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The text is organized into foundational two-electron examples and the theoretical extensions needed for larger molecular systems, followed by case studies that illustrate valence-bond descriptions of molecular structure. It also addresses how the stability of this description depends on basis sets, and it discusses using the public-domain CRUNCH program for further study. 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Gallup  \nVALENCE BOND METHODS  \nTheory and applications  \nValence bond theory is one of two commonly used methods in molecular quantum mechanics, the other is molecular orbital theory. This book focuses on the first of these methods, ab initio valence bond theory.  \nThe book is split into two parts. Part I gives simple examples of two-electron calculations and the necessary theory to extend these to larger systems. Part II gives a series of case studies of related molecule sets designed to show the nature of the valence bond description of molecular structure. It also highlights the stability of this description to varying basis sets. There are references to the CRUNCH computer program for molecular structure calculations, which is currently available in the public domain. Throughout the book there are suggestions for further study using CRUNCH to supplement discussions and questions raised in the text.  \nThe book will be of primary interest to researchers and students working on molecular electronic theory and computation in chemistry and chemical physics.  \nGORDON A . GALLUP was born (9 March 1927) and raised in St Louis, Missouri and attended the public schools there. After High School and a short stint in the US Navy, he attended Washington University (St Louis) and graduated with an AB in 1950. He received the PhD degree from the University of Kansas in 1953 and spent two years at Purdue University carrying out post-doctoral research. In 1955 he was appointed to the faculty of chemistry atthe University of Nebraska and rose through the ranks, becoming full professor in 1964. He spent a year at the Quantum Theory Project at the University of Florida, and a year in England at the University of Bristol on an SERC fellowship. In 1993 he retired from teaching and since then has spent time as a research professor with the Department of Physics and Astronomy at the University of Nebraska. His research interests over the years include infrared spectroscopy and molecule vibrations, theory of molecular electronic structure, valence bond theory, electron scattering from atoms and molecules, and dissociative electron attachment. During his career he has held grants from the National Science Foundation, the Department of Energy, and others. He has had over 100 articles published in 10–15 different chemistry and physics journals, as well as articles in edited compendia and review books.  \nThis Page Intentionally Left Blank  \nVALENCE BOND METHODS  \nTheory and applications  \nGORDON A. GALLUP  \nUniversity of Nebraska  \nPUBLISHED BY CAMBRIDGE UNIVERSITY PRESS (VIRTUAL PUBLISHING) FOR AND ON BEHALF OF THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE  \nThe Pitt Building, Trumpington Street, Cambridge CB2 IRP  \n40 West 20th Street, New York, NY 10011-4211, USA  \n477 Williamstown Road, Port Melbourne, VIC 3207, Australia  \n[http://www.cambridge.org](http://www.cambridge.org)  \n© Gordon A. Gallup 2002  \nThis edition © Gordon A. Gallup 2003 First published in printed format 2002  \nA catalogue record for the original printed book is available from the British Library and from the Library of Congress Original ISBN 0 521 80392 6 hardback  \nISBN 0 511 02037 6 virtual (netLibrary Edition)  \nTo my wife Grace, for all her encouragement, and to the memory of our son, Michael, 1956–1995 .  \nThis Page Intentionally Left Blank  \nContents  \nPreface page xiii  \nList of abbreviations xv  \nI Theory and two-electron systems  \n1 Introduction 3  \n1.1 History 3  \n1.2 Mathematical background 4  \n1.2.1 Schr¨odinger’s equation 5  \n1.3 The variation theorem 9  \n1.3.1 General variation functions 9  \n1.3.2 Linear variation functions 9  \n1.3.3 A 2 × 2 generalized eigenvalue problem 14  \n1.4 Weights of nonorthogonal functions 16  \n1.4.1 Weights without orthogonalization 18  \n1.4.2 Weights requiring orthogonalization 19  \n2 H2 and localized orbitals 23  \n2.1 The separation of spin and space variables 23  \n2.1.1 Th","cbCaid6GtKySKKDV","https://ap.wps.com/l/cbCaid6GtKySKKDV","pdf",2168574,255,"English","# Contents\n## I Theory and two-electron systems\n## 1 Introduction\n## 2 H2 and localized orbitals\n## 3 H2 and delocalized orbitals\n## 4 Three electrons in doublet states\n## 5 Advanced methods for larger molecules","[{\"question\":\"What is the focus of valence bond methods in this book?\",\"answer\":\"The book focuses on ab initio valence bond theory, contrasting it with molecular orbital theory and developing methods for molecular quantum mechanics.\"},{\"question\":\"How is the book structured across its two parts?\",\"answer\":\"Part I provides simple two-electron calculations and the theory needed to extend those ideas to larger systems, while Part II presents case studies of related molecule sets.\"},{\"question\":\"What role does the CRUNCH computer program play?\",\"answer\":\"The text references CRUNCH for molecular structure calculations and suggests using it to supplement discussions and questions throughout the book.\"}]","Valence Bond Methods - Theory and applications | PDF",1789974337,643]