Solid state theory

Madelung O 1996 Introduction to Solid State Theory (New York Springer)... 

W. A. Harrison, Solid State Theory Dover, New York (1979). 

Madelung, O., Solid State Theory, Springer-Verlag, Berlin, 1978. 

The orbitals and orbital energies produced by an atomic HF-Xa calculation differ in several ways from those produced by standard HF calculations. First of all, the Koopmans theorem is not valid and so the orbital energies do not give a direct estimate of the ionization energy. A key difference between standard HF and HF-Xa theories is the way we eoneeive the occupation number u. In standard HF theory, we deal with doubly oecupied, singly occupied and virtual orbitals for which v = 2, 1 and 0 respectively. In solid-state theory, it is eonventional to think about the oecupation number as a continuous variable that can take any value between 0 and 2. 

Dr. Roman V. Chepulskii Scientific Researcher Dept, of Solid State Theory Institute of Metal Physics National Acad. Sci. of Ukraine 36, Acad. Vernadsky Blvd. 

These limitations, most urgently felt in solid state theory, have stimulated the search for alternative approaches to the many-body problem of an interacting electron system as found in solids, surfaces, interfaces, and molecular systems. Today, local density functional (LDF) theory (3-4) and its generalization to spin polarized systems (5-6) are known to provide accurate descriptions of the electronic and magnetic structures as well as other ground state properties such as bond distances and force constants in bulk solids and surfaces. 

The SCF method for molecules has been extended into the Crystal Orbital (CO) method for systems with ID- or 3D- translational periodicityiMi). The CO method is in fact the band theory method of solid state theory applied in the spirit of molecular orbital methods. It is used to obtain the band structure as a means to explain the conductivity in these materials, and we have done so in our study of polyacetylene. There are however some difficulties associated with the use of the CO method to describe impurities or defects in polymers. The periodicity assumed in the CO formalism implies that impurities have the same periodicity. Thus the unit cell on which the translational periodicity is applied must be chosen carefully in such a way that the repeating impurities do not interact. In general this requirement implies that the unit cell be very large, a feature which results in extremely demanding computations and thus hinders the use of the CO method for the study of impurities. 

Here we briefly summarize some major results of solid state theory that are relevant for understanding the behavior of adsorption on surfaces. For a more detailed description please consult excellent books such as S. Elliot, The Physics and Chemistry of Solids (1998), Wiley Sons, New York N. Ashcroft and N.D Mermin, Solid... 

With this in mind, I have presented the information in this book in a form that can be easily understood. I think that it is quite important that any student of the body of knowledge that we call "science" needs to be cognizeuit of the history and effort that has been made by those who preceded us. It was Newton who said "If I have seen further, it is because I have stood on the shoulders of giants . Thus, I have tried to give a short history of each particular segment of solid state theory and technology. 

The Kronig-Penney model, although rather crude, has been used extensively to generate a substantial amount of useful solid-state theory [73]. Simple free-electron models have likewise been used to provide logical descriptions of a variety of molecular systems, by a method known in modified form as the Hiickel Molecular Orbital (HMO) procedure [74]. 

Wilkes, P., Solid State Theory in Metallurgy, Cambridge University Press,... 

Jens and I started an attempt at a systematic, rigorous inclusion of electron correlation effects on solid-state properties. We hailed both from a quantum chemistry tradition of formal clarity, analytical and numerical care, and attention for efficient programming techniques. On the other hand, the solid-state theory tradition followed, and continues to travel a very different route. This path is... 

It is therefore my conviction that, rather sooner then later, we will see a resurgence of the precise many-body approach to solid-state theory as we envisioned. Almost assuredly the GW method will be the tool of choice. I hope to see those days, and maybe Jens and I can enjoy them together. 

Madelung, O. (1978). In Introduction to Solid-State Theory, eds. M. Cardona, P. Fulde and H. J. Queisser. Berlin Springer-Verlag. 

Despite the growing importance of solid state chemistry, however, we fotrrrd that there were few textbooks that tackled solid state theory from a chemist s rather than a physicist s viewpoint. Of those that did most, if not all, were aimed at firral year undergraduates and postgraduates. We felt there was a need for a book written from a chemist s viewpoint that was accessible to undergradrrates earlier in their degree programme. This book is an attempt to provide such a text. 

