DFT ‐D4 counterparts of leading meta‐ generalized‐gradient approximation and hybrid density functionals for energetics and geometries

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).

Synthesis and Structure of 5-Methyl-9-(trifluoromethyl)-12H-quino[3,4-b][1,4]benzothiazinium Chloride as Anticancer Agent

In this work, the synthesis, structural analysis and anticancer properties of 5-methyl-9-trifluoromethyl-12H-quino[3,4-b][1,4]benzothiazinium chloride (3) are described. Compound 3 was synthesized by reacting 1-methyl-4-butylthio-3-(benzoylthio)quinolinium chloride with 4-(trifluoromethyl)aniline, respectively. The structure of the resulting product was determined using 1H-NMR and 13C-NMR spectroscopy as well as HR-MS spectrometry. The spatial geometry of agent 3 and the arrangement of molecules in the crystal (unit cell) were also confirmed using X-ray diffraction. The tetracyclic quinobenzothiazinium system is fairly planar because the dihedral angle between the planes formed by the benzene ring and the quinoline system is 173.47°. In order to obtain insight into the electronic charge distribution of the investigated molecule, electronic structure calculations employing the Density Functional Theory (DFT) were performed. Moreover, antiproliferative activity against a set of pancreatic cancer cell lines was tested, with compound 3 showing IC50 values against human primary pancreatic adenocarcinoma BxPC-3 and human epithelioid pancreatic carcinoma Panc-1 of 0.051 µM and 0.066 µM, respectively. The IC50 value of cytotoxicity/cell viability of the investigated compound assessed on normal human lung fibroblasts WI38 was 0.36 µM.

Toward Reliable Conformational Energies of Amino Acids and Dipeptides─The DipCONFS Benchmark and DipCONL Datasets

Simulating peptides and proteins is becoming increasingly important, leading to a growing need for efficient computational methods. These are typically semiempirical quantum mechanical (SQM) methods, force fields (FFs), or machine-learned interatomic potentials (MLIPs), all of which require a large amount of accurate data for robust training and evaluation. To assess potential reference methods and complement the available data, we introduce two sets, DipCONFL and DipCONFS, which cover large parts of the conformational space of 17 amino acids and their 289 possible dipeptides in aqueous solution. The conformers were selected from the exhaustive PeptideCS dataset by Andris et al. [ J. Phys. Chem. B 2022, 126, 5949-5958]. The structures, originally generated with GFN2-xTB, were reoptimized using the accurate r2SCAN-3c density functional theory (DFT) composite method including the implicit CPCM water solvation model. The DipCONFS benchmark set contains 918 conformers and is one of the largest sets with highly accurate coupled cluster conformational energies so far. It is employed to evaluate various DFT and wave function theory (WFT) methods, especially regarding whether they are accurate enough to be used as reliable reference methods for larger datasets intended for training and testing more approximated SQM, FF, and MLIP methods. The results reveal that the originally provided BP86-D3(BJ)/DGauss-DZVP conformational energies are not sufficiently accurate. Among the DFT methods tested as an alternative reference level, the revDSD-PBEP86-D4 double hybrid performs best with a mean absolute error (MAD) of 0.2 kcal mol-1 compared with the PNO-LCCSD(T)-F12b reference. The very efficient r2SCAN-3c composite method also shows excellent results, with an MAD of 0.3 kcal mol-1, similar to the best-tested hybrid ωB97M-D4. With these findings, we compiled the large DipCONFL set, which includes over 29,000 realistic conformers in solution with reasonably accurate r2SCAN-3c reference conformational energies, gradients, and further properties potentially relevant for training MLIP methods. This set, also in comparison to DipCONFS, is used to assess the performance of various SQM, FF, and MLIP methods robustly and can complement training sets for those.

A Benchmark Study of DFT-Computed p-Block Element Lewis Pair Formation Enthalpies Against Experimental Calorimetric Data

The quantification of Lewis acidity is of fundamental and applied importance in chemistry. While the computed fluoride ion affinity (FIA) is the most widely accepted thermodynamic metric, only sparse experimental values exist. Accordingly, a benchmark of methods for computing Lewis pair formation enthalpies, also with a broader set of Lewis bases against experimental data, is missing. Herein, we evaluate different density functionals against a set of 112 experimentally determined Lewis acid/base binding enthalpies and gauge influences such as solvation correction in structure optimization. From that, we can recommend r2SCAN-3c for robust quantification of this omnipresent interaction.

Antioxidant Activity of MgSO4 Ion Pairs by Spin-Electron Stabilization of Hydroxyl Radicals through DFT Calculations: Biological Relevance

Magnesium sulfate has been of great interest as an antioxidant for its ability to decrease the oxidizing capacity of the hydroxyl radical. Previously, it was shown that the contact ion pair of this salt could stabilize •OH by coordinating with Mg and delocalizing the unpaired electron over sulfate. The present study explores in detail the MgSO4 antioxidant properties, considering all its ion pairs with •OH in different conformations. The analyses were based on structural, spin, and energetic properties using the DFT approach. As a result, the high antioxidant potential of MgSO4 is related to the spin-electron transfer from SO4 -2 to •OH causing electron spin delocalization and electrostatic stabilization. This transfer occurs for all ion pairs when •OH approaches the Mg first solvation shell, without being coordinated to Mg. The direct Mg-•OH interaction further stabilizes the radical system. These results show that spin-electron transfers are feasible in all hydrated ion pairs MgSO4-•OH, even at a •OH-sulfate distance greater than 10 Å.

dxtb-An efficient and fully differentiable framework for extended tight-binding

Automatic differentiation (AD) emerged as an integral part of machine learning, accelerating model development by enabling gradient-based optimization without explicit analytical derivatives. Recently, the benefits of AD and computing arbitrary-order derivatives with respect to any variable were also recognized in the field of quantum chemistry. In this work, we present dxtb-an open-source, fully differentiable framework for semiempirical extended tight-binding (xTB) methods. Developed entirely in Python and leveraging PyTorch for array operations, dxtb facilitates extensibility and rapid prototyping while maintaining computational efficiency. Through comprehensive code vectorization and optimization, we essentially reach the speed of compiled xTB programs for high-throughput calculations of small molecules. The excellent performance also scales to large systems, and batch operability yields additional benefits for execution on parallel hardware. In particular, energy evaluations are on par with existing programs, whereas the speed of automatically differentiated nuclear derivatives is only 2 to 5 times slower compared to their analytical counterparts. We showcase the utility of AD in dxtb by calculating various molecular and spectroscopic properties, highlighting its capacity to enhance and simplify such evaluations. Furthermore, the framework streamlines optimization tasks and offers seamless integration of semiempirical quantum chemistry in machine learning, paving the way for physics-inspired end-to-end differentiable models. Ultimately, dxtb aims to further advance the capabilities of semiempirical methods, providing an extensible foundation for future developments and hybrid machine learning applications. The framework is accessible at https://github.com/grimme-lab/dxtb.

