Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet–Triplet Gaps of Biradicals

Drwal, Daria; Beran, Pavel; Hapka, Michał; Modrzejewski, Marcin; Sokół, Adam K.; Veis, Libor; Pernal, Katarzyna

doi:10.1021/acs.jpclett.2c00993

Cited by 18 publications

(38 citation statements)

References 57 publications

(115 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Capturing the dynamic correlation outside the active space is also of interest and this is one of the main challenges for future studies. One of the future directions would be to use the adiabatic connection based methods that have been recently used for capturing the dynamic correlation outside the active space using only up to two-body reduced density matrices. , …”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions

Abraham

Mayhall

2022

J. Chem. Theory Comput.

View full text Add to dashboard Cite

Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional configuration interaction (CI) methods are not size extensive, hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of a truncated CI that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional, and average quadratic coupled-cluster to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wave function as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH4 and F2 where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar π-conjugated systems. Overall, the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.

show abstract

Section: Resultsmentioning

confidence: 99%

“…One of the future directions would be to use the adiabatic connection based methods that have been recently used for capturing the dynamic correlation outside the active space using only up to two-body reduced density matrices. 84,85 3.4. Planar π-Conjugated Systems.…”

Section: Stillbene Isomerizationmentioning

confidence: 99%

Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions

Abraham

Mayhall

2022

J. Chem. Theory Comput.

View full text Add to dashboard Cite

show abstract

“…One of the future direction would be to use the adiabatic connection based methods that have been recently used for capturing the dynamic correlation outside the active space using only up to twobody reduced density matrices. 84,85 D. Planar π-conjugated systems…”

Section: Stillbene Isomerizationmentioning

confidence: 99%

Coupled electron pair-type approximations for tensor product state wavefunctions

Abraham,

Mayhall

2022

Preprint

View full text Add to dashboard Cite

Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional CI methods are not size extensive hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of truncated configuration interaction (CI) that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant-based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional (ACPF) and average quadratic coupled-cluster (AQCC) to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA-based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wavefunction as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH4 and F2 where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar π-conjugated systems. Overall the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.

show abstract

“…[6][7][8][9][10] Approximations developed in the AC(MC) framework offer a lower computational cost compared to second-order multireference perturbation methods, at the same time rivalling them in terms of accuracy. 11,12 Contrary to the AC(KS-DFT) and AC(HF) methods, which are limited to ground states of singlet spin symmetry, AC(MC) is applicable to both ground and excited states of arbitrary spin multiplicity. [13][14][15] The first step in the AC theory assumes choosing the model Hamiltonian Ĥ(0) under requirement that the reference wavefunction Ψ ref is one of its eigenfunctions Ĥ(0)…”

Section: Introductionmentioning

confidence: 99%

“…[20][21][22] Encouraging results from the AC(MC) approximations applied both to ground and excited states with the CASSCF and DMRG systems were obtained. 11,12 Even though the approximation that RDMs are constant with the coupling parameter α is justified if Ψ ref involves large active space, it is still one of the sources of inaccuracies of the AC(MC) methods. Thus, it is important to investigate possible ways of improving the AC models by lifting the fixed-RDM restriction.…”

Section: Introductionmentioning

confidence: 99%

Toward more accurate adiabatic connection approach for multireference wave functions

Matoušek¹,

Hapka²,

Veis³

et al. 2022

Preprint

View full text Add to dashboard Cite

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to computing dynamic correlation within CASSCF and DMRG models. Practical realizations of AC have been based on two approximations: i) fixing oneand two-electron reduced density matrices (1-and 2-RDMs) at the zero-coupling constant limit and ii) extended random phase approximation (ERPA). This work investigates the the effect of removing the "fixed-RDM" approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function-and the Dyall-Hamiltonians. Exact reference AC integrands are generated from the DMRG FCI solver. Two AC models are investigated, employing either exact 1-and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving accuracy of the existing AC approximations.

show abstract

Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet–Triplet Gaps of Biradicals

Cited by 18 publications

References 57 publications

Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions

Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions

Coupled electron pair-type approximations for tensor product state wavefunctions

Toward more accurate adiabatic connection approach for multireference wave functions

Contact Info

Product

Resources

About