Hyperspherical Harmonics and Generalized Sturmians: 4 (Progress in Theoretical Chemistry and Physics, 4) - Softcover

Avery, John S.

Softcover

ISBN 10: 1402004095 ISBN 13: 9781402004094

Publisher: Springer, 2002

Synopsis

n Angular Momentum Theory for Diatomic Molecules, R R method of trees, 3 construct the wave functions of more complicated systems for ex- ple many electron atoms or molecules. However, it was soon realized that unless the continuum is included, a set of hydrogenlike orbitals is not complete. To remedy this defect, Shull and Lowdin [273] - troduced sets of radial functions which could be expressed in terms of Laguerre polynomials multiplied by exponential factors. The sets were constructed in such a way as to be complete, i. e. any radial fu- tion obeying the appropriate boundary conditions could be expanded in terms of the Shull-Lowdin basis sets. Later Rotenberg [256, 257] gave the name "Sturmian" to basis sets of this type in order to emp- size their connection with Sturm-Liouville theory. There is a large and rapidly-growing literature on Sturmian basis functions; and selections from this literature are cited in the bibliography. In 1968, Goscinski [138] completed a study ofthe properties ofSt- rnian basis sets, formulating the problem in such a way as to make generalization of the concept very easy. In the present text, we shall follow Goscinski's easily generalizable definition of Sturmians.

About this title

Review

From the reviews:
"This book should find its place on the shelves of theoretical chemists as a good companion to other well-known books by this author: "Creation and annihilation operators" and "Quantum theory of atoms, molecules and photons"."
(Theoretical Chemistry Accounts, 106:236 (2001)

Synopsis

This book explores the connections between the theory of hyperspherical harmonics, momentum-space quantum theory, and generalized Sturmian basis functions; and it introduces methods which may be used to solve many-particle problems directly, without the use of the self-consistent-field approximation. The method of many-electron Sturmians offers an interesting and fresh alternative to the usual SCF-CI methods for calculating atomic and molecular structure. When many-electron Sturmians are used, and when the basis potential is chosen to be the attractive potential of the nuclei in the system, the following advantages are offered: the matrix representation of the nuclear attraction potential is diagonal; the kinetic energy term vanishes from the secular equation; the Slater exponents of the atomic orbitals are automatically optimized; convergence is rapid; a correlated solution to the many-electron problem can be obtained directly, without the use of the SCF approximation; and excited states can be obtained with good accuracy.

Edition details

• Publisher: Springer
• Publication date: 2002
• Language: English
• ISBN 10: 1402004095
• ISBN 13: 9781402004094
• Binding: Paperback
• Number of pages: 204