Extension of the D3 and D4 London dispersion corrections to the full actinides series

Efficient dispersion corrections are an indispensable component of modern density functional theory, semi-empirical quantum mechanical, and even force field methods. In this work, we extend the well established D3 and D4 London dispersion corrections to the full actinides series, francium, and radium. To keep consistency with the existing versions, the original parameterization strategy of the D4 model was only slightly modified. This includes improved reference Hirshfeld atomic partial charges at the ωB97M-V/ma-def-TZVP level to fit the required electronegativity equilibration charge (EEQ) model. In this context, we developed a new actinide data set called AcQM, which covers the most common molecular actinide compound space. Furthermore, the efficient calculation of dynamic polarizabilities that are needed to construct CAB6 dispersion coefficients was implemented into the ORCA program package. The extended models are assessed for the computation of dissociation curves of actinide atoms and ions, geometry optimizations of crystal structure cutouts, gas-phase structures of small uranium compounds, and an example extracted from a small actinide complex protein assembly. We found that the novel parameterizations perform on par with the computationally more demanding density-dependent VV10 dispersion correction. With the presented extension, the excellent cost-accuracy ratio of the D3 and D4 models can now be utilized in various fields of computational actinide chemistry and, e.g., in efficient composite DFT methods such as r2SCAN-3c. They are implemented in our freely available standalone codes (dftd4, s-dftd3) and the D4 version will be also available in the upcoming ORCA 6.0 program package.

A nucleophilic beryllyl complex via metathesis at [Be-Be]2

Owing to its high toxicity, the chemistry of element number four, beryllium, is poorly understood. However, as the lightest elements provide the basis for fundamental models of chemical bonding, there is a need for greater insight into the properties of beryllium. In this context, the chemistry of the homo-elemental Be-Be bond is of fundamental interest. Here the ligand metathesis chemistry of diberyllocene (1; CpBeBeCp)-a stable complex with a Be-Be bond-has been investigated. These studies yield two complexes with Be-Be bonds: Cp*BeBeCp (2) and [K{(HCDippN)2BO}2]BeBeCp (3; Dipp = 2,6-diisopropylphenyl). Quantum chemical calculations indicate that the Be-Be bond in 3 is polarized to such an extent that the complex could be formulated as a mixed-oxidation state Be0/BeII complex. Correspondingly, it is demonstrated that 3 can transfer the 'beryllyl' anion, [BeCp]-, to an organic substrate, by analogy with the reactivity of sp2-sp3 diboranes. Indeed, this work reveals striking similarities between the homo-elemental bonding linkages of beryllium and boron, despite the respective metallic and non-metallic natures of these elements.

The sugar cube: Network control and emergence in stereoediting reactions

Stereochemical editing strategies have recently enabled the transformation of readily accessible substrates into rare and valuable products. Typically, site selectivity is achieved by minimizing kinetic complexity by using protecting groups to suppress reactivity at undesired sites (substrate control) or by using catalysts with tailored shapes to drive reactivity at the desired site (catalyst control). We propose "network control," a contrasting paradigm that exploits hidden interactions between rate constants to greatly amplify modest intrinsic biases and enable precise multisite editing. When network control is applied to the photochemical isomerization of hexoses, six of the eight possible diastereomers can be selectively obtained. The amplification effect can be viewed as a mesoscale phenomenon between the limiting regimes of kinetic control in simple chemical systems and metabolic regulation in complex biological systems.

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.

Combining low-cost electronic structure theory and low-cost parallel computing architecture

The computational efficiency of low-cost electronic structure methods can be further improved by leveraging heterogenous computing architectures. The software package TeraChem has been developed since 2008 to make use of graphical processing units (GPUs), particularly their strong single-precision performance, for the acceleration of quantum chemical calculations. Here, we present the implementation of three low-cost methods, namely HF-3c, PBEh-3c, and the recently introduced ωB97X-3c. We show that these can benefit in terms of performance when combined with "consumer grade" GPUs by leveraging the mixed precision integral handling in TeraChem. The current limitation of the latter's GPU integral library is that Gaussian integrals only for functions with angular momentum l < 3 can be computed, which generally restricts the achievable accuracy in terms of the one-particle basis set. Particularly, the implementation of the ωB97X-3c method now enables higher accuracy with this setting which, in turn, provides the most efficient implementation accessible with consumer-grade hardware. We furthermore show that the implemented 3c methods can be combined with the hh-TDA formalism. This gives new and efficient low-cost multi-configurational excited states methods, which are benchmarked for the description of lowest vertical excitation energies in this work. All in all, the combination of these efficient electronic structure theory methods with affordable highly parallelized computing hardware provides an optimal computational and monetary cost to accuracy ratio.

