## Many-Electron Approaches in Physics, Chemistry and Mathematics: A Multidisciplinary ViewThis book provides a broad description of the development and (computational) application of many-electron approaches from a multidisciplinary perspective. In the context of studying many-electron systems Computer Science, Chemistry, Mathematics and Physics are all intimately interconnected. However, beyond a handful of communities working at the interface between these disciplines, there is still a marked separation of subjects. This book seeks to offer a common platform for possible exchanges between the various fields and to introduce the reader to perspectives for potential further developments across the disciplines. The rapid advances of modern technology will inevitably require substantial improvements in the approaches currently used, which will in turn make exchanges between disciplines indispensable. In essence this book is one of the very first attempts at an interdisciplinary approach to the many-electron problem. |

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### Contents

3 | |

2 Spurious Modes in Dirac Calculations and How to Avoid Them | 30 |

3 Tensor Product Approximation DMRG and Coupled Cluster Method in Quantum Chemistry | 53 |

4 Quantum Cluster Equilibrium | 77 |

5 Linear Response Methods in Quantum Chemistry | 97 |

Part IITopics in Density Functional Theoryand Related Approaches | 111 |

OrbitalFree Density Functionals | 113 |

7 TimeDependent Density Functional Theory | 135 |

14 The Computational Complexity of Density Functional Theory | 245 |

15 Computational Techniques for Density Functional Based Molecular Dynamics Calculations in PlaneWave and Localized Basis Sets | 261 |

Part IVInformation Theoryin ManyElectron Descriptions | 284 |

16 Towards the InformationTheoretic Construction of an OrbitalFree KineticEnergy Functional | 287 |

17 LiebRobinson Bounds and the Simulation of TimeEvolution of Local Observables in Lattice Systems | 301 |

Part VGreen FunctionBased Approaches | 319 |

18 Electronic Structure Calculations with LDA+DMFT | 320 |

19 The GW Approximation for the Electronic SelfEnergy | 343 |

8 Density Functional Theory for StronglyInteracting Electrons | 152 |

9 Towards the Computational Design of Compounds from First Principles | 169 |

10 Application of KohnSham DensityFunctional Theory to Real Materials | 191 |

11 The Quantum Energy Agrees with the Müller Energy up to Third Order | 207 |

12 Mathematical Aspects of Density Functionals and Density Matrix Functionals in Quantum Chemistry | 218 |

13 Some Important? Unsolved Mathematical Problems in Molecular Simulation | 235 |

Part IIITopics in Computer Science | 243 |

Part VITopics in Quantum Monte Carloand Related Approaches | 358 |

20 LevyLieb Principle Meets Quantum Monte Carlo | 361 |

21 The New Resonating Valence Bond Method for AbInitio Electronic Simulations | 376 |

22 Mathematical Perspective on Quantum Monte Carlo Methods | 393 |

Part VIIEpilogue | 410 |

23 On Some Open Problems in ManyElectron Theory | 411 |

### Other editions - View all

Many-Electron Approaches in Physics, Chemistry and Mathematics: A ... Volker Bach,Luigi Delle Site No preview available - 2014 |

Many-Electron Approaches in Physics, Chemistry and Mathematics: A ... Volker Bach,Luigi Delle Site No preview available - 2014 |

Many-Electron Approaches in Physics, Chemistry and Mathematics: A ... Volker Bach,Luigi Delle Site No preview available - 2016 |