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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

   Carvalho, Jhonatas R; Nieman, Reed; Kertesz, Miklos; Aquino, Adelia_J_A; Hansen, Andreas; Lischka, Hans (August 2024, Theoretical Chemistry accounts)

   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 densities NU. 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) has 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 between NFOD and NU values 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 temperature Tel for the FT-DFT calculation. We also established an optimal temperature for the semi-empirical extended tight-binding GFN2-xTB method. These findings significantly broaden the applicability of FOD analysis across various DFT functionals and semi-empirical methods. 

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2. 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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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. Low‐energy Sr ₂ MSbO_5.5 (M = Ca and Sr) structures show significant distortions near oxygen vacancies

   https://doi.org/10.1002/qua.26356  

   Patel, Megha; Zhong, Jiayun; Gomez‐Haibach, Konrad S.; Gomez, Maria A.; King, Graham (June 2020, International Journal of Quantum Chemistry)

   Abstract Inspired by significant local distortions found near vacancies in a neutron pair distribution function analysis study (G. King et al.,Inorg. Chem.2012, 51, 13060) of Sr₂MSbO_5.5(M = Ca and Sr), this computational study finds minimum‐energy structures with these and related distortions using density functional theory (DFT) with the Perdew‐Burke‐Ernzerhof (PBE) functional as implemented in the Vienna Ab Initio Simulations Package (VASP) (G. Kresse and J. Furthmüller,Phys. Rev. B, 1996, 54, 11169; G. Kresse and J. Hafner,Phys. Rev. B, 1993, 47, 558; G. Kresse and J. Furthmüller,Comput. Mater. Sci., 1996, 6, 15). All structures were optimized using the conjugate gradient method. The global minima found for both systems featured trigonal bipyramid SbO₅structures and edge sharing with M‐centered polyhedra. However, while calcium ions occupied full and partial octahedra, the larger strontium ions were more commonly found in full and partial pentagonal bipyramids. Molecular dynamics with velocity rescaling at1200K revealed movements of the oxygen vacancy via polyhedral rotations. This work highlights the need to consider both square pyramid to trigonal bipyramid rearrangements around small ions and rotational polyhedral movements in simulating oxygen vacancy conduction in oxygen‐deficient double perovskites. 

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5. 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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