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Author: Motoi Tobita Publisher: ISBN: Category : Languages : en Pages :
Book Description
ABSTRACT: This dissertation is focused on the development of highly accurate electron-correlation methods for one- and two-dimensional periodic systems. For one-dimensional systems, atomic-orbital based many-body perturbation theory and coupled cluster theory are developed and applied to polyacetylene and lithium-hydride model chain. Use of atomic orbitals instead of conventional crystalline (molecular) orbitals enables us to control runtime and accuracy of the calculation. The gain in the atomic-orbital based coupled cluster method originates from the locality and sparsity of matrices needed in the framework of the theory. Provided, efficient sparse matrix-matrix multiplication routines, we obtain good estimates of the correlation energy much faster than the conventional method for large systems. 90 percent of the correlation energy can be recovered very quickly, and 2 to 3 digit accuracy can be obtained for polymers with relatively simple unit cells such as polyacetylene. The formalism behind the atomic-orbital based coupled cluster theory is applicable for both large molecular systems and periodic systems. Formal aspects of the atomic-orbital based coupled cluster theory are discussed and correspondence between the atomic-orbital based framework and crystalline (molecular) orbital based framework are shown. Two-dimensional code development is based on Hartree-Fock and density functional theories due to the fact that coupled-cluster theory is too costly. Efficient inclusion of the Coulomb effects by the fast multipole method and analytical gradient techniques are the core elements that contribute robustness and computational efficiency for two-dimensional systems. The fast multipole method is an algorithm to include the long-range Coulomb effects for uniform systems with linear-scaling costs for molecular systems and with logarithmic scaling for infinite periodic systems. The analytical gradient technique is a powerful tool when optimized geometries or vibrational frequencies are computed. If optimum geometries or vibrational frequencies are required, then analytical gradients are for all practical purposes, a necessity.
Author: Motoi Tobita Publisher: ISBN: Category : Languages : en Pages :
Book Description
ABSTRACT: This dissertation is focused on the development of highly accurate electron-correlation methods for one- and two-dimensional periodic systems. For one-dimensional systems, atomic-orbital based many-body perturbation theory and coupled cluster theory are developed and applied to polyacetylene and lithium-hydride model chain. Use of atomic orbitals instead of conventional crystalline (molecular) orbitals enables us to control runtime and accuracy of the calculation. The gain in the atomic-orbital based coupled cluster method originates from the locality and sparsity of matrices needed in the framework of the theory. Provided, efficient sparse matrix-matrix multiplication routines, we obtain good estimates of the correlation energy much faster than the conventional method for large systems. 90 percent of the correlation energy can be recovered very quickly, and 2 to 3 digit accuracy can be obtained for polymers with relatively simple unit cells such as polyacetylene. The formalism behind the atomic-orbital based coupled cluster theory is applicable for both large molecular systems and periodic systems. Formal aspects of the atomic-orbital based coupled cluster theory are discussed and correspondence between the atomic-orbital based framework and crystalline (molecular) orbital based framework are shown. Two-dimensional code development is based on Hartree-Fock and density functional theories due to the fact that coupled-cluster theory is too costly. Efficient inclusion of the Coulomb effects by the fast multipole method and analytical gradient techniques are the core elements that contribute robustness and computational efficiency for two-dimensional systems. The fast multipole method is an algorithm to include the long-range Coulomb effects for uniform systems with linear-scaling costs for molecular systems and with logarithmic scaling for infinite periodic systems. The analytical gradient technique is a powerful tool when optimized geometries or vibrational frequencies are computed. If optimum geometries or vibrational frequencies are required, then analytical gradients are for all practical purposes, a necessity.
