MVO-10: A Gas-Phase Oxide Benchmark for Localization/Delocalization in Mixed-Valence Systems

2018

WIREs Comput Mol Sci

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130

224

The state of the art in the development, implementation, validation, and application of local hybrid functionals with position‐dependent exact‐exchange admixture is reviewed comprehensively. Starting from the general formulation of a local hybrid functional, possible constructions of local mixing functions to determine the position dependence are scrutinized in terms of their exact properties as well as their desirable features. The gauge problem pertaining to the ambiguity of exchange‐energy densities is discussed. “Smoking guns” for the gauge problem are identified, and the first calibration functions to improve the match of the exact and semi‐local exchange‐energy densities are compared. In view of the appearance of nonstandard exact‐exchange integrals, a crucial aspect is the efficient implementation of local hybrid functionals. This has been achieved recently using a resolution of the identity and/or semi‐numerical techniques, both for ground‐state energies and gradients, and for linear‐response time‐dependent density functional theory. The validation and early applications of local hybrids are reviewed, including thermochemistry, reaction barriers, structures and vibrational frequencies, electric and magnetic properties, as well as electronic excitation spectra. This article is categorized under: Electronic Structure Theory > Density Functional Theory Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry

“…A first preliminary application of the analytical gradient implementation for local hybrids focused on structure and energetics of the localized gas‐phase mixed‐valence anion

{Al}_{2} O_{4}^{-}

, suggesting local hybrids to become competitive tools in this field. This has been further corroborated in a recent larger benchmark study for gas‐phase mixed‐valence complexes …”

Section: Validation Studies and Performance Comparisonssupporting

confidence: 69%

Section: Structures and Vibrational Spectramentioning

confidence: 99%

Local hybrid functionals: Theory, implementation, and performance of an emerging new tool in quantum chemistry and beyond

Maier

Arbuznikov

2018

WIREs Comput Mol Sci

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130

224

“…112−114 Due to the flexible EXX admixture in local hybrids, these XC functionals were found to be particularly well suited for this task. 70,114 In this light, our results with U-LH12ct-SsirPW92 suggest that a localized T 1 state with a C 2 like structure is correct not only in solution but also for the gas phase. This agrees with the spectrum recorded in an organic glass matrix reported in ref 32 (and plotted in the figures of the present work) but contradicts the insights from experiments by Braun et al, in which one or more of the 2,2′-bipyridine ligands has been deuterated.…”

Section: ■ Resultsmentioning

confidence: 55%

“…As our calculations were performed without symmetry constraints, the symmetry of the optimized T 1 structure is determined just by the electronic-structure method. In that sense, the situation here is reminiscent of the challenge to predict localization/delocalization of the spin-density in mixed-valence compounds, where a proper balance between emulating left–right correlation and avoiding delocalization errors was found to be decisive. − Due to the flexible EXX admixture in local hybrids, these XC functionals were found to be particularly well suited for this task. , In this light, our results with U-LH12ct-SsirPW92 suggest that a localized T 1 state with a C 2 like structure is correct not only in solution but also for the gas phase. This agrees with the spectrum recorded in an organic glass matrix reported in ref (and plotted in the figures of the present work) but contradicts the insights from experiments by Braun et al, in which one or more of the 2,2′-bipyridine ligands has been deuterated .…”

Section: Resultsmentioning

confidence: 99%

Reliable TDDFT Protocol Based on a Local Hybrid Functional for the Prediction of Vibronic Phosphorescence Spectra Applied to Tris(2,2′-bipyridine)-Metal Complexes

Grotjahn

2021

J. Phys. Chem. A

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An efficient computational protocol for the prediction of vibrationally resolved phosphorescence spectra is developed and validated for five tris(2,2′-bipyridine)-metal complexes ([M(bpy)3] n+, where M = Zn, Ru, Rh, Os, Ir). The outstanding feature of this protocol is the use of full linear-response time-dependent density functional theory (TDDFT) for the excited-state triplet calculation, i.e., the commonly seen strategies employing the Tamm–Dancoff approximation (TDA) or unrestricted density functional theory (DFT) calculations for the T1 state are not needed. This is achieved by the use of a local hybrid functional (LH12ct-SsirPW92) that features a real-space dependent admixture of exact exchange governed by a local mixing function. The excellent performance of this LH for triplet excitation energies known from previous studies transfers to a remarkable mean absolute error of 0.06 eV for the phosphorescence 0–0 energies investigated herein, while the popular B3PW91 functional gives an error of 0.27 eV in TDDFT and 0.09 eV in unrestricted DFT calculations, respectively. The advantages of the local hybrid are particularly apparent for excited states with a mixed-valence character. The influence of spin–orbit coupling was found to be significant for [Os(bpy)3]2+ red-shifting the 0–0 energy for phosphorescence by 0.17 eV, while the effect is negligible for the other complexes (<0.03 eV). The influence of the basis-set and integration-grid sizes is evaluated, and a computationally lighter protocol is validated that leads to drastic savings in computation time with negligible loss in accuracy.

“…The LH nuclear shielding implementations of refs and are still incomplete in an important aspect: they have been limited to first-generation LHs based on the local spin-density approximation (LSDA) for the exchange-energy density, which lack a so-called calibration function (CF) to deal with the gauge ambiguity of exchange-energy densities. ,− In particular, the gauge problem manifests in spurious nondynamical correlation contributions and notably affects weak noncovalent interactions. ,− Our more recent LHs are thus based on GGA exchange-energy densities that are corrected by a semilocal CF. , The recent LH20t functional is particularly notable in this context as it has been found to be one of the most accurate rung-four functionals for general main-group energetics and is the first functional of any rung to properly balance localization and delocalization in the MVO-10 gas-phase mixed-valence benchmark. The CFs in such calibrated functionals contain terms that depend on the Laplacian and Hessian of the electron density.…”

Section: Introductionmentioning

confidence: 99%

Implementation and Validation of Local Hybrid Functionals with Calibrated Exchange-Energy Densities for Nuclear Shielding Constants

Schattenberg

2021

J. Phys. Chem. A

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A recently reported coupled-perturbed Kohn–Sham implementation to compute nuclear shielding constants with gauge-including atomic orbitals and local hybrid functionals has been extended to cover higher derivatives of the density in the local mixing function (LMF) of the local hybrid as well as the calibration function (CF) needed to deal with the ambiguity of exchange-energy densities. This allowed the first evaluation of state-of-the-art local hybrids with “calibrated” exchange-energy densities for nuclear shieldings. Compared to previously evaluated simpler local hybrids without a CF, appreciable improvements are found for proton shieldings. Furthermore, the recent LH20t functional is still competitive with the outstanding performance of the uncalibrated LH12ct-SsirSVWN and LH12ct-SsifSVWN LHs for heavier nuclei, suggesting that LH20t is possibly the most robust choice of any rung-four functional for computing the nuclear shieldings of main-group nuclei so far. Interestingly, the presence of a CF in the functional significantly reduces the number of artifacts introduced by the widely used Maximoff–Scuseria framework to treat the local kinetic energy τ. The latter occurs in so-called t-LMFs used in many of the present local hybrids. In any case, the use of Dobson’s current-density functional framework is also recommended with more advanced calibrated τ-dependent local hybrid functionals.