Range-separated Hybrid Functionals Research Articles

Basis Set Requirements of σ-Functionals for Gaussian- and Slater-Type Basis Functions and Comparison with Range-Separated Hybrid and Double Hybrid Functionals.

σ-Functionals belong to the class of Kohn-Sham (KS) correlation functionals based on the adiabatic-connection fluctuation-dissipation theorem and are technically closely related to the random phase approximation (RPA). They have the same computational demand as the latter, with the computational effort of an energy evaluation for both methods being lower than that of a preceding hybrid DFT calculation for typical systems but yield much higher accuracy, reaching chemical accuracy of 1 kcal/mol for quantities such as reactions and transition energies in main group chemistry. In previous work on σ-functionals, rather large Gaussian basis sets have been used. Here, we investigate the actual basis set requirements of σ-functionals and present three setups that employ smaller Gaussian basis sets ranging from quadruple-ζ (QZ) to triple-ζ (TZ) quality and represent a good compromise between accuracy and computational efficiency. Furthermore, we introduce an implementation of σ-functionals based on Slater-type basis sets and present two setups of QZ and TZ quality for this implementation. We test the accuracy of these setups on a large database of various physical properties and types of reactions, as well as equilibrium geometries and vibrational frequencies. As expected, the accuracy of σ-functional calculations becomes somewhat lower with a decreasing basis set size. However, for all setups considered here, calculations with σ-functionals are clearly more accurate than those within the RPA and even more so than those of the conventional KS methods. For the smallest setup using Gaussian-type basis functions and Slater-type basis functions, we introduce a reparametrization that reduces the loss in accuracy due to the basis set error to some extent. A comparison with the range-separated hybrid ωB97X-V and the double hybrid DSD-BLYP-D3 shows that σ functionals outperform in accuracy both of these accurate and, for their class, representative functionals.

The performance and efficiency of twelve range-separated hybrid DFT functionals for calculation of the magnetic exchange coupling constants of di-nuclear first row transition metal complexes

The performance and efficiency of twelve range-separated hybrid functionals are compared with each other in calculating magnetic exchange coupling constant (J) data on eleven di-nuclear first-row transition metal complexes having di-copper (Cu) and di-vanadium (V) as their central atoms. The J values are then compared with the experimental findings. In addition to that we also computed the B3LYP results of these complexes. We compared them with the results obtained from range-separated functionals as well as with the experimental results to understand their performances in predicting the magnetic exchange coupling constant. When computing, we reoptimized all the structures of the complexes taken from the crystal data, and then the values of Js were determined. The performances are predicted in terms of four statistical error matrices, namely, the mean absolute error (MAE), mean fractional error (MFE), mean signed error (MSE), root mean square error (RMSE) in cm−1.

Photoredox matching of earth-abundant photosensitizers with hydrogen evolving catalysts by first-principles predictions.

Photoredox properties of several earth-abundant light-harvesting transition metal complexes in combination with cobalt-based proton reduction catalysts have been investigated computationally to assess the fundamental viability of different photocatalytic systems of current experimental interest. Density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations using several GGA (BP86, BLYP), hybrid-GGA (B3LYP, B3LYP*), hybrid meta-GGA (M06, TPSSh), and range-separated hybrid (ωB97X, CAM-B3LYP) functionals were used to calculate relevant ground and excited state reduction potentials for photosensitizers, catalysts, and sacrificial electron donors. Linear energy correction factors for the DFT/TD-DFT results that provide the best agreement with available experimental reference results were determined in order to provide more accurate predictions. Among the selection of functionals, the B3LYP* and TPSSh sets of correction parameters were determined to give the best redox potentials and excited states energies, ΔEexc, with errors of ∼0.2eV. Linear corrections for both reduction and oxidation processes significantly improve the predictions for all the redox pairs. In particular, for TPSSh and B3LYP*, the calculated errors decrease by more than 0.5V against experimental values for catalyst reduction potentials, photosensitizer oxidation potentials, and electron donor oxidation potentials. Energy-corrected TPSSh results were finally used to predict the energetics of complete photocatalytic cycles for the light-driven activation of selected proton reduction cobalt catalysts. These predictions demonstrate the broader usefulness of the adopted approach to systematically predict full photocycle behavior for first-row transition metal photosensitizer-catalyst combinations more broadly.

