Author: John Scales Avery

Publisher: World Scientific

Published: 2011-10-31

Total Pages: 240

ISBN-13: 9814458953

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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. Contents:General ConsiderationsExamples from Atomic PhysicsExamples from Quantum ChemistryGeneralized Sturmians Applied to AtomsMolecular Orbitals Based on SturmiansAn Example from AcousticsAn Example from Heat ConductionSymmetry-Adapted Solutions by Iteration Readership: Researchers in quantum physics, theoretical/quantum chemistry and numerical and computational mathematics. Keywords:Group Theory;Quantum Theory;Configuration Interaction;Computational Algorithms;Generalized SturmiansKey Features:The book describes easy algorithms for automatic generation of symmetry-adapted basis functionsIt also discusses the Generalized Sturmian Method and its applications to both atomic and molecular calculations. The method leads to automatic scaling of basis functionsA new method is introduced which applies hyperspherical harmonic theory to the rapid calculation of interelectron repulsion integrals involving exponential-type orbitals

Download or read book Symmetry-Adapted Basis Sets written by John Scales Avery and published by World Scientific. This book was released on 2011-10-31 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:General ConsiderationsExamples from Atomic PhysicsExamples from Quantum ChemistryGeneralized Sturmians Applied to AtomsMolecular Orbitals Based on SturmiansAn Example from AcousticsAn Example from Heat ConductionSymmetry-Adapted Solutions by Iteration Readership: Researchers in quantum physics, theoretical/quantum chemistry and numerical and computational mathematics. Keywords:Group Theory;Quantum Theory;Configuration Interaction;Computational Algorithms;Generalized SturmiansKey Features:The book describes easy algorithms for automatic generation of symmetry-adapted basis functionsIt also discusses the Generalized Sturmian Method and its applications to both atomic and molecular calculations. The method leads to automatic scaling of basis functionsA new method is introduced which applies hyperspherical harmonic theory to the rapid calculation of interelectron repulsion integrals involving exponential-type orbitals