Highly accurate first-principles benchmark data sets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics

Anions Formed by Perchlorofluorobenzenes C6ClnF6-n (n = 0-6)

Anions formed by the perhalobenzene series C6ClnF6-n (n = 0-6) are studied computationally. All members of the series form both stable valence and stable nonvalence anions. At the geometry of the neutral parents, only nonvalence anions are bound, and the respective vertical electron affinities show values in the 20 to 60 meV range. Valence anions show distorted nonplanar structures, and one can distinguish two types of conformers. A-type conformers show puckered-ring structures and excess electrons delocalized over several C-Cl bonds [in the case of C6F6-, C-F bonds], while B-type conformers possess excess electrons essentially localized in a single C-Cl bond, which is accordingly strongly stretched and bent out of plane. For a specific anion, all conformers are close in energy (relative energies of less than 10 kJ/mol) and are connected by low-lying transition states. Accordingly, A-type and B-type conformers possess similar adiabatic electron affinities; however, their vertical detachment energies exhibit drastically different values, which should ease conformer distinction in photoelectron spectroscopy.

Exploring non-covalent interactions in excited states: beyond aromatic excimer models

Time-dependent density functional theory (TD-DFT) offers a relatively accurate and inexpensive approach for excited state calculations. However, conventional TD-DFT may suffer from the same poor description of non-covalent interactions (NCIs) which is known from ground-state DFT. In this work we present a comprehensive benchmark study of TD-DFT for excited-state NCIs. This is achieved by calculating dissociation curves for excited complexes ('exciplexes'), whose binding strength depends on excited-state NCIs including electrostatics, Pauli repulsion, charge-transfer, and London dispersion. Reference dissociation curves are calculated with the reasonably accurate wave function method SCS-CC2/CBS(3,4) which is used to benchmark a range of TD-DFT methods. Additionally, we test the effect of ground-state dispersion corrections, DFT-D3(BJ) and VV10, for exciplex binding. Overall, we find that TD-DFT methods generally under-bind exciplexes which can be explained by the missing dispersion forces. Underbinding errors reduce going up the rungs of Jacob's ladder. Further, the D3(BJ) dispersion correction is essential for good accuracy in most cases. Likewise, the VV10-type non-local kernel yields relatively low errors and has comparable performance in either its fully self-consistent implementation or as a post-SCF additive correction, but its impact is solely on ground-state energies and not on excitation energies. From our analysis, the most robust TD-DFT methods for exciplexes with localised excitations in their equilibrium and non-equilibrium geometries are the double hybrids B2GP-PLYP-D3(BJ) and B2PLYP-D3(BJ). Their range-separated versions ωB2(GP-)PLYP-D3(BJ) or the spin-opposite scaled, range-separated double hybrid SOS-ωB88PP86 can be recommended when charge transfer plays a role in the excitations. We also identify the need for a state-specific dispersion correction as the next step for improved TD-DFT performance.

Toward Efficient and Unified Treatment of Static and Dynamic Correlations in Generalized Kohn-Sham Density Functional Theory

Accurate description of the static correlation poses a persistent challenge in electronic structure theory, particularly when it has to be concurrently considered with the dynamic correlation. We develop here a method in the generalized Kohn-Sham density functional theory (DFT) framework, named R-xDH7-SCC15, which achieves an unprecedented accuracy in capturing the static correlation, while maintaining a good description of the dynamic correlation on par with the state-of-the-art DFT and wave function theory methods, all grounded in the same single-reference black-box methodology. Central to R-xDH7-SCC15 is a general-purpose static correlation correction (SCC) model applied to the renormalized XYG3-type doubly hybrid method (R-xDH7). The SCC model development involves a hybrid machine learning strategy that integrates symbolic regression with nonlinear parameter optimization, aiming to achieve a balance between generalization capability, numerical accuracy, and interpretability. Extensive benchmark studies confirm the robustness and broad applicability of R-xDH7-SCC15 across a diverse array of main-group chemical scenarios. Notably, it displays exceptional aptitude in accurately characterizing intricate reaction kinetics and dynamic processes in regions distant from equilibrium, where the influence of static correlation is most profound. Its capability to consistently and efficiently predict the whole energy profiles, activation barriers, and reaction pathways within a user-friendly "black-box" framework represents an important advance in the field of electronic structure theory.

Assessment of the applicability of DFT methods to [Cp*Rh]-catalyzed hydrogen evolution processes

The present computational study provides a benchmark of density functional theory (DFT) methods in describing hydrogen evolution processes catalyzed by [Cp*Rh]-containing organometallic complexes. A test set was composed of 26 elementary reactions featuring chemical transformations and bonding situations essential for the field, including the emerging concept of non-innocent Cp* behavior. Reference values were obtained from a highly accurate 3/4 complete basis set and 6/7 complete PNO space extrapolated DLPNO-CCSD(T) energies. The performance of lower-level extrapolation procedures was also assessed. We considered 84 density functionals (DF) (including 13 generalized gradient approximations (GGA), nine meta-GGAs, 33 hybrids, and 29 double-hybrids) and three composite methods (HF-3c, PBEh-3c, and r2SCAN-3c), combined with different types of dispersion corrections (D3(0), D3BJ, D4, and VV10). The most accurate approach is the PBE0-DH-D3BJ (MAD of 1.36 kcal mol-1) followed by TPSS0-D3BJ (MAD of 1.60 kcal mol-1). Low-cost r2SCAN-3c composite provides a less accurate but much faster alternative (MAD of 2.39 kcal mol-1). The widely used Minnesota-family M06-L, M06, and M06-2X DFs should be avoided (MADs of 3.70, 3.94, and 4.01 kcal mol-1, respectively).

An investigation into transition states of cyclic tetra-atomic silicon and germanium interstellar dust compounds: SixC4-x, GexC4-x, and GexSi4-x (x ∈ {1,2,3})

Presented in this work is a thorough determination of the transition states between the different isomers of cyclic tetra-atomic silicon carbide, germanium carbide, and germanium silicide clusters. Through use of density functional theory (B3LYP-D3BJ, M06-2X, ωB97X-D4, and B2GP-PLYP) in conjunction with the aug-cc-pVTZ basis set, transition state structures and their barrier heights are determined for the interconversions between the various isomers for the family of tetra-atomic SiC, GeC, and GeSi compounds. SiC dust grains are known to be prevalent in interstellar dust, and among this group, so far only diamond-shaped (d-)SiC3 has been detected in the interstellar medium (ISM). Determining which other structures might be detectable not only depends on their intrinsic spectroscopic features, but whether or not they are likely to exist as isomers in interstellar environments. By examining the energy barrier heights for transitions between isomers, we determined that many of these structures are unlikely to exhibit interconversion in the ISM, outside of hotter circumstellar environments. Although Boltzmann population ratios at approximate circumstellar temperatures suggest the presence of higher energy minima, it is likely that once interconversion happens, as molecules travel away from a star and cool, they will get kinetically trapped in the potential energy well they inhabit, making how the ratios freeze out dependent on the time and pathways the molecules take to cool down. As such, many of these higher energy minima may still be good candidates for detection including (rhomboidal) r-SiC3, r-GeC3, r-GeSi3, (trapezoidal) t-Si2C2, r-Ge2C2, and d-Si3C.

