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Density Matrix Renormalization Group (DMRG)-based Approaches in Computational Chemistry

1st Edition - August 21, 2022

Authors: Haibo Ma, Ulrich Schollwöck, Zhigang Shuai

Paperback ISBN:

9 7 8 - 0 - 3 2 3 - 8 5 6 9 4 - 2

eBook ISBN:

9 7 8 - 0 - 3 2 3 - 8 5 6 9 5 - 9

Density Matrix Renormalization Group (DMRG)-based Approaches in Computational Chemistry outlines important theories and algorithms of DMRG-based approaches and explores their use… Read more

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Density Matrix Renormalization Group (DMRG)-based Approaches in Computational Chemistry outlines important theories and algorithms of DMRG-based approaches and explores their use in computational chemistry. Beginning with an introduction to DMRG and DMRG-based approaches, the book goes on to discuss the key theories and applications of DMRG, from DMRG for semi-empirical and ab-initio quantum chemistry, to DMRG in embedded environments, frequency spaces and quantum dynamics. Drawing on the experience of its expert authors, sections detail recent ideas and key developments, providing an up-to-date view of current developments in the field for students and researchers in quantum chemistry.

Cover image
Title page
Table of Contents
Copyright
Preface
Chapter 1. Density matrix renormalization group
Abstract
1.1 Introduction
1.2 Infinite-system density matrix renormalization group
1.3 Finite-system density matrix renormalization group
References
Chapter 2. Tensor network states: matrix product states and relatives
Abstract
2.1 Tensor decompositions
2.2 Schmidt decomposition and quantum entanglement
2.3 Matrix product state
2.4 Matrix product operator
2.5 Ground state calculations with MPS
References
Chapter 3. Density matrix renormalization group for semiempirical quantum chemistry
Abstract
3.1 Introduction
3.2 Semiempirical model Hamiltonian
3.3 Symmetrized density matrix renormalization group algorithm
3.4 Applications
3.5 Summary
Acknowledgments
References
Chapter 4. Density matrix renormalization group for ab initio quantum chemistry Hamiltonian
Abstract
4.1 Renormalized operator-based density matrix renormalization group implementation
4.2 Matrix product operator-based density matrix renormalization group implementation
4.3 Optimal construction for matrix product operators
4.4 Symmetries and spin adaption
4.5 Reduced density matrix
4.6 Orbital selection and ordering
4.7 Error estimation
4.8 Component analysis of density matrix renormalization group wave function
4.9 Quantum information theory analysis
4.10 Density matrix renormalization group for larger active spaces
4.11 Relativistic density matrix renormalization group
4.12 High-performance ab initio density matrix renormalization group
4.13 Tensor network states
References
Chapter 5. Density matrix renormalization group with orbital optimization
Abstract
5.1 Orbital rotation
5.2 The multiconfigurational self-consistent field methods
5.3 Density matrix renormalization group self-consistent field methods
5.4 Excited state calculation
5.5 Analytic gradient and geometry optimization
5.6 Molecular spectra
5.7 Beyond Born–Oppenheimer approximation
5.8 Applications
References
Chapter 6. Post-density matrix renormalization group
Abstract
6.1 Fundamentals for multireference quantum chemical calculations
6.2 Density matrix renormalization group-multireference configuration interaction
6.3 Density matrix renormalization group-multireference perturbation theory
6.4 Density matrix renormalization group-coupled cluster theory
6.5 Hybridization of density matrix renormalization group with density functional theory
6.6 Density matrix renormalization group-adiabatic connection
6.7 Embedding density matrix renormalization group in environments
6.8 Summary and outlook
References
Chapter 7. DMRG in frequency space
Abstract
7.1 Introduction
7.2 Spectral function in linear response regime
7.3 Algorithms at zero temperature
7.4 Finite temperature algorithms
7.5 Applications
7.6 Summary and outlook
References
Further reading
Chapter 8. Time-dependent density matrix renormalization group
Abstract
8.1 Overview
8.2 Time evolution algorithms
8.3 Finite temperature algorithms
8.4 Applications
8.5 Summary and outlook
References
Index

Haibo Ma

Haibo Ma is Professor of Theoretical Chemistry at Nanjing University. He has a B.S. and a Ph.D. from Nanjing University in 2002 and 2007 respectively. He has received the Humboldt research Fellowship from the Alexander von Humboldt foundation (2007-2009) and Tang Au-Qing youth award on theoretical chemistry from Chinese chemical society (2018). His main research interests focus on the development and implementation of renormalization group-based quantum chemical methods as well as their applications in the study of strongly correlated systems and excited state processes.

Affiliations and expertise

Professor of Theoretical Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, China

Ulrich Schollwöck

Ulrich Schollwöck is Professor of Theoretical Physics at the Ludwig-Maximilian University of Munich. He has a MSc from Balliol College, University of Oxford in 1991, a Diploma in Physics from the University of Munich in 1993, and a PhD from the French Atomic Energy Commission in 1995. His key interest are strongly correlated quantum systems with a focus on the development of new algorithms for large-scale simulations. He is a leading expert for the density-matrix renormalization group and was a pioneer in applying it to quantum systems far from equilibrium. He is a Fellow of the American Physical Society (2006) and Academy of Science member in Germany (2007). He has received the Gerhard Hess prize of the German Research Foundation (2000) and has been Fellow of the Institute of Advanced Study in Berlin (2009/2010). He is vice-president of the German Association of University Professors and Lecturers, scientific advisory board member of the Krupp foundation and of the Alexander von Humboldt foundation, and trustee of the German Museum of Science and Technology.

Affiliations and expertise

Department of Physics, Ludwig-Maximilian University of Munich, Munchen, Germany

Zhigang Shuai

Zhigang Shuai is a Changjiang Scholar Professor at Tsinghua University. He received B. Sc. (physics major) from Sun Yat-sen University in 1983 and his Ph.D. degree (in theoretical physics) from Fudan University in 1989. His research interests focus on the development of computational methodologies for modelling organic and polymeric functional materials. He has devised computational methods for the luminescence spectra and quantum efficiency, carrier mobility, thermoelectric conversion, and photovoltaic processes in organic/polymeric and layered nanomaterials. He extended the density matrix renormalization group theory for investigating the excited state structures and dynamical processes, light-emitting property, and nonlinear optical responses for conjugated polymers since 1996. He is the Vice President of the International Academy of Quantum Molecular Science, and the Vice President of the Chinese Chemical Society.

Affiliations and expertise

Department of Chemistry, Tsinghua University, Beijing, China