Author: Harold David ToddPublisher:
ISBN:
Category :
Languages : en
Pages : 436
Book Description
Analytical Evaluation and Computation of Molecular Integrals, and Application to the 3B1 State of Methylene
Author: Harold David ToddRecent Advances In Computational Chemistry: Molecular Integrals Over Slater Orbitals
Author: Telhat OzdoganPublisher:
ISBN: 9788178953700
Category :
Languages : en
Pages : 255
Book Description
The object of this book is to present the methods used in the evaluation of molecular integrals over Slater orbitals, which occur in quantum chemical calculations of atoms, molecules and solids. The evaluation of molecular integrals is a dynamic research field at the heart of the computational chemistry, namely quantum theory of molecular electronic structure. One of the main difficulties in the application of rigorous quantum mechanical methods to the study of the electronic structure of polyatomic molecules has been the evaluation of molecular integrals. The use of Slater functions in molecular calculations was hindered in the 1950s by the enormous computational complexity of molecular integrals, due to the lack of advances in applied mathematics and computer technology. Soon in the 1950s the pragmatic solution was chosen: Slater orbitals were replaced by Gaussian ones in molecular calculations. This situation has been maintained along the last four decades, but it is changing at present and it seems to be inverted in the near future. The fundamental properties of atomic and molecular wave functions, such as nuclear and electron-electron cusps, exponential decay at infinity are known and it is relatively hard to find trial functions to satisfy them. Atom centered Slater functions help to describe the critical region around the nuclei efficiently, hence these have been used in a majority of quantum chemical studies of molecules. This type of basis function is particularly well-suited for atomic and molecular calculations. From the 1990s up to today, many efforts have been made by several groups to elaborate effective procedures for efficient calculation of molecular integrals over Slater orbitals and fructified in new programs for polyatomic molecules that already perform more efficiently than those using Gaussian orbitals in some applications. One of the most promising applications of Slater functions is the highly accurate determination of the electronic energy of ground and excited states, and diverse properties of atoms and molecules using explicit correlated wave functions. In particular the Hylleraas-Configuration Interaction (Hy-CI) method is considered as a generalization of the conventional CI procedure and can be extended to larger systems. Several chapters of this book are devoted to the analytical evaluation of the appearing integrals in the Hy-CI method. We have organized the molecular integrals in this book into the parts: history, atomic integrals, molecular integrals, relativistic integrals and integrals of properties. The integrals are correlated und uncorrelated. In all chapters new recent methods are presented by the authors, and a main topic is reviewed. The first chapter is a delighting historical review about Slater orbitals and the first and recent computer programs. The second chapter is a magnificent mathematical review of all integration methods over correlated atomic wave functions, which is extremely valuable for present and future scientists in this field. The evaluation of new molecular integrals over Slater orbitals with the flexibility of including also non-integer powers is the topic of the third chapter. Some mathematical techniques which can be helpful in the evaluation of correlated and uncorrelated molecular integrals, like the Hamiltonian in Hylleraas coordinates, appear in the fourth chapter. The fifth chapter accounts all the techniques which have been actually programmed in a molecular computer program, including discussions of their efficiency and performance. It gives a deep insight into the actual practical situation. The sixth chapter compiles the results of the only general method of evaluation of all appearing integrals in two-center molecules using the Hy-CI method. Relativistic integrals occurring in the Hy-CI method for the Dirac-Coulomb Hamiltonian are developed in the seventh chapter. In the chapter eight Coulomb integrals for the case of different orbital exponents are evaluated using the Fourier transform method. Finally, the last chapter is dedicated to the calculation of electric multipole moments using Slater orbitals. We believe that the advance of quantum chemistry depends on the efficient evaluation of molecular integrals over Slater orbitals. It is a pleasant duty to acknowledge here in part the wide assistance we have received from Prof. Peter Otto from the University Erlangen-Nürnberg, Germany, Prof. Nazmi Turan Okumusoglu, Rector of Rize University, Turkey, and The Scientific and Technological Research Council of Turkey (TUBITAK), and Prof. Philip E. Hoggan, Clermont University, France.