Anion Photoelectron Imaging Spectroscopy of C6F5X- (X = F, Cl, Br, I)

The photoelectron (PE) spectra of C6F5X- (X = Cl, Br, I) and computational results on the anions and neutrals are presented and compared to previously reported results on C6F6- [McGee, C. J. J. Phys. Chem. A 2023, 127, 8556-8565.]. The spectra all exhibit broad, vibrationally unresolved detachment transitions, indicating that the equilibrium structures of the anions are significantly different from the neutrals. The PE spectrum of C6F5Cl- exhibits a parallel photoelectron angular distribution (PAD), similar to that of the previously reported C6F6- spectrum, while the PE spectra of C6F5Br- and C6F5I- have isotropic PADs, and also exhibit a prominent X- PE feature due to photodissociation of C6F5X- resulting in X- formation. Identification of the C6F5X- detachment transition origins, which is equivalent to the neutral electron affinity (EA), in all three cases is difficult, since the broadness of the detachment feature is accompanied by vanishingly small detachment cross section near the origin. Upper limits on the EAs were determined to be 1.70 eV for C6F5Cl, 2.10 eV for C6F5Br, and 2.00 eV for C6F5I, all significantly higher than the 0.76 eV upper limit determined for C6F6 with the same experiment. The broad detachment transitions are consistent with computational results, which predict very large differences between the neutral and anionic C-X (X = Cl, Br, I) bond lengths. Based on differences between the MBIS atom charges in the anions and neutrals, the excess charge in the anion is on the unique C atom and X, in contrast to the nonplanar C2v structured C6F6- anion, for which the charge is delocalized over the molecule. In C6F5Cl-, the C-Cl bond is predicted to be bent out of the plane, while both C6F5Br- and C6F5I- are predicted to be planar on average. The impact of the interruption of the symmetry in the hexafluorobenzene neutral and anion on the molecular and electronic structure of C6F5X/C6F5X- is considered, as well as the possible dissociative state leading to X- (X = Br, I) formation, and the nature of the C-X bond.

How do spin-scaled double hybrids designed for excitation energies perform for noncovalent excited-state interactions? An investigation on aromatic excimer models

Time-dependent double hybrids with spin-component or spin-opposite scaling to their second-order perturbative correlation correction have demonstrated competitive robustness in the computation of electronic excitation energies. Some of the most robust are those recently published by our group (M. Casanova-Páez, L. Goerigk, J. Chem. Theory Comput. 2021, 20, 5165). So far, the implementation of these functionals has not allowed correctly calculating their ground-state total energies. Herein, we define their correct spin-scaled ground-state energy expressions which enables us to test our methods on the noncovalent excited-state interaction energies of four aromatic excimers. A range of 22 double hybrids with and without spin scaling are compared to the reasonably accurate wavefunction reference from our previous work (A. C. Hancock, L. Goerigk, RSC Adv. 2023, 13, 35964). The impact of spin scaling is highly dependent on the underlying functional expression, however, the smallest overall errors belong to spin-scaled functionals with range separation: SCS- and SOS- ω PBEPP86, and SCS-RSX-QIDH. We additionally determine parameters for DFT-D3(BJ)/D4 ground-state dispersion corrections of these functionals, which reduce errors in most cases. We highlight the necessity of dispersion corrections for even the most robust TD-DFT methods but also point out that ground-state based corrections are insufficient to completely capture dispersion effects for excited-state interaction energies.

Chemical Potentials and the One-Electron Hamiltonian of the Second-Order Perturbation Theory from the Functional Derivative Approach

We develop a functional derivative approach to calculate the chemical potentials of second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the derivative of the MP2 correlation energy with respect to the occupation number of frontier orbitals, is obtained from the chain rule via the noninteracting Green's function. First, the MP2 correlation energy is expressed in terms of the noninteracting Green's function, and its functional derivative to the noninteracting Green's function is the second-order self-energy. Then, the derivative of the noninteracting Green's function to the occupation number is obtained by including the orbital relaxation effect. We show that the MP2 chemical potentials obtained from the functional derivative approach agree with that obtained from the finite difference approach. The one-electron Hamiltonian, defined as the derivative of the MP2 energy with respect to the one particle density matrix, is also derived using the functional derivative approach, which can be used in the self-consistent calculations of MP2 and double-hybrid density functionals. The developed functional derivative approach is promising for calculating the chemical potentials and the one-electron Hamiltonian of approximate functionals and many-body perturbation approaches dependent explicitly on the noninteracting Green's function.

Big data benchmarking: how do DFT methods across the rungs of Jacob's ladder perform for a dataset of 122k CCSD(T) total atomization energies?

Total atomization energies (TAEs) are a central quantity in density functional theory (DFT) benchmark studies. However, so far TAE databases obtained from experiment or high-level ab initio wavefunction theory included up to hundreds of TAEs. Here, we use the GDB-9 database of 133k CCSD(T) TAEs generated by Curtiss and co-workers [B. Narayanan, P. C. Redfern, R. S. Assary and L. A. Curtiss, Chem. Sci., 2019, 10, 7449] to evaluate the performance of 14 representative DFT methods across the rungs of Jacob's ladder (namely, PBE, BLYP, B97-D, M06-L, τ-HCTH, PBE0, B3LYP, B3PW91, ωB97X-D, τ-HCTHh, PW6B95, M06, M06-2X, and MN15). We first use the A25[PBE] diagnostic for nondynamical correlation to eliminate systems that potentially include significant multireference effects, for which the CCSD(T) TAEs might not be sufficiently reliable. The resulting database (denoted by GDB9-nonMR) includes 122k species. Of the considered functionals, B3LYP attains the best performance relative to the G4(MP2) reference TAEs, with a mean absolute deviation (MAD) of 4.09 kcal mol-1. This first-generation hybrid functional, in which the three mixing coefficients were fitted against a small set of TAEs, is one of the few functionals that are not systematically biased towards overestimating the G4(MP2) TAEs, as demonstrated by a mean-signed deviation (MSD) of 0.45 kcal mol-1. The relatively good performance of B3LYP is followed by the heavily parameterized M06-L meta-GGA functional, which attains a MAD of 6.24 kcal mol-1. The PW6B95, M06, M06-2X, and MN15 functionals tend to systematically overestimate the G4(MP2) TAEs and attain MADs ranging between 18.69 (M06) and 28.54 (MN15) kcal mol-1. However, PW6B95 and M06-2X exhibit particularly narrow error distributions. Thus, scaling their TAEs by an empirical scaling factor reduces their MADs to merely 3.38 (PW6B95) and 2.85 (M06-2X) kcal mol-1. Empirical dispersion corrections (e.g., D3 and D4) are attractive, and therefore, their inclusion worsens the performance of methods that systematically overestimate the TAEs.

