Recent Advances In Computational Chemistry Molecular Integrals Over Slater Orbitals

Download or read book Recent Advances In Computational Chemistry: Molecular Integrals Over Slater Orbitals written by Telhat Ozdogan and published by . This book was released on 2008-01-01 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.