Controlling product selectivity during dioxygen reduction with Mn complexes using pendent proton donor relays and added base

The catalytic reduction of dioxygen (O2) is important in biological energy conversion and alternative energy applications. In comparison to Fe- and Co-based systems, examples of catalytic O2 reduction by homogeneous Mn-based systems is relatively sparse. Motivated by this lack of knowledge, two Mn-based catalysts for the oxygen reduction reaction (ORR) containing a bipyridine-based non-porphyrinic ligand framework have been developed to evaluate how pendent proton donor relays alter activity and selectivity for the ORR, where Mn(p-tbudhbpy)Cl (1) was used as a control complex and Mn(nPrdhbpy)Cl (2) contains a pendent -OMe group in the secondary coordination sphere. Using an ammonium-based proton source, N,N'-diisopropylethylammonium hexafluorophosphate, we analyzed catalytic activity for the ORR: 1 was found to be 64% selective for H2O2 and 2 is quantitative for H2O2, with O2 binding to the reduced Mn(ii) center being the rate-determining step. Upon addition of the conjugate base, N,N'-diisopropylethylamine, the observed catalytic selectivity of both 1 and 2 shifted to H2O as the primary product. Interestingly, while the shift in selectivity suggests a change in mechanism for both 1 and 2, the catalytic activity of 2 is substantially enhanced in the presence of base and the rate-determining step becomes the bimetallic cleavage of the O-O bond in a Mn-hydroperoxo species. These data suggest that the introduction of pendent relay moieties can improve selectivity for H2O2 at the expense of diminished reaction rates from strong hydrogen bonding interactions. Further, although catalytic rate enhancements are observed with a change in product selectivity when base is added to buffer proton activity, the pendent relays stabilize dimer intermediates, limiting the maximum rate.

Conformational energies of biomolecules in solution: Extending the MPCONF196 benchmark with explicit water molecules

A prerequisite for the computational prediction of molecular properties like conformational energies of biomolecules is a reliable, robust, and computationally affordable method usually selected according to its performance for relevant benchmark sets. However, most of these sets comprise molecules in the gas phase and do not cover interactions with a solvent, even though biomolecules typically occur in aqueous solution. To address this issue, we introduce a with explicit water molecules solvated version of a gas-phase benchmark set containing 196 conformers of 13 peptides and other relevant macrocycles, namely MPCONF196 [J. Řezáč et al., JCTC 2018, 14, 1254-1266], and provide very accurate PNO-LCCSD(T)-F12b/AVQZ' reference values. The novel solvMPCONF196 benchmark set features two additional challenges beyond the description of conformers in the gas phase: conformer-water and water-water interactions. The overall best performing method for this set is the double hybrid revDSDPBEP86-D4/def2-QZVPP yielding conformational energies of almost coupled cluster quality. Furthermore, some (meta-)GGAs and hybrid functionals like B97M-V and ω B97M-D with a large basis set reproduce the coupled cluster reference with an MAD below 1 kcal mol- 1  . If more efficient methods are required, the composite DFT-method r2 SCAN-3c (MAD of 1.2 kcal mol- 1 ) is a good alternative, and when conformational energies of polypeptides or macrocycles with more than 500-1000 atoms are in the focus, the semi-empirical GFN2-xTB or the MMFF94 force field (for very large systems) are recommended.

Photoswitchable imines: aryliminopyrazoles quantitatively convert to long-lived Z-isomers with visible light

Arylimines offer promise in dynamic-covalent materials due to their recyclability and ease of synthesis. However, their light-triggered E/Z isomerism has received little attention. This is attributed to challenges that include low thermal stability of their metastable state (<60 s at 20 °C), incomplete photoswitching (<50% to the metastable state), and the need for UV light (≤365 nm). We overcome these limitations with a novel class of imine photoswitch, the aryliminopyrazoles (AIPs). These AIPs can be switched using visible light (470 nm), attain photostationary states with over 95% of the Z-isomer, exhibit great resistance to fatigue, and have thermal half-lives up to 19.2 hours at room temperature. Additionally, they display T-type and negative photochromism under visible light irradiation-a useful property. The photochromic properties, quantitative assembly and accessibility of precursors set these photoswitches apart from their azo-based analogues. These findings open avenues for next-generation photoresponsive dynamic-covalent materials driven solely by these new photochromic linkages and further exploration of photocontrolled dynamic combinatorial chemistry.

Scalar Relativistic All-Electron and Pseudopotential Ab Initio Study of a Minimal Nitrogenase [Fe(SH)4H]- Model Employing Coupled-Cluster and Auxiliary-Field Quantum Monte Carlo Many-Body Methods

Nitrogenase is the only enzyme that can cleave the triple bond in N2, making nitrogen available to organisms. The detailed mechanism of this enzyme is currently not known, and computational studies are complicated by the fact that different density functional theory (DFT) methods give very different energetic results for calculations involving nitrogenase models. Recently, we designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S to mimic different possible protonation states of the nitrogenase active site. We showed that the energy difference between these two isomers (ΔE) is hard to estimate with quantum-mechanical methods. Based on nonrelativistic single-reference coupled-cluster (CC) calculations, we estimated that the ΔE is 101 kJ/mol. In this study, we demonstrate that scalar relativistic effects play an important role and significantly affect ΔE. Our best revised single-reference CC estimates for ΔE are 85-91 kJ/mol, including energy corrections to account for contributions beyond triples, core-valence correlation, and basis-set incompleteness error. Among coupled-cluster approaches with approximate triples, the canonical CCSD(T) exhibits the largest error for this problem. Complementary to CC, we also used phaseless auxiliary-field quantum Monte Carlo calculations (ph-AFQMC). We show that with a Hartree-Fock (HF) trial wave function, ph-AFQMC reproduces the CC results within 5 ± 1 kJ/mol. With multi-Slater-determinant (MSD) trials, the results are 82-84 ± 2 kJ/mol, indicating that multireference effects may be rather modest. Among the DFT methods tested, τ-HCTH, r2SCAN with 10-13% HF exchange with and without dispersion, and O3LYP/O3LYP-D4, and B3LYP*/B3LYP*-D4 generally perform the best. The r2SCAN12 (with 12% HF exchange) functional mimics both the best reference MSD ph-AFQMC and CC ΔE results within 2 kJ/mol.

Hybrid DFT Geometries and Properties for 17k Lanthanoid Complexes─The LnQM Data Set

The unique properties of lanthanoids and their diverse applications make them an indispensable part of modern research and industry. While the field has garnered attention, there remains a gap in available molecule data sets that facilitate both classical quantum chemistry calculations and the burgeoning field of machine learning in data science applications. This research addresses the need for a comprehensive data set that allows for a comparative analysis of various lanthanoids. The herein presented, curated data set includes 17269 monolanthanoid complexes derived from 1205 distinct ligand motifs. Structures encompass all 15 lanthanoids in the +3 oxidation state and exhibit molecular charges ranging from -1 to +3, including structures with a high spin multiplicity up to 8. Starting from lanthanum complexes, samples were processed with a permutation of the central lanthanoid atom, resulting in highly comparable subsets, facilitating comparative studies in which the influence of the lanthanoid can be investigated independently of ligand effects. The data set provides a broad range of features such as PBE0-D4/def2-SVP optimized geometries and optimization trajectories, while also covering ωB97M-V/def2-SVPD energies, rotational constants, dipole moments, highest occupied molecular orbital-lowest-unoccupied molecular orbital (HOMO-LUMO) energies, and Mulliken, Löwdin, and Hirshfeld population analyses. Additionally, coordination numbers, polarizabilities, and partial charges from D4, electronegativity equilibration (EEQ), GFN2-xTB, and charge extended Hückel (CEH) calculations are included. The data set is openly accessible and may serve as a basis for further investigations into the properties of lanthanoids.

