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Second Quantized Approach to Quantum Chemistry: An Elementary Introduction Softcover reprint of the original 1st ed. 1989 [Pehme köide]

  • Formaat: Paperback / softback, 184 pages, kõrgus x laius: 235x155 mm, kaal: 318 g, XIII, 184 p., 1 Paperback / softback
  • Ilmumisaeg: 13-Dec-2011
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642747574
  • ISBN-13: 9783642747571
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  • Formaat: Paperback / softback, 184 pages, kõrgus x laius: 235x155 mm, kaal: 318 g, XIII, 184 p., 1 Paperback / softback
  • Ilmumisaeg: 13-Dec-2011
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642747574
  • ISBN-13: 9783642747571
The aim of this book is to give a simple, short, and elementary introduction to the second quantized formalism as applied to a many-electron system. It is intended for those, mainly chemists, who are familiar with traditional quantum chemistry but have not yet become acquainted with second quantization. The treatment is, in part, based on a series of seminars held by the author on the subject. It has been realized that many quantum chemists either interested in theory or in applications, being educated as chemi~ts and not as physicists, have never devoted themselves to taking a course on the second quantized approach. Most available textbooks on this topic are not very easy to follow for those who are not trained in theory, or they are not detailed enough to offer a comprehensive treatment. At the same time there are several papers in quantum chemical literature which take advantage of using second quantization, and it would be worthwhile if those papers were accessible for a wider reading public. For this reason, it is intended in this survey to review the basic formalism of second quantization, and to treat some selected chapters of quantum chemistry in this language. Most derivations will be carried out in a detailed manner, so the reader need not accept gaps to understand the result.

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Springer Book Archives
List of Symbols
xiii
1 Introduction
1(5)
1.1 Importance of Second Quantization
1(1)
1.2 The One-Electron Model
2(4)
2 Concept of Creation and Annihilation Operators
6(12)
2.1 The Vacuum State
6(1)
2.2 Creating Electrons
6(3)
2.3 Particle Number Representation
9(1)
2.4 Annihilating Electrons
10(2)
2.5 Commutator Relation between Creation and Annihilation Operators
12(2)
2.6 The Adjoint Relation -- Role of Orthogonality of One-Particle States
14(2)
2.7 Summary of the Properties of Creation/Annihilation Operators
16(2)
3 Particle Number Operators
18(4)
4 Second Quantized Representation of Quantum Mechanical Operators
22(11)
4.1 General
22(1)
4.2 One-Electron Operators
23(3)
4.3 Two-Electron Operators
26(3)
4.4 Second Quantized Form of the Born-Oppenheimer Hamiltonian
29(1)
4.5 Hermiticity of Second Quantized Operators
30(3)
5 Evaluation of Matrix Elements
33(7)
5.1 Basic Matrix Elements
33(2)
5.2 Concept of the Fermi Vacuum
35(5)
6 Advantages of Second Quantization - Illustrative Examples
40(6)
6.1 General
40(1)
6.2 Overlap of two Determinants
41(1)
6.3 Huckel Energy Expression
42(2)
6.4 Interaction of Two Electrons
44(2)
7 Density Matrices
46(7)
7.1 First-Order Density Matrix
46(3)
7.2 Second-Order Density Matrix
49(2)
7.3 Hartree-Fock Energy Expression
51(2)
8 Connection to "Bra and Ket" Formalism
53(6)
9 Using Spatial Orbitals
59(7)
10 Some Model Hamiltonians in Second Quantized Form
66(21)
10.1 π-Electron Hamiltonians
66(7)
10.1.1 Huckel Level
66(4)
10.1.2 Hubbard Model
70(2)
10.1.3 Pariser-Parr-Pople (PPP) Model
72(1)
10.2 Particle-Hole Symmetry
73(7)
10.3 All-Valence Electron Hamiltonians
80(3)
10.4 The Hartree-Fock Hamiltonian
83(4)
11 The Brillouin Theorem
87(6)
12 Many-Body Perturbation Theory
93(10)
13 Second Quantization for Nonorthogonal Orbitals
103(11)
13.1 Anticommutation Rules
103(5)
13.2 The Hamiltonian in Nonorthogonal Representations
108(3)
13.3 Extended Huckel Theory
111(3)
14 Second Quantization and Hellmann-Feynman Theorem
114(7)
14.1 General
114(2)
14.2 Variation of Energy-Orthogonal Basis Set
116(1)
14.3 Variation of Energy-Nonorthogonal Basis Set
117(2)
14.4 Special Case: The SCF Gradient Formula
119(2)
15 Intermolecular Interactions
121(16)
15.1 The Operator for Interaction
121(10)
15.2 Symmetry-Adapted Perturbation Theory
131(6)
16 Quasiparticle Transformations
137(16)
16.1 One-Particle Transformations
137(4)
16.2 Two-Particle Transformations
141(4)
16.3 A Theory of the Local Chemical Bond
145(8)
17 Miscellaneous Topics Related to Second Quantization
153(10)
17.1 Spin Operators and Spin Hamiltonians
153(6)
17.2 Unitary Group Approach
159(4)
18 Problem Solutions
163(12)
19 References
175(6)
Index 181