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

Efficient Ab Initio Estimation of Formation Enthalpies for Organic Compounds: Extension to Sulfur and Critical Evaluation of Experimental Data

The efficient protocol for the estimation of gas-phase enthalpies of formation developed previously for C, H, O, N, and F elements was extended to sulfur. The protocol is based on a local coupled cluster with single, double, and perturbative triple excitation [CCSD(T)] approximation and allows rapid evaluation of compounds with sizes computationally prohibitive to canonical CCSD(T) using quadruple zeta basis sets. As a part of model development, a comprehensive review and critical evaluation of experimental data were performed for 87 sulfur-containing organic and inorganic compounds. A compact model with only three empirical parameters for sulfur introduced to address the effects beyond frozen core CCSD(T) was developed. The model exhibits approximately 2 kJ·mol-1 standard deviation over a set of experimental values for a diverse collection of sulfur-containing compounds. The complete basis set version of the model demonstrates a similar performance and requires only one empirical parameter. Multiple problems with the existing experimental data were identified and discussed. In addition, a lack of reliable data for certain important classes of sulfur compounds was found to impede the model generalization and confident performance assessment.

Quantum Chemical Investigation of Perchloric Acid Decomposition Releasing Oxygen

The primary objectives of this study are to identify the initiation steps of perchloric acid (HClO₄) decomposition and to validate and provide insights into the reaction pathways of O₂ formation. To this end, we have performed quantum chemical calculations using the Gaussian 09 program package to identify new reaction pathways and species formed during decomposition. The thermodynamic quantities of the species, such as Gibbs free energy and enthalpy, are calculated using a double-hybrid density functional theory method, B2PLYP, with Jensen's basis set, aug-pc2. For heavy atoms, such as chlorine, the basis set is augmented by adding 2 d functions with a stride factor of 2.5. To incorporate the solvation effect, the conductor-like polarizable continuum model, which is an implicit solvation model, is used. Numerical simulations using a control-volume analysis of an experiment are also performed using the proposed mechanism. In these simulations, rates of the reactions are calculated using transition state theory, incorporating diffusion effects on the rate constants. In order to consider the nonideal behavior of a concentrated HClO₄ solution, activity coefficients are used to calculate the effective concentration of acid in solution. The activity coefficient of HClO₄ plays a critical role in the calculation of the induction period involved in the HClO₄ decomposition. A comparison of numerically predicted O₂ evolution and duration of the induction period with experimental data shows that the numerical simulation using the proposed mechanism predicts both the three-stage decomposition characteristics and the induction period observed during HClO₄ decomposition, thus validating the proposed mechanism.

On the origins of the mechanistic variants in the thermal reactions of Sx+ (x = 1-3) with benzene

The S-π interaction between sulfur atom(s) and aromatic ring prevails in chemical and biochemical processes. The thermal gas-phase reactions of the S_n⁺ (n = 1-3) ions with benzene have been explored by using Quadrupole-Ion Trap (Q-IT) mass spectrometry complemented by quantum chemical calculations. Charge transfer was found to be the only reaction channel for S₂⁺/C₆H₆, while both charge transfer and bond activation are available for the S⁺/C₆H₆ and S₃⁺/C₆H₆ couples. Upon interrogating the associated electronic origins, multiple factors were found to matter for these processes. In contrast to the σ-type two-center three-electron (2c-3e) S-π hemibond as reported previously, unusual S-π hemibonds were addressed for the S_n⁺/C₆H₆ couples, i.e. the 2c-3e π(S061Eπ) and the three-center three-electron (3c-3e) σ(S₂061Eπ) hemibonds. Such S-π interaction was found to be responsible for the charge transfer processes in S⁺/C₆H₆ and S₂⁺/C₆H₆, but uninvolved in any transformation for S₃⁺/C₆H₆.

Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet-Singlet and Singlet-Triplet Excitation Energies

Following the work on spin-component and spin-opposite scaled (SCS/SOS) global double hybrids for singlet-singlet excitations by Schwabe and Goerigk [ J. Chem. Theory Comput. 2017, 13, 4307-4323] and our own works on new long-range corrected (LC) double hybrids for singlet-singlet and singlet-triplet excitations [ J. Chem. Theory Comput. 2019, 15, 4735-4744 and J. Chem. Phys. 2020, 153, 064106], we present new LC double hybrids with SCS/SOS that demonstrate further improvement over previously published results and methods. We introduce new unscaled and scaled versions of different global and LC double hybrids based on Becke88 or PBE exchange combined with LYP, PBE, or P86 correlation. For singlet-singlet excitations, we cross-validate them on six benchmark sets that cover small to medium-sized chromophores with different excitation types (local-valence, Rydberg, and charge transfer). For singlet-triplet excitations, we perform the cross-validation on three different benchmark sets following the same analysis as in our previous work in 2020. In total, 203 excitations are analyzed. Our results confirm and extend those of Schwabe and Goerigk regarding the superior performance of SCS and SOS variants compared to their unscaled parents by decreasing mean absolute deviations, root-mean-square deviations, or error spans by more than half and bringing absolute mean deviations closer to zero. Our SCS/SOS variants are shown to be highly efficient and robust for the computation of vertical excitation energies, which even outperform specialized double hybrids that also contain an LC in their perturbative part. In particular, our new SCS/SOS-ωPBEPP86 and SCS/SOS-ωB88PP86 functionals are four of the most accurate and robust methods tested in this work, and we fully recommend them for future applications. However, if the relevant SCS and SOS algorithms are not available to the user, we suggest ωPBEPP86 as the best unscaled method in this work.

