New Theoretical Developments

7 New Theoretical Developments. - In the preceding sections, even where new variations of computational methods have been used, the papers have involved applications of computer modelling to particular molecules or series of molecules. In this section a few publications are described that are concerned with novel approaches which have not yet reached the stage where a body of data from applications is available. 

Nakano and Yamaguchi255-258 are developing a method based on numerical solutions of Liouville s equation to describe the frequency-dependent response of an assembly of dipoles to an electric field. The aggregates are of a size such that retardation effects are significant. One novel result is that there is a sharp change of the polarizability, reminiscent of a phase transition, that occurs as the intensity of a near-resonant field is increased. 

Hattig259,260 gives expressions for the frequency dispersion of the / - and y-hyperpolarizability components in terms of the derivatives of the hyperpolarizability with respect to the frequency arguments (see also the comment by Bishop261). 

Gorling et al.262,263 have been concerned with the development of new forms of time-dependent DFT using coupled Kohn-Sham equations. The theory should be suitable for the calculation of the response functions. Itskowitz and 

Berkowitz264 have formulated a DFT method in terms of perturbations of atomic densities. 

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A list of previous books and reviews on block copolymers is given in the bibliography. There have been no authored books in the field since the volume by Noshay and McGrath in 1977, and this was primarily concerned with the chemistry and materials science. Most of the literature consists of outdated edited books, although a number of review articles have appeared recently. The field has advanced rapidly during the last two decades, with major new theoretical developments, discoveries of new morphologies and the initiation of research in new fields such as thin films, crystalline solids and gels in concentrated solutions. It is thus hoped that this book is timely and fulfils the need for an up-to-date summary of the fundamental physics of block copolymers. 

In summary, we have enlarged the concepts of chemical structure and resonance in such a way as to make then conform the more general theories of molecular quantum mechanics. Classical VB concepts have been extremely useful in rationalizing empirical facts but became inadequate in the light of the new theoretical developments. The new concepts presented here are consistent both with the mathematical models of quantum chemistry and with empirical chemical facts, and their formulation recognize the latest research advancements. 

A second interesting new theoretical development of a quite different kind has been the application of an information theory approach to the classification of experimental results [478-488]. The outcome of collisions, for example, the distribution of product translational or vibrational energies, is compared with the statistically predicted result for a closed system and the difference between the two is recorded as the surprisal. The surprisal is defined by an expression of the type found in information theory for example, if the probability of a reaction producing a molecular product in a final vibrational state v, corresponding to a fractional energy yield/,., is P fv.) and the corresponding statistical expression for a closed system is P°(fV ), then the surprisal is given by... 

I encourage lipid chemists to invest the resources to develop ultrasonic measurement methods. Existing technology can compete with existing solid fat measurement methods, and new theoretical developments offer the promise of much more. 

One-Component Lennard-Jones Clusters. Lennard-Jones clusters remain being the reference model system for testing new theoretical developments. For clusters consisting of only one type of atoms, the total energy is written as... 

Silicon is the element in semiconductor industry. Due to the miniaturization of all semiconductor devices, it is also technological relevant to study the properties of very small structures based on only Si. Therefore, very many studies have been devoted to Si clusters. This also means that it is natural to apply new theoretical developments to Si clusters. Accordingly, Ballone et al 6 used the Car-Parrinello method, shortly after its introduction, to the study of the structural properties of Spy clusters with A up to 10. 

VI. NEW THEORETICAL DEVELOPMENTS BEYOND THE LANDAU-ZENER-STUCKELBERG THEORY... 

The new theoretical developments described in Sec. VI were done in collaboration with Dr. C. Zhu. This work was supported in part by a Grant-in-Aid for Scientific Research on Priority Area Theory of Chemical Reactions from the Ministry of Education, Science and Culture of Japan. 

In this paper, we extend the classical 2-dimensional Ostwald ripening model in the light of new theoretical developments, and present novel solutions, compatible with the experimental particle size distributions. A family of solutions is available for each limiting case studied, i.e. when sintering dynamics are controlled by either crystallite-support interface interaction or by the rate of diffusion of adatoms on the support. 

IPN s and scrutinize the results in the light of new theoretical developments (1-6). For clarity, all PS/PS IPN s will be denoted by two pairs of numbers actual volume % DVB in polymer I/actual volume % DVB in polymer II, % polymer I/% polymer II,... 

Density-functional theory is a very active field and the number of papers reporting results of calculations based on this theory is enormous. In many cases these theoretical studies are used in supplementing experimental work, in others to obtain alternative theoretical information compared to that obtained with more traditional wavefimction-based methods, and in yet others to explore new systems and/or properties that are not or have not been accessed with other approaches. Due to this huge amount of density-functional studies on specific systems we felt that a report simply listing all these studies at best would be useless. Instead we have in this report discussed some of the issues that currently are the topic of new theoretical developments. 

Until recently the realization of a D- He or a D-D burning reactor had been considered a goal to be achieved in the next century, since a near-term experiment to test the possibility of igniting these kinds of plasmas could not be foreseen. However, recent experimental observations, as well as new theoretical developments, have led to the identification of a class of experiments that can lead to the realization of ignition conditions for a D- He system on the basis of present-day technology. ... 

Attempts to understand polymer-solvent and polymer-polymer mutual solution behavior led to many new theoretical developments, particularly in thermodynamics. To an increasing extent, the polymer scientist is now able to predict phase relationships involving polymers. The development of polymer solution and phase separation behavior is the subject of this chapter. 

The workshop brought together experts from different fields which, we hope, benefited from their mutual interaction around the central theme of the Dynamics of Van der Waals complexes. It was especially fruitful for experimentalists and theoreticians to interact which each other. New experiments raised new challenges to the theory and new theoretical developments provided answers to some old questions and raised new ones for the experimentalist to study. 

Fig. 7.36) indicate that departures from Gaussian statistics (8 = 0.5) are observed both in the ordered phase and in the disordered phase. This is consistent with the shift in position of the peak as the ODT is approached [212] and shows that the coils undergo a Gaussian-stretched coil transition in the disordered state, where 8 = 0.8=b 0.04. Such data have indicated the deficiencies of the original theory [208] and have subsequently been used as the basis for new theoretical developments [214-218]. This study indicates the close interaction between theory and experiment which has often been stimulated by the information provided by SANS over the past two decades. The possibility of measuring previously inaccessible parameters has stimulated theoretical developments, which have led to new experiments (e.g. Fig. 7.36), which have in turn prompted improvements in theory. 

Therefore, calculations on model systems for which EtotW has a very simple, functional form of R are extremely useful in identifying trends. Furthermore, due to the simple form of Etot(R) it is easier to perform extensive searches in structure spaces, what hardly is possible with more elaborate expressions for EtotiR). Therefore, such model systems can also be used in studying new theoretical developments. As one of the most important points in this direction is that of developing new theoretical methods for unbiased and efficient determination of the structure of the global total-energy minimum. In our earlier report we gave some examples in this direction. Here, we shall just briefly discuss some more recent studies. 

New theoretical developments based on modern statistic theories of liquids are now in progress. At the same time, much effort must be made exqperimentally to find reactive models to which the theory can be applied, and to refine the new advanced technologies of pulse radiolysis and photolysis. ... 

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