Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 38
Book Description
Solution of Multi-center Molecular Integrals of Slater-type Orbitals
Author: Recent 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.
Analytical Methods Using Slater-Type Orbitals in Quantum Chemistry
Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 89
Book Description
Our main concern is with the development of a Slater-type orbital (STO) multicenter molecular integral package for use with standard ab initio quantum chemistry codes such as the Columbus code and Alchemy. Significant advances have been made toward this goal. A new strategy has been adopted: First program all molecular integrals in Mathematics (a computer algebra language that can give arbitrary precision with our alpha-function method); then, using assured accurate results as a guide, use FORTRAN to obtain speed and acceptable accuracy. We believe that this dual thrust will finally crack the 'intractable' problem of STO multicenter integrals. Applications will soon be made to real molecules.
ETO Multicenter Molecular Integrals
Author: C.A. WeatherfordPublisher: Springer Science & Business Media
ISBN: 9400979215
Category : Science
Languages : en
Pages : 188
Book Description
The First International Conference on ETO Multicenter Molecular Integrals was held August 3-6, 1981, on the Florida A&M university campus in Tallahassee, Florida, USA. Thirty four scientists from eight countries assembled in Tallahassee under the sponsorship of the Institute for Molecular Computations and the Physics Department at Florida A&M. Financial support is gratefully acknowledged from the National Science Foundation, U.S. Army Research Office (Durham), Office of Naval Research, the National Aeronautics and Space Admini stration (NASA), and Florida A&M University. In particular, the editors would like to thank Dr. Joe Majowicz and Dr. David Squire of the U.S. Army, and Dr. Aaron Temkin of NASA for their support and encouragement. We would also like to acknowledge the Atlanta University Resource Center for Science and Engineering for financial support in the pre paration of the manuscript. Also, of course, we sincerely appreciate the participation of the attendees and especially the contributors to this work. As a result of their presentations, the conference was a very intense and fertile forum for the exchange of ideas on a very important and historic problem of quantum chemistry. Finally, we want to thank Ms. Sonja Richardson for the enthusiastic, diligent and competent preparation of a very difficult manuscript. Charles A. Weatherford Herbert W. Jones vii C. A. Weatherford and H. W. Jones (eds.), ETO Multicenter Molecular Inteffrals, vii.
Advances in Quantum Chemistry
Author: Publisher: Elsevier
ISBN: 0443186642
Category : Science
Languages : en
Pages : 400
Book Description
Advances in Quantum Chemistry, Volume 88 presents the latest ongoing research at the forefront of Electronic structure theory. Chapters in the updated release include Spin-constrained Hartree-Fock and the generator coordinate method for the 2-site Hubbard model, Analytical evaluation of Hylleraas-CI Coulomb and Hybrid two-center Integrals over Slater orbitals, Hartree-Fock-Roothaan Theory of Molecular Compton Profiles Via Position Space Method, Analysis of Research Trend on the Molecular Integrals Over Slater Type Orbitals, An efficient approximation for accelerating convergence of numerical power series, Results for the 1D-Schroedinger equation, The aims and objectives of algebraic molecular orbital theory, and much more. Includes new theoretical methods Provides state-of-the art electron correlation, methods and effects Covers the challenge of excited electronic states
Scientific and Technical Aerospace Reports
Author: The DV-Xα Molecular-Orbital Calculation Method
Author: Tomohiko IshiiPublisher: Springer
ISBN: 331911185X
Category : Science
Languages : en
Pages : 358
Book Description
This multi-author contributed volume contains chapters featuring the development of the DV-Xα method and its application to a variety of problems in Materials Science and Spectroscopy written by leaders of the respective fields. The volume contains a Foreword written by the Chairs of Japanese and Korea DV-X alpha Societies. This book is aimed at individuals working in Quantum Chemistry.
Advances in Quantum Chemistry: Lowdin Volume
Author: Publisher: Academic Press
ISBN: 0128104007
Category : Science
Languages : en
Pages : 408
Book Description
Advances in Quantum Chemistry: Lowdin Volume presents a series of articles exploring aspects of the application of quantum mechanics to atoms, molecules, and solids. Celebrates Per-Olov Lowdin, who would have been 100 in 2016 Contains papers by many who use his ideas in theoretical chemistry and physics today
Research in Progress
Author: Ab Initio Molecular Orbital Calculations for Chemists
Author: William Graham RichardsPublisher: Oxford University Press, USA
ISBN:
Category : Science
Languages : en
Pages : 116
Book Description