Development and Validation of a Parameter-Free Model Chemistry for the Computation of Reliable Reaction Rates

A recently developed model chemistry (jun-Cheap) has been slightly modified and proposed as an effective, reliable, and parameter-free scheme for the computation of accurate reaction rates with special reference to astrochemical and atmospheric processes. Benchmarks with different sets of state-of-the-art energy barriers spanning a wide range of values show that, in the absence of strong multireference contributions, the proposed model outperforms the most well-known model chemistries, reaching a subchemical accuracy without any empirical parameter and with affordable computer times. Some test cases show that geometries, energy barriers, zero point energies, and thermal contributions computed at this level can be used in the framework of the master equation approach based on the ab initio transition-state theory for obtaining accurate reaction rates.

Accurate density functional made more versatile

We propose a one-electron self-interaction-free correlation energy functional compatible with the order-of-limit problem-free Tao-Mo (TM) semilocal functional (regTM) [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016) and Patra et al., J. Chem. Phys. 153, 184112 (2020)] to be used for general purpose condensed matter physics and quantum chemistry. The assessment of the proposed functional for large classes of condensed matter and chemical systems shows its improvement in most cases compared to the TM functional, e.g., when applied to the relative energy difference of MnO₂ polymorphs. In this respect, the present exchange-correction functional, which incorporates the TM technique of the exchange hole model combined with the slowly varying density correction, can achieve broad applicability, being able to solve difficult solid-state problems.

Spin-Scaled Range-Separated Double-Hybrid Density Functional Theory for Excited States

Our recently presented range-separated (RS) double-hybrid (DH) time-dependent density functional approach [J. Chem. Theory Comput. 17, 927 (2021)] is combined with spin-scaling techniques. The proposed spin-component-scaled (SCS) and scaled-opposite-spin (SOS) variants are thoroughly tested for almost 500 excitations including the most challenging types. This comprehensive study provides useful information not only about the new approaches but also about the most prominent methods in the DH class. The benchmark calculations confirm the robustness of the RS-DH ansatz, while several tendencies and deficiencies are pointed out for the existing functionals. Our results show that the SCS variant consistently improves the results, while the SOS variant preserves the benefits of the original RS-DH method reducing its computational expenses. It is also demonstrated that, besides our approaches, only the nonempirical functionals provide balanced performance for general applications, while particular methods are only suggested for certain types of excitations.

Spin-Opposite-Scaled Range-Separated Exchange Double-Hybrid Models (SOS-RSX-DHs): Marriage Between DH and RSX/SOS-RSX Is Not Always a Happy Match

The range-separated version of double-hybrid density functional theory (DH-DFT) with a remarkable efficiency for both ground-state and excited-state characteristics has recently come into spotlight. In this work, based on theoretical arguments, several variants of spin-opposite-scaled range-separated exchange double-hybrid models (SOS-RSX-DHs) have been proposed and validated. More specifically, we first extend the RSX-DHs to design some other related models. Next, the SOS version of the resulting approximations is constructed and thoroughly evaluated using standard benchmark compilations of various properties. It is shown that although there are properties for which the RSX-DH and SOS-RSX-DH frameworks are rival, there are still some problems particularly prone to the self-interaction error issues where our proposed models seem to be beneficial. Furthermore, some of the presented models devoid of any additional corrections can also surpass the recently proposed approximations from different rungs of "Jacob's Ladder". Nonetheless, perusing the results of different methods and detailed comparisons with the predecessors discloses that all things may not necessarily be well with the RSX and SOS-RSX schemes, where the parent DHs as well as their SOS counterparts can still come into play.

Density Functional Theory Calculations of Core-Electron Binding Energies at the K-Edge of Heavier Elements

The capability to determine core-electron binding energies (CEBEs) is vital in the analysis of X-ray photoelectron spectroscopy, and the continued development of light sources has made inner shell spectroscopy of heavier elements increasingly accessible. Density functional theory is widely used to determine CEBEs of lighter elements (boron-fluorine). It is shown that good performance of exchange-correlation functionals for these elements does not necessarily translate to the calculation of CEBEs for the heavier elements from the next row of the periodic table, and in general, larger errors are observed. Two strategies are explored that improve the accuracy of the calculated CEBEs. The first is to apply element and functional dependent energy corrections, and the second is a reparametrization of a short-range corrected functional. This functional is able to reproduce experimental phosphorus and sulfur K-edge CEBEs with an average error of 0.15 eV demonstrating the importance of reducing the self-interaction error associated with the core electrons and represents progress toward a density functional theory calculation that performs equally well for ionization at the K-edge of all elements.

