Many-Body Methods for Atoms, Molecules and Clusters

1. Front Matter

   Pages i-xii

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2. Many-Electron Systems and the Electron Propagator

   1. Front Matter

      Pages 1-1

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   2. Systems of Identical Particles

      • Jochen Schirmer

      Pages 3-17

   3. Second Quantization

      • Jochen Schirmer

      Pages 19-30

   4. One-Particle Green’s Function

      • Jochen Schirmer

      Pages 31-41

3. Formalism of Diagrammatic Perturbation Theory

   1. Front Matter

      Pages 43-43

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   2. Perturbation Theory for the Electron Propagator

      • Jochen Schirmer

      Pages 45-60

   3. Introducing Diagrams

      • Jochen Schirmer

      Pages 61-73

   4. Feynman Diagrams

      • Jochen Schirmer

      Pages 75-93

   5. Time-Ordered or Goldstone Diagrams

      • Jochen Schirmer

      Pages 95-108

4. Approximations and Computational Schemes

   1. Front Matter

      Pages 109-109

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   2. Self-Energy and the Dyson Equation

      • Jochen Schirmer

      Pages 111-134

   3. Algebraic–Diagrammatic Construction (ADC)

      • Jochen Schirmer

      Pages 135-146

   4. Direct ADC Procedure for the Electron Propagator

      • Jochen Schirmer

      Pages 147-159

   5. Intermediate-State Representation (ISR)

      • Jochen Schirmer

      Pages 161-175

   6. Order Relations and Separability

      • Jochen Schirmer

      Pages 177-191

5. N-Electron Excitations

   1. Front Matter

      Pages 193-193

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   2. Polarization Propagator

      • Jochen Schirmer

      Pages 195-204

   3. ADC and ISR Approaches to the Polarization Propagator

      • Jochen Schirmer

      Pages 205-221

   4. Random-Phase Approximation (RPA)

      • Jochen Schirmer

      Pages 223-237

This book provides an introduction to many-body methods for applications in quantum chemistry. These methods, originating in field-theory, offer an alternative to conventional quantum-chemical approaches to the treatment of the many-electron problem in molecules. Starting with a general introduction to the atomic and molecular many-electron problem, the book then develops a stringent formalism of field-theoretical many-body theory, culminating in the diagrammatic perturbation expansions of many-body Green's functions or propagators in terms of Feynman diagrams. It also introduces and analyzes practical computational methods, such as the field-tested algebraic-diagrammatic construction (ADC) schemes. The ADC concept can also be established via a wave-function based procedure, referred to as intermediate state representation (ISR), which bridges the gap between propagator and wave-function formulations. Based on the current rapid increase in computer power and the development of efficient computational methods, quantum chemistry has emerged as a potent theoretical tool for treating ever-larger molecules and problems of chemical and physical interest. Offering an introduction to many-body methods, this book appeals to advanced students interested in an alternative approach to the many-electron problem in molecules, and is suitable for any courses dealing with computational methods in quantum chemistry.

• Many-body methods in quantum chemistry
• Field-theoretical many-body methods
• Electronic states and transitions in molecules
• Feynman diagrams
• Algebraic-diagrammatic construction (ADC)
• Fundamentals of many-body physics
• Many-electron systems
• Electron propagator
• Diagrammatic perturbation theory
• Green’s function
• Goldstone diagrams
• Dyson equation

• Institute of Physical Chemistry, Heidelberg University, Heidelberg, Germany

  Jochen Schirmer

Prof. Dr. Jochen Schirmer studied physics at the universities of Munich and Göttingen (Germany). He obtained his physics diploma from the University of Munich and earned his PhD at Physics Department of the Technical University of Munich in 1977. Subsequently he held research positions as post-doctoral fellow at the University in Freiburg and at the Theoretical Chemistry group of L.S. Cederbaum in Heidelberg. From 1983-87, he worked at the Fritz-Haber-Institute of the Max Planck Society in Berlin, but finished his habilitation in Heidelberg in 1985. Prof. Schirmer further visited the University in Kaiserslautern (1987-89) and the California Institute of Technology, Pasadena, USA (1987/88) before finally returning to Heidelberg as professor for Physical Chemistry. He retired from this position in 2009.

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