Author: Publisher: Academic Press ISBN: 0128235470 Category : Science Languages : en Pages : 354
Book Description
Advances in Quantum Chemistry presents surveys of current topics in this rapidly developing field one that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. It features detailed reviews written by leading international researchers. In this volume the readers are presented with an exciting combination of themes. - Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology - Features detailed reviews written by leading international researchers
Author: Publisher: ISBN: Category : Languages : en Pages : 10
Book Description
The objective of our work for ONR has been to develop and apply new, correlated electronic structure methods for infinite periodic systems. The methods of interest include many body perturbation theory (MBPT) and its infinite order coupled cluster generalizations and complementary density functional methods. Today we routinely do highly correlated studies of molecules (including making reliable predictions of structure, photoelectron, vibrational, and electronic spectra). The next frontier in electronic structure theory is the treatment (with the same level of confidence) of polymers, surfaces, and crystals, which are semiconductors or insulators and are collectively termed "extended systems." The current paradigm for molecules is SCF, MBPT(2), CCSD, CCSD(T), CCSDT, and full CI. Though convergence is not monotonic, such a sequence, augmented by experience and approximate error bars, typically offers purely ab inito, extrapolated solutions that are predictive. In contrast, no such paradigm exists for extended systems. Furthermore, there is no full CI so only high-level CC methods can offer reference results. The only methods currently available for extended systems are periodic Hartree Fock (i.e., SCF) and density functional theory (DFT), usually in the local density approximation (LDA). The former lacks the critical electron correlation effects responsible for so many of the interesting phenomena in solids, from band gaps to high Tc superconductivity, while the latter might introduce some correlation effects, but an unclear amount. In fact, the greatest weakness of DFT is that, unlike the above CC/MBPT paradigm, there is no way to systematically converge to the correct result.
Author: Jamal Berakdar Publisher: John Wiley & Sons ISBN: 3527618538 Category : Science Languages : en Pages : 205
Book Description
An up-to-date selection of applications of correlation spectroscopy, in particular as far as the mapping of properties of correlated many-body systems is concerned. The book starts with a qualitative analysis of the outcome of the two-particle correlation spectroscopy of localized and delocalized electronic systems as they occur in atoms and solids. The second chapter addresses how spin-dependent interactions can be imaged by means of correlation spectroscopy, both in spin-polarized and extended systems. A further chapter discusses possible pathways for the production of interacting two-particle continuum states. After presenting some established ways of quantifying electronic correlations and pointing out the relationship to correlation spectroscopy, the author addresses in a separate chapter the electron-electron interaction in extended systems, and illustrates the ideas by some applications to fullerenes and metal clusters. The last two chapters are devoted to the investigation of the potential of two-particle spectroscopy in studying ordered surfaces and disordered samples. Throughout the book the material is analyzed using rather qualitative arguments, and the results of more sophisticated theories serve the purpose of endorsing the suggested physical scenarios. The foundations of some of these theories have been presented in a corresponding volume entitled "Concepts of Highly Excited Electronic Systems" (3-527-40335-3).
Author: E.Y. Andrei Publisher: Springer Science & Business Media ISBN: 9401512868 Category : Science Languages : en Pages : 398
Book Description
Recent studies on two-dimensional systems have led to new insights into the fascinating interplay between physical properties and dimensionality. Many of these ideas have emerged from work on electrons bound to the surface of a weakly polarizable substrate such as liquid helium or solid hydrogen. The research on this subject continues to be at the forefront of modern condensed matter physics because of its fundamental simplicity as well as its connection to technologically useful devices. This book is the first comprehensive overview of experimental and theoretical research in this exciting field. It is intended to provide a coherent introduction for graduate students and non-experts, while at the same time serving as a reference source for active researchers in the field. The chapters are written by individuals who made significant contributions and cover a variety of specialized topics. These include the origin of the surface states, tunneling and magneto-tunneling out of these states, the phase diagram, collective excitations, transport and magneto-transport.