Confined Lewis Pairs: Investigation of the X- →Si20 Interaction in Halogen-Encapsulating Silafulleranes

A joint theoretical and experimental study on 32 endohedral silafullerane derivatives [X@Si20 Y20 ]- (X=F-I; Y=F-I, H, Me, Et) andT h ${T_h }$ -[Cl@Si20 H12 Y8 ]- (Y=F-I) is presented. First, we evaluated the structure-determining template effect of Cl- in a systematic series of concave silapolyquinane model systems. Second, we investigated the X- →Si20 interaction energy (E int ${E_{{\rm{int}}} }$ ) as a function of X- and Y and found the largestE int ${E_{{\rm{int}}} }$ values for electron-withdrawing exohedral substituents Y. Given that X- ions can be considered as Lewis bases and empty Si20 Y20 clusters as Lewis acids, we classify our inseparable host-guest complexes [X@Si20 Y20 ]- as "confined Lewis pairs". Third, 35 Cl NMR spectroscopy proved to be highly diagnostic for an experimental assessment of the Cl- →Si20 interaction as the paramagnetic shielding and, in turn, δ ${\delta }$ (35 Cl) of the endohedral Cl- ion correlate inversely withE int ${E_{{\rm{int}}} }$ . Finally, we disclose the synthesis of [PPN][Cl@Si20 Y20 ] (Y=Me, Et, Br) and provide a thorough characterization of these new silafulleranes.

Exploring CPS-Extrapolated DLPNO-CCSD(T1) Reference Values for Benchmarking DFT Methods on Enzymatically Catalyzed Reactions

Domain-based local pair natural orbital coupled-cluster singles doubles with perturbative triples [DLPNO-CCSD(T)] is regularly used to calculate reliable benchmark reference values at a computational cost significantly lower than that of canonical CCSD(T). Recent work has shown that even greater accuracy can be obtained at only a small additional cost through extrapolation to the complete PNO space (CPS) limit. Herein, we test two levels of CPS extrapolation, CPS(5,6), which approximates the accuracy of standard TightPNO, and CPS(6,7), which surpasses it, as benchmark values to test density functional approximations (DFAs) on a small set of organic and transition-metal-dependent enzyme active site models. Between the different reference levels of theory, there are changes in the magnitudes of the absolute deviations for all functionals, but these are small and there is minimal impact on the relative rankings of the tested DFAs. The differences are more significant for the metalloenzymes than the organic enzymes, so we repeat the tests on our entire ENZYMES22 set of organic enzyme active site models [Wappett, D. A.; Goerigk, L. J. Phys. Chem. A 2019, 123, 7057-7074] to confirm that using the CPS extrapolations for the reference values has negligible impact on the benchmarking outcomes. This means that we can particularly recommend CPS(5,6) as an alternative to standard TightPNO settings for calculating reference values, increasing the applicability of DLPNO-CCSD(T) in benchmarking reaction energies and barrier heights of larger models of organic enzymes. DLPNO-CCSD(T1)/CPS(6,7) energies for ENZYMES22 are finally presented as updated reference values for the set, reflecting the recent improvements in the method.

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.

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

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

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.

Halogen-Dependent Diversity and Weak Interactions in the Heterometallic Ni/Cd Complex Solids: Structural and Theoretical Investigation

Three novel heterometallic Ni/Cd coordination compounds [Ni(en)3][CdCl4]∙3dmso (1), [Ni(en)2(dmf)2][CdBr4] (2), and [Ni(en)3]2[CdI4](I)2 (3) have been synthesized through the self-assembly process in a one-pot reaction of cadmium oxide, nickel salt (or nickel powder), NH4X (X = Cl, Br, I), and ethylenediamine in non-aqueous solvents dmso (for 1) or dmf (for 2 and 3). Formation of the one- (1) or three-dimensional (2 and 3) hydrogen-bonded frameworks has been observed depending on the nature of the [CdX4]2- counter-anion, as well as on the nature of the solvent. The electronic structures of [Ni(en)3]2+ and [Ni(en)2(dmf)2]2+ cations were studied at the DFT and CASSCF levels, including the ab initio ligand field theory (AILFT) calculations. The non-covalent intermolecular contacts between the cationic nickel and anionic cadmium blocks in the solid state were investigated by the QTAIM analysis. The mechanism of ligand substitution at the nickel center in [Ni(en)2(dmf)2]2+ was theoretically investigated at the ωB97X-D4/ma-def2-TZVP//DLPNO-CCSD(T)/ma-def2-TZVPP level. The results demonstrate that thermodynamic factors are structure-determining ones due to low energy barriers of the rotation of dmf ligands in [Ni(en)2(dmf)2]2+ (below 3 kcal mol-1) and the reversible transformation of [Ni(en)2(dmf)2]2+ into [Ni(en)3]2+ (below 20 kcal mol-1).

Molecular orbital and topological electron density study of n → π* interactions: amides and thioamides cases

The n → π* interactions were studied in amides and thioamides systems models, through the analysis of the electron density topology along with the Natural Bonding Orbital (NBO) approach. The effect of the dispersion terms was assessed using different DFT functionals. The NBO, independent gradient model (IGM), and the analysis of the reduced density gradient outcomes show that dispersion forces play a significant role in the strength of n → π* interactions. The IGM results indicate that δg height values for n → π* interactions do not extend beyond 0.025. All the methods used in this work predict that n → π* interaction between pairs of thioamides is stronger than those between amides. However, the electron density topology-based methods were not able to replicate the trends in the relative force of this interaction found in the experimental and NBO results.

