues. For instance, for antimony(III) more distorted structures are known than for bismuth(III) ]29]. 

This view somehow seems dubious in the case of heavier elements like 6 row metals. The high energy separation, as well as the very different spatial distribution of the 6s/6p wavefunctions, which are found for these elements because of the strong influence of relativity, stand against an efficient s-p hybridization. The first excited state of Th (in the gas phase), s p lies 7.4 eV above the 

In order to estabhsh the true nature of lone-pair distortions for 6 row elements, a number of theoretical calculations were undertaken recently. 

An asymmetric surrounding of thallium(I) in a crown ether (or cryptand) is especially surprising as these polyethers generally provide a highly symmetric surrounding for the coordinated cation. In fact, alkali-metal cations Hke sodium. 

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The field of gas phase reaction dynamics has been extensively reviewed elsewhere [1, 2 and 3] in considerably greater detail than is appropriate for this chapter. Here, we begin by simnnarizing the key theoretical concepts and experimental teclmiques used in reaction dynamics, followed by a case study , the reaction F + H2 HF + H, which serves as an illustrative example of these ideas. 

Schlegel H B 1989. Some Practical Suggestions for Optimizing Geometries and Locating Transition States. In Bertran J and IG Csizmadia (Editors). New Theoretical Concepts for Understanding Organic Reactions. Dordrecht, Kluwer, pp. 33-53. 

New Theoretical Concepts for Understanding Organic Reactions J. Beilran, I. G. Csiz-madia, Eds., Kluwer, Dordrecht (1988). 

It is the purpose of this chapter to provide a resume of theoretical concepts which are used in discussing aromatic reactivity. Extended discussion is imnecessary, for many of the concepts are the common currency of organic chemistry, and have been frequently expounded. - ... 

In this section we examine some examples of cross-linked step-growth polymers. The systems we shall describe are thermosetting polymers of considerable industrial importance. The chemistry of these polymerization reactions is more complex than the hypothetical AB reactions of our models. We choose to describe these commercial polymers rather than model systems which might conform better to the theoretical developments of the last section both because of the importance of these materials and because the theoretical concepts provide a framework for understanding more complex systems, even if they are not quantitatively successful. 

Extension of the appHcations of polymethine dyes has required special spectral and other characteristics. As a rule, the search for and synthesis of promising new compounds having desired properties imply the preliminary estimation of their most important parameters on the basis of elaborated theoretical conceptions. Thus, an effective way of governing electron properties consists of the variation of molecular topology of polymethines. 

Internal and External Phases. When dyeing hydrated fibers, for example, hydrophUic fibers in aqueous dyebaths, two distinct solvent phases exist, the external and the internal. The external solvent phase consists of the mobile molecules that are in the external dyebath so far away from the fiber that they are not influenced by it. The internal phase comprises the water that is within the fiber infrastmcture in a bound or static state and is an integral part of the internal stmcture in terms of defining the physical chemistry and thermodynamics of the system. Thus dye molecules have different chemical potentials when in the internal solvent phase than when in the external phase. Further, the effects of hydrogen ions (H" ) or hydroxyl ions (OH ) have a different impact. In the external phase acids or bases are completely dissociated and give an external or dyebath pH. In the internal phase these ions can interact with the fiber polymer chain and cause ionization of functional groups. This results in the pH of the internal phase being different from the external phase and the theoretical concept of internal pH (6). 

Thus the concentration of cell-0 is dependent on the internal pH (—log[i/) ]) of the fiber. This is essentiaHy a theoretical concept because H ] caimot be measured directiy. 

An acceptable reconciliation of inherent flaw and fracture energy concepts has not been achieved and provides an area of current study. The two theoretical concepts will be discussed, and several applications in fragment-size prediction will be described. We will make comparisons between the two fragmentation approaches and attempt to identify some conditions which determine when one or the other method applies. 

In this situation computer simulation is useful, since the conditions of the simulation can be chosen such that full equihbrium is established, and one can test the theoretical concepts more stringently than by experiment. Also, it is possible to deal with ideal and perfectly flat surfaces, very suitable for testing the general mechanisms alluded to above, and to disregard in a first step all the complications that real substrate surfaces have (corrugation on the atomistic scale, roughness on the mesoscopic scale, surface steps, adsorbed impurities, etc.). Of course, it may be desirable to add such complications at a later stage, but this will not be considered here. In fact, computer simulations, i.e., molecular dynamics (MD) and Monte Carlo (MC) calculations, have been extensively used to study both static and dynamic properties [11] in particular, structural properties at interfaces have been considered in detail [12]. 

