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E-raamat: Electronic, Atomic and Molecular Calculations: Applying the Generator Coordinate Method

(Instituto de Quimica de Sao Carlos (IQSC), Universidade de Sao Paulo, Sao Carlos, Brazil), (Instituto de Quimica de Sao Carlos (IQSC), Universidade de Sao Paulo, Sao Carlos, SP, Brazil)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 30-Aug-2011
  • Kirjastus: Elsevier Science Ltd
  • Keel: eng
  • ISBN-13: 9780080547084
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Electronic, Atomic and Molecular Calculations: Applying the Generator Coordinate MethodSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 30-Aug-2011
  • Kirjastus: Elsevier Science Ltd
  • Keel: eng
  • ISBN-13: 9780080547084
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The Generator Coordinate Method (GCM) is a mathematical tool for the understanding of stable atomic nuclei. Electronic, Atomic and Molecular Calculations is designed to assist scientists applying GCM in the analysis of the electronic structure of atoms and molecules. There have been numerous publications covering nuclear physics and electronic structure of atoms and molecules, but this book is unique in the sense that it specifically addresses the application of GCM for such purposes. Using this book, researchers will be able to understand and calculate the electronic structure in a novel manner.

* Only book that covers the Generator Coordinate Method and applications for atoms, molecules and nuclei
* Clearly describes how the GCM can be used as a powerful tool for design of atomic basis sets
* Reviews current literature on GCM in atomic and molecular fields and a large part of the literature of the method in nuclear physics

Muu info

The first book on the GCM and applications
Preface xi
Acknowledgements xiii
Introduction
1(2)
The Generator Coordinate Method
3(6)
Introduction
3(1)
Background for the Formulation of the Method
3(1)
Formulation of the Method
4(1)
Applications in Nuclear Physics
5(1)
Some Alternative Proposals to the Generator Coordinate Method
6(3)
Analytical and Numerical Experiments for Simple Systems
9(10)
Introduction
9(1)
Analytical Solutions for the Griffin--Hill--Wheeler Equation
9(5)
Numerical Experiments for the Griffin--Hill--Wheeler Equation
14(5)
The Generator Coordinate Hartree--Fock Formalism
19(12)
Introduction
19(1)
The Background of the Hartree--Fock Scheme
19(2)
The Generator Coordinate Hartree--Fock Method
21(1)
Numerical Integration
22(3)
First Applications to the He and Be Atoms
25(6)
The He Atom with a Slater Orbital
25(1)
The He Atom with a Gaussian Orbital
26(1)
The Be Atom with GTOs
26(5)
Discretization Techniques
31(24)
Introduction
31(1)
A Model Problem: The Harmonic Oscillator
32(2)
Discretization of the Griffin--Hill--Wheeler Equation for the Harmonic Oscillator Problem
34(4)
The Integral Discretization
38(8)
Introduction
38(4)
The Harmonic Oscillator with Translated Gaussians
42(2)
The Hydrogen Atom with a Gaussian Generator Function
44(2)
A New Proposal for the Discretization of the Griffin--Hill--Wheeler--Hartree--Fock Equations
46(9)
Introduction
46(3)
The Polynomial Integral Discretization
49(6)
Role of the Weight Function in the Design of Efficient Basis Sets for Atomic and Molecular Nonrelativistic Calculations
55(24)
Introduction
55(1)
Weight Function and the Generation of Universal Basis Sets
56(19)
Slater and Gaussian Universal Basis Sets for the Ground and Certain Low-lying Excited States of the Neutral Atoms from Hydrogen to Xenon
56(5)
The Weight Functions
61(4)
Slater and Gaussian Universal Basis Sets for the Ground and Certain Low-lying Excited States of Positive and Negative Ions of the Atoms from Hydrogen to Xenon
65(7)
Role of the Weight Functions in the Evaluation of Total Electronic Energies
72(3)
Is the Generator Coordinate Weight Function a Distribution?
75(1)
The Future of Generating Basis Sets for Atomic and Molecular Calculations Using the GCHF Method
76(3)
The Generator Coordinate Dirac--Fock Method and Relativistic Calculations for Atoms and Molecules
79(72)
Introduction
79(1)
The Generator Coordinate Dirac--Fock--Coulomb Formalism
80(7)
The Generator Coordinate Dirac--Fock Method and the Generation of a Universal Gaussian Basis Set for the Relativistic Closed-Shell Atoms from Zinc to Nobelium
87(6)
The Generator Coordinate Dirac--Fock Method and the Generation of a Relativistic Universal Gaussian Basis Set for Atoms from Hydrogen to Nobelium
93(15)
Variational Prolapse Analysis for the Relativistic Universal Gaussian Basis Set Generated with the Generator Coordinate Dirac--Fock Method
100(8)
The Generator Coordinate Dirac--Fock--Breit Formalism
108(5)
A Polynomial Version of the Generator Coordinate Dirac--Fock Method
113(6)
The Polynomial Version of the Generator Coordinate Dirac--Fock Method and the Generation of Relativistic Adapted Gaussian Basis Sets
119(32)
Relativistic Adapted Gaussian Basis Sets for Hydrogen through Xenon
119(16)
Relativistic Adapted Gaussian Basis Sets for Cesium through Radon
135(16)
The Generator Coordinate Method and Connections with Natural Orbitals and Density Functional Theory
151(12)
Introduction
151(1)
Natural Orbitals
151(1)
An Integral Transform View of Natural Orbitals
151(5)
Density Functional Theory
156(1)
First Applications of the Generator Coordinate Method to Density Functional Theory
157(6)
FINAL REMARKS AND PERSPECTIVES
163(2)
APPENDIX: SELECTED UNIVERSAL AND ATOM-ADAPTED SLATER AND GAUSSIAN BASIS SETS FOR ATOMIC AND MOLECULAR CALCULATIONS
165(134)
Appendix 1
167(2)
Appendix 2
169(2)
Appendix 3
171(4)
Appendix 4
175(4)
Appendix 5
179(120)
Subject Index 299


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