Umfang:
Online-Ressource (XI, 192 p)
,
online resource
Ausgabe:
Reproduktion Springer eBook Collection. Chemistry and Materials Science
ISBN:
9781461542919
Inhalt:
The current volume is a very practical book, consisting primarily of many examples and exercises. In particular, The Construction of Spin Eigenfunctions presents all aspects connected with the construction of spin eigenfunctions, and their relationship with many-electron antisymmetric wave functions. This book treats new aligorithms in a way that no previous books have. The Construction of Spin Eigenfunctions opens with a brief theoretical introduction. Due to the increasing importance of spin eigenfunctions in quantum chemistry, Dr. Pauncz has followed up with two helpful chapters on the symmetric group and its representations. The author has also calculated matrix elements of the Hamiltonian using spin eigenfunctions. Dr. Pauncz wraps up the book with an important new technique: the spin-coupled valence bond method. This book should be very useful to graduate students working in the field of molecular quantum mechanics. It also could be used as a text for a one-semester graduate course in physics or in chemistry
Anmerkung:
1. The Spin Operator and Spin Functions1.1 Introduction -- 1.2 Spin operators and Pauli matrices -- 1.3 Spin functions -- 1.4 The Dirac identity -- 1.5 Square brackets of spin functions -- 1.6 Graphical representation of the primitive spin functions -- 2. Genealogical Construction of Spin Eigenfunctions -- 2.1 Addition theorem of angular momenta -- 2.2 Addition theorem of spin forNelectrons -- 2.3 The spin degeneracy -- 2.4 Branching diagram symbol -- 2.5 Special properties of the branching diagram functions -- 2.6 The coefficient of a primitive spin function in a given branching diagram function -- 3. Serber Spin Functions -- 3.1 Serber spin functions -- 3.2 Geminal spin product functions. Serber path diagram -- 3.3 Serber branching diagram -- 3.4 Recursion formulas for the highest component -- 3.5 Special properties of the Serber functions -- 3.6 The coefficient of a geminal product in a given Serber function -- 3.7 The algorithm of Carrington and Doggett -- 4. Projected Spin Eigenfunctions -- 4.1 Projection operator -- 4.2 Expanded form of the projected function (Löwdin) -- 4.3 Projection of other primitive functions -- 4.4 Relation between the projected functions and the branching diagram functions -- 4.5 Calculation of the overlap matrix of the projected functions -- 5. Spin-Paired Spin Eigenfunctions -- 5.1 Spin-paired spin functions -- 5.2 The Rumer algorithm for the selection of linearly independent spin-paired spin functions -- 5.3 Extended Rumer diagrams (Simonetta) -- 5.4 The leading term (Simonetta) -- 5.5 Linear independence of spin-paired eigenfunctions -- 5.6 Overlap integrals between Rumer functions. -- 6. The Symmetric Group -- 6.1 Basic notions of the symmetric group -- 6.2 Classes of the symmetric group -- 6.3 Representations of the symmetric group -- 6.4 Young tableaux -- 6.5 Young’s orthogonal representation -- 6.6 The conjugate representation -- 6.7 The symmetric group algebra -- 6.8 The Young operator -- 7. Representations of SNGenerated by Spin Eigenfunctions -- 7.1 Representations of the symmetric group generated by the branching diagram functions -- 7.2 Yamanouchi-Kotani method for the representations -- 7.3 Branching diagram functions and Young tableaux -- 7.4 Representations of SNgenerated by the projected spin functions -- 7.5 Calculations of A(P) by the Rettrup-Pauncz algorithm -- 7.6 Correspondence between spin-paired functions and Young tableaux -- 7.7 Generation of projected spin functions by Young operators -- 8. Combination of Spatial and Spin Functions -- 8.1 Introduction -- 8.2 Antisymmetric wave function -- 8.3 Combination of spatial and spin functions -- 8.4 Representations of SNby the spatial functions ? jiS -- 9. Calculation of the Hamiltonian Matrix -- 9.1 Spin-free Hamiltonian -- 9.2 Branching diagram spin functions -- 9.3 The determinantal form of the wave function -- 9.4 Serber spin functions -- 9.5 Projected spin functions -- 9.6 Valence-bond spin function -- 9.7 Many-configuration wave functions -- 10. Spin-Coupled Functions -- 10.1 Introduction -- 10.2 Historical development -- 10.3 Spin-coupled wave functions -- 10.4 Spin-coupled valence-bond method -- 10.5 Core-valence separation -- 10.6 SPINS, computer program -- 11. Solutions to the Exercises -- 11.1 Chapter 1 -- 11.2 Chapter 2 -- 11.3 Chapter 3 -- 11.4 Chapter 4 -- 11.5 Chapter 5 -- 11.6 Chapter 6 -- 11.7 Chapter 7 -- 11.8 Chapter 8 -- 12. Index.
Weitere Ausg.:
ISBN 9781461369257
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 9780306464003
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 9781461369257
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 9781461542926
Sprache:
Englisch
DOI:
10.1007/978-1-4615-4291-9
URL:
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