Many-Body Methods for Atoms, Molecules and Clusters

ISBN-13: 9783030066918 / Angielski / Miękka / 2018 / 332 str.

Jochen Schirmer

Spis treści

I. Many-Electron Systems and the Electron Propagator

1. Systems of identical particles 

2. Second quantization 

3. One-particle Green’s function 

II. Formalism of Diagrammatic Perturbation Theory 

4. Perturbation theory for the electron propagator 

5. Introducing diagrams 

6. Feynman diagrams 

7. Time-ordered or Goldstone diagrams

III. Approximations and Computational Schemes 

8. Self-energy and the Dyson equation 

9. Algebraic-diagrammatic construction (ADC) 

10. Direct ADC procedure for the electron propagator 

11. Intermediate-state representation (ISR) 

12. Order relations and separability 

IV. N-Electron Excitations 

13. Polarization propagator  

14. ADC and ISR approaches to the polarization propagator 

15. Random-phase approximation (RPA) 

V. A Look at Related Methods 

16. Algebraic propagator methods

17. Coupled-cluster methods for generalized excitations 

Appendix 

A1 Basic tools 

A2 Proof of the Gell-Mann and Low theorem 

A3 Proof of Wick’s theorem 

A4 Time-ordered diagrams: derivation of Goldstone rules 

A5 Dyson expansion method for the static self-energy part 

A6 Proofs of order relations 

A7 Linear response theory and the polarization propagator 

A8 Superoperator approach to the electron propagator 

A9 Compilation of ADC expressions 

O autorze

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.

Blurb

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.