Performance of the DLPNO-CCSD and recent DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals

In the present study, the performance of a set of density functionals: BP86, PBE, OLYP, BEEF, PBEpow, TPSS, SCAN, PBEGXPBE, M06L, MN15L, B3LYP, PBE0, mPW1PW, B97, BHandHLYP, mPW1PW, B98, TPSS0, PBE1KCIS, SCAN0, M06, M06-2X, MN15, CAM-B3LYP, ωB97x, B2PLYP, and the B3LYP/N07D and PBE/N07D schemes in the calculation of the ¹⁴N anisotropic hyperfine coupling (HFC) constants of a set of 23 nitroxide radicals is evaluated. The results are compared with those obtained with the DLPNO-CCSD method and experimental HFC values. Harmonic contribution to the ¹⁴N HFC vibrational correction was calculated at the revPBE0/def2-TZVPP level and included in the evaluation. With the vibrational correction, the DLPNO-CCSD method yielded HFC values in good agreement with the experiment (mean absolute deviation (MAD) = 0.3 G for the dipole-dipole contribution and MAD = 0.8 G for the contact coupling contribution). The best DFT results are obtained using the M06 functional with MAD = 0.2 G for the dipole-dipole contribution and MAD = 0.7 G for the contact coupling contribution. In general, vibrational correction significantly improved most DFT functionals' performance but did not change its overall ranking.

Exploring the Superhalogen Properties of Polynuclear Structures without Halogen Ligands: A Combined Ab Initio and DFT Study on Triple-Bridged [Mg2L5]-1 (L = -OCN, -SCN) Anions

Via combined ab initio and DFT calculations, 16 [Mg₂(OCN)₅]^-1 and [Mg₂(SCN)₅]^-1 isomers are studied to explore their potentials as superhalogens. The results of high-level OVGF calculations verify that these systems are superhalogen anions due to their high VDE values which lie within 6.74-7.04 eV and 5.73-6.27 eV for [Mg₂(OCN)₅]^-1 and [Mg₂(SCN)₅]^-1, respectively. The results of low-cost methods, either ab initio or DFT, are generally consistent with those of OVGF, and some of them demonstrate promising accuracy. The best performance of low-cost ab initio methods comes from (HF+MP2)/2, which represents the average value of the MP2 and HF results. In the aspect of DFT, five functionals (CAM-B3LYP, ωB97X-D3, M06, M06-2X, and B2PLYP) provide the most accurate results when compared to OVGF. Thus, these low-cost methods could be used to calculate the VDE value of the future systems of larger size. Useful information about the VDEs of [Mg₂(OCN)₅]^-1 and [Mg₂(SCN)₅]^-1 could be obtained from the analysis of the extra electron density and HOMO as well as spin density.

CHAL336 Benchmark Set: How Well Do Quantum-Chemical Methods Describe Chalcogen-Bonding Interactions?

We present the CHAL336 benchmark set-the most comprehensive database for the assessment of chalcogen-bonding (CB) interactions. After careful selection of suitable systems and identification of three high-level reference methods, the set comprises 336 dimers each consisting of up to 49 atoms and covers both σ- and π-hole interactions across four categories: chalcogen-chalcogen, chalcogen-π, chalcogen-halogen, and chalcogen-nitrogen interactions. In a subsequent study of DFT methods, we re-emphasize the need for using proper London dispersion corrections when treating noncovalent interactions. We also point out that the deterioration of results and systematic overestimation of interaction energies for some dispersion-corrected DFT methods does not hint at problems with the chosen dispersion correction but is a consequence of large density-driven errors. We conclude this work by performing the most detailed DFT benchmark study for CB interactions to date. We assess 109 variations of dispersion-corrected and dispersion-uncorrected DFT methods and carry out a detailed analysis of 80 of them. Double-hybrid functionals are the most reliable approaches for CB interactions, and they should be used whenever computationally feasible. The best three double hybrids are SOS0-PBE0-2-D3(BJ), revDSD-PBEP86-D3(BJ), and B2NCPLYP-D3(BJ). The best hybrids in this study are ωB97M-V, PW6B95-D3(0), and PW6B95-D3(BJ). We do not recommend using the popular B3LYP functional nor the MP2 approach, which have both been frequently used to describe CB interactions in the past. We hope to inspire a change in computational protocols surrounding CB interactions that leads away from the commonly used, popular methods to the more robust and accurate ones recommended herein. We would also like to encourage method developers to use our set for the investigation and reduction of density-driven errors in new density functional approximations.