Author: Alex C. Hewson Publisher: Springer Science & Business Media ISBN: 9401002134 Category : Science Languages : en Pages : 364
Book Description
The NATO sponsored Advanced Research Workshop on "Concepts in Electron Correlation" took place on the Croatian island of Hvar during the period from the 29th of September to the 3rd of October, 2002. The topic of electron correlation is a fundamental one in the field of condensed matter, and one that is being very actively studied both experimentally and theoretically at the present time. The manifestations of electron cor relation are diverse, and play an important role in systems ranging from high temperature superconductors, heavy fermions, manganite compounds with colossal magnetoresistance, transition metal compounds with metal insulator transitions, to mesoscopic systems and quantum dots. The aim of the workshop was to provide an opportunity for a dialogue between exper imentalists and theoreticians to assess the current state of understanding, and to set an agenda for future work. There was also a follow-up workshop on the same topic where the presentations included more background and introductory material for younger researchers in the field. The papers presented in these proceedings clearly demonstrate the di versity of current research on electron correlation. They show that real progress is being made in characterising systems experimentally and in developing theoretical approaches for a quantitative comparison with ex periment. The more one learns, however, the more there is to understand, and many of the contributions help to map out the territory which has yet to be explored. We hope that the articles in this volume will be a stimulus for such future work.
Author: Petr Cársky Publisher: Springer Science & Business Media ISBN: 9048128854 Category : Science Languages : en Pages : 672
Book Description
I feel very honored that I have been asked to write a Foreword to this book. The subject of the book – “Coupled cluster theory” – has been around for about half a century. The basic theory and explicit equations for closed-shell ground states were formulated before 1970. At the beginning of the seventies the rst ab initio calcu- tion were carried out. At that time speed and memory of computers were very limited compared to today’s standards. Moreover, the size of one-electron bases employed was small, so that it was only possible to achieve an orientation in methodical aspects rather than to generate new signi cant results. Extensive use of the coupled-cluster method started at the beginning of the eighties. With the help of more powerful computers the results of coupled-cluster approaches started to yield more and more interesting results of relevance to the interpretation of experimental data. New ideas in methodology kept appearing and computer codes became more and more ef cient. This exciting situation continues to this very day. Remarkably enough, even the - quired equations can now be generated by a computer with the help of symbolic languages. The size of this monograph and the rich variety of articles it contains attests to the usefulness and viability of the couple-cluster formalism for the h- dling of many-electron correlation effects. This represents a vivid testimony of a tremendous work that has been accomplished in coupled-cluster methodology and its exploitation.
Author: Angela K. Wilson Publisher: ISBN: Category : Language Arts & Disciplines Languages : en Pages : 236
Book Description
Modeling is becoming a significant component in the design and analysis of chemical systems in areas such as catalysis, nanomaterials, and biological systems. With rapidly advancing technology, there is an increasing need to model molecules that are quite large and complex, and to model such systems with reasonable accuracy. However, computational methods are generally more numerous and reliable for lighter, smaller molecules since calculations on smaller molecules are less computationally demanding than for larger molecules, and can take advantage of high accuracy, but prohibitively expensive, computational approaches. Two widely used approaches for chemical modeling are ab initio correlated methods and density functional theory. Though there is great interest in using these methods for high accuracy calculations on increasingly larger and more complex chemical systems, each approach currently has limitations. Ab initio methods suffer from a high "N-scaling" problem, where the N-scaling represents the computational cost (memory, disk space, and time requirements of the calculations), thus making high accuracy calculations. Density functional methods have a much lower N-scaling, and thus calculations can be done on much larger molecules. Unfortunately, density functional calculations are generally not as reliable as ab initio approaches, and sometimes, at best can only provide a qualitative description of properties of interest. This volume brings together researchers from throughout the world to assess recent progress in the field of electronic structure methodology, focusing upon ab initio and density functional developments, and to discuss future direction. This publication will impact a number of fields including computational chemistry, organic chemistry, and inorganic chemistry. It will help to provide a closer commonality of ab initio and density functional approaches, as it brings together many of the top senior and junior scientists in both fields to address a common problem: high accuracy modeling of larger chemical systems.
Author: Motoi Tobita
Author: Motoi Tobita
Author: 
Author: 
Author: Jamal Berakdar
Author: E.Y. Andrei
Author: Alex C. Hewson
Author: Petr Cársky
Author: 
Author: Robin Kay Jurgens-Lutovsky
Author: Angela K. Wilson