Author: John M. HerbertPublisher:
ISBN:
Category :
Languages : en
Pages : 492
Book Description
Reconstructive Approaches to One-and Two-electron Density Matrix Theory
Author: John M. HerbertReduced-Density-Matrix Mechanics
Author: David A. MazziottiPublisher: John Wiley & Sons
ISBN: 047010659X
Category : Science
Languages : en
Pages : 300
Book Description
An up-to-date account of this cutting-edge research in a consistent and understandable framework, of special interest to experts in other areas of electronic structure and/or quantum many-body theory. It will serve equally well as a self-contained guide to learning about reduced density matrices either through self-study or in a classroom as well as an invaluable resource for understanding the critical advancements in the field.
Many-Electron Densities and Reduced Density Matrices
Author: Jerzy CioslowskiPublisher: Springer Science & Business Media
ISBN: 1461542111
Category : Science
Languages : en
Pages : 311
Book Description
Science advances by leaps and bounds rather than linearly in time. I t is not uncommon for a new concept or approach to generate a lot of initial interest, only to enter a quiet period of years or decades and then suddenly reemerge as the focus of new exciting investigations. This is certainly the case of the reduced density matrices (a k a N-matrices or RDMs), whose promise of a great simplification of quantum-chemical approaches faded away when the prospects of formulating the auxil iary yet essential N-representability conditions turned quite bleak. How ever, even during the period that followed this initial disappointment, the 2-matrices and their one-particle counterparts have been ubiquitous in the formalisms of modern electronic structure theory, entering the correlated-level expressions for the first-order response properties, giv ing rise to natural spinorbitals employed in the configuration interaction method and in rigorous analysis of electronic wavefunctions, and al lowing direct calculations of ionization potentials through the extended Koopmans'theorem. The recent research of Nakatsuji, Valdemoro, and Mazziotti her alds a renaissance of the concept of RDlvls that promotes them from the role of interpretive tools and auxiliary quantities to that of central variables of new electron correlation formalisms. Thanks to the economy of information offered by RDMs, these formalisms surpass the conven tional approaches in conciseness and elegance of formulation. As such, they hold the promise of opening an entirely new chapter of quantum chemistry.
The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State
Author: N.I. GidopoulosPublisher: Springer Science & Business Media
ISBN: 9401704090
Category : Science
Languages : en
Pages : 233
Book Description
This volume records the proceedings of a Forum on The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State held at the Coseners' House, Abingdon-on-Thames, Oxon. over the period 31st May - 2nd June, 2002. The forum consisted of 26 oral and poster presentations followed by a discussion structure around questions and comments submitted by the participants (and others who had expressed an interest) in advance of the meeting. Quantum mechanics provides a theoretical foundation for our under standing of the structure and properties of atoms, molecules and the solid state in terms their component particles, electrons and nuclei. (Rel ativistic quantum mechanics is required for molecular systems contain ing heavy atoms.) However, the solution of the equations of quantum mechanics yields a function, a wave function, which depends on the co ordinates, both space and spin, of all of the particles in the system. This functions contains much more information than is required to yield the energy or other property.
Modern Charge-Density Analysis
Author: Carlo GattiPublisher: Springer Science & Business Media
ISBN: 9048138361
Category : Science
Languages : en
Pages : 800
Book Description
Modern Charge-Density Analysis focuses on state-of-the-art methods and applications of electron-density analysis. It is a field traditionally associated with understanding chemical bonding and the electrostatic properties of matter. Recently, it has also been related to predictions of properties and responses of materials (having an organic, inorganic or hybrid nature as in modern materials and bio-science, and used for functional devices or biomaterials). Modern Charge-Density Analysis is inherently multidisciplinary and written for chemists, physicists, crystallographers, material scientists, and biochemists alike. It serves as a useful tool for scientists already working in the field by providing them with a unified view of the multifaceted charge-density world. Additionally, this volume facilitates the understanding of scientists and PhD students planning to enter the field by acquainting them with the most significant and promising developments in this arena.