What Types of Chemical Problems Benefit from Density-Corrected DFT? A Probe Using an Extensive and Chemically Diverse Test Suite

For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA exchange–correlation (XC) functionals (PBE, BLYP, TPSS, and SCAN) as a function of the percentage of HF exchange in the hybrid. The D4 empirical dispersion correction has been added throughout. For subsets dominated by dynamical correlation, HF-DFT is highly beneficial, particularly at low HF exchange percentages. This is especially true for noncovalent interactions where the electrostatic component is dominant, such as hydrogen and halogen bonds: for π-stacking, HF-DFT is detrimental. For subsets with significant nondynamical correlation (i.e., where a Hartree–Fock determinant is not a good zero-order wavefunction), HF-DFT may do more harm than good. While the self-consistent series show optima at or near 37.5% (i.e., 3/8) for all four XC functionals—consistent with Grimme’s proposal of the PBE38 functional—HF-BnLYP-D4, HF-PBEn-D4, and HF-TPSSn-D4 all exhibit minima nearer 25% (i.e., 1/4) as the use of HF orbitals greatly mitigates the error at 25% for barrier heights. Intriguingly, for HF-SCANn-D4, the minimum is near 10%, but the weighted mean absolute error (WTMAD2) for GMTKN55 is only barely lower than that for HF-SCAN-D4 (i.e., where the post-HF step is a pure meta-GGA). The latter becomes an attractive option, only slightly more costly than pure Hartree–Fock, and devoid of adjustable parameters other than the three in the dispersion correction. Moreover, its WTMAD2 is only surpassed by the highly empirical M06-2X and by the combinatorially optimized empirical range-separated hybrids ωB97X-V and ωB97M-V.

π-π Catalysis in Carbon Flatland-Flipping [8]Annulene on Graphene

Noncovalent interactions are an integral part of the modern catalysis toolbox. Although stronger noncovalent interactions such as hydrogen bonding are commonly the main driving force of catalysis, π-π interactions typically provide smaller additional stabilizations, for example, to afford selectivity enhancements. Here, it is shown computationally that pristine graphene flakes may efficiently catalyze the skeletal inversions of various benzannulated cyclooctatetraene derivatives, providing an example of a catalytic process driven solely by π-π stacking interactions. Hereby, the catalytic effect results from disproportionate shape complementarity between catalyst and transition structure compared with catalyst and reactant. An energy decomposition analysis reveals electrostatic and, especially with increasing system size, to a larger extent, dispersion interactions as the origin of stabilization.

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States

A simple and robust range-separated (RS) double-hybrid (DH) time-dependent density functional approach is presented for the accurate calculation of excitation energies of molecules within the Tamm-Dancoff approximation. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decomposition of the Coulomb potential, for which both the exchange and correlation contributions are range-separated. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approximation is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on standard DHs in most cases, and it can provide a more robust and accurate alternative. In addition, on average, it noticeably surpasses the existing RS hybrid and RS DH functionals.

Reaction mechanism of the farnesyl pyrophosphate C-methyltransferase towards the biosynthesis of pre-sodorifen pyrophosphate by Serratia plymuthica 4Rx13

Classical terpenoid biosynthesis involves the cyclization of the linear prenyl pyrophosphate precursors geranyl-, farnesyl-, or geranylgeranyl pyrophosphate (GPP, FPP, GGPP) and their isomers, to produce a huge number of natural compounds. Recently, it was shown for the first time that the biosynthesis of the unique homo-sesquiterpene sodorifen by Serratia plymuthica 4Rx13 involves a methylated and cyclized intermediate as the substrate of the sodorifen synthase. To further support the proposed biosynthetic pathway, we now identified the cyclic prenyl pyrophosphate intermediate pre-sodorifen pyrophosphate (PSPP). Its absolute configuration (6R,7S,9S) was determined by comparison of calculated and experimental CD-spectra of its hydrolysis product and matches with those predicted by semi-empirical quantum calculations of the reaction mechanism. In silico modeling of the reaction mechanism of the FPP C-methyltransferase (FPPMT) revealed a S_N2 mechanism for the methyl transfer followed by a cyclization cascade. The cyclization of FPP to PSPP is guided by a catalytic dyad of H191 and Y39 and involves an unprecedented cyclopropyl intermediate. W46, W306, F56, and L239 form the hydrophobic binding pocket and E42 and H45 complex a magnesium cation that interacts with the diphosphate moiety of FPP. Six additional amino acids turned out to be essential for product formation and the importance of these amino acids was subsequently confirmed by site-directed mutagenesis. Our results reveal the reaction mechanism involved in methyltransferase-catalyzed cyclization and demonstrate that this coupling of C-methylation and cyclization of FPP by the FPPMT represents an alternative route of terpene biosynthesis that could increase the terpenoid diversity and structural space.

