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In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding eigenfunctions and eigenvalues for the Hamiltonian of a many-particle system is usually so difficult that it requires approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed in such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets automatically with computer techniques. The method has a wide range of applicability, and can be used to solve difficult eigenvalue problems in a number of fields. The book is of special interest to quantum theorists, computer scientists, computational chemists and applied mathematicians.
In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding eigenfunctions and eigenvalues for the Hamiltonian of a many-particle system is usually so difficult that it requires approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed in such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets automatically with computer techniques. The method has a wide range of applicability, and can be used to solve difficult eigenvalue problems in a number of fields. The book is of special interest to quantum theorists, computer scientists, computational chemists and applied mathematicians.
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
Novel Electronic Structure Theory: General Innovations and Strongly Correlated Systems, Volume 76, the latest release in the Advances in Quantum Chemistry series presents work and reviews of current work in quantum chemistry (molecules), but also includes scattering from atoms and solid state work of interest in physics. Topics covered in this release include the Present Status of Selected Configuration Interaction with Truncation Energy Error, Recent Developments in Asymptotic Expansions from Numerical Analysis and Approximation Theory, The kinetic energy Pauli enhancement factor and its role in determining the shell structure of atoms and molecules, Numerical Hartree-Fock and Many-Body Calculations for Diatomic Molecules, and more. - Provides reports on current work in molecular and atomic quantum mechanics - Contains work reported by many of the best scientists in the field - Presents the latest release in the Advances in Quantum Chemistry series
Hyperspherical harmonics are extremely useful in nuclear physics and reactive scattering theory. However, their use has been confined to specialists with very strong backgrounds in mathematics. This book aims to change the theory of hyperspherical harmonics from an esoteric field, mastered by specialists, into an easily-used tool with a place in the working kit of all theoretical physicists, theoretical chemists and mathematicians. The theory presented here is accessible without the knowledge of Lie-groups and representation theory, and can be understood with an ordinary knowledge of calculus. The book is accompanied by programs and exercises designed for teaching and practical use.
Quantum chemistry is simulating atomistic systems according to the laws of quantum mechanics, and such simulations are essential for our understanding of the world and for technological progress. Machine learning revolutionizes quantum chemistry by increasing simulation speed and accuracy and obtaining new insights. However, for nonspecialists, learning about this vast field is a formidable challenge. Quantum Chemistry in the Age of Machine Learning covers this exciting field in detail, ranging from basic concepts to comprehensive methodological details to providing detailed codes and hands-on tutorials. Such an approach helps readers get a quick overview of existing techniques and provides an opportunity to learn the intricacies and inner workings of state-of-the-art methods. The book describes the underlying concepts of machine learning and quantum chemistry, machine learning potentials and learning of other quantum chemical properties, machine learning-improved quantum chemical methods, analysis of Big Data from simulations, and materials design with machine learning. Drawing on the expertise of a team of specialist contributors, this book serves as a valuable guide for both aspiring beginners and specialists in this exciting field. - Compiles advances of machine learning in quantum chemistry across different areas into a single resource - Provides insights into the underlying concepts of machine learning techniques that are relevant to quantum chemistry - Describes, in detail, the current state-of-the-art machine learning-based methods in quantum chemistry
This text unravels those fundamental physical principles which explain how all matter behaves. It takes us from the foundations of quantum mechanics, through quantum models of atomic, molecular, and electronic structure, and on to discussions of spectroscopy, and the electronic and magnetic properties of molecules.
Chemists are used to the operational definition of symmetry, which crystallographers introduced long before the advent of quantum mechanics. The ball-and-stick models of molecules naturally exhibit the symmetrical properties of macroscopic objects. However, the practitioner of quantum chemistry and molecular modeling is not concerned with balls and sticks, but with subatomic particles: nuclei and electrons. This textbook introduces the subtle metaphors which relate our macroscopic understanding of symmetry to the molecular world. It gradually explains how bodily rotations and reflections, which leave all inter-particle distances unaltered, affect the study of molecular phenomena that depend only on these internal distances. It helps readers to acquire the skills to make use of the mathematical tools of group theory for whatever chemical problems they are confronted with in the course of their own research.
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.