DLPNO-CCSD(T) and DFT study of the acetate-assisted C-H activation of benzaldimine at [RuCl2(p-cymene)]2: the relevance of ligand exchange processes at ruthenium(II) complexes in polar protic media

To gain mechanistic insights into the acetate-assisted cyclometallations of arylimines promoted by [RuCl2(p-cymene)]2 in polar protic media, DFT geometry optimizations (with M06 and ωB97X-D3 functionals and the cc-pVDZ-PP[Ru] basis set) followed by DLPNO-CCSD(T)/CBS energy evaluations were performed using benzaldimine as a model substrate and methanol as the solvent (with CPCM or SMD models). The calculation results show that coordination of the imine to an acetate ruthenium precursor is followed by anion (chloride or acetate) dissociation as the rate-determining step of the process. H-Bonding of two explicit MeOH to the anion reduces the calculated activation energy to ca. 23 kcal mol-1, in good agreement with the experimental half-life at room temperature. Subsequent AMLA/CMD C-H activation of the intermediate cationic complexes is a faster, reversible process. Alternative reaction pathways involving neutral diacetate ruthenium complexes offer AMLA/CMD transition state structures of lower energy but are precluded due to higher energy barriers for the initial ligand exchange processes at ruthenium. Solvent assistance accelerates the final chloride/acetate exchange processes on the cycloruthenate intermediates, particularly when compression in the condensed phase is taken into consideration. The performance of six DFT functionals (with the aug-pVTZ-PP[Ru] basis set) was assessed using the DLPNO-CCSD(T)/CBS reference energies. Neutral diacetate ruthenium complexes were incorrectly predicted as being kinetically relevant when using hybrid DFT methods (PBE0-D3(BJ), M06-2X or ωB97M-V). Good agreement between the calculated barrier heights and our benchmark energy results was obtained by using double-hybrid DFT methods. PWPB95 with D3(BJ) or D4 dispersion energy corrections was found to be the most accurate (ΔG≠ MUE of ca. 1 kcal mol-1). This study may aid our understanding of and help with further experimental investigations of synthetically useful carboxylate-assisted C-H bond functionalizations involving (N,C)-cyclometallated (p-cymene)Ru(II) intermediate complexes in sustainable polar protic solvents.

On the sensitivity of computed partial charges toward basis set and (exchange-)correlation treatment

Partial charges are a central concept in general chemistry and chemical biology, yet dozens of different computational definitions exist. In prior work [Cho et al., ChemPhysChem 21, 688-696 (2020)], we showed that these can be reduced to at most three 'principal components of ionicity'. The present study addressed the dependence of computed partial charges q on 1-particle basis set and (for WFT methods) n -particle correlation treatment or (for DFT methods) exchange-correlation functional, for several representative partial charge definitions such as QTAIM, Hirshfeld, Hirshfeld-I, HLY (electrostatic), NPA, and GAPT. Our findings show that semi-empirical double hybrids can closely approach the CCSD(T) 'gold standard' for this property. In fact, owing to an error compensation in MP2, CCSD partial charges are further away from CCSD(T) than is MP2. The nonlocal correlation is important, especially when there is a substantial amount of nonlocal exchange. Employing range separation proves to be "mostly" not advantageous, while global hybrids perform optimally for 20%-30% Hartree-Fock exchange across all charge types. Basis set convergence analysis shows that an augmented triple-zeta heavy-aug-cc-pV(T+d)Z basis set or a partially augmented jun-cc-pV(T+d)Z basis set is sufficient for Hirshfeld, Hirshfeld-I, HLY, and GAPT charges. In contrast, QTAIM and NPA display slower basis set convergence. It is noteworthy that for both NPA and QTAIM, HF exhibits markedly slower basis set convergence than the correlation components of MP2 and CCSD. Triples corrections in CCSD(T), denoted as CCSD(T)-CCSD, exhibit even faster basis set convergence.

Copper(II) coordination to the intrinsically disordered region of SARS-CoV-2 Nsp1

The intrinsically disordered C-terminal peptide region of severe acute respiratory syndrome coronavirus 2 nonstructural protein-1 (Nsp1-CT) inhibits host protein synthesis by blocking messenger RNA (mRNA) access to the 40S ribosome entrance tunnel. Aqueous copper(II) ions bind to the disordered peptide with micromolar affinity, creating a possible strategy to restore protein synthesis during host infection. Electron paramagnetic resonance (EPR) and tryptophan fluorescence measurements on a 10-residue model of the disordered protein region (Nsp1-CT10), combined with advanced quantum mechanics calculations, suggest that the peptide binds to copper(II) as a multidentate ligand. Two optimized computational models of the copper(II)-peptide complexes were derived: One corresponding to pH 6.5 and the other describing the complex at pH 7.5 to 8.5. Simulated EPR spectra based on the calculated model structures are in good agreement with experimental spectra.

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.

High-Performance Multi-GPU Analytic RI-MP2 Energy Gradients

This article presents a novel algorithm for the calculation of analytic energy gradients from second-order Møller-Plesset perturbation theory within the Resolution-of-the-Identity approximation (RI-MP2), which is designed to achieve high performance on clusters with multiple graphical processing units (GPUs). The algorithm uses GPUs for all major steps of the calculation, including integral generation, formation of all required intermediate tensors, solution of the Z-vector equation and gradient accumulation. The implementation in the EXtreme Scale Electronic Structure System (EXESS) software package includes a tailored, highly efficient, multistream scheduling system to hide CPU-GPU data transfer latencies and allows nodes with 8 A100 GPUs to operate at over 80% of theoretical peak floating-point performance. Comparative performance analysis shows a significant reduction in computational time relative to traditional multicore CPU-based methods, with our approach achieving up to a 95-fold speedup over the single-node performance of established software such as Q-Chem and ORCA. Additionally, we demonstrate that pairing our implementation with the molecular fragmentation framework in EXESS can drastically lower the computational scaling of RI-MP2 gradient calculations from quintic to subquadratic, enabling further substantial savings in runtime while retaining high numerical accuracy in the resulting gradients.

W4Λ: Leveraging Λ Coupled-Cluster for Accurate Computational Thermochemistry Approaches

High-accuracy composite wave function methods like Weizmann-4 (W4) theory, high-accuracy extrapolated ab initio thermochemistry (HEAT), and the Feller-Peterson-Dixon (FPD) approach enable sub-kJ/mol accuracy in gas-phase thermochemical properties. Their biggest computational bottleneck is the evaluation of the valence post-CCSD(T) correction term. We demonstrate here, for the W4-17 thermochemistry benchmark and subsets thereof, that the Λ coupled-cluster expansion converges more rapidly and smoothly than the regular coupled-cluster series. By means of CCSDT(Q)Λ and CCSDTQ(5)Λ, we can considerably (up to an order of magnitude) accelerate W4- and W4.3-type calculations without loss in accuracy, leading to the W4Λ and W4.3Λ computational thermochemistry protocols.

Diffusion Monte Carlo method for barrier heights of multiple proton exchanges and complexation energies in small water, ammonia, and hydrogen fluoride clusters

Proton exchange reactions are of key importance in many processes in water. However, it is nontrivial to achieve reliable barrier heights for multiple proton exchanges and complexation energies in hydrogen-bonded systems theoretically. Performance of the fixed-node diffusion quantum Monte Carlo (FN-DMC) with the single-Slater-Jastrow trial wavefunction on total energies, barrier heights of multiple proton exchanges, and complexation energies of small water, ammonia, and hydrogen fluoride clusters is investigated in this study. Effects of basis sets and those of locality approximation (LA), T-move approximation (T-move), and determinant localization approximation (DLA) schemes in dealing with the nonlocal part of pseudopotentials on FN-DMC results are evaluated. According to our results, diffuse basis functions are important in achieving reliable barrier heights and complexation energies with FN-DMC, although the cardinal number of the basis set is more important than diffuse basis functions on total energies of these systems. Our results also show that the time step bias with DLA and LA is smaller than T-move; however, the time step bias of DMC energies with respect to time steps using the T-move is roughly linear up to 0.06 a.u., while this is not the case with LA and DLA. Barrier heights and complexation energies with FN-DMC using these three schemes are always within chemical accuracy. Taking into account the fact that T-move and DLA are typically more stable than LA, FN-DMC calculations with the T-move or DLA scheme and basis sets containing diffuse basis functions are suggested for barrier heights of multiple proton exchanges and complexation energies of hydrogen-bonded clusters.