Time-Dependent Density Functional Theory Study of Copper(II) Oxo Active Sites for Methane-to-Methanol Conversion in Zeolites

Copper-exchanged zeolites are useful materials for step-wise methane-to-methanol conversion (MMC). However, methanol yields on copper-exchanged zeolites are often modest, spurring interest in the development of active-site species that are activated at moderate temperatures, afford greater yields, and provide excellent methanol selectivities. Ultraviolet-visible (UV-vis) spectroscopy is a major tool for characterizing the active-sites and their evolution during the step-wise MMC process. However, computation of the UV-vis spectra of the copper-oxo active sites using Tamm-Dancoff time-dependent density functional theory (TDA-DFT) can be quite problematic. This has led to utilization of expensive methods based on multireference approaches, Green functions, and the Bethe-Salpeter equation. In this work, we examined the optical spectra of [CuO]⁺, [Cu₂O]²⁺, [Cu₂O₂]²⁺, and [Cu₃O₃]²⁺ species implicated in MMC in zeolites. For the larger species, we examined how agreement with experimental data is improved with increasingly larger cluster models. For [CuO]⁺, we compared TDA-DFT against restricted active space 2nd-order perturbation theory, RASPT2. We found that signature peaks for [CuO]⁺ have multireference behavior. The excited states have many configuration state functions with a double excitation character. These effects are likely responsible for the poor utility of conventional TDA-DFT methods. Indeed, we obtain good agreement with experimental data and RASPT2 after accounting for 2h/2p excitations within TDA-DFT with a previously described configuration interaction singles and doubles, CIS(D)-style scheme. This was the case for [CuO]⁺, [Cu₂O]²⁺, as well as a [Cu₂O₂]²⁺ species. Using a long-range corrected double-hybrid, ωB2PLYP, we provide for the first time computational evidence for the experimental UV-vis spectrum of the [Cu₃O₃]²⁺ active site motif.

Global double hybrids do not work for charge transfer: A comment on "Double hybrids and time-dependent density functional theory: An implementation and benchmark on charge transfer excited states"

We comment on the results published by Ottochian et al. in J. Comput Chem. 2020, 41, 1242. Therein, the authors claim that the second-order, perturbative correlation correction applied to the time-dependent version of the PBE-QIDH global double-hybrid functional approximation (DHDFA) enables the description of charge-transfer (CT) excitations. Herein, we point out some inadvertent oversights related to what had already been previously known and achieved in the field of time-dependent DHDFAs. Exemplified for the same four systems that Ottochian et al. have used to analyze intermolecular CT excitations, we show how a systematic and unacceptably large redshift in global DHDFAs is rectified when using the latest long-range corrected DHDFAs published earlier in J. Chem. Theory Comput. 2019, 15, 4735.

The Trip to the Density Functional Theory Zoo Continues: Making a Case for Time-Dependent Double Hybrids for Excited-State Problems

This account is written for general users of time-dependent density functional theory (TD-DFT) methods as well as chemists who are unfamiliar with the field. It includes a brief overview of conventional TD-DFT approaches and recommendations for applications to organic molecules based on our own experience. The main emphasis of this work, however, lies in providing the first in-depth review of time-dependent double-hybrid density functionals. They were first established in 2007 with very promising follow-up studies in the subsequent four years before developments or applications became scarce. The topic has regained more interest since 2017, and this account reviews those latest developments led by our group. These developments have shown unprecedented robustness for a variety of different types of electronic excitations when compared to more conventional TD-DFT methods. In particular, time-dependent double hybrids do not suffer from artificial ghost states and are able to reproduce exciton-coupled absorption spectra. Our latest methods include range separation and belong to the currently best TD-DFT methods for singlet-singlet excitations in organic molecules. While there is still room for improvement and further development in this space, we hope that this account encourages users to adjust their computational protocols to such new methods to provide more real-life testing and scenarios.

Comprehensive Benchmark Study on the Calculation of 29Si NMR Chemical Shifts

A comprehensive and diverse benchmark set for the calculation of ²⁹Si NMR chemical shifts is presented. The SiS146 set includes 100 silicon containing compounds with 146 experimentally determined reference ²⁹Si NMR chemical shifts measured in nine different solvents in a range from -400 to +828 ppm. Silicon atoms bound to main group elements as well as transition metals with coordination numbers of 2-6 in various bonding patterns including multiple bonds and coordinative and aromatic bonding are represented. The performance of various common and specialized density functional approximations including (meta-)GGA, hybrid, and double-hybrid functionals in combination with different AO basis sets and for differently optimized geometries is evaluated. The role of scalar-relativistic effects is further investigated by inclusion of the zeroth order regular approximation (ZORA) method into the calculations. GGA density functional approximations (DFAs) are found to outperform hybrid DFAs with B97-D3 performing best with an MAD of 7.2 ppm for the subset including only light atoms (Z < 18), while TPSSh is the best tested hybrid functional with an MAD of 10.3 ppm. For ²⁹Si cores in the vicinity of heavier atoms, the application of ZORA proved indispensable. Inclusion of spin-orbit effects into the ²⁹Si NMR chemical shift calculation decreases the mean absolute deviations by up to 74% compared to calculations applying effective core potentials.

