Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Journal of Chemical Physics

The ab-initio density matrix renormalization group in practice

Roberto Olivares‐Amaya, Weifeng Hu, Naoki Nakatani, Sandeep Sharma, Jun Yang, Garnet Kin‐Lic Chan

Published Jan 15, 2015• 364 citations
Publisher

Abstract

The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

DOI
10.1063/1.4905329

Related papers

The Density Matrix Renormalization Group Algorithm in Quantum Chemistry

Konrad Heinrich Marti, Markus Reiher

Quantum Chemistry / Electron Correlation / Density Matrix Renormalization Group / Transition Metal Chemistry In this work, we derive the density matrix renormalization group (DMRG) algorithm in the language of configuration interaction. Furthermore, the development of DMRG in quantum chemistry is reviewed and DMRG-specific peculiarities are discussed. Finally, we discuss new results for a dinuclear μ -oxo bridged copper cluster, which is an important active-site structure in transition-metal chemistry, an area in which we pioneered the application of DMRG.

Oldenbourg Wissenschaftsverlag eBooks•Jan 1, 2010•26 citations

The Density Matrix Renormalization Group Algorithm in Quantum Chemistry

Konrad Heinrich Marti, Markus Reiher

Abstract In this work, we derive the density matrix renormalization group (DMRG) algorithm in the language of configuration interaction. Furthermore, the development of DMRG in quantum chemistry is reviewed and DMRG-specific peculiarities are discussed. Finally, we discuss new results for a dinuclear μ-oxo bridged copper cluster, which is an important active-site structure in transition-metal chemistry, an area in which we pioneered the application of DMRG.

Zeitschrift für Physikalische Chemie•Apr 1, 2010•210 citations

Ab Initio Density Matrix Renormalization Group Methodology And Computational Transition Metal Chemistry

Johannes Hachmann

This thesis is concerned with two topics from the field of computational electronic structure theory. In the first part we will describe our contributions to the ab initio density matrix renormalization group (DMRG) methodology in quantum chemistry, in particular our quadratically scaling local algorithm. We will present applications aimed towards new insights into the physics of conjugated π-electron systems as found, e.g., in organic electronic materials. The second part of this thesis covers our computational study of 3d-M(smif)2 complexes synthesized and characterized in the Wolczanski Group. These compounds exhibit unusual electronic structure phenomena which we address from a theoretical perspective.

•Apr 9, 2010•0 citations

Clifford augmented density matrix renormalization group for ab initio quantum chemistry

Lizhong Fu, Honghui Shang, Jinlong Yang +1 more

The recently proposed Clifford augmented density matrix renormalization group (CA-DMRG) method seamlessly integrates Clifford circuits with matrix product states and takes advantage of the expression power from both. CA-DMRG has been shown to be able to achieve higher accuracy than standard DMRG on commonly used lattice models, with only moderate computational overhead compared to the latter. In this work, we propose an efficient scheme in CA-DMRG to deal with ab initio quantum chemistry Hamiltonians and apply it to study several molecular systems. Our numerical results show that CA-DMRG can reach higher accuracy than DMRG using the same bond dimension, pointing out a promising route to push the boundary of solving ab initio quantum chemistry with strong static correlations.

Physical review. B./Physical review. B•Nov 12, 2025•2 citations

New trends in density matrix renormalization

Karen A. Hallberg

The density matrix renormalization group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applicability has now extended beyond condensed matter, and is successfully used in quantum chemistry, statistical mechanics, quantum information theory, and nuclear and high-energy physics as well. In this article, we briefly review the main aspects of the method and present some of the most relevant applications so as to give an overview of the scope and possibilities of DMRG. We focus on the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, finite-temperature simulations, phonons and disorder, field theory, time-dependent properties and the ab initio calculation of electronic states in molecules. The recent quantum information interpretation, the development of highly accurate time-dependent algorithms and the possibility of using the DMRG as the impurity-solver of the dynamical mean field method (DMFT) give new insights into its present and potential uses. We review the numerous very recent applications of these techniques where the DMRG has shown to be one of the most reliable and versatile methods in modern computational physics.