A DFT study on photodissociation of the palladium tetrachloride anion PdCl42− in solution

Photodissociation of PdCl42− in water is investigated using the time-dependent DFT method with the polarized continuum model. First, to find out the exchange–correlation functional that can well describe the present system we make following two comparisons using many functionals: (i) the DFT absorption spectrum vs. experiment; (ii) the DFT one-dimensional (1D) potential energy curves (PECs) vs. the previous MRCI 1D PECs. As a result of comparison, it is found that the range-separated hybrid functionals well reproduce the observed spectrum and, among these, the M11 functional may be the most reasonable choice. Next, using M11, we calculate ground and excited-state 1D PECs for single Cl loss in water and the ground-state two-dimensional (2D) potential energy surface (PES) for double Cl loss in water. It is revealed in the 1D PECs in water that electronic excitations to the PECs that have large transition dipole moments with the ground electronic state may easily lead to the PdCl3− + Cl− dissociation channel, which is similar to single Cl loss in the gas phase. It is also found that the ground-state 2D PES in water correlates with the PdCl2 + 2Cl− dissociation channel with no transition state on the way to it. This is different from the prediction in the gas phase; the ground-state 2D PES correlates with the PdCl2 + Cl2− dissociation channel with a transition state on the minimum energy path leading to it.

Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities.

In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA), as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)]. Our study was later extended to local hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al. also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density (τ) in mGGA calculations by comparing the Maximoff-Scuseria formulation of τ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH, and scLH functionals outperform all of the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character, such as the ozone molecule, which is traditionally excluded from statistical error evaluations due to its large errors with common density functionals.

Range-Separated Local Hybrid Functionals with Small Fractional-Charge and Fractional-Spin Errors: Escaping the Zero-Sum Game of DFT Functionals

Range-Separated Local Hybrid Functionals with Small Fractional-Charge and Fractional-Spin Errors: Escaping the Zero-Sum Game of DFT Functionals

Do Optimally Tuned Range-Separated Hybrid Functionals Require a Reparametrization of the Dispersion Correction? It Depends.

For ground- and excited-state studies of large molecules, it is the state of the art to combine (time-dependent) DFT with dispersion-corrected range-separated hybrid functionals (RSHs), which ensures an asymptotically correct description of exchange effects and London dispersion. Specifically for studying excited states, it is common practice to tune the range-separation parameter ω (optimal tuning), which can further improve the accuracy. However, since optimal tuning essentially changes the functional, it is unclear if and how much the parameters used for the dispersion correction depend on the chosen ω value. To answer this question, we explore this interdependency by refitting the DFT-D4 dispersion model for six established RSHs over a wide range of ω values (0.05-0.45 a0-1) using a set of noncovalently bound molecular complexes. The results reveal some surprising differences among the investigated functionals: While PBE-based RSHs and ωB97M-D4 generally exhibit a weak interdependency and robust performance over a wide range of ω values, B88-based RSHs, specifically LC-BLYP, are strongly affected. For these, even a minor reduction of ω from the default value manifests in strong systematic overbinding and poor performance in the typical range of optimally tuned ω values. Finally, we discuss strategies to mitigate these issues and reflect the results in the context of the employed D4 parameter optimization algorithm and fit set, outlining strategies for future improvements.

Exact two-component theory becoming an efficient tool for NMR shieldings and shifts with spin–orbit coupling

We present a gauge-origin invariant exact two-component (X2C) approach within a modern density functional framework, supporting meta-generalized gradient approximations such as TPSS and range-separated hybrid functionals such as CAM-B3LYP. The complete exchange-correlation kernel is applied, including the direct contribution of the field-dependent basis functions and the reorthonormalization contribution from the perturbed overlap matrix. Additionally, the finite nucleus model is available for the electron-nucleus potential and the vector potential throughout. Efficiency is ensured by the diagonal local approximation to the unitary decoupling transformation in X2C as well as the (multipole-accelerated) resolution of the identity approximation for the Coulomb term (MARI-J, RI-J) and the seminumerical exchange approximation. Errors introduced by these approximations are assessed and found to be clearly negligible. The applicability of our implementation to large-scale calculations is demonstrated for a tin pincer-type system as well as low-valent tin and lead complexes. Here, the calculation of the Sn nuclear magnetic resonance shifts for the pincer-type ligand with about 2400 basis functions requires less than 1 h for hybrid density functionals. Further, the impact of spin–orbit coupling on the nucleus-independent chemical shifts and the corresponding ring currents of all-metal aromatic systems is studied.

