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 Physical Chemistry Letters

Equation-of-Motion Block-Correlated Coupled Cluster Method for Excited Electronic States of Strongly Correlated Systems

Haodong Zhang, Jingxiang Zou, Xiaochuan Ren, Shuhua Li

Published Jul 21, 2023• 10 citations
Publisher

Abstract

An equation-of-motion block-correlated coupled cluster method based on the generalized valence bond wave function (EOM-GVB-BCCC) is proposed to describe low-lying excited states for strongly correlated systems. The EOM-GVB-BCCC2b method with up to two-pair correlation has been implemented and tested for a few strongly correlated systems. For a water hexamer with stretched O-H bonds, which is beyond the capability of the CASSCF method, EOM-GVB-BCCC2b provides very close results as the density matrix renormalization group (DMRG). For four conjugated diradical species with triplet ground states, we found that their vertical S-T gaps from EOM-GVB-BCCC2b are also quite consistent with the DMRG results. This new method is expected to be a promising theoretical tool for describing the low-lying excited states of strongly correlated systems with large active spaces.

DOI
10.1021/acs.jpclett.3c01474

Related papers

Equation-of-Motion Block-Correlated Coupled Cluster Method with up to Three-Block Correlation for Excited Electronic States of Strongly Correlated Systems

Haodong Zhang, Jingxiang Zou, Xiaochuan Ren +1 more

The equation-of-motion generalized valence bond (GVB) based block-correlated coupled cluster approach with up to three-block correlation (termed EOM-GVB-BCCC3) has been implemented to describe low-lying excited states of strongly correlated systems with large active spaces. The computational time of EOM-GVB-BCCC3 scales as the fifth power of the system size. The method is then applied to investigate low-lying excited states in several strongly correlated systems. Our results demonstrate that EOM-GVB-BCCC3 could provide satisfactory results for the excited states with different spin multiplicities as the complete active space configuration interaction or the density matrix renormalization group method. EOM-GVB-BCCC3 shows significant improvement compared to EOM-GVB-BCCC2b proposed previously. This work demonstrates the potential of EOM-GVB-BCCC3 as a promising tool in investigating low-lying excited states of strongly correlated systems with large active spaces.

The Journal of Physical Chemistry Letters•May 2, 2025•6 citations

Equation-of-Motion Block-Correlated Coupled Cluster Theory with up to Four-Block Correlation for Excited Electronic States of Strongly Correlated Systems

Jun Lin, Xiaochuan Ren, Haodong Zhang +2 more

The theoretical treatment of low-lying excited states in strongly correlated (SC) systems, particularly those with multi-electron excitation character, typically requires computational methods with exponential scaling. To address this bottleneck, we develop the equation-of-motion generalized valence bond based block-correlated coupled cluster approach with up to four-block correlation (EOM-GVB-BCCC4). This method is capable of capturing low-lying excited states of SC systems with large active spaces with a polynomial O ( N 6 ) cost. We show that this approach provides a noticeable improvement over its lower-order truncated schemes, successfully identifying the doubly excited triplet–triplet pair state in singlet-fission candidates that were missed by its EOM-GVB-BCCC3 variant. Furthermore, the method achieves remarkably high accuracy for transition-metal complexes and organic diradicals, yielding excitation energies in excellent agreement with density matrix renormalization group (DMRG) benchmarks. These results highlight EOM-GVB-BCCC4 as a powerful method for investigating SC systems with large active spaces that are beyond the reach of conventional multireference approaches.

The Journal of Physical Chemistry Letters•Mar 4, 2026•3 citations

Efficient Implementation of Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Strongly Correlated Systems

Jingxiang Zou, Qingchun Wang, Xiaochuan Ren +3 more

An optimized implementation of block-correlated coupled cluster theory based on the generalized valence bond wave function (GVB-BCCC) for the singlet ground state of strongly correlated systems is presented. The GVB-BCCC method with two-pair correlation (GVB-BCCC2b) or up to three-pair correlation (GVB-BCCC3b) will be the focus of this work. Three major techniques have been adopted to dramatically accelerate GVB-BCCC2b and GVB-BCCC3b calculations. First, the GVB-BCCC2b and GVB-BCCC3b codes are noticeably optimized by removing redundant calculations. Second, independent amplitudes are identified by constraining excited configurations to be pure singlet states and only independent amplitudes need to be solved. Third, an incremental updating scheme for the amplitudes in solving the GVB-BCCC equations is adopted. With these techniques, accurate GVB-BCCC3b calculations are now accessible for systems with relatively large active spaces (50 electrons in 50 orbitals) and GVB-BCCC2b calculations are affordable for systems with much larger active spaces. We have applied GVB-BCCC methods to investigate three typical kinds of systems: polyacenes, pentaprismane, and [Cu 2 O 2 ] 2+ isomers. For polyacenes, we demonstrate that GVB-BCCC3b can capture more than 94% of the total correlation energy even for 12-acene with 50 π electrons. For the potential energy curve of simultaneously stretching 15 C–C bonds in pentaprismane, our calculations show that the GVB-BCCC3b results are quite close to the results from the density matrix renormalization group (DMRG) over the whole range. For two dinuclear copper oxide isomers, their relative energy predicted by GVB-BCCC3b is also in good accord with the DMRG result. All calculations show that the inclusion of three-pair correlation in GVB-BCCC is critical for accurate descriptions of strongly correlated systems.

