Minimal Active Space for Diradicals Using Multistate Density Functional Theory

Han, Jingting; Zhao, Ruoqi; Guo, Yujie; Qu, Zhi‐Rong; Gao, Jiali

doi:10.3390/molecules27113466

Cited by 2 publications

(4 citation statements)

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“…Although the N -matrix density D ( r ) could be directly optimized using N 2 Slater determinants, here, we take an alternative route by constructing a set of N auxiliary multistate wave functions {Φ A ; A = 1, ..., N } for representing D ( r ). The auxiliary wave functions are expressed as a linear combination of Slater determinants in the MAS, V MAS = {Ξ ξ ; ξ = 1, ..., M } with M ∼ N 2 . – Φ A = ∑ ξ normalM c ξ normalA Ξ ξ where Ξ ξ is the ξth Slater determinant, constructed from n e (the number of electrons) one-body spin orbitals {ψ iσ ξ }, and c ξA is a configuration coefficient for auxiliary state A . Ξ ξ false( r 1 , · · · , r n normale false) = 1 n e ! A ^ false{ ψ 1 σ 1 ξ ( r 1 ) · · · ψ n normale σ n normale ξ ( r n e ) false} …”

Section: Theorymentioning

confidence: 99%

“…The multistate density functional theory (MSDFT) offers opportunities to develop novel density functional approximations beyond the realm of traditional KS-DFT and to treat both the ground state and excited states on an equal footing . By introducing a minimal active space (MAS) according to Theorem 3 of Lu and Gao, – we have the original benefits of DFT with a balanced treatment of computational efficiency and accuracy in light of increased complexity of multiple states. In this article, we present the results from a nonorthogonal state interaction (NOSI) method in the framework of MSDFT. , The findings are compared with the TBE of WFT on a list of benchmark molecules that has been established previously …”

Section: Introductionmentioning

confidence: 99%

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Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

Zhu,

Zhao,

et al. 2023

J. Phys. Chem. A

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The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018. Two optimization techniques, namely, block-localized excitation and target state optimization, are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spinmultiplet degeneracy constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D ∞ ), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn−Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.

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Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

Zhu,

Zhao,

et al. 2023

J. Phys. Chem. A

Self Cite

View full text Add to dashboard Cite

show abstract

“…28 The multistate density functional theory (MSDFT) offers opportunities to develop novel density functional approximations beyond the realm of traditional HKS-DFT and to treat both the ground state and excited states on an equal footing. 29 By introducing a minimal active space (MAS) according to the theorem of Lu and Gao, [30][31][32] we can retain the original benefits of DFT with a balanced treatment of computational efficiency and accuracy in light of increased complexity of multiple states. In this article, we present the results from a nonorthogonal state interaction (NOSI) method in the framework of MSDFT.…”

Section: Introductionmentioning

confidence: 99%

“…Although the N-matrix density 𝑫𝑫(𝒓𝒓) could be directly optimized using 𝑁𝑁 2 Slater determinants, here, we take an alternative route by constructing a set of N auxiliary multistate wavefunctions {Φ 𝐴𝐴 ; 𝐴𝐴 = 1, ⋯ , 𝑁𝑁} for representing 𝑫𝑫(𝒓𝒓) . The auxiliary wave functions are expressed as a linear combination of Slater determinants in the MAS, 𝑉𝑉 𝑀𝑀𝐴𝐴𝑀𝑀 = {Ξ 𝜉𝜉 ; 𝜉𝜉 = 1, ⋯ , 𝑀𝑀} with 𝑀𝑀~𝑁𝑁 2 [29][30][31].…”

mentioning

confidence: 99%

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

Zhu¹,

Zhao²,

Liu³

et al. 2023

Preprint

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The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates (TBE) extracted to the full configuration interaction accuracy on the database developed by Loos, P.F., at al. in 2018 (Loos2018). Two optimization techniques, namely block-localized excitation (BLE) and target state optimization (TSO), are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy (SMD) constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, better than CIS(D_∞), CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat less than STEOM-CCSD (RMSE of 0.14 eV) and CCSD (RMSE of 0.11 eV) wave function methods. Interestingly, MSDFT-NOSI performs noticeably better than TDDFT at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with the ground state and the lowest triplet energies from KS-DFT calculations, it was found that the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a non-interacting reference may be adopted in MSDFT calculations in which state interaction is key.

show abstract

Minimal Active Space for Diradicals Using Multistate Density Functional Theory

Cited by 2 publications

References 71 publications

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

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