Canonical and DLPNO-Based Composite Wavefunction Methods Parametrized against Large and Chemically Diverse Training Sets. 2: Correlation-Consistent Basis Sets, Core-Valence Correlation, and F12 Alternatives

A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for elements H through Rn, was recently reported by the present authors [J. Chem. Theor. Comput.2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Møller–Plesset correction and replacing the Weigend–Ahlrichs def2-mZVPP(D) basis sets used with complete basis set extrapolation from augmented correlation-consistent core–valence triple-ζ, aug-cc-pwCVTZ(-PP), and quadruple-ζ, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4-type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion’s share of the improvement comes from better capture of valence correlation; the inclusion of core–valence correlation is almost an order of magnitude less important. These robust correlation-consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly, the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at a modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component.

Third-Order Møller-Plesset Theory Made More Useful? The Role of Density Functional Theory Orbitals

The practical utility of Møller-Plesset (MP) perturbation theory is severely constrained by the use of Hartree-Fock (HF) orbitals. It has recently been shown that the use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error [Bertels, L. W.; J. Phys. Chem. Lett. 2019, 10, 4170 4176]. In this work, we examine whether density functional theory (DFT)-optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that the use of DFT orbitals leads to significantly improved performance for prediction of thermochemistry, barrier heights, noncovalent interactions, and dipole moments relative to the standard HF-based MP theory. Indeed, MP3 (with or without scaling) with DFT orbitals is found to surpass the accuracy of coupled-cluster singles and doubles (CCSD) for several data sets. We also found that the results are not particularly functional sensitive in most cases (although range-separated hybrid functionals with low delocalization error perform the best). MP3 based on DFT orbitals thus appears to be an efficient, noniterative O(N⁶) scaling wave-function approach for single-reference electronic structure computations. Scaled MP2 with DFT orbitals is also found to be quite accurate in many cases, although modern double hybrid functionals are likely to be considerably more accurate.

Accurate Hybrid Density Functionals with UW12 Correlation

In previous work, we suggested a single-parameter hybrid functional containing a novel correlation contribution based on the Unsöld approximation, UW12. This model resembles the explicitly correlated part of MP2-F12 theory and can be written as an explicit formula in terms of the single-particle reduced density matrix. Here, we further investigate hybrid functionals containing UW12 correlation and in particular look at functionals with a large fraction of exact exchange to reduce the self-interaction error. We suggest two new hybrid functionals B-LYP-osUW12 and fB-LYP-osUW12. On the test sets we use, our best hybrid functional overall (B-LYP-osUW12) is of similar accuracy to the best double hybrids considered while eliminating the need for virtual orbitals.

Natural Polyketides Isolated from the Endophytic Fungus Phomopsis sp. CAM212 with a Semisynthetic Derivative Downregulating the ERK/IκBα Signaling Pathways

Three previously undescribed natural products, phomopsinin A - C (1:  - 3: ), together with three known compounds, namely, cis-hydroxymellein (4: ), phomoxanthone A (5: ) and cytochalasin L-696,474 (6: ), were isolated from the solid culture of Phomopsis sp. CAM212, an endophytic fungus obtained from Garcinia xanthochymus. Their structures were determined on the basis of spectroscopic data, including IR, NMR, and MS. The absolute configurations of 1: and 2: were assigned by comparing their experimental and calculated ECD spectra. Acetylation of compound 1: yielded 1A: , a new natural product derivative that was tested together with other isolated compounds on lipopolysaccharide-stimulated RAW 264.7 cells. Cytochalasin L-696,474 (6: ) was found to significantly inhibit nitric oxide production, but was highly cytotoxic to the treated cells, whereas compound 1: slightly inhibited nitric oxide production, which was not significantly different compared to lipopolysaccharide-treated cells. Remarkably, the acetylated derivative of 1: , compound 1A: , significantly inhibited nitric oxide production with an IC₅₀ value of 14.8 µM and no cytotoxic effect on treated cells, thereby showing the importance of the acetyl group in the anti-inflammatory activity of 1A: . The study of the mechanism of action revealed that 1A: decreases the expression of inducible nitric oxide synthase, cyclooxygenase 2, and proinflammatory cytokine IL-6 without an effect on IL-1β expression. Moreover, it was found that 1A: exerts its anti-inflammatory activity in lipopolysaccharide-stimulated RAW 264.7 macrophage cells by downregulating the activation of ERK1/2 and by preventing the translocation of nuclear factor κB. Thus, derivatives of phomopsinin A (1: ), such as compound 1A: , could provide new anti-inflammatory leads.

Atomically Dispersed Iridium on Indium Tin Oxide Efficiently Catalyzes Water Oxidation

Heterogeneous catalysts in the form of atomically dispersed metals on a support provide the most efficient utilization of the active component, which is especially important for scarce and expensive late transition metals. These catalysts also enable unique opportunities to understand reaction pathways through detailed spectroscopic and computational studies. Here, we demonstrate that atomically dispersed iridium sites on indium tin oxide prepared via surface organometallic chemistry display exemplary catalytic activity in one of the most challenging electrochemical processes, the oxygen evolution reaction (OER). In situ X-ray absorption studies revealed the formation of IrV=O intermediate under OER conditions with an Ir-O distance of 1.83 Å. Modeling of the reaction mechanism indicates that IrV=O is likely a catalyst resting state, which is subsequently oxidized to IrVI enabling fast water nucleophilic attack and oxygen evolution. We anticipate that the applied strategy can be instrumental in preparing and studying a broad range of atomically dispersed transition metal catalysts on conductive oxides for (photo)electrochemical applications.