Journal of Chemical Theory and Computation•Aug 3, 2022•19 citations

Block-Correlated Coupled Cluster Theory with up to Four-Pair Correlation for Accurate Static Correlation of Strongly Correlated Systems

Xiaochuan Ren, Jingxiang Zou, Haodong Zhang +2 more

A block-correlated coupled cluster method with up to four-pair correlation based on the generalized valence bond wave function (GVB-BCCC4) is first implemented, which offers an alternative method for electronic structure calculations of strongly correlated systems. We developed some techniques to derive a set of compact and cost-effective equations for GVB-BCCC4, which include the definition of n -block ( n = 1–4) Hamiltonian matrices, the combination of excitation operators, and the definition of independent amplitudes. We then applied the GVB-BCCC4 method to investigate several potential energy surfaces of strongly correlated systems with singlet ground states. Our calculations demonstrate that the GVB-BCCC4 method can provide nearly exact static correlation energies as the density matrix renormalization group method (on the basis of the same GVB orbitals). This work highlights the significance of four-pair correlation in quantitative descriptions of static correlation energy for strongly correlated systems.

The Journal of Physical Chemistry Letters•Jan 11, 2024•17 citations

Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Singlet–Triplet Energy Gaps of Strongly Correlated Systems

Xiaochuan Ren, Jingxiang Zou, Wei Li +1 more

A block-correlated coupled cluster (BCCC) method based on the triplet generalized valence bond (GVB) wave function (GVB-BCCC) has been implemented for the first time. By introducing several techniques, we have developed a practical and efficient GVB-BCCC code. The GVB-BCCC3 method (with up to three-pair correlation) can be used to deal with strongly correlated (SC) systems with triplet or singlet ground states, allowing singlet-triplet (S-T) energy gaps in the active space of SC systems computationally available. For selected SC systems, our calculations show that GVB-BCCC3 can always provide correct ground-state spin multiplicity as the complete active space configuration interaction (CASCI) or density matrix renormalization group (DMRG). Furthermore, we found that the S-T energy gaps from GVB-BCCC3 are quite consistent with CASCI or DMRG results. This work demonstrates that GVB-BCCC3 is a promising theoretical tool for describing S-T energy gaps within the active space of SC systems with large active spaces.

The Journal of Physical Chemistry Letters•Nov 5, 2024•8 citations

Describing Strong Correlation with Block-Correlated Coupled Cluster Theory

Qingchun Wang, Mingzhou Duan, Enhua Xu +2 more

A block-correlated coupled cluster (BCCC) method based on the generalized valence bond (GVB) wave function (GVB-BCCC in short) is proposed and implemented at the ab initio level, which represents an attractive multireference electronic structure method for strongly correlated systems. The GVB-BCCC method is demonstrated to provide satisfactory descriptions for multiple bond breaking in small molecules, although the GVB reference function is qualitatively wrong for the studied processes. For a challenging prototype of strongly correlated systems, tridecane with all 12 single C–C bonds at various distances, our calculations have shown that the GVB-BCCC2b method can provide highly comparable results as the density matrix renormalization group method for potential energy surfaces along simultaneous dissociation of all C–C bonds.