Analytic Evaluation of Multicenter Molecular Integrals
Author: Donald Edwin EllisApplications of Electronic Structure Theory
Author: Henry SchaeferPublisher: Springer Science & Business Media
ISBN: 1468485415
Category : Science
Languages : en
Pages : 470
Book Description
These two volumes deal with the quantum theory of the electronic structure of ab initio is the notion that approximate solutions molecules. Implicit in the term of Schrodinger'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 a sense, 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 developing new theoretical and computational methods and models. Henry F. Schaefer vii Contents Contents of Volume 3 xv Chapter 1. A Priori Geometry Predictions 1. A. Pople 1. Introduction . . . . . . . . . . . . . . . . . . . 1 2. Equilibrium Geometries by Hartree-Fock Theory 2 2. 1. Restricted and Unrestricted Hartree-Fock Theories 2 2. 2. Basis Sets for Hartree-Fock Studies . . . . . 4 2. 3. Hartree-Fock Structures for Small Molecules . 6 2. 4. Hartree-Fock Structures for Larger Molecules 12 3. Equilibrium Geometries with Correlation . . 18 4. Predictive Structures for Radicals and Cations 20 5. Conclusions 23 References 24 Chapter 2. Barriers to Rotation and Inversion Philip W. Payne and Leland C.
Quantities, Units and Symbols in Physical Chemistry
Author: International Union of Pure and Applied Chemistry. Physical and Biophysical Chemistry DivisionPublisher: Royal Society of Chemistry
ISBN: 0854044337
Category : Reference
Languages : en
Pages : 240
Book Description
Prepared by the IUPAC Physical Chemistry Division this definitive manual, now in its third edition, is designed to improve the exchange of scientific information among the readers in different disciplines and across different nations. This book has been systematically brought up to date and new sections added to reflect the increasing volume of scientific literature and terminology and expressions being used. The Third Edition reflects the experience of the contributors with the previous editions and the comments and feedback have been integrated into this essential resource. This edition has been compiled in machine-readable form and will be available online.
Reviews in Computational Chemistry, Volume 30
Author: Abby L. ParrillPublisher: John Wiley & Sons
ISBN: 1119355435
Category : Science
Languages : en
Pages : 404
Book Description
The Reviews in Computational Chemistry series brings together leading authorities in the field to teach the newcomer and update the expert on topics centered on molecular modeling. • Provides background and theory, strategies for using the methods correctly, pitfalls to avoid, applications, and references • Contains updated and comprehensive compendiums of molecular modeling software that list hundreds of programs, services, suppliers and other information that every chemist will find useful • Includes detailed indices on each volume help the reader to quickly discover particular topics • Uses a tutorial manner and non-mathematical style, allowing students and researchers to access computational methods outside their immediate area of expertise
Bulletin of the Chemical Society of Japan
Author: Nihon KagakkaiPublisher:
ISBN:
Category : Chemistry
Languages : en
Pages : 996
Book Description
Energy Research Abstracts
Author: Publisher:
ISBN:
Category : Power resources
Languages : en
Pages : 632
Book Description
Semiannual, with semiannual and annual indexes. References to all scientific and technical literature coming from DOE, its laboratories, energy centers, and contractors. Includes all works deriving from DOE, other related government-sponsored information, and foreign nonnuclear information. Arranged under 39 categories, e.g., Biomedical sciences, basic studies; Biomedical sciences, applied studies; Health and safety; and Fusion energy. Entry gives bibliographical information and abstract. Corporate, author, subject, report number indexes.
Semiempirical Methods of Electronic Structure Calculation
Author: Gerald SegalPublisher: Springer
ISBN: 9780306335075
Category : Science
Languages : en
Pages : 302
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.
Recent Progress in Coupled Cluster Methods
Author: Petr CárskyPublisher: Springer Science & Business Media
ISBN: 9048128854
Category : Science
Languages : en
Pages : 672
Book Description
I feel very honored that I have been asked to write a Foreword to this book. The subject of the book – “Coupled cluster theory” – has been around for about half a century. The basic theory and explicit equations for closed-shell ground states were formulated before 1970. At the beginning of the seventies the rst ab initio calcu- tion were carried out. At that time speed and memory of computers were very limited compared to today’s standards. Moreover, the size of one-electron bases employed was small, so that it was only possible to achieve an orientation in methodical aspects rather than to generate new signi cant results. Extensive use of the coupled-cluster method started at the beginning of the eighties. With the help of more powerful computers the results of coupled-cluster approaches started to yield more and more interesting results of relevance to the interpretation of experimental data. New ideas in methodology kept appearing and computer codes became more and more ef cient. This exciting situation continues to this very day. Remarkably enough, even the - quired equations can now be generated by a computer with the help of symbolic languages. The size of this monograph and the rich variety of articles it contains attests to the usefulness and viability of the couple-cluster formalism for the h- dling of many-electron correlation effects. This represents a vivid testimony of a tremendous work that has been accomplished in coupled-cluster methodology and its exploitation.