Clash between Experimental Parameters and Simple Theoretical Concepts... 

Theoretical concepts for generating electricity from ocean currents such, as the Gulf Stream, and salinity gradients (differences in salt content) are being investigated. More research and development is required before these concepts reach the stage of demonstration power plants. 

Part A, dealing with the Fundamentals of Quantitative Chemical Analysis, has been extended to incorporate sections of basic theory which were originally spread around the body of the text. This has enabled a more logical development of theoretical concepts to be possible. Part B, concerned with errors, statistics, and sampling, has been extensively rewritten to cover modern approaches to sampling as well as the attendant difficulties in obtaining representative samples from bulk materials. The statistics has been restructured to provide a logical, stepwise approach to a subject which many people find difficult. 

The modern approach to chemical education appears to be strongly biased toward theories, particularly quantum mechanics. Many authors have remarked that classical chemistry and its invaluable predictive rules have been downgraded since chemistry was put into orbit around physics. School and undergraduate courses as well as textbooks show an increasing tendency to begin with the establishment of theoretical concepts such as orbitals and hybridization. There is a continuing debate in the chemical literature on the relative merits of theory as opposed to qualitative or descriptive chemistry 1-6). To quote the late J. J. Zucker-man who supported the latter approach (3). 

The problems which the orbital approximation raises in chemical education have been discussed elsewhere by the author (Scerri [1989], [1991]). Briefly, chemistry textbooks often fail to stress the approximate nature of atomic orbitals and imply that the solution to all difficult chemical problems ultimately lies in quantum mechanics. There has been an increassing tendency for chemical education to be biased towards theories, particularly quantum mechanics. Textbooks show a growing tendency to begin with the establishment of theoretical concepts such as atomic orbitals. Only recently has a reaction begun to take place, with a call for more qualitatively based courses and texts (Zuckermann [1986]). A careful consideration of the orbital model would therefore have consequences for chemical education and would clarify the status of various approximate theories purporting to be based on quantum mechanics. 

As indicated in the Preface, this book does not claim to be comprehensive. Fortunately there are a number of other books which cover all or some aspects of diazo chemistry and can be recommended for further reading. Some of these will be mentioned briefly in this section. Older books are not included. The latter are still useful, however, for chemists who are interested in the future of their science not just from a pragmatic viewpoint, but also with regard to identifying potentially fruitful future scientific developments based on old problems. Such problems were frequently not followed up in the past because no suitable methods or theoretical concepts were available at that time - but the necessary methods may be already available today or may become so in the future ... 

No unifying theoretical concepts have been recognized which can be used to provide satisfactory criteria for the comprehensive classification of the kinetics and mechanisms of reactions involving solids. Thus the scope and treatment of the subject cannot be entirely systematic. General problems encountered during any attempt to review the field include the following. 

True detector linearity is, in fact, a theoretical concept, and despite the claims by many manufacturers, LC detectors can only tend to exhibit this ideal response. As the linearity of the detector will determine the accuracy of the analysis, it is important to have some method for measuring detector linearity that can describe it in numerical terms. A method for linearity measurement was proposed by Scott and Fowlis (3), who assumed that for a nearly linear detector the response of the detector could be expressed by the following equation. 

To address these challenges, chemical engineers will need state-of-the-art analytical instruments, particularly those that can provide information about microstmctures for sizes down to atomic dimensions, surface properties in the presence of bulk fluids, and dynamic processes with time constants of less than a nanosecond. It will also be essential that chemical engineers become familiar with modem theoretical concepts of surface physics and chemistry, colloid physical chemistry, and rheology, particrrlarly as it apphes to free surface flow and flow near solid bormdaries. The application of theoretical concepts to rmderstanding the factors controlling surface properties and the evaluation of complex process models will require access to supercomputers. 

Sxx is the sum of squares of the residuals, r, that are obtained when the average value Xmean is subtracted from each observation a ,. Xmean is the best estimate for the true mean fj.. When discussing theoretical concepts or when the standard deviation is precisely known, a small Greek sigma, a, is used in all other cases, the estimate Sx appears instead. 

Schmidbaur, H. (2000) The Aurophilicity Phenomenon A Decade of Experimental Findings, Theoretical Concepts and Emerging Applications. Gold Bulletin, 33, 3-10. 

Values for the heats of hydration of a number of ions that were calculated by the aforementioned methods on the basis of theoretical models and experimental data are reported in Table 7.2. We see that there is a certain general agreement, but in individual cases the discrepancies are large, due to inadequacies of the theoretical concepts used in the calculations. 

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