Chemical Investigation on the Mechanism and Kinetics of the Atmospheric Degradation Reaction of Trichlorofluoroethene by OH⋅ and Its Subsequent Fate in the Presence of O2 /NOx

The M06-2X/6-311++G(d,p) level of theory was used to examine the degradation of Trichlorofluoroethene (TCFE) initiated by OH⋅ radicals. Additionally, the coupled-cluster single-double with triple perturbative [CCSD(T)] method was employed to refine the single-point energies using the complete basis set extrapolation approach. The results indicated that OH-addition is the dominant pathway. OH⋅ adds to both the C1 and C2 carbons, resulting in the formation of the C(OH)Cl2 -⋅CClF and ⋅CCl2 -C(OH)ClF species. The associated barrier heights were determined to be 1.11 and -0.99 kcal mol-1 , respectively. Furthermore, the energetic and thermodynamic parameters show that pathway 1 exhibits greater exothermicity and exergonicity compared to pathway 2, with differences of 8.11 and 8.21 kcal mol-1 , correspondingly. The primary pathway involves OH addition to the C2 position, with a rate constant of 6.2×10-13  cm3 molecule-1 sec-1 at 298 K. This analysis served to estimate the atmospheric lifetime, along with the photochemical ozone creation potential (POCP) and ozone depletion potential (ODP). It yielded an atmospheric lifetime of 8.49 days, an ODP of 4.8×10-4 , and a POCP value of 2.99, respectively. Radiative forcing efficiencies were also estimated at the M06-2X/6-311++G(d,p) level. Global warming potentials (GWPs) were calculated for 20, 100, and 500 years, resulting in values of 9.61, 2.61, and 0.74, respectively. TCFE is not expected to make a significant contribution to the radiative forcing of climate change. The results obtained from the time-dependent density functional theory (TDDFT) indicated that TCFE and its energized adducts are unable to photolysis under sunlight in the UV and visible spectrum. Secondary reactions involve the [TCFE-OH-O2 ]⋅ peroxy radical, leading subsequently to the [TCFE-OH-O]⋅ alkoxy radical. It was found that the alkoxy radical resulting from the peroxy radical can lead to the formation of phosgene (COCl2 ) and carbonyl chloride fluoride (CClFO), with phosgene being the primary product.

A 21st Century View of Allowed and Forbidden Electrocyclic Reactions

In 1965, Woodward and Hoffmann proposed a theory to predict the stereochemistry of electrocyclic reactions, which, after expansion and generalization, became known as the Woodward-Hoffmann Rules. Subsequently, Longuet-Higgins and Abrahamson used correlation diagrams to propose that the stereoselectivity of electrocyclizations could be explained by the correlation of reactant and product orbitals with the same symmetry. Immediately thereafter, Hoffmann and Woodward applied correlation diagrams to explain the mechanism of cycloadditions. We describe these discoveries and their evolution. We now report an investigation of various electrocyclic reactions using DFT and CASSCF. We track the frontier molecular orbitals along the intrinsic reaction coordinate and modeled trajectories and examine the correlation between HOMO and LUMO for thermally forbidden systems. We also investigate the electrocyclizations of several highly polarized systems for which the Houk group had predicted that donor-acceptor substitution can induce zwitterionic character, thereby providing low-energy pathways for formally forbidden reactions. We conclude with perspectives on the field of pericyclic reactions, including a refinement as the meaning of Woodward and Hoffmann's "Violations. There are none!" Lastly, we comment on the burgeoning influence of computations on all fields of chemistry.

Correlated proton dynamics in hydrogen bonding networks: the benchmark case of 3-hydroxyglutaric acid

Proton and hydrogen-bonded networks sustain a broad range of structural and charge transfer processes in supramolecular materials. The modelling of proton dynamics is however challenging and demands insights from prototypical benchmark systems. The intramolecular H-bonding networks induced by either protonation or deprotonation of 3-hydroxyglutaric acid provide intriguing case studies of correlated proton dynamics. The vibrational signatures associated with the fluxional proton bonding and its coupling with the hydroxyglutaric backbone are investigated here with infrared action ion spectroscopy experiments and Born-Oppenheimer molecular dynamics (BOMD) computations. Despite the formally similar symmetry of protonated and deprotonated hydroxyglutaric acid, the relative proton affinities of the oxygen centers of the carboxylic and carboxylate groups with respect to that of the central hydroxyl group lead to distinct proton dynamics. In the protonated acid, a tautomeric arrangement of the type HOCO·[HOH]+·OCOH is preferred with the proton binding tighter to the central hydroxyl moiety and the electronic density being shared between the two nearly symmetric H-bonds with the carboxylic end groups. In the deprotonated acid, the asymmetric [OCO]-·HO·HOCO configuration is more stable, with a stronger H-bonding on the bare carboxylate end. Both systems display active backbone dynamics and concerted Grothuss-like proton motions, leading to diffuse band structures in their vibrational spectra. These features are accurately reproduced by the BOMD computations.

Toward a correct treatment of core properties with local hybrid functionals

In local hybrid functionals (LHs), a local mixing function (LMF) determines the position-dependent exact-exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt-LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn-Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high-density and iso-orbital limits relevant for the innermost core region. Using TDDFT calculations for a set of K-shell core excitations of second- and third-period systems including accurate state-of-the-art relativistic orbital corrections, the core part of the LMF is optimized, while the valence part is optimized as previously reported for test sets of atomization energies and reaction barriers (Haasler et al., J Chem Theory Comput 2020, 16, 5645). The LHs are completed by a calibration function that minimizes spurious nondynamical correlation effects caused by the gauge ambiguities of exchange-energy densities, as well as by B95c meta-GGA correlation. The resulting LH23pt functional relates to the previous LH20t functional but specifically improves upon the core region.

Noncovalently bound excited-state dimers: a perspective on current time-dependent density functional theory approaches applied to aromatic excimer models

Excimers are supramolecular systems whose binding strength is influenced by many factors that are ongoing challenges for computational methods, such as charge transfer, exciton coupling, and London dispersion interactions. Treating the various intricacies of excimer binding at an adequate level is expected to be particularly challenging for time-dependent Density Functional Theory (TD-DFT) methods. In addition to well-known limitations for some TD-DFT methods in the description of charge transfer or exciton coupling, the inherent London dispersion problem from ground-state DFT translates to TD-DFT. While techniques to appropriately treat dispersion in DFT are well-developed for electronic ground states, these dispersion corrections remain largely untested for excited states. Herein, we aim to shed light on current TD-DFT methods, including some of the newest developments. The binding of four model excimers is studied across nine density functionals with and without the application of additive dispersion corrections against a wave function reference of SCS-CC2/CBS(3,4) quality, which approximates select CCSDR(3)/CBS data adequately. To our knowledge, this is the first study that presents single-reference wave function dissociation curves at the complete basis set level for the assessed model systems. It is also the first time range-separated double-hybrid density functionals are applied to excimers. In fact, those functionals turn out to be the most promising for the description of excimer binding followed by global double hybrids. Range-separated and global hybrids-particularly with large fractions of Fock exchange-are outperformed by double hybrids and yield worse dissociation energies and inter-molecular equilibrium distances. The deviation between each assessed functional and reference increases with system size, most likely due to missing dispersion interactions. Additive dispersion corrections of the DFT-D3(BJ) and DFT-D4 types reduce the average errors for TD-DFT methods but do so inconsistently and therefore do not offer a black-box solution in their ground-state parametrised form. The lack of appropriate description of dispersion effects for TD-DFT methods is likely hindering the practical application of the herein identified more efficient methods. Dispersion corrections parametrised for excited states appear to be an important next step to improve the applicability of TD-DFT methods and we hope that our work assists with the future development of such corrections.