Spin state and magnetic coupling in polynuclear Ni(II) complexes from density functional theory: is there an optimal amount of Fock exchange?

Reliable prediction of the ground-state spin and magnetic coupling constants in transition-metal complexes is a well-known challenge for density functional theory (DFT). One popular strategy for addressing this long-standing issue involves the modification of the fraction of Fock exchange in a hybrid functional. Here we explore the viability of this approach using three polynuclear metal-organic complexes based on a Ni4O4 cubane motif, having different ground state spin values (S = 0, 2, 4) owing to the use of different ligands. We systematically search for an optimum fraction of Fock exchange, across various global, range-separated, and double hybrid functionals. We find that for all functionals tested, at best there only exists a very narrow range of Fock exchange fractions which results in a correct prediction of the ground-state spin for all three complexes. The useful range is functional dependent, but general trends can be identified. Typically, at least two similar systems must be used in order to determine both an upper and lower limit of the optimal range. This is likely owing to conflicting demands of minimizing delocalization errors, which typically requires a higher percentage of Fock exchange, and addressing static correlation, which typically requires a lower one. Furthermore, we find that within the optimal range of Fock exchange, the signand relative magnitude of Ni-Ni magnetic coupling constants are reasonably well reproduced, but there is still room for quantitative improvement in the prediction. Thus, the prediction of spin state and magnetic coupling in polynuclear complexes remains an ongoing challenge for DFT.

Automatic Generation of Auxiliary Basis Sets in Spherical Representation Using the Cholesky Decomposition.

Density fitting techniques that use automatically generated auxiliary basis sets generally rely on the formation of basis function products. Recently, Lehtola [ J. Chem. Theory Comput. 2021, 17, 6886-6900] presented a procedure making use of a purely spherical representation by adding auxiliary basis functions coupled to the required angular momentum quantum numbers for the product of spherical harmonics and then removing linear dependencies by means of a Cholesky decomposition. In this work, we extend this idea by making use of the explicit equations for the product of two spherical harmonics in the angular part of the basis function product. Some of the resulting terms are not directly accessible when popular standard integral libraries are used, which could prevent the widespread use of the exact product form. For these terms, we introduce four approximations of increasing sophistication that require integrals involving only standard Gaussian-type orbitals and thus can be computed with standard libraries. We assess the accuracy of the different schemes in the context of the aCD for the reconstruction of the electron repulsion integral matrix and absolute and relative single point energies and in the framework of optimally tuned range-separated hybrid functionals.

Transferable screened range-separated hybrid functionals for electronic and optical properties of van der Waals materials

Transferable screened range-separated hybrid functionals for electronic and optical properties of van der Waals materials

Unraveling the Complex Interplay of Phase Transitions in Spinel Ferrites: A Comprehensive Quantum Mechanical Vibrational Study of ZnFe2O4.