Remarkable Accuracy of an O(N6) Perturbative Correction to Opposite-Spin CCSD: Are Triples Necessary for Chemical Accuracy in Coupled Cluster?

The focus of this work is OS-CCSD-SPT(2), which is a second-order similarity transformed perturbation theory correction to opposite spin coupled cluster singles doubles, where in the latter the same-spin amplitudes are removed and the opposite-spin ones are solved self-consistently. OS-CCSD-SPT(2) is free of empirical parameters, has an instrinsic scaling of O(N⁶), and makes no use of triples. We demonstrate that, for non-multireference molecules, OS-CCSD-SPT(2) produces relative energies whose accuracy is significantly higher than what is generally expected of a triples-free model. For example, using PBE0 orbitals in the reference, OS-CCSD-SPT(2) exhibits a mean absolute deviation (MAD) of 1.13 kcal/mol with respect to CCSD(2_F) benchmark values for the non-multireference subset of W4-08 atomization energies (cf. a MAD > 6.5 kcal/mol for CCSD) and a MAD of 0.68 kcal/mol for the energies of reactions generated from the W4-08 molecules. These MADs are reduced to 0.61 and 0.63 kcal/mol, respectively, by a simple one-parameter spin-component scaling of the OS-CCSD-SPT(2) same-spin correlation energy. OS-CCSD is also naturally amenable to higher order corrections: the associated third-order correction, OS-CCSD-SPT(3), which does involve connected triples and quadruples, exhibits a MAD of 0.44 kcal/mol for the same atomization-energy benchmark.

Difficulties of Popular Density Functionals to Describe the Conformational Isomerism in Iodoacetic Acid

Matrix isolation studies in solid argon and neon at 4.2 K reveal that iodoacetic acid initially only exists as its ground state (c,x) conformer with an almost perpendicular I-C-C═O dihedral angle, but UV irradiation in the 240-255 nm range leads to population of the 0.8 kcal mol^-1 less stable (c,c) isomer. The latter structure exhibits a close 3.23 Å contact of the iodine and carbonyl oxygen atoms decidedly below the sum of their van der Waals radii (3.50 Å). Increasing the matrix temperature by only a few Kelvin triggers the thermal back reaction of (c,c) to (c,x) and leads to an estimated upper limit of 0.38 kcal mol^-1 for the associated torsional barrier. While wave function methods including completely uncorrelated Hartree-Fock theory have no problem to identify (c,c) as a proper minimum, many popular density functionals fail to describe the C-C torsional potential in cis-iodoacetic acid qualitatively correct. We assessed the performance of 12 density functionals of different levels of sophistication, namely, the BLYP, PBE, TPSS, B3LYP, BHandHLYP, PBE0, M06-2X, CAM-B3LYP, ωB97X-D3, B2-PLYP, B2GP-PLYP, and DSD-PBEP86 methods, against accurate extrapolated CCSD(T)/CBS(T-Q)//MP2/def2-TZVPP energies and found that almost all of them yield acceptable relative energies. Still, even some of the best performers fail to find a reasonably deep minimum in the region of the (c,c) conformer, and addition of the empirical D3-dispersion correction does not remedy the qualitative shortcoming. Instead, inclusion of a sufficient amount of (long-range) exact exchange and likely a proper treatment of medium-range correlation effects all along the torsional coordinate play an important role in the proper description of the sub-van der Waals iodine-oxygen contact. More modern, recommended functionals do not suffer from the described shortcoming.

Double hybrid DFT calculations with Slater type orbitals

On a comprehensive database with 1,644 datapoints, covering several aspects of main-group as well as of transition metal chemistry, we assess the performance of 60 density functional approximations (DFA), among them 36 double hybrids (DH). All calculations are performed using a Slater type orbital (STO) basis set of triple-ζ (TZ) quality and the highly efficient pair atomic resolution of the identity approach for the exchange- and Coulomb-term of the KS matrix (PARI-K and PARI-J, respectively) and for the evaluation of the MP2 energy correction (PARI-MP2). Employing the quadratic scaling SOS-AO-PARI-MP2 algorithm, DHs based on the spin-opposite-scaled (SOS) MP2 approximation are benchmarked against a database of large molecules. We evaluate the accuracy of STO/PARI calculations for B3LYP as well as for the DH B2GP-PLYP and show that the combined basis set and PARI-error is comparable to the one obtained using the well-known def2-TZVPP Gaussian-type basis set in conjunction with global density fitting. While quadruple-ζ (QZ) calculations are currently not feasible for PARI-MP2 due to numerical issues, we show that, on the TZ level, Jacob's ladder for classifying DFAs is reproduced. However, while the best DHs are more accurate than the best hybrids, the improvements are less pronounced than the ones commonly found on the QZ level. For conformers of organic molecules and noncovalent interactions where very high accuracy is required for qualitatively correct results, DHs provide only small improvements over hybrids, while they still excel in thermochemistry, kinetics, transition metal chemistry and the description of strained organic systems.

