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1. Multireference calculations on bond dissociation and biradical polycyclic aromatic hydrocarbons as guidance for fractional occupation number weighted density analysis in DFT calculations

   https://doi.org/10.1007/s00214-024-03143-8  

   Carvalho, Jhonatas_R; Nieman, Reed; Kertesz, Miklos; Aquino, Adelia_J_A; Hansen, Andreas; Lischka, Hans (September 2024, Theoretical Chemistry Accounts)

   Abstract This study explores open-shell biradical and polyradical molecular compounds based on extended multireference (MR) methods (MR-configuration interaction with singles and doubles (CISD) and MR-averaged quadratic coupled cluster (AQCC) approach) using the numbers of unpaired densitiesN_U. These results were used to guide the analysis of the fractional occupation number weighted density (FOD) calculated within the finite temperature (FT) density functional theory (DFT) approach. As critical test examples, the dissociation of carbon–carbon (CC) single, double and triple bonds and a benchmark set of polycyclic aromatic hydrocarbons (PAHs) have been chosen. By examining single, double, and triple bond dissociations, we demonstrate the utility and accuracy but also limitations of the FOD analysis for describing these dissociation processes. In significant extension of previous work (Phys Chem Chem Phys 25: 27380–27393), the assessment of FOD applications for different classes of DFT functionals was performed examining the range-separated functionals ωB97XD, ωB97M-V, CAM-B3LYP, LC-ωPBE, and MN12-SX, the hybrid (M06-2X) functional and the double hybrid (B2P-LYP) functional. In all cases, strong correlations betweenN_FODandN_Uvalues are found. The major task was to develop a new linear regression formula for range-separated functionals allowing a convenient determination of the optimal electronic temperatureT_elfor the FT-DFT calculation. We also established an optimal temperature for the semiempirical extended tight-binding GFN2-xTB method. These findings significantly broaden the applicability of FOD analysis across various DFT functionals and semiempirical methods. 

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2. Assessment of the Performance of Optimally Tuned Range‐Separated Hybrid Functionals for Nuclear Magnetic Shielding Calculations

   https://doi.org/10.1002/adts.202000083  

   Prokopiou, Georgia; Autschbach, Jochen; Kronik, Leeor (July 2020, Advanced Theory and Simulations)

   Abstract The performance of optimally tuned range‐separated hybrid (OT‐RSH) functional calculations in predicting accurate isotropic nuclear magnetic shielding (σ) and chemical shift values is examined. To that end, the results of OT‐RSH and other approximate density functional theory calculations are assessed against recently published benchmark CCSD(T) calculations for a test set consisting of several molecules and bond types. It is found that for atoms in single bonds with a large paramagnetic contribution to σ, OT‐RSH offers a significant improvement in prediction of shielding constants over popular semi‐local and hybrid density functionals, yielding non‐empirical results that are as accurate as those of semi‐empirical density functionals often used for prediction of shielding constants. This success is attributed to the improved fundamental gap prediction of the OT‐RSH approach. For atoms in multiple bonds, however, larger errors often persist. By comparing OT‐RSH and recently reported double‐hybrid functional results, the remaining difficulties are traced to significant non‐local correlation. 

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3. Self-consistent equations for nonempirical tight-binding theory

   https://doi.org/10.1063/5.0276043  

   Mironenko, Alexander V; Leung, Lanie; Zhuang, Jiqing (October 2025, The Journal of Chemical Physics)

   A new reference state for density functional theory (DFT), termed the independent atom ansatz, is introduced in this work. This ansatz allows for the formally exact representation of electron density in terms of atom-localized orbitals. Self-consistent equations for such states are derived in general and asymptotic forms. The resultant total energy functional is found to closely resemble tight-binding theory. The independent atom ansatz facilitates partial cancellation of inter-atomic electron–electron and nucleus–electron interactions, which allows for the derivation of analytical tight-binding Hamiltonian matrix elements in a weak interaction limit. The formalism provides energy decomposition and charge analyses at no additional cost and links tight-binding, localized orbital, and electronegativity concepts. Numerical accuracy of the total energy functional has been previously reported for hydrogenic systems [Mironenko, J. Phys. Chem. A 127, 7836 (2023)] and is demonstrated here for He2, Li2, Be2, B2, N2, O2, F2, and Ne2. The method accurately reproduces the shapes of potential energy curves, capturing large-basis CCSD(T)-level bond lengths and bond dissociation energies for N2, O2, and F2 using only a minimal basis set. It outperforms both CCSD(T) and some mainstream approximate restricted Kohn–Sham DFT functionals in describing bond dissociation behavior away from equilibrium geometries. 

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4. Implementation of symmetry-adapted perturbation theory based on density functional theory and using hybrid exchange–correlation kernels for dispersion terms

   https://doi.org/10.1063/5.0090688  

   Xie, Yi; Smith, Daniel G.; Sherrill, C. David (July 2022, The Journal of Chemical Physics)

   We report the implementation of a symmetry-adapted perturbation theory algorithm based on a density functional theory [SAPT(DFT)] description of monomers. The implementation adopts a density-fitting treatment of hybrid exchange–correlation kernels to enable the description of monomers with hybrid functionals, as in the algorithm by Bukowski, Podeszwa, and Szalewicz [Chem. Phys. Lett. 414, 111 (2005)]. We have improved the algorithm by increasing numerical stability with QR factorization and optimized the computation of the exchange–correlation kernel with its 2-index density-fitted representation. The algorithm scales as O( N 5 ) formally and is usable for systems with up to ∼3000 basis functions, as demonstrated for the C 60 –buckycatcher complex with the aug-cc-pVDZ basis set. The hybrid-kernel-based SAPT(DFT) algorithm is shown to be as accurate as SAPT(DFT) implementations based on local effective exact exchange potentials obtained from the local Hartree–Fock (LHF) method while avoiding the lower-scaling [ O( N 4 )] but iterative and sometimes hard-to-converge LHF process. The hybrid-kernel algorithm outperforms Hartree–Fock-based SAPT (SAPT0) for the S66 test set, and its accuracy is comparable to the many-body perturbation theory based SAPT2+ approach, which scales as O( N 7 ), although SAPT2+ exhibits a more narrow distribution of errors. 

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5. Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry

   https://doi.org/10.1063/5.0089460  

   Bajaj, Akash; Duan, Chenru; Nandy, Aditya; Taylor, Michael_G; Kulik, Heather_J (May 2022, The Journal of Chemical Physics)

   Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d1 MOPs to be suitable for nearly eliminating all energetic delocalization and static correlation errors. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization and static correlation errors within a non-empirical framework. 

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