Inverted Lowest Singlet and Triplet Excitation Energy Ordering of Graphitic Carbon Nitride Flakes

In organic light-emitting diodes (OLEDs), only 25% of electrically generated excitons are in a singlet state, S1, and the remaining 75% are in a triplet state, T1. In thermally activated delayed fluorescence (TADF) chromophores the transition from the nonradiative T1 state to the radiative S1 state can be thermally activated, which improves the efficiency of OLEDs. Chromophores with inverted energy ordering of S1 and T1 states, S1 < T1, are superior to TADF chromophores, thanks to the absence of an energy barrier for the transition from T1 to S1. We benchmark the performance of time-dependent density functional theory using different exchange-correlation functionals and find that scaled long-range corrected double-hybrid functionals correctly predict the inverted singlet-triplet gaps of N-substituted phenalene derivatives. We then show that the inverted energy ordering of S1 and T1 is an intrinsic property of graphitic carbon nitride flakes. A design strategy of new chromophores with inverted singlet-triplet gaps is proposed. The color of emitted light can be fine-tuned through flake size and amine substitution on flake vertices.

Benchmarking Density Functional Theory Methods for Metalloenzyme Reactions: The Introduction of the MME55 Set

We present a new benchmark set of metalloenzyme model reaction energies and barrier heights that we call MME55. The set contains 10 different enzymes, representing eight transition metals, both open and closed shell systems, and system sizes of up to 116 atoms. We use four DLPNO-CCSD(T)-based approaches to calculate reference values against which we then benchmark the performance of a range of density functional approximations with and without dispersion corrections. Dispersion corrections improve the results across the board, and triple-ζ basis sets provide the best balance of efficiency and accuracy. Jacob's ladder is reproduced for the whole set based on averaged mean absolute (percent) deviations, with the double hybrids SOS0-PBE0-2-D3(BJ) and revDOD-PBEP86-D4 standing out as the most accurate methods for the MME55 set. The range-separated hybrids ωB97M-V and ωB97X-V also perform well here and can be recommended as a reliable compromise between accuracy and efficiency; they have already been shown to be robust across many other types of chemical problems, as well. Despite the popularity of B3LYP in computational enzymology, it is not a strong performer on our benchmark set, and we discourage its use for enzyme energetics.

Mehrere Triplett-Metall-zentrierte Jahn-Teller-Isomere bestimmen die temperaturabhängigen Lumineszenzlebensdauern in [Ru(bpy)3]2

Ein genaues Verständnis der Faktoren, welche die Lumineszenzlebensdauer von Übergangsmetallverbindungen bestimmen, ist für Anwendungen in der Photokatalyse und der photodynamischen Therapie von entscheidender Bedeutung. Die im Falle von [Ru(bpy)3]2+ (bpy=2,2’‐Bipyridin) allgemein akzeptierte Theorie besagt, dass die Emissionslebensdauer durch Optimierung der Energiebarriere zwischen dem emittierenden Triplett‐Zustand des Metall‐Liganden‐Ladungstransfers (3MLCT) und dem thermisch aktivierten Triplett‐Zustand des Metall‐Zentrums (3MC), oder der Energielücke zwischen beiden Zuständen gesteuert werden kann. Hier zeigen wir, dass dies nicht allgemeingültig ist. Darüber hinaus demonstrieren wir, dass die Betrachtung eines einzelnen Relaxationspfades, der vom energetisch niedrigsten Minimum aus bestimmt wird, zu falschen Vorhersagen der temperaturabhängigen Emissionslebensdauer führt. Stattdessen erhalten wir eine ausgezeichnete Übereinstimmung mit den experimentellen temperaturabhängigen Lebensdauern, wenn ein erweitertes kinetisches Modell herangezogen wird, welches alle Pfade im Zusammenhang mit mehreren Jahn–Teller‐Isomeren und ihren effektiven Reaktionsbarrieren beinhaltet. Diese Konzepte sind für das Design weiterer lumineszierender Übergangsmetallkomplexe mit individuell angepassten Emissionslebensdauern auf der Grundlage theoretischer Vorhersagen unerlässlich.

Multiple Triplet Metal-Centered Jahn-Teller Isomers Determine Temperature-Dependent Luminescence Lifetimes in [Ru(bpy)3 ]2

Understanding the factors that determine the luminescence lifetime of transition metal compounds is key for applications in photocatalysis and photodynamic therapy. Here we show that for[ Ru ( bpy ) 3 ] 2 + ${[{\rm{Ru}}({\rm{bpy}})_{\rm{3}} ]^{{\rm{2 + }}} }$ (bpy = 2,2'-bipyridine), the generally accepted idea that emission lifetimes can be controlled optimizing the energy barrier from the emissive triplet metal-to-ligand charge-transfer (3 MLCT) state to the thermally-activated triplet metal-centered (3 MC) state or the energy gap between both states is a misconception. Further, we demonstrate that considering a single relaxation pathway determined from the minimum that is lowest in energy leads to wrong temperature-dependent emission lifetimes predictions. Instead, we obtain excellent agreement with experimental temperature-dependent lifetimes when an extended kinetic model that includes all the pathways related to multiple Jahn-Teller isomers and their effective reaction barriers is employed. These concepts are essential to correctly design other luminescent transition metal complexes with tailored emission lifetimes based on theoretical predictions.

Refining the thermochemical properties of CF, SiF, and their cations by combining photoelectron spectroscopy, quantum chemical calculations, and the Active Thermochemical Tables approach

Fluorinated species have a pivotal role in semiconductor material chemistry and some of them have been detected beyond the Earth's atmosphere. Achieving good energy accuracy on fluorinated species using quantum chemical calculations has long been a challenge. In addition, obtaining direct experimental thermochemical quantities has also proved difficult. Here, we report the threshold photoelectron and photoion yield spectra of SiF and CF radicals generated with a fluorine reactor. The spectra were analysed with the support of ab initio calculations, resulting in new experimental values for the adiabatic ionisation energies of both CF (9.128 ± 0.006 eV) and SiF (7.379 ± 0.009 eV). Using these values, the underlying thermochemical network of Active Thermochemical Tables was updated, providing further refined enthalpies of formation and dissociation energies of CF, SiF, and their cationic counterparts.

A Computational Study on Halogen/Halide Redox Mediators and Their Role in 1O2 Release in Aprotic Li-O2 Batteries

We present a computational study on the redox reactions of small clusters of Li superoxide and peroxide in the presence of halogen/halide redox mediators. The study is based on DFT calculations with a double hybrid functional and an implicit solvent model. It shows that iodine is less effective than bromine in the oxidation of Li2O2 to oxygen. On the basis of our thermodynamic data, in solvents with a low dielectric constant, iodine does not spontaneously promote either the oxidation of Li2O2 or the release of singlet oxygen, while bromine could spontaneously trigger both events. When a solvent with a large dielectric constant is used, both halogens appear to be able, at least on the basis of thermodynamics, to react spontaneously with the oxides, and the ensuing reaction sequence turned out to be strongly exoergic, thereby providing a route for the release of significant amounts of singlet oxygen. The role of spin-orbit coupling in providing a mechanism for singlet-triplet intersystem crossing has also been assessed.