Reactivities of singlet oxygen: open-shell or closed-shell?

This work explores the reactivity of singlet oxygen with respect to two typical reactions: cycloaddition to anthracene and excitation energy transfer (EET) to a carotenoid using diabatic states with multistate density functional theory (MSDFT). Noticeably, the degenerate state 1Δg has distinct open-shell (OS) and closed-shell (CS) components, and the closed-shell component showed more reactivity than the open-shell one due to the strong diabatic couplings to the product diabatic states. The diabatic perspective presented in this work could also apply to general singlet fission processes.

Improved Basis-Set Incompleteness Potentials for Accurate Density-Functional Theory Calculations in Large Systems

The accurate calculation of chemical properties using density-functional theory (DFT) requires the use of a nearly complete basis set. In chemical systems involving hundreds to thousands of atoms, the cost of the calculations place practical limitations on the number of basis functions that can be used. Therefore, in most practical applications of DFT to large systems, there exists a basis-set incompleteness error (BSIE). In this article, we present the next iteration of the basis-set incompleteness potentials (BSIPs), one-electron potentials designed to correct for basis-set incompleteness error. The ultimate goal associated with the development of BSIPs is to allow the calculation of molecular properties using DFT with near-complete-basis-set results at a computational cost that is similar to a small basis set calculation. In this work, we develop BSIPs for 10 atoms in the first and second rows (H, B-F, Si-Cl) and 15 common basis sets of the Pople, Dunning, Karlsruhe, and Huzinaga types. Our new BSIPs are constructed to minimize BSIE in the calculation of reaction energies, barrier heights, noncovalent binding energies, and intermolecular distances. The BSIPs were obtained using a training set of 15 944 data points. The fitting approach employed a regularized linear least-squares method with variable selection (the LASSO method), which results in a much better fit to the training data than our previous BSIPs while, at the same time, reducing the computational cost of BSIP development. The proposed BSIPs are tested on various benchmark sets and demonstrate excellent performance in practice. Our new BSIPs are also transferable; i.e., they can be used to correct BSIE in calculations that employ density functionals other than the one used in the BSIP development (B3LYP). Finally, BSIPs can be used in any quantum chemistry program that have implemented effective-core potentials without changes to the software.

Canonical and DLPNO-Based G4(MP2)XK-Inspired Composite Wave Function Methods Parametrized against Large and Chemically Diverse Training Sets: Are They More Accurate and/or Robust than Double-Hybrid DFT?

The large and chemically diverse GMTKN55 benchmark was used as a training set for parametrizing composite wave function thermochemistry protocols akin to G4(MP2)XK theory (Chan, B.; Karton, A.; Raghavachari, K. J. Chem. Theory Comput. 2019, 15, 4478–4484). On account of their availability for elements H through Rn, Karlsruhe def2 basis sets were employed. Even after reparametrization, the GMTKN55 WTMAD2 (weighted mean absolute deviation, type 2) for G4(MP2)-XK is actually inferior to that of the best rung-4 DFT functional, ωB97M-V. By increasing the basis set for the MP2 part to def2-QZVPPD, we were able to substantially improve performance at modest cost (if an RI-MP2 approximation is made), with WTMAD2 for this G4(MP2)-XK-D method now comparable to the better rung-5 functionals (albeit at greater cost). A three-tier approach with a scaled MP3/def2-TZVPP intermediate step, however, leads to a G4(MP3)-D method that is markedly superior to even the best double hybrids ωB97M(2) and revDSD-PBEP86-D4. Evaluating the CCSD(T) component with a triple-ζ, rather than split-valence, basis set yields only a modest further improvement that is incommensurate with the drastic increase in computational cost. G4(MP3)-D and G4(MP2)-XK-D have about 40% better WTMAD2, at similar or lower computational cost, than their counterparts G4 and G4(MP2), respectively: detailed comparison reveals that the difference lies in larger molecules due to basis set incompleteness error. An E2/{T,Q} extrapolation and a CCSD(T)/def2-TZVP step provided the G4-T method of high accuracy and with just three fitted parameters. Using KS orbitals in MP2 leads to the G4(MP3|KS)-D method, which entirely eliminates the CCSD(T) step and has no steps costlier than scaled MP3; this shows a path forward to further improvements in double-hybrid density functional methods. None of our final selections require an empirical HLC correction; this cuts the number of empirical parameters in half and avoids discontinuities on potential energy surfaces. G4-T-DLPNO, a variant in which post-MP2 corrections are evaluated at the DLPNO-CCSD(T) level, achieves nearly the accuracy of G4-T but is applicable to much larger systems.