A number of general-purpose, reasonably accurate and well-tested ab-initio codes for crystals are discussed in this book. The aim is to expand competence of their application in material sciences and solid-state physics. The book addresses particularly readers with a general knowledge in quantum chemistry and intends to give a deeper insight into the special algorithms and computational techniques in ab-initio computer codes for crystals. Three different programs which are available to all interested potential users on request are presented.
On the occasion of the fourth International Conference on Industrial and Applied Mathematics!, we decided to organize a sequence of 4 minisymposia devoted to the mathematical aspects and the numerical aspects of Quantum Chemistry. Our goal was to bring together scientists from different communities, namely mathematicians, experts at numerical analysis and computer science, chemists, just to see whether this heterogeneous set of lecturers can produce a rather homogeneous presentation of the domain to an uninitiated audience. To the best of our knowledgde, nothing of this kind had never been tempted so far. It seemed to us that it was the good time for doing it, both . because the interest of applied mathematicians into the world of computational chemistry has exponentially increased in the past few years, and because the community of chemists feels more and more concerned with the numerical issues. Indeed, in the early years of Quantum Chemistry, the pioneers (Coulson, Mac Weeny, just to quote two of them) used to solve fundamental equations modelling toy systems which could be simply numerically handled in view of their very limited size. The true difficulty arose with the need to model larger systems while possibly taking into account their interaction with their environment. Hand calculations were no longer possible, and computing science came into the picture.
The thermodynamic limit is a mathematical technique for modeling crystals or other macroscopic objects by considering them as infinite periodic arrays of molecules. The technique allows models in solid state physics to be derived directly from models in quantum chemistry. This book presents new results, many previously unpublished, for a large class of models and provides a survey of the mathematics of thermodynamic limit problems. The authors both work closely with Fields Medal-winner Pierre-Louis Lion, and the book will be a valuable tool for applied mathematicians and mathematical physicists studying nonlinear partial differential equations.
This is the first edited volume that features two important frameworks, Hückel and quantum chemical topological analyses. The contributors, which include an array of academics of international distinction, describe recent applications of such topological methods to various fields and topics that provide the reader with the current state-of-the-art and give a flavour of the wide range of their potentialities.
Potential Energy Surfaces is a collection of lectures given at the 1996 Mariapfarr Workshop in Theoretical Chemistry, organized by Alexander F. Sax. The Mariapfarr Workshops' aim is to discuss in-depth topics in Theoretical Chemistry. The target group of these workshops is graduate students and postdocs.
The authors demonstrate that the essential information about order in, and energy levels of physical systems is encapsulated in the second order reduced density matrix. They have discovered an algorithm to obtain a reasonable accurate expression for the 2-matrix of an N-particle state to make nearly all properties of matter which are of interest to chemists and physicists accessible.
Despite the tremendous advances in the techniques and equipment for carrying out high-pressure crystallography, the application or exploration of the high-pressure variable in detailed structural studies remains rare. The chapters in this book provide a set of lecture notes and supplementary material for a course on high pressure crystallography. The material comprises state-of-the-art reviews of high-pressure experiments using X-ray and neutron diffraction techniques at synchrotron and neutron facilities and in the laboratory, as well as complementary experimental high-pressure techniques and theoretical methods for investigating matter at elevated pressures. The materials studies range from elemental solids and liquids to inorganic compounds, minerals, organic compounds, clathrates and pharmaceutical compounds, to large biological molecules such as proteins and viruses. The book provides a reference for workers in high-pressure science wishing to learn more about crystallography and for established crystallographers potentially interested in high pressure as a variable, as well as an introductory guide to new researchers in the field.
With the development of potent x-ray sources at many synchrotron laboratories worldwide, Compton scattering has become a standard tool for studying electron densities in materials. This book provides condensed matter and materials physicists with an authoritative, up-to-date, and very accessible account of the Compton scattering method, leading to a fundamental understanding of the electrical and magnetic properties of solid materials. The spectrum of Compton scattered x-rays is particularly sensitive to this behaviour and thus can be used as a direct probe and to test the predictions of theory. The current generation of synchrotron facilities allows this method to be readily exploited to study the ground state electron density in both elements and in complex compounds. It is important that those working in related fields, as well as the increasing number directly using the Compton method, have a comprehensive assessment of what is now possible and how to achieve it, in addition to a full understanding of its theoretical basis. This monograph is unique and timely, since little of what is described, was practicable a decade ago. The development of synchrotron radiation facilities has ensured that the technique described here will remain a powerful probe of electron charge and spin density for many years to come.
This book explores the potential of quantum crystallography. The field accompanied the major milestones of x-ray diffraction and it has undergone a rapid evolution in the past few years. For this reason, some reflections are necessary in order to scrutinize the next steps and anticipate the future developments. After a short survey of the historical background and in depth description of the state of the art, some examples are provided of current and future applications of the know-how in this discipline. This implies attracting readership of both experts in the field and neophytes. The former will test their own views with the one exposed in the book; the newcomers, instead, will learn both what has been done and what could be done with quantum crystallography.
Linear current-voltage pattern, has been and continues to be the basis for characterizing, evaluating performance, and designing integrated circuits, but is shown not to hold its supremacy as channel lengths are being scaled down. In a nanoscale circuit with reduced dimensionality in one or more of the three Cartesian directions, quantum effects transform the carrier statistics. In the high electric field, the collision free ballistic transform is predicted, while in low electric field the transport remains predominantly scattering-limited. In a micro/nano-circuit, even a low logic voltage of 1 V is above the critical voltage triggering nonohmic behavior that results in ballistic current saturation. A quantum emission may lower this ballistic velocity.