A theoretical study on π-stacking and ferromagnetism of the perylene diimide radical anion dimer and tetramer

Ferromagnetism is rare in pure organic materials. Recently, the perylene diimide radical anion (PDI-) salt prepared through solvothermal reduction by hydrazine hydrate has shown room-temperature ferromagnetism in our work [Jiang et al., Adv. Mater., 2022, 34, 2108103]. Based on this, herein we conduct a theoretical study based on density functional theory (DFT) to reveal the stacked geometries between two NH4PDI monomers for low-spin (LS) and high-spin (HS) states and their magnetic exchange interactions (JAB) using Yamaguchi's approximate spin projection. It is observed that the pancake-bonded dimer of NH4PDI is the most stable pimer compared to others on both LS and HS potential energy surfaces. A transition of magnetic properties from strong antiferromagnetic (-1333.9 cm-1) to moderate ferromagnetic (67.0 cm-1) appears after increasing the interplanar distance between monomers and their relative rotation angle to access the HS state. According to energy decomposition analysis, the enhanced hydrogen bond formation and decrease of Pauli repulsion is able to counteract the decrease of attraction induced by electron correlation after accessing the HS state. Stacking patterns of exchange-coupled chain consisting of the NH4PDI tetramer are obtained for the HS state after geometry optimization of the structure constructed by two most stable HS pimers. The exchange interactions (51.8 cm-1, 381.2 cm-1 and 53.2 cm-1) between adjacent NH4PDI monomers are ferromagnetic in the HS state, which is in accordance with the experimentally observed room-temperature ferromagnetism.

Accurate Thermochemical and Kinetic Parameters at Affordable Cost by Means of the Pisa Composite Scheme (PCS)

A new strategy for the computation at an affordable cost of geometrical structures, thermochemical parameters, and rate constants for medium-sized molecules in the gas phase is proposed. The most distinctive features of the new model are the systematic use of cc-pVnZ-F12 basis sets, the addition of MP2 core-valence correlation in geometry optimizations by a double-hybrid functional, the separate extrapolation of MP2 and post-MP2 contributions, and the inclusion of anharmonic contributions in zero-point energies and thermodynamic functions. A thorough benchmark based on a wide range of prototypical systems shows that the new scheme outperforms the most well-known model chemistries without the need for any empirical parameter. Additional tests show that the computed zero-point energies and thermal contributions can be confidently used for obtaining accurate thermochemical and kinetic parameters. Since the whole computational workflow is translated in a black-box procedure, which can be followed with standard electronic structure codes, the way is paved for the accurate yet not prohibitively expensive study of medium- to large-sized molecules also by nonspecialists.

The influence of substituents in governing the strength of the P-X bonds of substituted halophosphines R1R2P-X (X = F and Cl)

In this study, the gas-phase homolytic P-F and P-Cl bond dissociation energies (BDEs) of a set of thirty fluorophosphine (R1R2P-F) and thirty chlorophosphine-type (R1R2P-Cl) molecules have been obtained using the high-level W2 thermochemical protocol. For the R1R2P-F species, the P-F BDEs (at 298 K) differ by up to 117.0 kJ mol-1, with (H3Si)2P-F having the lowest BDE (439.5 kJ mol-1) and F2P-F having the largest BDE (556.5 kJ mol-1). In the case of the chlorophosphine-type molecules, the difference in BDEs is considerably smaller (i.e., 72.6 kJ mol-1), with (NC)2P-Cl having the lowest P-Cl BDE (299.8 kJ mol-1) and (HO)2P-Cl having the largest (372.4 kJ mol-1). We have further analyzed the effect of substituents in governing the P-F and P-Cl BDEs by considering the effect of substituents in the parent halogenated precursors (using molecule stabilization enthalpies) and the effect of substituents in the product radicals (using radical stabilization enthalpies). Finally, we have also assessed the performance of a wide range of DFT methods for their ability to compute the gas-phase P-F and P-Cl BDEs contained in this dataset. We find that, overall, the double hybrid functional DSD-PBEB95 offers the best performance for both bond types, with mean absolute deviations of just 2.1 (P-F BDEs) and 2.2 (P-Cl BDEs) kJ mol-1.

Correlation Consistent Basis Sets for Explicitly Correlated Theory: The Transition Metals

We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f2g] for the 3d-block elements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters.

Catalytic effect of graphene on the inversion of corannulene using a continuum approach with the Lennard-Jones potential

The catalytic effect of graphene on the corannulene bowl-to-bowl inversion is confirmed in this paper using a pair-wise dispersion interaction model. In particular, a continuum approach together with the Lennard-Jones potential are adopted to determine the interaction energy between corannulene and graphene. These results are consistent with previous quantum chemical studies, which showed that a graphene sheet reduces the barrier height for the bowl-to-bowl inversion in corannulene. However, the results presented here demonstrate, for the first time, that the catalytic activity of graphene can be reproduced using pair-wise dispersion interactions alone. This demonstrates the major role that pair-wise dispersion interactions play in the catalytic activity of graphene.

Sub 20 cm-1 computational prediction of the CH bond energy - a case of systematic error in computational thermochemistry

The bond dissociation energy of methylidyne, D0(CH), is studied using an improved version of the High-Accuracy Extrapolated ab initio Thermochemistry (HEAT) approach as well as the Feller-Peterson-Dixon (FPD) model chemistry. These calculations, which include basis sets up to nonuple (aug-cc-pCV9Z) quality, are expected to be capable of providing results substantially more accurate than the ca. 1 kJ mol-1 level that is characteristic of standard high-accuracy protocols for computational thermochemistry. The calculated 0 K CH bond energy (27 954 ± 15 cm-1 for HEAT and 27 956 ± 15 cm-1 for FPD), along with equivalent treatments of the CH ionization energy and the CH+ dissociation energy (85 829 ± 15 cm-1 and 32 946 ± 15 cm-1, respectively), were compared to the existing benchmarks from Active Thermochemical Tables (ATcT), uncovering an unexpected difference for D0(CH). This has prompted a detailed reexamination of the provenance of the corresponding ATcT benchmark, allowing the discovery and subsequent correction of a systematic error present in several published high-level calculations, ultimately yielding an amended ATcT benchmark for D0(CH). Finally, the current theoretical results were added to the ATcT Thermochemical Network, producing refined ATcT estimates of 27 957.3 ± 6.0 cm-1 for D0(CH), 32 946.7 ± 0.6 cm-1 for D0(CH+), and 85 831.0 ± 6.0 cm-1 for IE(CH).

A Systematic Exploration of B-F Bond Dissociation Enthalpies of Fluoroborane-Type Molecules at the CCSD(T)/CBS Level

Fluoroborane-type molecules (R1R2B-F) are of interest in synthetic chemistry, but to date, apart from a handful of small species (such as H2BF, HBF2, and BF3), little is known concerning the effect of substituents in governing the strength of the B-F bonds of such species toward homolytic dissociation in the gas phase. In this study, we have calculated the bond dissociation enthalpies (BDEs) of thirty unique B-F bonds at the CCSD(T)/CBS level using the high-level W1w thermochemical protocol. The B-F bonds in all species considered are very strong, ranging from 545.9 kJ mol-1 in (H2B)2B-F to 729.2 kJ mol-1 HBF2. Nevertheless, these BDEs still vary over a wide range of 183.3 kJ mol-1. The structural properties that affect the BDEs are examined in detail, and the homolytic BDEs are rationalized based on molecule stabilization enthalpies and radical stabilization enthalpies. Since polar B-F bonds may represent a challenging test case for density functional theory (DFT) methods, we proceed to examine the performance of a wide range of DFT methods across the rungs of Jacob's Ladder for their ability to compute B-F BDEs. We find that only a handful of DFT methods can reproduce the CCSD(T)/CBS BDEs with mean absolute deviations (MADs) below the threshold of chemical accuracy (i.e., with average deviations below 4.2 kJ mol-1). The only functionals capable of achieving this feat were (MADs given in parentheses): ωB97M-V (4.0), BMK (3.5), DSD-BLYP (3.8), and DSD-PBEB95 (1.8 kJ mol-1).