The rich phase transition landscape of spinel ferrites and its profound impact on their physical properties have garnered significant interest in recent years. The complex interplay of divalent and trivalent cations distributed across A- and B-sites gives rise to a captivating variety of interactions. In this study, we delve into the structural, electronic, magnetic, and vibrational properties of ZnFe2O4 as a function of the degree of inversion, employing first-principles density functional theory with global and range-separated hybrid functionals and a local basis set. The ground state of ZnFe2O4 is an open-shell system, characterized by Zn atoms occupying tetrahedral sites, Fe atoms residing in octahedral sites, and Fe atom spins exhibiting ligand parallel alignment. In the normal structure, the antiparallel arrangement is less stable than the ferro arrangement by 0.058 eV (673 K) for fully relaxed structures, decreasing to 0.034 eV (395 K) upon incorporating a zero-point vibrations contribution. For normal ferromagnetic ZnFe2O4, we calculated scattering for A1g, Eg, and 3T2g symmetry at 676.6, 367.1, and (189.7, 457.7, 602.3) cm-1, respectively. Additionally, four T1u vibrational frequencies predicted by group theory were obtained at 524.59, 358.48, 312.49, and 192.9 cm-1, demonstrating excellent agreement with the experimental studies. We also explored the influence of spin rearrangement and inversion (X = 0.5 and 1) on Raman and infrared spectra. By analyzing the infrared spectra of isotopic substitutions, we reevaluated the assignments of the four T1u modes in light of available experimental data. Notably, the sensitivity of peak positions and intensities for some Raman modes, particularly A1g and T2g(2), to spin arrangement could provide a convenient experimental tool for detecting phase transitions induced by changes in temperature or external electric fields. This investigation shines a light on the complex interplay of phase transitions in spinel ferrites, paving the way for a deeper understanding of their properties and potential applications.

CCSD(T) Rotational Constants for Highly Challenging C5H2 Isomers-A Comparison between Theory and Experiment.

We evaluate the accuracy of CCSD(T) and density functional theory (DFT) methods for the calculation of equilibrium rotational constants (Ae, Be, and Ce) for four experimentally detected low-lying C5H2 isomers (ethynylcyclopropenylidene (2), pentatetraenylidene (3), ethynylpropadienylidene (5), and 2-cyclopropen-1-ylidenethenylidene (8)). The calculated rotational constants are compared to semi-experimental rotational constants obtained by converting the vibrationally averaged experimental rotational constants (A0, B0, and C0) to equilibrium values by subtracting the vibrational contributions (calculated at the B3LYP/jun-cc-pVTZ level of the theory). The considered isomers are closed-shell carbenes, with cumulene, acetylene, or strained cyclopropene moieties, and are therefore highly challenging from an electronic structure point of view. We consider both frozen-core and all-electron CCSD(T) calculations, as well as a range of DFT methods. We find that calculating the equilibrium rotational constants of these C5H2 isomers is a difficult task, even at the CCSD(T) level. For example, at the all-electron CCSD(T)/cc-pwCVTZ level of the theory, we obtain percentage errors ≤0.4% (Ce of isomer 3, Be and Ce of isomer 5, and Be of isomer 8) and 0.9-1.5% (Be and Ce of isomer 2, Ae of isomer 5, and Ce of isomer 8), whereas for the Ae rotational constant of isomers 2 and 8 and Be rotational constant of isomer 3, high percentage errors above 3% are obtained. These results highlight the challenges associated with calculating accurate rotational constants for isomers with highly challenging electronic structures, which is further complicated by the need to convert vibrationally averaged experimental rotational constants to equilibrium values. We use our best CCSD(T) rotational constants (namely, ae-CCSD(T)/cc-pwCVTZ for isomers 2 and 5, and ae-CCSD(T)/cc-pCVQZ for isomers 3 and 8) to evaluate the performance of DFT methods across the rungs of Jacob's Ladder. We find that the considered pure functionals (BLYP-D3BJ, PBE-D3BJ, and TPSS-D3BJ) perform significantly better than the global and range-separated hybrid functionals. The double-hybrid DSD-PBEP86-D3BJ method shows the best overall performance, with percentage errors below 0.5% in nearly all cases.

Dissecting the ingredients of optimally tuned range-separated hybrid models for reliable description of non-adiabatic couplings.

