Many-Body Methods for Atoms, Molecules and Clusters

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.

Presents many-body theory using the language of quantum chemistry and molecular physics Provides a concise, yet rigorous guide to many-body Green's functions, propagators, and Feynman diagrams Bridges the gap between the genuine many-body and conventional wave-function-based methods

Auteur

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.

Contenu
Part I Many-Electron Systems and the Electron Propagator.- Systems of identical particles.- Second quantization.- One-particle Green's function.- Part II Formalism of Diagrammatic Perturbation Theory.- Perturbation theory for the electron propagator.- Introducing diagrams.- Feynman diagrams.- Time-ordered or Goldstone diagrams.- Part III Approximation and Computational Schemes.- Self-energy and the Dyson equation.- Algebraic-diagrammatic construction (ADC).- Direct ADC procedure for the electron propagator.- Intermediate-state representation (ISR).- Order relations and separability.- Part IV N-Electronic excitations.- Polarization propagator.- ADC and ISR approaches to the polarization propagator.- Random-phase approximation (RPA).- Part V. A look at related methods.- Algebraic propagator methods.- Coupled-cluster methods for generalized excitations.- Appendix.