Methods for Directly Determining the Two-electron Reduced Density Matrix with Applications to Quantum Phase Transitions and Chemical Reactions
Author: Christine Ann SchwerdtfegerPublisher:
ISBN: 9781267247780
Category :
Languages : en
Pages : 168
Book Description
An N-particle system can be described without approximation using a two-particle reduced density matrix (2-RDM) if the particles are indistinguishable and interact pairwise. If a 2-RDM is determined without using an N-particle wavefunction, the computational advantage of using a two-particle representation is realized. Directly minimizing the energy as a functional of the 2-RDM, however, does not yield a 2-RDM that describes an N -particle system (N-representable). In this thesis we discuss two approaches for determining approximately N-representable 2-RDMS without using wavefunctions. In the first approach, known as the variational 2-RDM method, we minimize the energy as a function of the 2-RDM while explicitly enforcing a subset of N-representability conditions on the 2-RDM to obtain a lower bound to the exact energy. We apply this approach to the strongly correlated quantum phase transition in the 1D transverse Ising model and demonstrate that compared to the exact solution, the variational 2-RDM method provides an accurate description of the Ising lattice and is an alternative tool for locating a quantum phase transition using only the ground electronic state. The second approach used in this work is the parametric 2-RDM method. The 2-RDM is parameterized using a reference 2-RDM and a subset of N-representability conditions. We apply the method to several isomerization reactions including those of oxywater, ammonia oxide, carbonic acid and diazene. Results obtained using the parametric 2-RDM method reproduce experimental results in predicting the equilibrium ratio of cis- to trans-carbonic acid isomers and describe the multireference transition state in the isomerization of diazene as well as multireference wavefunction methods. We extend the 2-RDM parameterization to describe electronic systems in arbitrary spin states and demonstrate similar accuracy at equilibrium and nonequilibrium geometries as was seen in describing singlet electronic states. Lastly, we reparameterize the 2-RDM to obtain a new parameterization that scales with the fourth power of the size of the basis set and improves on the accuracy of second-order Moller-Plesset perturbation theory, particularly for electronic systems that are strongly correlated.
Solving the Schrdinger Equation
Author: Paul L. A. PopelierPublisher: World Scientific
ISBN: 1848167245
Category : Science
Languages : en
Pages : 375
Book Description
The Schrdinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrdinger equation. Each method is based on a set of core ideas and this volume aims to explain these ideas clearly so that they become more accessible. By bringing together these non-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of novel approaches. Is there a method out there that we have not thought of yet? Can we design a new method that combines the best of all worlds?
Density-Functional Methods for Excited States
Author: Nicolas FerréPublisher: Springer
ISBN: 3319220810
Category : Science
Languages : en
Pages : 487
Book Description
The series Topics in Current Chemistry presents critical reviews of the present and future trends in modern chemical research. The scope of coverage is all areas of chemical science including the interfaces with related disciplines such as biology, medicine and materials science. The goal of each thematic volume is to give the non-specialist reader, whether in academia or industry, a comprehensive insight into an area where new research is emerging which is of interest to a larger scientific audience. Each review within the volume critically surveys one aspect of that topic and places it within the context of the volume as a whole. The most significant developments of the last 5 to 10 years are presented using selected examples to illustrate the principles discussed. The coverage is not intended to be an exhaustive summary of the field or include large quantities of data, but should rather be conceptual, concentrating on the methodological thinking that will allow the non-specialist reader to understand the information presented. Contributions also offer an outlook on potential future developments in the field. Review articles for the individual volumes are invited by the volume editors. Readership: research chemists at universities or in industry, graduate students
Dissertation Abstracts International
Author: Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 902
Book Description
Electron Density and Bonding in Crystals
Author: V.G TsirelsonPublisher: CRC Press
ISBN: 1000157164
Category : Science
Languages : en
Pages : 534
Book Description
Electron Density and Bonding in Crystals: Principles, Theory and X-Ray Diffraction Experiments in Solid State Physics and Chemistry provides a comprehensive, unified account of the use of diffraction techniques to determine the distribution of electrons in crystals. The book discusses theoretical and practical techniques, the application of electron density studies to chemical bonding, and the determination of the physical properties of condensed matter. The book features the authors' own key contributions to the subject as well a thorough, critical summary of the extensive literature on electron density and bonding. Logically organized, coverage ranges from the theoretical and experimental basis of electron density determination to its impact on investigations of the nature of the chemical bond and its uses in determining electromagnetic and optical properties of crystals. The main text is supplemented by appendices that provide clear, concise guidance on aspects such as systems of units, quantum theory of atomic vibrations, atomic orbitals, and creation and annihilation operators. The result is a valuable compendium of modern knowledge on electron density distributions, making this reference a standard for crystallographers, condensed matter physicists, theoretical chemists, and materials scientists.