Perusing the non-radiative processes requires a reliable prediction of non-adiabatic couplings (NACs) describing the interaction of two Born-Oppenheimer surfaces. In this regard, the development of appropriate and affordable theoretical methods that accurately account for the NAC terms between different excited-states is desirable. In this work, we develop and validate several variants of the optimally tuned range-separated hybrid functionals (OT-RSHs) for investigating NACs and related properties, such as excited states energy gaps and NAC forces, within the time-dependent density functional theory framework. Particular attention is paid to the influence of the underlying density functional approximations (DFAs), the short- and long-range Hartree-Fock (HF) exchange contributions, and the range-separation parameter. Considering several radical cations and sodium-doped ammonia clusters with the available reference data for the NACs and related quantities as the working models, we have evaluated the applicability and accountability of the proposed OT-RSHs. The obtained results unveil that any combination of the ingredients in the proposed models is not proper for describing the NACs, but a particular compromise among the involved parameters is needed to achieve reliable accuracy. Scrutinizing the results of our developed methods, the OT-RSHs based on the PBEPW91, BPW91, and PBE exchange and correlation DFAs, including about 30% HF exchange at the short-range regime, appeared to be the best performers. We also find that the newly developed OT-RSHs with correct asymptotic exchange-correlation potential have superior performances as compared to their standard counterparts with the default parameters and many earlier hybrids with both fixed and interelectronic distance-dependent HF exchange. The recommended OT-RSHs in this study can hopefully be applicable as computationally efficient alternatives to the expensive wave function-based methods for the systems prone to non-adiabatic properties as well as to screen out the novel candidates prior to their challenging synthesis.

Strategies to Calculate Fukui Functions and Applications to Radicals with SOMO-HOMO Inversion.

This work explores an efficient and numerically accurate procedure to obtain the Fukui function from fractional orbital occupation calculations. The energy- and density-linearity conditions are investigated in the context of using optimally tuned range-separated hybrid functionals for the calculation of the Fukui function. The methodology is then used to study the reactivity of organic radicals exhibiting energetic inversion between the singly occupied molecular orbital (SOMO) and the highest occupied molecular orbital (HOMO), that is, SOMO-HOMO inversion (SHI). The Fukui function correctly identifies the reactive sites of the molecules investigated, but additional computed quantities, such as radical reaction energies and vertical ionization potentials, are needed to distinguish SHI systems from conventional radicals.

Range-separated hybrid functionals for accurate prediction of band gaps of extended systems

In this work, we systematically evaluate the accuracy in band gap prediction of range-separated hybrid functionals on a large set of semiconducting and insulating materials and carry out comparisons with the performance of their global counterparts. We observe that all the range-separated hybrid functionals that correctly describe the long-range dielectric screening significantly improve upon standard hybrid functionals such as PBE0 and HSE06. The choice of the short-range Fock exchange fraction and the screening length can further reduce the predicted error. We then propose a universal expression for the selection of the inverse screening parameter as a function of the short-range and long-range Fock exchange fractions, which results in a mean absolute error as small as 0.15 eV for band gap prediction.

Hybrid functionals for periodic systems in the density functional tight-binding method

Screened range-separated hybrid (SRSH) functionals within generalized Kohn-Sham density functional theory (GKS-DFT) have been shown to restore a general $1/(r\ensuremath{\varepsilon})$ asymptotic decay of the electrostatic interaction in dielectric environments. Major achievements of SRSH include an improved description of optical properties of solids and correct prediction of polarization-induced fundamental gap renormalization in molecular crystals. The density functional tight-binding method (DFTB) is an approximate DFT that bridges the gap between first-principles methods and empirical electronic structure schemes. While purely long-range corrected RSH are already accessible within DFTB for molecular systems, this work generalizes the theoretical foundation to also include screened range-separated hybrids, with conventional pure hybrid functionals as a special case. The presented formulation and implementation is also valid for periodic boundary conditions (PBC) beyond the $\mathrm{\ensuremath{\Gamma}}$ point. To treat periodic Fock exchange and its integrable singularity in reciprocal space, we resort to techniques successfully employed by DFT, in particular a truncated Coulomb operator and the minimum image convention. Starting from the first-principles Hartree-Fock operator, we derive suitable expressions for the DFTB method, using standard integral approximations and their efficient implementation in the $\mathrm{dftb}+$ software package. Convergence behavior is investigated and demonstrated for the polyacene series as well as two- and three-dimensional materials. Benzene and pentacene molecular and crystalline systems show the correct polarization-induced gap renormalization by SRSH-DFTB at heavily reduced computational cost compared to first-principles methods.