arXiv:2007.05989•The Journal of Physical Chemistry Letters•Aug 18, 2020•37 citations
An equation-of-motion block-correlated coupled cluster method based on the generalized valence bond wave function (EOM-GVB-BCCC) is proposed to describe low-lying excited states for strongly correlated systems. The EOM-GVB-BCCC2b method with up to two-pair correlation has been implemented and tested for a few strongly correlated systems. For a water hexamer with stretched O-H bonds, which is beyond the capability of the CASSCF method, EOM-GVB-BCCC2b provides very close results as the density matrix renormalization group (DMRG). For four conjugated diradical species with triplet ground states, we found that their vertical S-T gaps from EOM-GVB-BCCC2b are also quite consistent with the DMRG results. This new method is expected to be a promising theoretical tool for describing the low-lying excited states of strongly correlated systems with large active spaces.
The equation-of-motion generalized valence bond (GVB) based block-correlated coupled cluster approach with up to three-block correlation (termed EOM-GVB-BCCC3) has been implemented to describe low-lying excited states of strongly correlated systems with large active spaces. The computational time of EOM-GVB-BCCC3 scales as the fifth power of the system size. The method is then applied to investigate low-lying excited states in several strongly correlated systems. Our results demonstrate that EOM-GVB-BCCC3 could provide satisfactory results for the excited states with different spin multiplicities as the complete active space configuration interaction or the density matrix renormalization group method. EOM-GVB-BCCC3 shows significant improvement compared to EOM-GVB-BCCC2b proposed previously. This work demonstrates the potential of EOM-GVB-BCCC3 as a promising tool in investigating low-lying excited states of strongly correlated systems with large active spaces.
The theoretical treatment of low-lying excited states in strongly correlated (SC) systems, particularly those with multi-electron excitation character, typically requires computational methods with exponential scaling. To address this bottleneck, we develop the equation-of-motion generalized valence bond based block-correlated coupled cluster approach with up to four-block correlation (EOM-GVB-BCCC4). This method is capable of capturing low-lying excited states of SC systems with large active spaces with a polynomial O ( N 6 ) cost. We show that this approach provides a noticeable improvement over its lower-order truncated schemes, successfully identifying the doubly excited triplet–triplet pair state in singlet-fission candidates that were missed by its EOM-GVB-BCCC3 variant. Furthermore, the method achieves remarkably high accuracy for transition-metal complexes and organic diradicals, yielding excitation energies in excellent agreement with density matrix renormalization group (DMRG) benchmarks. These results highlight EOM-GVB-BCCC4 as a powerful method for investigating SC systems with large active spaces that are beyond the reach of conventional multireference approaches.
An optimized implementation of block-correlated coupled cluster theory based on the generalized valence bond wave function (GVB-BCCC) for the singlet ground state of strongly correlated systems is presented. The GVB-BCCC method with two-pair correlation (GVB-BCCC2b) or up to three-pair correlation (GVB-BCCC3b) will be the focus of this work. Three major techniques have been adopted to dramatically accelerate GVB-BCCC2b and GVB-BCCC3b calculations. First, the GVB-BCCC2b and GVB-BCCC3b codes are noticeably optimized by removing redundant calculations. Second, independent amplitudes are identified by constraining excited configurations to be pure singlet states and only independent amplitudes need to be solved. Third, an incremental updating scheme for the amplitudes in solving the GVB-BCCC equations is adopted. With these techniques, accurate GVB-BCCC3b calculations are now accessible for systems with relatively large active spaces (50 electrons in 50 orbitals) and GVB-BCCC2b calculations are affordable for systems with much larger active spaces. We have applied GVB-BCCC methods to investigate three typical kinds of systems: polyacenes, pentaprismane, and [Cu 2 O 2 ] 2+ isomers. For polyacenes, we demonstrate that GVB-BCCC3b can capture more than 94% of the total correlation energy even for 12-acene with 50 π electrons. For the potential energy curve of simultaneously stretching 15 C–C bonds in pentaprismane, our calculations show that the GVB-BCCC3b results are quite close to the results from the density matrix renormalization group (DMRG) over the whole range. For two dinuclear copper oxide isomers, their relative energy predicted by GVB-BCCC3b is also in good accord with the DMRG result. All calculations show that the inclusion of three-pair correlation in GVB-BCCC is critical for accurate descriptions of strongly correlated systems.
A block-correlated coupled cluster method with up to four-pair correlation based on the generalized valence bond wave function (GVB-BCCC4) is first implemented, which offers an alternative method for electronic structure calculations of strongly correlated systems. We developed some techniques to derive a set of compact and cost-effective equations for GVB-BCCC4, which include the definition of n -block ( n = 1–4) Hamiltonian matrices, the combination of excitation operators, and the definition of independent amplitudes. We then applied the GVB-BCCC4 method to investigate several potential energy surfaces of strongly correlated systems with singlet ground states. Our calculations demonstrate that the GVB-BCCC4 method can provide nearly exact static correlation energies as the density matrix renormalization group method (on the basis of the same GVB orbitals). This work highlights the significance of four-pair correlation in quantitative descriptions of static correlation energy for strongly correlated systems.
A block-correlated coupled cluster (BCCC) method based on the triplet generalized valence bond (GVB) wave function (GVB-BCCC) has been implemented for the first time. By introducing several techniques, we have developed a practical and efficient GVB-BCCC code. The GVB-BCCC3 method (with up to three-pair correlation) can be used to deal with strongly correlated (SC) systems with triplet or singlet ground states, allowing singlet-triplet (S-T) energy gaps in the active space of SC systems computationally available. For selected SC systems, our calculations show that GVB-BCCC3 can always provide correct ground-state spin multiplicity as the complete active space configuration interaction (CASCI) or density matrix renormalization group (DMRG). Furthermore, we found that the S-T energy gaps from GVB-BCCC3 are quite consistent with CASCI or DMRG results. This work demonstrates that GVB-BCCC3 is a promising theoretical tool for describing S-T energy gaps within the active space of SC systems with large active spaces.
A block-correlated coupled cluster (BCCC) method based on the generalized valence bond (GVB) wave function (GVB-BCCC in short) is proposed and implemented at the ab initio level, which represents an attractive multireference electronic structure method for strongly correlated systems. The GVB-BCCC method is demonstrated to provide satisfactory descriptions for multiple bond breaking in small molecules, although the GVB reference function is qualitatively wrong for the studied processes. For a challenging prototype of strongly correlated systems, tridecane with all 12 single C–C bonds at various distances, our calculations have shown that the GVB-BCCC2b method can provide highly comparable results as the density matrix renormalization group method for potential energy surfaces along simultaneous dissociation of all C–C bonds.