Skip to main content

Über dieses Buch

The first volume of Lecture Notes in Quantum Chemistry (Lecture Notes in Chemistry 58, Springer Verlag, Berlin 1992) contained a compilation of selected lectures given at the two first European Summer Schools in Quantum Chemistry (ESQC), held in southern Sweden in August 1989 and 1991, respectively. The notes were written by the teachers at the school and covered a large range of topics in ab initio quantum chemistry. After the third summer school (held in 1993) it was decided to put together a second volume with additional material. Important lecture material was excluded in the first volume and has now been added. Such added topics are: integrals and integral derivatives, SCF theory, coupled-cluster theory, relativity in quantum chemistry, and density functional theory. One chapter in the present volume contains the exercise material used at the summer school and in addition solutions to all the exercises. It is the hope of the authors that the two volumes will find good use in the scientific community as textbooks for students, who are interested in learn­ ing more about modern methodology in molecular quantum chemistry. The books will be used as teaching material in the European Summer Schools in Quantum Chemistry, which are presently planned. Lund in July 1994 Bjorn Roos NOTES ON HARTREE-FOCK THEORY AND RELATED TOPICS JanAlmlof Department of Chemistry University of Minnesota Minneapolis, MN 55455. USA Contents: 1 • Introduction. 2 . The Born-Oppenheimer Approximation. 3. Determinant Wavefunctions and the Pauli Principle. 4. Expectation Values With a Determinant Wavefunction.



Notes on Hartree-Fock Theory and Related Topics

The numerical challenges encountered when addressing electronic structure problems from first principles in computational quantum chemistry are humbling. Solving the Schrödinger equation for a large molecular system amounts to handling sets of second-order differential or integro-differential equations, often with thousands of variables. Indeed, the large number of particles that have to be treated in a quantum-mechanical description of a chemical system is certainly one of the greatest obstacles to quantum chemistry. The equations may have millions of singularities, and an accuracy of a few parts per billion is usually required. While a lot of sophisticated method development has been devoted to this problem with spectacular progress in the last couple of decades, the current state of the art nevertheless leaves both room and need for improvement. Many problems where a theoretical-computational approach could have an immense potential would require a quantitative description of extended molecular systems, i.e., molecules in the range 102–104 atoms.
Jan Almlöf

Density Functional Theory

The subject of quantum chemistry may have reached an impasse. Keeping the discussion to ab initio quantum chemistry we now know how to do very large SCF calculations, thanks to the introduction of the Direct methodology by Almlöf[1]. We can also manage to work with good basis sets for such calculations, although I consider that 6–31G* are not good enough, and probably something nearer to TZ2P is required for definitive SCF calculations.
Nicholas C. Handy

Coupled-cluster Methods in Quantum Chemistry

The purpose of this course is to review extensively the methods and the motivations behind coupled-cluster approaches to molecular electronic structure. These methods had their origins — or, at least, were first used — in nuclear many-body theory. They were introduced into quantum chemistry in the 1960’s, but were relatively little used until the late 1970’s, perhaps in part because the original formulations used techniques, like second quantization and diagrammatic methods, that were unfamiliar to quantum chemists. As time passed, however, these methods were recast in more palatable mathematical forms; more importantly, efficient computational implementations appeared and demonstrated great robustness and high accuracy. In the last ten years coupled-cluster methods, or approximations to them, have become widely used when the aim is to obtain very accurate results for molecules that are well-described qualitatively at the Hartree-Fock level.
Peter R. Taylor

Methods of Relativistic Quantum Chemistry

The consideration of the electronic structure of atoms and molecules at the level of the relativistic quantum mechanics is a rather new area of quantum chemistry. The growing interest in relativistic methods for electronic structure calculations is strongly linked to the developments in chemistry of heavy atom compounds and their use in industry. Moreover, there is a number of chemical observations which show that for heavy atom compounds the interpretation of their electronic structure and properties cannot be achieved without the relativistic treatment.
Andrzej J. Sadlej

Exercises with solutions

The exercises in this book have been selected from those used at the European Summer-school in Quantum Chemistry, with a few additions. The proveniences of these exercises are sometimes unclear; however, we gratefully acknowledge contributions, work and communications with Lars Pettersson, Jeppe Olsen, Trygve Helgaker, Peter Taylor, Björn Roos, and Nicholas Handy. To you, and to any of the inevitably forgotten problem-text authors, thank you very much, and forgive us the liberties taken.
Roland Lindh, Per-Åke Malmqvist


Weitere Informationen