Accurate Ionization Potentials, Electron Affinities, and Band Gaps from the ωLH22t Range-Separated Local Hybrid Functional: No Tuning Required.

The optimal tuning (OT) of range-separated hybrid (RSH) functionals has been proposed as the currently most accurate DFT-based way to compute the relevant quantities required for charge-transfer processes in organic chromophores used in organic photovoltaics and related fields. The main drawback of OT-RSHs is that the system-specific tuning of the range-separation parameter is not size-consistent. It therefore also lacks transferability, e.g., when considering processes involving orbitals not involved in the tuning or for reactions between different chromophores. Here we show that the recently reported ωLH22t range-separated local hybrid functional provides ionization energies, electron affinities, and fundamental gaps on par with OT-RSH treatments, approaching the quality of GW results, without any need for system-specific tuning. This holds from relevant organic chromophores of varying sizes all the way to atomic electron affinities. ωLH22t also gives excellent outer-valence quasiparticle spectra and is a generally accurate functional for both main-group and transition-metal energetics, as well as for a variety of excitation types. Range-separated local hybrid functionals are suggested as promising new quantum-chemical tools in molecular electronics.

Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization.

This work introduces a new class of hybrid density functional theory (DFT) approximations, which incorporate different fractions of nonlocal exact exchange in predefined states such as core atomic orbitals (AOs). These projected hybrid density functionals are related to range-separated hybrid functionals, which incorporate different fractions of nonlocal exchange at different electron-electron separations. This work derives projected hybrids using the Adiabatic Projection formalism. One projects the electron-electron interaction operator onto the chosen predefined states, introduces the projected operator into the noninteracting Kohn-Sham reference system, and employs a formally exact density functional to model the remaining electron-electron interactions. Projected hybrids, like range-separated hybrids, approximate the partially interacting reference system's ground-state wave function as a single Slater determinant. Projected hybrids are readily implemented into existing density functional codes, requiring only a projection of the one-particle density matrices and exchange operators entering existing routines. This work also presents an application to core electron ionization. Projecting onto core atomic orbitals allows us to introduce additional nonlocal exchange into atomic core regions. This reduces the impact of self-interaction error on computed core electron properties. Benchmark studies are reported for PBE0c70, a core-projected variant of the Perdew-Burke-Ernzerhof global hybrid PBE0, in which the fraction of nonlocal exchange is increased from 25% to 70% in atomic core regions. PBE0c70-predicted core orbital energies accurately recover nonrelativistic core-electron binding energies of second-period elements Li-Ne and third-period elements Na-Ar, without degrading the good performance of PBE0 for atomization energies and valence ionization potentials.

Full Implementation, Optimization, and Evaluation of a Range-Separated Local Hybrid Functional with Wide Accuracy for Ground and Excited States.

We report the first full and efficient implementation of range-separated local hybrid functionals (RSLHs) into the TURBOMOLE program package. This enables the computation of ground-state energies and nuclear gradients as well as excitation energies. Regarding the computational effort, RSLHs scale like regular local hybrid functionals (LHs) with system or basis set size and increase timings by a factor of 2-3 in total. An advanced RSLH, ωLH22t, has been optimized for atomization energies and reaction barriers. It is an extension of the recent LH20t local hybrid and is based on short-range PBE and long-range HF exchange-energy densities, a pig2 calibration function to deal with the gauge ambiguity of exchange-energy densities, and reoptimized B95c correlation. ωLH22t has been evaluated for a wide range of ground-state and excited-state quantities. It further improves upon the already successful LH20t functional for the GMTKN55 main-group energetics test suite, and it outperforms any global hybrid while performing close to the top rung-4 functional, ωB97M-V, for these evaluations when augmented by D4 dispersion corrections. ωLH22t performs excellently for transition-metal reactivity and provides good balance between delocalization errors and left-right correlation for mixed-valence systems, with a somewhat larger bias toward localized states compared to LH20t. It approaches the accuracy of the best local hybrids to date for core, valence singlet and triplet, and Rydberg excitation energies while improving strikingly on intra- and intermolecular charge-transfer excitations, comparable to the most successful range-separated hybrids available.