The diacetyliminoxyl radical in oxidative functionalization of alkenes

The intermolecular oxime radical addition to CC bonds was observed and studied for the first time. The diacetyliminoxyl radical was proposed as a model radical reagent for the study of oxime radical reactivity towards unsaturated substrates, which is important in the light of the active development of synthetic applications of oxime radicals. In the present work it was found that the diacetyliminoxyl radical reacts with vinylarenes and conjugated dienes to give radical addition products, whereas unconjugated alkenes can undergo radical addition or allylic hydrogen substitution by diacetyliminoxyl depending on the substrate structure. Remarkably, substituted alkenes give high yields of C-O coupling products despite the significant steric hindrance, whereas unsubstituted alkenes give lower yields of the C-O coupling products. The observed atypical C-O coupling yield dependence on the alkene structure was explained by the discovered ability of the diacetyliminoxyl radical to attack alkenes with the formation of a C-N bond instead of a C-O bond giving side products. This side process is not expected for sterically hindered alkenes due to lower steric availability of the N-atom in diacetyliminoxyl than that of the O-atom.

Free Radicals in the Queue: Selective Successive Addition of Azide and N-Oxyl Radicals to Alkenes

The selective successive addition of azide (•N3) and N-oxyl radicals to alkenes is demonstrated, despite each of the two radicals being known to attack C═C bonds and the mixture of radical adducts possibly being expected. The proposed radical mechanism was supported by density functional theory calculations, electron paramagnetic resonance, and radical trapping experiments. The reaction proceeds at room temperature with the available reagents: NaN3, N-hydroxy compounds, and PhI(OAc)2 as the oxidant. The method can be applied for N-hydroxyimides, N-hydroxyamides, N-hydroxybenzotriazole, and oximes as N-oxyl radical precursors. Vinylarenes, aliphatic alkenes, and even electron-deficient methyl methacrylate were successfully functionalized.

DeePMD-kit v2: A software package for deep potential models

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

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.

Bismuth Infrared Star: Being at a Glance

Bismuth polycations have garnered significant attention from researchers due to their extraordinary and counter-intuitive structures and stoichiometries. Despite extensive experimental and theoretical investigations, understanding of the bonding in such clusters remains insufficient. An AdNDP bonding analysis was conducted to elucidate the bonding characteristics using both homoatomic and heteroatomic bismuth clusters with various stoichiometries. Analysis of the calculated nucleus-independent chemical shift data confirmed the aromatic nature of these species. Universal bonding patterns were identified that can be applied to a range of homoatomic and heteroatomic bismuth clusters. Additionally, calculations of absorbance and fluorescence spectra were performed to gain insights into the near-infrared emission and establish a potential correlation between absorbance and the identified bonding patterns.

Comparison of the Performance of Density Functional Methods for the Description of Spin States and Binding Energies of Porphyrins

This work analyzes the performance of 250 electronic structure theory methods (including 240 density functional approximations) for the description of spin states and the binding properties of iron, manganese, and cobalt porphyrins. The assessment employs the Por21 database of high-level computational data (CASPT2 reference energies taken from the literature). Results show that current approximations fail to achieve the "chemical accuracy" target of 1.0 kcal/mol by a long margin. The best-performing methods achieve a mean unsigned error (MUE) <15.0 kcal/mol, but the errors are at least twice as large for most methods. Semilocal functionals and global hybrid functionals with a low percentage of exact exchange are found to be the least problematic for spin states and binding energies, in agreement with the general knowledge in transition metal computational chemistry. Approximations with high percentages of exact exchange (including range-separated and double-hybrid functionals) can lead to catastrophic failures. More modern approximations usually perform better than older functionals. An accurate statistical analysis of the results also casts doubts on some of the reference energies calculated using multireference methods. Suggestions and general guidelines for users are provided in the conclusions. These results hopefully stimulate advances for both the wave function and the density functional side of electronic structure calculations.

Thermal site energy fluctuations in photosystem I: new insights from MD/QM/MM calculations

Cyanobacterial photosystem I (PSI) is one of the most efficient photosynthetic machineries found in nature. Due to the large scale and complexity of the system, the energy transfer mechanism from the antenna complex to the reaction center is still not fully understood. A central element is the accurate evaluation of the individual chlorophyll excitation energies (site energies). Such an evaluation must include a detailed treatment of site specific environmental influences on structural and electrostatic properties, but also their evolution in the temporal domain, because of the dynamic nature of the energy transfer process. In this work, we calculate the site energies of all 96 chlorophylls in a membrane-embedded model of PSI. The employed hybrid QM/MM approach using the multireference DFT/MRCI method in the QM region allows to obtain accurate site energies under explicit consideration of the natural environment. We identify energy traps and barriers in the antenna complex and discuss their implications for energy transfer to the reaction center. Going beyond previous studies, our model also accounts for the molecular dynamics of the full trimeric PSI complex. Via statistical analysis we show that the thermal fluctuations of single chlorophylls prevent the formation of a single prominent energy funnel within the antenna complex. These findings are also supported by a dipole exciton model. We conclude that energy transfer pathways may form only transiently at physiological temperatures, as thermal fluctuations overcome energy barriers. The set of site energies provided in this work sets the stage for theoretical and experimental studies on the highly efficient energy transfer mechanisms in PSI.

Pyridine Dimers and Their Low-Temperature Isomerization: A High-Resolution Matrix-Isolation Spectroscopy Study

The bonding between two neutral aromatic compounds, especially small ones, has been controversially debated in the last decades, and terms like "π-stacking" had to be revised. Surprisingly, despite of many experimental and computational work, there is still no clear consensus about the structure of and the bonding in the pyridine dimer. In this work, for different isomeric forms of the pyridine dimer, the structures and bonding were elucidated by combining high-resolution matrix-isolation spectroscopic results with quantum-chemical calculations. High-resolution IR spectra of Ne matrices at 4 K containing pyridine were recorded for different concentrations and upon annealing to 10 and 12 K, relying on three isotopologues of pyridine. The spectra show the presence of hydrogen-bonded, T-shaped, and stacked forms of weakly-bound pyridine dimers. Among these, the hydrogen-bonded isomer is identified as the lowest-energy form. The results provide for the first time conclusive information about the interaction between two pyridine dimers.