Assessment of DFT functionals for a minimal nitrogenase [Fe(SH)4H]- model employing state-of-the-art ab initio methods

We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (∆E) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ∆E estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree-Fock included (0%-54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ∆E is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn-Sham orbitals gives results within 4-11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ∼5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.

Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level

The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.

Tracking C-H activation with orbital resolution

Transition metal reactivity toward carbon-hydrogen (C-H) bonds hinges on the interplay of electron donation and withdrawal at the metal center. Manipulating this reactivity in a controlled way is difficult because the hypothesized metal-alkane charge-transfer interactions are challenging to access experimentally. Using time-resolved x-ray spectroscopy, we track the charge-transfer interactions during C-H activation of octane by a cyclopentadienyl rhodium carbonyl complex. Changes in oxidation state as well as valence-orbital energies and character emerge in the data on a femtosecond to nanosecond timescale. The x-ray spectroscopic signatures reflect how alkane-to-metal donation determines metal-alkane complex stability and how metal-to-alkane back-donation facilitates C-H bond cleavage by oxidative addition. The ability to dissect charge-transfer interactions on an orbital level provides opportunities for manipulating C-H reactivity at transition metals.

Predicting Magnetic Coupling and Spin-Polarization Energy in Triangulene Analogues

Triangulene and its analogue metal-free magnetic systems have garnered increasing attention since their discovery. Predicting the magnetic coupling and spin-polarization energy with quantitative accuracy is beyond the predictive power of today's density functional theory (DFT) due to their intrinsic multireference character. Herein, we create a benchmark dataset of 25 magnetic systems with nonlocal spin densities, including the triangulene monomer, dimer, and their analogues. We calculate the magnetic coupling (J) and spin-polarization energy (ΔE_spin) of these systems using complete active space self-consistent field (CASSCF) and coupled-cluster methods as high-quality reference values. This reference data is then used to benchmark 22 DFT functionals commonly used in material science. Our results show that, while some functionals consistently correctly predict the qualitative character of the ground state, achieving quantitative accuracy with small relative errors is currently not feasible. PBE0, M06-2X, and MN15 are predicting the correct electronic ground state for all systems investigated here and also have the lowest mean absolute error for predicting both ΔE_spin (0.34, 0.32, and 0.31 eV) and J (11.74, 12.66, and 10.64 meV). They may therefore also serve as starting points for higher-level methods such as the GW or the random phase approximation. As other functionals fail for the prediction of the ground state, they cannot be recommended for metal-free magnetic systems.

The vertical excitation energies and a lifetime of the two lowest singlet excited states of the conjugated polyenes from C2 to C22: Ab initio, DFT, and semiclassical MNDO-MD simulations

Electronic excited states in the series of polyene molecules were explored. Optimal ground-state geometry was used for the evaluation of vertical excitation energies. Results of a chosen set of functionals were compared to post-HF methods (EOM-CCSD, NEVPT2, CASPT2, and MRCI). In addition, the semiempirical OM2/MNDO method using MRCISD computational level was confronted with the above-mentioned techniques. Despite the fact that the first excited state has a significant double-excitation character some functionals were able to qualitatively determine the correct state order (where the lowest excited state has a A g - character). The most successful functionals in transition energies predictions were PBE, TPSS and BLYP in Tamm-Dancoff approach (TDA), which had the smallest root-mean-square deviation (RMSD) scoring towards the experimental values. Regarding RMSD scoring, the OM2/MNDO method performed fairly well, too. Besides absorption spectra, lifetimes of the first two excited states were estimated based on a stochastic approach exploring a swarm of OM2/MNDO hopping dynamics using the Tully fewest switch algorithm for each molecule. The longest lifetime of the first excited state (S₁ ) was found for decapentaene (about 5 ps). Further elongation of the conjugated chain caused a mild decrease of this value to ca 1.5 ps for docosaundecaene.

Double-Hybrid Density Functional Theory for Core Excitations: Theory and Benchmark Calculations

The double-hybrid (DH) time-dependent density functional theory is extended to core excitations. Two different DH formalisms are presented utilizing the core-valence separation (CVS) approximation. First, a CVS-DH variant is introduced relying on the genuine perturbative second-order correction, while an iterative analogue is also presented using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH ansatz. The performance of the new approaches is tested for the most popular DH functionals using the recently proposed XABOOM [J. Chem. Theory Comput.2021, 17, 1618] benchmark set. In order to make a careful comparison, the accuracy and precision of the methods are also inspected. Our results show that the genuine approaches are highly competitive with the more advanced CVS-ADC(2)-based methods if only excitation energies are required. In contrast, as expected, significant differences are observed in oscillator strengths; however, the precision is acceptable for the genuine functionals as well. Concerning the performance of the CVS-DH approaches, the PBE0-2/CVS-ADC(2) functional is superior, while its spin-opposite-scaled variant is also recommended as a cost-effective alternative. For these approaches, significant improvements are realized in the error measures compared with the popular CVS-ADC(2) method.

Excitation energies of polycylic aromatic hydrocarbons by double-hybrid functionals: Assessing the PBE0-DH and PBE-QIDH models and their range-separated versions

A family of non-empirical double-hybrid (DH) density functionals, such as Perdew-Burke-Ernzerhof (PBE)0-DH, PBE-QIDH, and their range-separated exchange (RSX) versions RSX-0DH and RSX-QIDH, all using Perdew-Burke-Ernzerhof(PBE) exchange and correlationfunctionals, is applied here to calculate the excitation energies for increasingly longer linear and cyclic acenes as part of their intense benchmarking for excited states of all types. The energies for the two lowest-lying singlet ¹L_a and ¹L_b states of linear oligoacenes as well as the triplet ³L_a and ³L_b states, are calculated and compared with experimental results. These functionals clearly outperform the results obtained from hybrid functionals and favorably compare with other double-hybrid expressions also tested here, such as B2-PLYP, B2GP-PLYP, ωB2-PLYP, and ωB2GP-PLYP. The study is complemented by the computation of adiabatic S₀-T₁ singlet-triplet energy difference for linear acenes as well as the extension of the study to strained cyclic oligomers, showing how the family of non-empirical expressions robustly leads to competitive results.

Inversion Theory Leveling as a New Methodological Approach to Antioxidant Thermodynamics: A Case Study on Phenol

Antioxidants are various types of compounds that represent a link between biology and chemistry. With the development of theoretical and computational methods, antioxidants are now being studied theoretically. Here, a novel method is presented that aims to reduce the estimated wall times for DFT calculations that result in the same or higher degree of accuracy in the second derivatives over energy than is the case with the regular computational route (i.e., optimizing the reaction system at a lower model and then recalculating the energies at a higher level of theory) by applying the inversion of theory level to the universal chemical scavenger model, i.e., phenol. The resulting accuracy and wall time obtained with such a methodological setup strongly suggest that this methodology could be generally applied to antioxidant thermodynamics for some costly DFT methods with relative absolute deviation.