There are other topics that might be considered, such as solid state theory and classical statistical mechanics. You must decide how much time to spend on each of your chosen topics. You can identify subtopics that you might omit or to which you can give only an introduction. One of the difficult decisions involves how much to teach about your own research area. You are obviously excited about this area, and will be tempted to spend too much class time on it. Another difficult decision is how much time to spend on topics of current interest such as nanomaterials and environmental chemistry. Your decisions should be guided by the composition of your class. If the class has a lot of premedical students and biochemistry majors in it, they are probably well served by a thorough treatment of thermodynamics and dynamics, and perhaps less well served by a thorough treatment of quantum mechanics and statistical mechanics. If the class is mostly composed of future chemistry graduate students, quantum mechanics and statistical mechanics are more important. 

At this stage of the discussion it must be emphasized that Philippoff (53, 54) has published a considerable amount of work carried out on solutions. For the determination of shear recovery he used a special coaxial cylinder apparatus. He arrived at the embarassing conclusion that Lodge s equation (2.11) is not valid, but that the equation of "solid state theory , i.e. eq. (2.12) is in accordance with the experimental results. Fig. 2.3 gives some of the results recently published by Philippoff and Stratton (55) for a 4.15 wt. per cent solution of polyisobutylene... 

BORN, MAX (1882-1970). A German-born British physicist. Max Born studied mathematics and physics and in 1904 became David Hilbert is private assistant for. While at the University of Breslau, he won a competition on the stability of elastic wires and it became the dissertation for his Ph.D. After graduate school, he studied special relativity for a while, then became interested in the physics of crystals. In 1912. he published the Born-Karman theory of specific heats and his work on crystals is a cornerstone of solid-state theory. 

Nevertheless, solid-state theory has made excellent progiess during the past decade. Just a few examples would include ... 

For example, Local Density Approximations in Quantum Chemistry and Solid State Physics. Proceedings of a Symposium on Local Density Approximations in Quantum Chemistry and Solid State Theory, Copenhagen, Denmark, 10-12 June 1982, edited by J. P. Dahl, J. Avery, Plenum, New York, 1984. 

The usual BO method (see eqs. A.5, A.6, A.9, A.10 as well as the "crude" approach (eqs. A.21-A.24) are characterized by a common shortcoming. Namely, it is difficult to evaluate higher nonadiabatic corrections based on these versions of adiabatic method. Neither of these approaches is adaptable to the usual perturbation theory development. In this connection, the development of a method that would enable the application of perturbation theory is of interest. Such a method has been determined by Geilikman (47) in solid state theory. An analogous method can be developed for molecules (81). 

Unlike solid state theory, it is necessary here to take... 

Solid-state theories ascribe electron relaxation to the coupling of electronic spin transitions with transitions between lattice vibrational levels, or more generally with phonons. Disappearance (depopulation of a vibrational level) or creation (population of a vibrational level) of phonons modulate the orbital component of the electron magnetic moment. 

Following the solid-state approach, equations have been derived [8,9] also for the electron spin relaxation of 5 = V2 ions in solution determined by the aforementioned processes. Instead of phonons, collisions with solvent should be taken into consideration, whose correlation time is usually in the range 10"11 to 10 12 s. However, there is no satisfactory theory that unifies relaxation in the solid state and in solution. The reason for this is that the solid state theory was developed for low temperatures, while solution theories were developed for room temperature. The phonon description is a powerful one when phonons are few. By increasing temperature, the treatment becomes cumbersome, and it is more convenient to use stochastic theory (see Section 3.2) instead of analyzing the countless vibrational transitions that become active. 

FOR RESEARCH IN ATOMIC, MOLECULAR AND SOLID-STATE THEORY UPPSALA UNIVERSITY, UPPSALA, SWEDEN... 

Landsberg, P. T. (ed.) (1969) Solid State Theory. London Wiley Interscience. 

Miller, S. C. and Love, W. F. (1967) Tables of Irreducible Representations of Space Groups and Co-representations of Magnetic Space Groups. Boulder, CO Pruett. Morgan, D. J. (1969) Group theory and electronic states in perfect crystals. In Landsberg, P. T. (ed.) Solid State Theory, chaps. IV and V. London Wiley Interscience. 

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