Ordering of monomers, dimers and polymers of deposited Br2I2Py molecules: a modeling study

We propose a lattice model describing the ordering of 1,6-dibromo-3,8-diiodopyrene (Br₂I₂Py) molecules on the Au(111) surface into two-dimensional structures and correlated one dimensional rows. Our model employs three (intact, singly and doubly deiodinated) types of Br₂I₂Py molecules and mimics the situation which occurs with increasing temperature, where the majority of intact molecules form ordered two-dimensional networks, while most of the doubly deiodinated molecules assemble into long organometallic polymeric rows. We use DFT calculations to determine the values of intermolecular interactions for intact molecules and propose a strategy for estimating the interactions for deiodinated molecules, where the organometallic interaction with Au atoms plays the dominant role. Our model is solved using Monte Carlo calculations and allows us to obtain the monomeric structure of intact molecules, the dimeric structure of singly deiodinated molecules and the polymeric row structure of (mostly) doubly deiodinated molecules. We obtain the coexistence of ordered intact Br₂I₂Py molecules and organometallic dimers, as well as their separation at large values of intermolecular interaction with Au. Similar results are obtained by studying mixtures of singly and doubly deiodinated molecules: dimer rows can be either incorporated into the two dimensional pattern of correlated polymeric chains or separated into their own dimeric structures.

Benchmarking the quadrupolar coupling tensor for chlorine to probe weak-bonding interactions

Rotational spectroscopy relies on quantum chemical calculations to interpret observed spectra. Among the most challenging molecules to assign are those with additional angular momenta coupling to the rotation, contributing to the complexity of the spectrum. This benchmark study of computational methods commonly used by rotational spectroscopists targets the nuclear quadrupole coupling constants of chlorine containing molecules and the geometry of its complexes and clusters. For each method, the quality of both structural and electronic parameter predictions is compared with the experimental values. Ab initio methods are found to perform best overall in predicting both the geometry of the complexes and the coupling constants of chlorine with moderate computational cost. This cost can be reduced by combining these methods with density functional theory structure optimization, which still yields adequate predictions. This work constitutes a first step in expanding Bailey's quadrupole coupling data set to encompass molecular clusters. [W. C. Bailey, Calculation of Nuclear Quadrupole Coupling Constants in Gaseous State Molecule, 2019, https://nqcc.wcbailey.net/].

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.

How do density functionals affect the Hirshfeld atom refinement?

In this work, the effect of mixing different amounts of Hartree-Fock (HF) exchange with hybrid density functionals applied to the Hirshfeld atom refinement (HAR) of urea and oxalic acid dihydrate is explored. Together, the influence of using different basis sets, methods (including MP2 and HF) and cluster sizes (to model bulk effects) is studied. The results show that changing the amount of HF exchange, no matter the level of theory, has an impact almost exclusively on the H atom refinement parameters. Contrary to pure quantum mechanical calculations where good geometries are obtained with intermediate HF exchange mixtures, in the HAR the best match with neutron diffraction reference values is not necessarily found for these admixtures. While the non-hydrogen covalent bond lengths are insensitive to the combination of method or basis set employed, the X-H bond lengths always increase proportionally to the HF exchange for the analysed systems. This outcome is opposite to what is normally observed from geometry optimisations, i.e., shorter bonds are obtained with greater HF exchange. Additionally, the thermal ellipsoids tend to shrink with larger HF exchange, especially for the H atoms involved in strong hydrogen bonding. Thus, it may be the case that the development of density functionals or basis sets suitable for quantum crystallography should take a different path than those fitted for quantum chemistry calculations.

5,8-Di-tert-butyl-2-hydroxy-1H-benzo[de]isoquinoline-1,3(2H)-dione—A New Lipophilic N-oxyl Radical Precursor

N-hydroxyimides are widely known as organocatalysts for aerobic oxidation and oxidative coupling reactions, in which corresponding imide-N-oxyl radicals play the role of catalytically active hydrogen atom abstracting species. The drawbacks of many N-hydroxyimides are poor solubility in low polarity solvents and limited activity in the cleavage of unactivated C–H bonds. To overcome these shortcomings, we have synthesized a new lipophilic N-hydroxyimide, 5,8-di-tert-butyl-2-hydroxy-1H-benzo[de]isoquinoline-1,3(2H)-dione, with high solubility in low-polarity solvents such as DCM. According to the EPR study, the stability of the corresponding imide-N-oxyl radical is comparable to that of the non-tert-butylated analogue, naphthalimide-N-oxyl radical. DFT calculations showed that the NO–H bond dissociation enthalpy (BDE) in the synthesized tert-butylated-N-hydroxynaphthalimide is one of the highest in N-hydroxyimide series, which corresponds to high hydrogen atom abstracting reactivity and may be useful in catalysis of strong C–H bond oxidative cleavage. The synthesized compound can be considered as catalyst for liquid-phase free-radical oxidation and oxidative coupling reactions in non-polar media where solubility was previously the limiting factor.

ωB97X-3c: A composite range-separated hybrid DFT method with a molecule-optimized polarized valence double-ζ basis set

A new composite density functional theory (DFT) method is presented. It is based on ωB97X-V as one of the best-performing density functionals for the GMTKN55 thermochemistry database and completes the family of "3c" methods toward range-separated hybrid DFT. This method is consistently available for all elements up to Rn (Z = 1-86). Its further key ingredients are a polarized valence double-ζ (vDZP) Gaussian basis set, which was fully optimized in molecular DFT calculations, in combination with large-core effective core potentials and a specially adapted D4 dispersion correction. Unlike most existing double-ζ atomic orbital sets, vDZP shows only small basis set superposition errors (BSSEs) and can compete with standard sets of triple-ζ quality. Small residual BSSE effects are efficiently absorbed by the D4 damping scheme, which overall eliminates the need for an explicit treatment or empirical corrections for BSSE. Thorough tests on a variety of thermochemistry benchmark sets show that the new composite method, dubbed ωB97X-3c, is on par with or even outperforms standard hybrid DFT methods in a quadruple-zeta basis set at a small fraction of the computational cost. Particular strengths of this method are the description of non-covalent interactions and barrier heights, for which it is among the best-performing density functionals overall.