Effect of the QM Size, Basis Set, and Polarization on QM/MM Interaction Energy Decomposition Analysis

Herein, an Energy Decomposition Analysis (EDA) scheme extended to the framework of QM/MM calculations in the context of electrostatic embeddings (QM/MM-EDA) including atomic charges and dipoles is applied to assess the effect of the QM region size on the convergence of the different interaction energy components, namely, electrostatic, Pauli, and polarization, for cationic, anionic, and neutral systems interacting with a strong polar environment (water). Significant improvements are found when the bulk solvent environment is described by a MM potential in the EDA scheme as compared to pure QM calculations that neglect bulk solvation. The predominant electrostatic interaction requires sizable QM regions. The results reported here show that it is necessary to include a surprisingly large number of water molecules in the QM region to obtain converged values for this energy term, contrary to most cluster models often employed in the literature. Both the improvement of the QM wave function by means of a larger basis set and the introduction of polarization into the MM region through a polarizable force field do not translate to a faster convergence with the QM region size, but they lead to better results for the different interaction energy components. The results obtained in this work provide insight into the effect of each energy component on the convergence of the solute-solvent interaction energy with the QM region size. This information can be used to improve the MM FFs and embedding schemes employed in QM/MM calculations of solvated systems.

A comprehensive benchmark investigation of quantum chemical methods for carbocations

The application of various density functional approximations (DFAs) and an emphasis on popular methods without any consensus have prevailed in computational studies dedicated to carbocations. More importantly, an extensive and rigorous benchmark investigation on density functionals for the class is still lacking. To close this gap, we present a comprehensive benchmark study of quantum chemical methods on a series of classical and nonclassical carbocations, the CARBO33 dataset. We evaluate a total of 107 DFT methods from all rungs giving particular attention to double hybrid density functionals as the potential of the class has been largely undermined in the context of carbocations. To support our findings, DLPNO-CCSD(T) at the complete basis set (CBS) limit and W1-F12 are used as reference methods. Our results indicate that the composite CBS-QB3 method performs poorly and should not be adopted for target energies. Oftentimes, the tested DFAs of a lower rung perform better than several DFAs in a higher rung of Perdew's "Jacob's ladder". Nonetheless, double hybrids DSD-PBEP86-NL and ωB97X-2-D3(BJ) stand out by showing the overall best performance. Among the hybrids evaluated, about half of them show mean absolute deviation (MAD) below 1.1 kcal mol^-1, including the popular hybrids M06-2X and mPW1PW91. In this family, MN15-D3(BJ) performs particularly well (MAD = 0.77 kcal mol^-1) displaying reliable results across various tests. Highly popular B3LYP exhibited one of the worst performances (MAD = 4.74 kcal mol^-1), and we do not recommend its application to carbocations. We also assess the 24 general-purpose basis sets of single- up to quadruple-ζ quality. The best compromise between accuracy and computational cost is achieved with cc-pVTZ followed by def2-TZVP. Computations on larger structures of general interest, including terpene carbocations, are also presented for selected DFT methods confirming general trends in the results.

Double Hybrid Density Functionals for the Electronic Excitation Energies of Linear Cyanines

The lowest bright electronic excitations of seven model linear cyanines (CN3-CN15) using 28 double-hybrid (DH) density functionals are benchmarked against accurate and recent CC3 results. Some of these DH functionals are recently designed specifically for excited electronic state calculations. In addition, CIS, CIS(D), SCS-CIS(D), and SOS-CIS(D) were also tested. Four different basis sets were used for the vertical electronic excitation calculations: cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis. Augmented basis sets (e.g. aug-cc-pVDZ and aug-cc-pVTZ) are found to be required for accurate and consistent results using DH functionals. The DH functionals tested in this work are classified into four main groups: global double-hybrids (GDH), range-separated double-hybrids (RSDH), spin-component and spin-opposite scaling global double-hybrids (SCS/SOS-GDH), and spin-component and spin-opposite scaling range-separated double-hybrids (SCS/SOS-RSDH). Within these groups, the SCS/SOS-RSDH group of functionals is found to provide the lowest mean absolute error (MAE) values (in the range 0.020-0.148 eV) in comparison with the GDH group (0.195-0.441 eV), the RSDH group (0.186-0.511 eV), and the SCS/SOS-GDH group (0.079-0.461 eV). Of all the DH functionals and ab initio methods investigated in the present contribution, the following functionals are found to be the most accurate and consistent: SCS-ωB2GPPLYP (MAE = 0.036 eV), SOS-ωB2GPPLYP (MAE = 0.020 eV), SOS-ωB88PP86 (MAE = 0.035 eV), and SOS-ωPBEPP86 (MAE = 0.037 eV). In general, the ab initio methods tested here show mediocre performance as compared to many DH functionals.

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.

Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n ≥ 1 and can slightly reduce computational costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. We select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low computational costs to make practical recommendations. Our assessment covers conventional electronic structure methods (density functional theory and wave function) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.

Supervised learning of a chemistry functional with damped dispersion

Kohn-Sham density functional theory is widely used in chemistry, but no functional can accurately predict the whole range of chemical properties, although recent progress by some doubly hybrid functionals comes close. Here, we optimized a singly hybrid functional called CF22D with higher across-the-board accuracy for chemistry than most of the existing non-doubly hybrid functionals by using a flexible functional form that combines a global hybrid meta-nonseparable gradient approximation that depends on density and occupied orbitals with a damped dispersion term that depends on geometry. We optimized this energy functional by using a large database and performance-triggered iterative supervised training. We combined several databases to create a very large, combined database whose use demonstrated the good performance of CF22D on barrier heights, isomerization energies, thermochemistry, noncovalent interactions, radical and nonradical chemistry, small and large systems, simple and complex systems and transition-metal chemistry.

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Benchmarking Approximate Methods for Adiabatic Spin-State Energy Differences in Fe(II) Complexes

The CASPT2+δMRCI composite approach reported in a companion paper has been extended and used to provide high-quality reference data for a series of adiabatic spin gaps (defined as ΔE = E_quintet - E_singlet) of [Fe^IIL₆]²⁺ complexes (L = CNH, CO, NCH, NH₃, H₂O), either at nonrelativistic level or including scalar relativistic effects. These highly accurate data have been used to evaluate the performance of various more approximate methods. Coupled-cluster theory with singles, doubles, and perturbative triples, CCSD(T), is found to agree well with the new reference data for Werner-type complexes but exhibits larger underestimates by up to 70 kJ/mol for the π-acceptor ligands, due to appreciable static correlation in the low-spin states of these systems. Widely used domain-based local CCSD(T) calculations, DLPNO-CCSD(T), are shown to depend very sensitively on the cutoff values used to construct the localized domains, and standard values are not sufficient. A large number of density functional approximations have been evaluated against the new reference data. The B2PLYP double hybrid gives the smallest deviations, but several functionals from different rungs of the usual ladder hierarchy give mean absolute deviations below 20 kJ/mol. This includes the B97-D semilocal functional, the PBE0* global hybrid with 15% exact-exchange admixture, as well as the local hybrids LH07s-SVWN and LH07t-SVWN. Several further functionals achieve mean absolute errors below 30 kJ/mol (M06L-D4, SSB-D, B97-1-D4, LC-ωPBE-D4, LH12ct-SsirPW92-D4, LH12ct-SsifPW92-D4, LH14t-calPBE-D4, LHJ-HFcal-D4, and several further double hybrids) and thereby also still overall outperform CCSD(T) or uncorrected CASPT2. While exact-exchange admixture is a crucial factor in favoring high-spin states, the present evaluations confirm that other aspects can be important as well. A number of the better-performing functionals underestimate the spin gaps for the π-acceptor ligands but overestimate them for L = NH₃, H₂O. In contrast to a previous suggestion, non-self-consistent density functional theory (DFT) computations on top of Hartree-Fock orbitals are not a promising path to produce accurate spin gaps in such complexes.