Theory and Hardware

Assuming isotropic and harmonic vibration the thermal parameter B becomes the quantity shown in equation 3.8, where if is the mean square displacement of the atomic vibration. 

For anisotropic vibration the temperature factor is more complex because f now depends on the direction of S. The anisotropic temperature factor is often 

In addition to the dynamic disorder caused by temperature-dependent vibration of atoms, protein crystals have static disorder due to the fact that molecules, or parts of molecules, do not occupy exactly the same position or do not have exactly the same orientation in the crystal unit cell. However, unless data are collected at different temperatures, one cannot distinguish between 

The end result of an X-ray structural determination reports the electron density in the crystal. The fundamental equation for its calculation follows in 

The isomorphous replacement method requires attachment of heavy atoms to protein molecules in the crystal. In this method, atoms of high atomic number are attached to the protein, and the coordinates of these heavy atoms in the unit cell are determined. The X-ray diffraction pattern of both the native protein and its heavy atom derivative(s) are determined. Application of the so-called Patterson function determines the heavy atom coordinates. Following the refinement of heavy atom parameters, the calculation of protein phase angles proceeds. In the final step the electron density of the protein is calculated. 

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Parallel to the developments achieved in methodology and hardware, the conventional methods and some of the new approaches have been employed to study several types of photoinduced processes which are relevant mainly in biology and nanotechnology. In particular, important contributions have been made related to the topics of photodissociations, photostability, photodimerizations, photoisomerizations, proton/hydrogen transfer, photodecarboxylations, charge transport, bioexcimers, chemiluminescence and bioluminescence. In contrast to earlier studies in the field of computational photochemistry, recent works include in many cases analyses in solution or in the natural environment (protein or DNA) of the mechanisms found in the isolated chromophores. In addition, semi-classical non-adiabatic molecular dynamics simulations have been performed in some studies to obtain dynamical attributes of the photoreactions. These latter calculations are however still not able to provide quantitative accuracy, since either the level of theory is too low or too few trajectories are generated. Within this context, theory and hardware developments aimed to decrease the time for accurate calculations of the PESs will certainly guide future achievements in the field of photodynamics. 

Considerable research efforts have been undertaken to develop reliable and cost-effective means to actively (or electronically) control noise produced by equipment. Though it is not a new concept, modem theory and hardware for adaptive digital signal processing have recently made the commercial use of active noise control worth considering for certain appU-cations with special requirements. 

Various instruments of theoretical chemistry have been widely to describe separate steps of solvent extraction of metal ions. Because of the complexity of solvent extraction systems, there is still no unified theory and no successful approach aimed at merging the extraction steps. It has already been pointed out that the challenging problem for theoreticians dealing with solvent extraction of metals, in particular with thermodynamic calculations, is to evaluate correctly solvent effects by the use of the most accurate explicit solvation models and QM calculations. However, such calculations on extremely large sets consisting of hundreds or even thousands of molecules, necessary to model all aspects of the extraction systems, are still impossible due to both hardware and software limitations. 

There has been an explosion of activity (as measured by number of published papers, books, symposia, workshops, dedicated journals, etc.) in the development of polymer modeling recently. This trend is expected to continue as new algorithms and advances in computer hardware allow the study of more realistic systems for example, the chapter by Kendall et al. in this volume. Two journals are worth mentioning because they are dedicated to publishing peer-reviewed results of work exclusively on polymer modeling. One is the Journal of Computational Polymer Science, which started in 1991 and the other is Die Makromolekulare Chemie Theory and Simulation, which began publication in 1992. 

The text books, encyclopedias and handbooks listed in the previous section are complemented by the computer software and hardware through which practical schemes of computation are realized. In this section, we consider the computer software for carrying out molecular many-body perturbation theory calculations. The computer hardware appropriate for such calculations is considered in section 3.7. 

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