Electronic, Atomic and Molecular Calculations


Book Description

The Generator Coordinate Method (GCM) is a mathematical tool for the understanding of stable atomic nuclei. Electronic, Atomic and Molecular Calculations is designed to assist scientists applying GCM in the analysis of the electronic structure of atoms and molecules. There have been numerous publications covering nuclear physics and electronic structure of atoms and molecules, but this book is unique in the sense that it specifically addresses the application of GCM for such purposes. Using this book, researchers will be able to understand and calculate the electronic structure in a novel manner.* Only book that covers the Generator Coordinate Method and applications for atoms, molecules and nuclei* Clearly describes how the GCM can be used as a powerful tool for design of atomic basis sets* Reviews current literature on GCM in atomic and molecular fields and a large part of the literature of the method in nuclear physics




Methods of Electronic Structure Theory


Book Description

These two volumes deal with the quantum theory of the electronic structure of molecules. Implicit in the term ab initio is the notion that approximate solutions of Schrödinger's equation are sought "from the beginning," i. e. , without recourse to experimental data. From a more pragmatic viewpoint, the distin guishing feature of ab initio theory is usually the fact that no approximations are involved in the evaluation of the required molecular integrals. Consistent with current activity in the field, the first of these two volumes contains chapters dealing with methods per se, while the second concerns the application of these methods to problems of chemical interest. In asense, the motivation for these volumes has been the spectacular recent success of ab initio theory in resolving important chemical questions. However, these applications have only become possible through the less visible but equally important efforts of those develop ing new theoretical and computational methods and models. Henry F Schaefer Vll Contents Contents of Volume 4 XIX Chapter 1. Gaussian Basis Sets for Molecular Calculations Thom. H. Dunning, Ir. and P. Ieffrey Hay 1. Introduction . . . . . . . . . . . . . . . . 1 1. 1. Slater Functions and the Hydrogen Moleeule 1 1. 2. Gaussian Functions and the Hydrogen Atom 3 2. Hartree-Fock Calculations on the First Row Atoms 5 2. 1. Valence States of the First Row Atoms 6 7 2. 2. Rydberg States of the First Row Atoms 9 2. 3.




Methods of Electronic-Structure Calculations


Book Description

Electronic-structure calculations of the properties of specific materials have become increasingly important over the last 30 years. Although several books on the subject have been published, it is rare to find one that covers in detail both the traditional quantum chemistry and the solid-state physics methods of electronic-structure calculations. This title bridges that gap, focusing equally on both types of method, including density-functional and Hartree-Fock-based approaches. The book is aimed at final-year undergraduate and postgraduate students of both chemistry and of physics. It describes in detail the fundamentals behind the various methods that are used in calculating electronic properties of materials, and that to some extent are commercially available. It should also be of interest to professional scientists working in related theoretical or experimental fields.




Atoms, Molecules and Clusters in Electric Fields


Book Description

With the central importance of electric polarizability and hyperpolarizability for a wide spectrum of activities, this book charts the trends in the accurate theoretical determination of these properties in specialized fields. The contributions include reviews and original papers that extend from methodology to applications in specific areas of primary importance such as cluster science and organic synthesis of molecules with specific properties.




Electronic Structure Calculations for Solids and Molecules


Book Description

Electronic structure problems are studied in condensed matter physics and theoretical chemistry to provide important insights into the properties of matter. This 2006 graduate textbook describes the main theoretical approaches and computational techniques, from the simplest approximations to the most sophisticated methods. It starts with a detailed description of the various theoretical approaches to calculating the electronic structure of solids and molecules, including density-functional theory and chemical methods based on Hartree-Fock theory. The basic approximations are thoroughly discussed, and an in-depth overview of recent advances and alternative approaches in DFT is given. The second part discusses the different practical methods used to solve the electronic structure problem computationally, for both DFT and Hartree-Fock approaches. Adopting a unique and open approach, this textbook is aimed at graduate students in physics and chemistry, and is intended to improve communication between these communities. It also serves as a reference for researchers entering the field.