arXiv:cond-mat/0609039•Advances In Physics•Jul 1, 2006•339 citations

New Trends in Density Matrix Renormalization

K. Hallberg

(April 2006) The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applicability has now extended beyond Condensed Matter, and is successfully used in Quantum Chemistry, Statistical Mechanics, Quantum Information Theory, Nuclear and High Energy Physics as well. In this article, we briefly review the main aspects of the method and present some of the most relevant applications so as to give an overview on the scope and possibilities of DMRG. We focus on the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, finite temperature simulations, phonons and disorder, field theory, time-dependent properties and the ab initio calculation of electronic states in molecules. The recent quantum information interpretation, the development of highly accurate time-dependent algorithms and the possibility of using the DMRG as the impurity-solver of the Dynamical Mean Field Method (DMFT) give new insights into its present and potential uses. We review the numerous very recent applications of these techniques where the DMRG has shown to be one of the most reliable and

•Jan 1, 2006•183 citations
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
Quantum Chemistry / Electron Correlation / Density Matrix Renormalization Group / Transition Metal Chemistry In this work, we derive the density matrix renormalization group (DMRG) algorithm in the language of configuration interaction. Furthermore, the development of DMRG in quantum chemistry is reviewed and DMRG-specific peculiarities are discussed. Finally, we discuss new results for a dinuclear μ -oxo bridged copper cluster, which is an important active-site structure in transition-metal chemistry, an area in which we pioneered the application of DMRG.
This thesis is concerned with two topics from the field of computational electronic structure theory. In the first part we will describe our contributions to the ab initio density matrix renormalization group (DMRG) methodology in quantum chemistry, in particular our quadratically scaling local algorithm. We will present applications aimed towards new insights into the physics of conjugated π-electron systems as found, e.g., in organic electronic materials. The second part of this thesis covers our computational study of 3d-M(smif)2 complexes synthesized and characterized in the Wolczanski Group. These compounds exhibit unusual electronic structure phenomena which we address from a theoretical perspective.
The recently proposed Clifford augmented density matrix renormalization group (CA-DMRG) method seamlessly integrates Clifford circuits with matrix product states and takes advantage of the expression power from both. CA-DMRG has been shown to be able to achieve higher accuracy than standard DMRG on commonly used lattice models, with only moderate computational overhead compared to the latter. In this work, we propose an efficient scheme in CA-DMRG to deal with ab initio quantum chemistry Hamiltonians and apply it to study several molecular systems. Our numerical results show that CA-DMRG can reach higher accuracy than DMRG using the same bond dimension, pointing out a promising route to push the boundary of solving ab initio quantum chemistry with strong static correlations.
The density matrix renormalization group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applicability has now extended beyond condensed matter, and is successfully used in quantum chemistry, statistical mechanics, quantum information theory, and nuclear and high-energy physics as well. In this article, we briefly review the main aspects of the method and present some of the most relevant applications so as to give an overview of the scope and possibilities of DMRG. We focus on the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, finite-temperature simulations, phonons and disorder, field theory, time-dependent properties and the ab initio calculation of electronic states in molecules. The recent quantum information interpretation, the development of highly accurate time-dependent algorithms and the possibility of using the DMRG as the impurity-solver of the dynamical mean field method (DMFT) give new insights into its present and potential uses. We review the numerous very recent applications of these techniques where the DMRG has shown to be one of the most reliable and versatile methods in modern computational physics.
(April 2006) The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applicability has now extended beyond Condensed Matter, and is successfully used in Quantum Chemistry, Statistical Mechanics, Quantum Information Theory, Nuclear and High Energy Physics as well. In this article, we briefly review the main aspects of the method and present some of the most relevant applications so as to give an overview on the scope and possibilities of DMRG. We focus on the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, finite temperature simulations, phonons and disorder, field theory, time-dependent properties and the ab initio calculation of electronic states in molecules. The recent quantum information interpretation, the development of highly accurate time-dependent algorithms and the possibility of using the DMRG as the impurity-solver of the Dynamical Mean Field Method (DMFT) give new insights into its present and potential uses. We review the numerous very recent applications of these techniques where the DMRG has shown to be one of the most reliable and