Performance of Localized-Orbital Coupled-Cluster Approaches for the Conformational Energies of Longer n-Alkane Chains

We report an update and enhancement of the ACONFL (conformer energies of large alkanes [J. Phys. Chem. A2022,126, 3521-3535]) dataset. For the ACONF12 (n-dodecane) subset, we report basis set limit canonical coupled-cluster with singles, doubles, and perturbative triples [i.e., CCSD(T)] reference data obtained from the MP2-F12/cc-pV{T,Q}Z-F12 extrapolation, [CCSD(F12*)-MP2-F12]/aug-cc-pVTZ-F12, and a (T) correction from conventional CCSD(T)/aug-cc-pV{D,T}Z calculations. Then, we explored the performance of a variety of single and composite localized-orbital CCSD(T) approximations, ultimately finding an affordable localized natural orbital CCSD(T) [LNO-CCSD(T)]-based post-MP2 correction that agrees to 0.006 kcal/mol mean absolute deviation with the revised canonical reference data. In tandem with canonical MP2-F12 complete basis set extrapolation, this was then used to re-evaluate the ACONF16 and ACONF20 subsets for n-hexadecane and n-icosane, respectively. Combining those with the revised canonical reference data for the dodecane conformers (i.e., ACONF12 subset), a revised ACONFL set was obtained. It was then used to assess the performance of different localized-orbital coupled-cluster approaches, such as pair natural orbital localized CCSD(T) [PNO-LCCSD(T)] as implemented in MOLPRO, DLPNO-CCSD(T0) and DLPNO-CCSD(T1) as implemented in ORCA, and LNO-CCSD(T) as implemented in MRCC, at their respective "Normal", "Tight", "vTight", and "vvTight" accuracy settings. For a given accuracy threshold and basis set, DLPNO-CCSD(T1) and DLPNO-CCSD(T0) perform comparably. With "VeryTightPNO" cutoffs, explicitly correlated DLPNO-CCSD(T1)-F12/VDZ-F12 is the best pick among all the DLPNO-based methods tested. To isolate basis set incompleteness from localized-orbital-related truncation errors (domain, LNOs), we have also compared the localized coupled-cluster approaches with canonical DF-CCSD(T)/aug-cc-pVTZ for the ACONF12 set. We found that gradually tightening the cutoffs improves the performance of LNO-CCSD(T), and using a composite scheme such as vTight + 0.50[vTight - Tight] improves things further. For DLPNO-CCSD(T1), "TightPNO" and "VeryTightPNO" offer a statistically similar accuracy, which gets slightly better when TCutPNO is extrapolated to the complete PNO space limit. Similar to Brauer et al.'s [Phys. Chem. Chem. Phys.2016,18 (31), 20905-20925] previous report for the S66x8 noncovalent interactions, the dispersion-corrected direct random phase approximation (dRPA)-based double hybrids perform remarkably well for the ACONFL set. While the revised reference data do not affect any conclusions on the less accurate methods, they may upend orderings for more accurate methods with error statistics on the same order as the difference between reference datasets.

Unusually Chemoselective Photocyclization of 2-(Hydroxyimino)aldehydes to Cyclobutanol Oximes: Synthetic, Stereochemical, and Mechanistic Aspects

Photocyclization of carbonyl compounds (known as the Norrish-Yang reaction) to yield cyclobutanols is, in general, accompanied by fragmentation reactions. The latter are predominant in the case of aldehydes so that secondary cyclobutanols are not considered accessible via the straightforward Norrish-Yang reaction. A noteworthy exception has been reported in our laboratory, where cyclobutanols bearing a secondary alcohol function were observed upon UV light irradiation of 2-(hydroxyimino)aldehydes (HIAs). This reaction is here investigated in detail by combining synthesis, spectroscopic data, molecular dynamics, and DFT calculations. The synthetic methodology is generally applicable to a series of HIAs, affording the corresponding cyclobutanol oximes (CBOs) chemoselectively (i.e., without sizable fragmentation side-reactions), diastereoselectively (up to >99:1), and in good to excellent yields (up to 95%). CBO oxime ether derivatives can be purified and diastereomers isolated by standard column chromatography. The mechanistic and stereochemical picture of this photocyclization reaction, as well as of the postcyclization E/Z isomerization of the oxime double bond is completed.

Between Two Chairs: Combination of Theory and Experiment for the Determination of the Conformational Dynamics of Xylosides

The conformational properties of monosaccharides constitute fundamental features of oligosaccharides. While the energy landscape of monosaccharides can be altered by a specific biochemical environment or by chemical modifications, the analysis of resulting dynamic conformational equilibria is not feasible by experimental means alone. In this work, a series of β-d-xylopyranosides is used to outline how a combination of experimental NMR parameters and computed molecular properties can be used to determine conformers and quantify the composition of conformational equilibria. We demonstrate that identifying the most stable conformers using energy calculations is challenging and computing of NMR shieldings is typically not sensitive enough. On the other hand, computed spin-spin coupling constants for the xyloside ring can be used to unambiguously assign experimental NMR data of dynamic conformational equilibria and quantify the ratio of different conformers in the mixture. As a proof of principle, this procedure allowed to analyze a hitherto unknown dynamic equilibrium of a diamino-xyloside as a precursor of a molecular switch.

"Vermellogens" and the Development of CB[8]-Based Supramolecular Switches Using pH-Responsive and Non-Toxic Viologen Analogues

We present herein the "vermellogens", a new class of pH-responsive viologen analogues, which replace the direct linking between para-substituted pyridinium moieties within those by a hydrazone functional group. A series of such compounds have been efficiently synthesized in aqueous media by hydrazone exchange reactions, displaying a marked pH-responsivity. Furthermore, the parent N,N'-dimethylated "vermellogen": the "red thread", an analogue of the herbicide paraquat and used herein as a representative model of the series, showed anion-recognition abilities, non-reversible electrochemical behavior, and non-toxicity of the modified bis-pyridinium core. The host-guest chemistry for the "red thread" with the CB[7,8] macrocyclic receptors has been extensively studied experimentally and by dispersion corrected density functional theory methods, showing a parallel behavior to that previously described for the herbicide but, crucially, swapping the well-known redox reactive capabilities of the viologen-based inclusion complexes by acid-base supramolecular responsiveness.