Semiempirical Methods of Electronic Structure Calculation


Book Description

If one reflects upon the range of chemical problems accessible to the current quantum theoretical methods for calculations on the electronic structure of molecules, one is immediately struck by the rather narrow limits imposed by economic and numerical feasibility. Most of the systems with which experimental photochemists actually work are beyond the grasp of ab initio methods due to the presence of a few reasonably large aromatic ring systems. Potential energy surfaces for all but the smallest molecules are extremely expensive to produce, even over a restricted group of the possible degrees of freedom, and molecules containing the higher elements of the periodic table remain virtually untouched due to the large numbers of electrons involved. Almost the entire class of molecules of real biological interest is simply out of the question. In general, the theoretician is reduced to model systems of variable appositeness in most of these fields. The fundamental problem, from a basic computational point of view, is that large molecules require large numbers of basis functions, whether Slater type orbitals or Gaussian functions suitably contracted, to provide even a modestly accurate description of the molecular electronic environment. This leads to the necessity of dealing with very large matrices and numbers of integrals within the Hartree-Fock approximation and quickly becomes both numerically difficult and uneconomic.




Relativistic Quantum Theory of Atoms and Molecules


Book Description

This book is intended for physicists and chemists who need to understand the theory of atomic and molecular structure and processes, and who wish to apply the theory to practical problems. As far as practicable, the book provides a self-contained account of the theory of relativistic atomic and molecular structure, based on the accepted formalism of bound-state Quantum Electrodynamics. The author was elected a Fellow of the Royal Society of London in 1992.




Computational Methods for Electron—Molecule Collisions


Book Description

The collision of electrons with molecules and molecular ions is a fundamental pro cess in atomic and molecular physics and in chemistry. At high incident electron en ergies, electron-molecule collisions are used to deduce molecular geometries, oscillator strengths for optically allowed transitions, and in the case of electron-impact ionization, to probe the momentum distribution of the molecule itself. When the incident electron energy is comparable to or below those of the molecular valence electrons, the physics involved is particularly rich. Correlation and exchange effects necessary to describe such collision processes bear a close resemblance to similar efft:cts in the theory of electronic structure in molecules. Compound state formations, in the form of resonances and vir tual states, manifest themselves in experimental observables which provide details of the electron-molecule interactions. Ro-vibrational excitations by low-energy electron collisions exemplify energy transfer between the electronic and nuclear motion. The role of nonadiabatic interaction is raised here. When the final vibrational state is in the continuum, molecular dissociation occurs. Dissociative recombination and dissociative attachment are examples of such fragmentation processes. In addition to its fundamental nature, the study of electron-molecule collisions is also motivated by its relation to other fields of study and by its technological appli cations. The study of planetary atmospheres and the interstellar medium necessarily involve collision processes of electrons with molecules and molecular ions.




Gaussian Basis Sets for Molecular Calculations


Book Description

Physical Sciences Data, Volume 16: Gaussian Basis Sets for Molecular Calculations provides information pertinent to the Gaussian basis sets, with emphasis on lithium, radon, and important ions. This book discusses the polarization functions prepared for lithium through radon for further improvement of the basis sets. Organized into three chapters, this volume begins with an overview of the basis set for the most stable negative and positive ions. This text then explores the total atomic energies given by the basis sets. Other chapters consider the distinction between diffuse functions and polarization function. This book presents as well the exponents of polarization function. The final chapter deals with the Gaussian basis sets. This book is a valuable resource for chemists, scientists, and research workers.




Atoms and Molecules


Book Description

Atoms and Molecules describes the basic properties of atoms and molecules in terms of group theoretical methods in atomic and molecular physics. The book reviews mathematical concepts related to angular momentum properties, finite and continuous rotation groups, tensor operators, the Wigner-Eckart theorem, vector fields, and vector spherical harmonics. The text also explains quantum mechanics, including symmetry considerations, second quantization, density matrices, time-dependent, and time-independent approximation methods. The book explains atomic structure, particularly the Dirac equation in which its nonrelativistic approximation provides the basis for the derivation of the Hamiltonians for all important interactions, such as spin-orbit, external fields, hyperfine. Along with multielectron atoms, the text discusses multiplet theory, the Hartree-Fock formulation, as well as the electromagnetic radiation fields, their interactions with atoms in first and higher orders. The book explores molecules and complexes, including the Born-Oppenheimer approximation, molecular orbitals, the self-consistent field method, electronic states, vibrational and rotational states, molecular spectra, and the ligand field theory. The book can prove useful for graduate or advanced students and academicians in the field of general and applied physics.