Density Matrix Renormalization Group with Dynamical Correlation via Adiabatic Connection

Beran, Pavel; Matoušek, Mikuláš; Hapka, Michał; Pernal, Katarzyna; Veis, Libor

doi:10.1021/acs.jctc.1c00896

Cited by 39 publications

(52 citation statements)

References 91 publications

(204 reference statements)

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“…The accurate treatment of excited states is critical for understanding photochemical phenomena, − and it has been a long-standing goal of the electronic structure community. − Although treating excited states is difficult in general, it is particularly challenging when single-determinant methods such as Hartree–Fock or Kohn–Sham density functional theory provide a poor reference state for predicting excited states. This can occur either because the excited states vary greatly from the ground state (e.g., double excitations) or because the ground state itself is not well described (e.g., strongly correlated systems − ). One can overcome these deficiencies by using multiple-determinant reference states, and the methods that take this approach are called multireference methods.…”

Section: Introductionmentioning

confidence: 99%

Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection

King

Hermes

Truhlar

et al. 2022

J. Chem. Theory Comput.

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We have calculated state-averaged complete-active-space self-consistent-field (SA-CASSCF), multiconfiguration pair-density functional theory (MC-PDFT), hybrid MC-PDFT (HMC-PDFT), and n-electron valence state second-order perturbation theory (NEVPT2) excitation energies with the approximate pair coefficient (APC) automated active-space selection scheme for the QUESTDB benchmark database of 542 vertical excitation energies. We eliminated poor active spaces (20–40% of calculations) by applying a threshold to the SA-CASSCF absolute error. With the remaining calculations, we find that NEVPT2 performance is significantly impacted by the size of the basis set the wave functions are converged in, regardless of the quality of their description, which is a problem absent in MC-PDFT. Additionally, we find that HMC-PDFT is a significant improvement over MC-PDFT with the translated PBE (tPBE) density functional and that it performs about as well as NEVPT2 and second-order coupled cluster on a set of 373 excitations in the QUESTDB database. We optimized the percentage of SA-CASSCF energy to include in HMC-PDFT when using the tPBE on-top functional, and we find the 25% value used in tPBE0 to be optimal. This work is by far the largest benchmarking of MC-PDFT and HMC-PDFT to date, and the data produced in this work are useful as a validation of HMC-PDFT and of the APC active-space selection scheme. We have made all the wave functions produced in this work (orbitals and CI vectors) available to the public and encourage the community to utilize this data as a tool in the development of further multireference model chemistries.

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Section: Introductionmentioning

confidence: 99%

Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection

King

Hermes

Truhlar

et al. 2022

J. Chem. Theory Comput.

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“…The electronic structural description of iron porphyrins is also of fundamental interest, as these systems are prototypical of large, strongly correlated systems where determining the spin-state ordering is still challenging. For even the simplest, unfunctionalized iron(II) porphyrin (FeP), the ordering of the lowest lying spin states is still being studied with recently developed, sophisticated electronic structure methods. − …”

Section: Introductionmentioning

confidence: 99%

Multiconfiguration Pair-Density Functional Theory Calculations of Iron(II) Porphyrin: Effects of Hybrid Pair-Density Functionals and Expanded RAS and DMRG Active Spaces on Spin-State Orderings

et al. 2022

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Iron(II) porphyrins play critical roles in enzymes and synthetic catalysts. Computationally determining the spin-state ordering for even the unsubstituted iron(II) porphyrin (FeP) is challenging due to its large size. Multiconfiguration pair-density functional theory (MC-PDFT), a method capable of accurately capturing correlation with lower cost than comparably accurate methods, was previously used to predict a triplet ground state for FeP across a wide range of active spaces up to (34e, 35o). The purpose of this present MC-PDFT study is to determine the effects of including nonlocal exchange in the energy calculation and of using a larger active space size [DMRG(40e, 42o) and RAS(40, 2, 2; 16, 6, 20)] on the calculated FeP spin-state ordering. The recently developed hybrid MC-PDFT method, which uses a weighted average of the MC-PDFT energy and the energy expectation value of the reference wave function, is applied with a weight of the reference wave function energy of λ. We find that increasing λ stabilizes the quintet relative to the triplets. The hybrid tPBE0 functional (tPBE with λ set to 0.25) consistently predicts a triplet ground state with the quintet lying above by 0.10–0.16 eV, depending on the reference wave function. These values are particularly interesting in light of tPBE0’s very strong performance for a diverse set of other systems.

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“…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%

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

Abraham

Mayhall

2022

J. Chem. Theory Comput.

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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.

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Density Matrix Renormalization Group with Dynamical Correlation via Adiabatic Connection

Cited by 39 publications

References 91 publications

Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection

Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection

Multiconfiguration Pair-Density Functional Theory Calculations of Iron(II) Porphyrin: Effects of Hybrid Pair-Density Functionals and Expanded RAS and DMRG Active Spaces on Spin-State Orderings

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

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