Theoretical calculations of formation and reactivity of o-quinomethide derivatives of resorcin[4]arene with reference to empirical data

This paper describes theoretical reaction pathways of alkoxybenzyl derivatives of resorcin[4]arene leading to the formation of o-quinomethide derivatives of resorcin[4]arene (o-QMR[4]A). For each case, the activation energies for the formation of one o-QMR[4]A unit and the activation energies for the backward reaction were calculated. Based on the calculated reaction pathways, the reaction mechanism of o-QMR[4]A formation was proposed. Using the example of o-QMR[4]A generated from a methoxy derivative of resorcin[4]arene, the activation energies with selected nucleophiles were calculated and the reaction mechanisms discussed. Reaction path calculations were performed using the nudged elastic band method and semiempirical extended tight-binding method (GFN2-xTB). Using hydroxybenzyl derivatives of resorcin[4]arene as an example, a comparison of calculated activation energies by selected density-functional theory methods with GFN2-xTB and B97-3c geometries was performed. B97-3c and wB97XD methods were used to calculate the energies of the reactants (R), transition states (TS) and products (P) of the analysed reactions. Theoretical reaction mechanisms were discussed with respect to the orbital-weighted Fukui dual descriptor (Δfw ) and experimental data.

Intermolecular Interactions of Pyrene and Its Oxides in Toluene Solution

In this work, the conformer-rotamer ensemble sampling tool (CREST), with the underlying semiempirical GFN2-xtb method, was used for automated geometry exploration of the homodimers of pyrene, pyrene-4,5-dione, and pyrene-4,5,9,10-tetraone, along with the heterodimer of pyrene and pyrene-4,5,9,10-tetraone. Geometries and energies of the dimers were further refined at the ωB97X-D4/def2-TZVP level of theory, both in the gas phase and in toluene solution. Computations in solution were handled using the CPCM (conductor-like polarizible continuum model) and SMD (solvation model based on density) models. Two previously unidentified pyrene-homodimer conformations were identified, and the effects of oxidation on the geometries and energies of dimerization were explored; in general, oxidation leads to stronger intermolecular interactions and decreased solubility in toluene. For selected dimers, DLPNO-CCSD(T)/cc-pVTZ/SMD(Toluene) energies were determined at the DFT geometries and illustrated the accuracy of the ωB97X-D4 approach, with an MAD of 1.47 kJ/mol.

Conformational Energy Benchmark for Longer n-Alkane Chains

We present the first benchmark set focusing on the conformational energies of highly flexible, long n-alkane chains, termed ACONFL. Unbranched alkanes are ubiquitous building blocks in nature, so the goal is to be able to calculate their properties most accurately to improve the modeling of, e.g., complex (biological) systems. Very accurate DLPNO-CCSD(T1)/CBS reference values are provided, which allow for a statistical meaningful evaluation of even the best available density functional methods. The performance of established and modern (dispersion corrected) density functionals is comprehensively assessed. The recently introduced r²SCAN-V functional shows excellent performance, similar to efficient composite DFT methods like B97-3c and r²SCAN-3c, which provide an even better cost-accuracy ratio, while almost reaching the accuracy of much more computationally demanding hybrid or double hybrid functionals with large QZ AO basis sets. In addition, we investigated the performance of common wave function methods, where MP2/CBS surprisingly performs worse compared to the simple D4 dispersion corrected Hartree-Fock. Furthermore, we investigate the performance of several semiempirical and force field methods, which are commonly used for the generation of conformational ensembles in multilevel workflows or in large scale molecular dynamics studies. Outstanding performance is obtained by the recently introduced general force field, GFN-FF, while other commonly applied methods like the universal force field yield large errors. We recommend the ACONFL as a helpful benchmark set for parametrization of new semiempirical or force field methods and machine learning potentials as well as a meaningful validation set for newly developed DFT or dispersion methods.

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.

Quantification of Geometric Errors Made Simple: Application to Main-Group Molecular Structures

Nearly all electronic structure simulations begin with obtaining approximate geometries, making a systematic quantification of errors in approximate molecular structures of key importance. Recently, the geometric energy offset (GEO) framework based on a single and natural measure for quantifying and analyzing these errors has been proposed ( J. Phys. Chem. Lett. 2020, 11, 99579964). An accurate and far less costly approximation to GEO is utilized here to readily quantify errors in main-group structures and analyze them in a chemically intuitive way. The use of semiexperimental geometries as a reference further simplifies the analysis. The analysis reveals new insights into the geometric performance of methods, their rankings, as well as patterns across different classes of methods and basis sets that arise from the analysis.

Chiral Phosphoric Acid Catalyzed Conversion of Epoxides into Thiiranes: Mechanism, Stereochemical Model, and New Catalyst Design

Computations and experiments leading to new chiral phosphoric acids (CPAs) for epoxide thionations are reported. Density functional theory calculations reveal the mechanism and origin of the enantioselectivity of such CPA-catalyzed epoxide thionations. The calculated mechanistic information was used to design new efficient CPAs that were tested experimentally and found to be highly effective. Bulky ortho-substituents on the 3,3'-aryl groups of the CPA are important to restrict the position of the epoxide in the key transition states for the enantioselectivity-determining step. Larger para-substituents significantly improve the enantioselectivity of the reaction.

The inversion of tetrahedral p-block element compounds: general trends and the relation to the second-order Jahn-Teller effect

The tetrahedron is the primary structural motif among the p-block elements and determines the architecture of our bio- and geosphere. However, a broad understanding of the configurational inversion of tetrahedral compounds is missing. Here, we report over 250 energies (DLPNO-CCSD(T)) for square planar inversion of third- and fourth-period element species of groups 13, 14, and 15. Surprisingly low inversion barriers are identified for compounds of industrial relevance (e.g., ≈100 kJ mol-1 for Al(OH)4 -). More fundamentally, the second-order Jahn-Teller theorem is disclosed as suitable to rationalize substituent and central element effects. Bond analysis tools give further insights into the preference of eight valence electron systems with four substituents to be tetrahedral. Hence, this study develops a model to understand, memorize, and predict the angular flexibility of tetrahedral species. Perceiving the tetrahedron not as forcingly rigid but as a dynamic structural entity might leverage new approaches and visions for adaptive matter.