Predicting valence tautomerism in diverse cobalt-dioxolene complexes: elucidation of the role of ligands and solvent.

The ability of molecular switches to reversibly interconvert between different forms promises potential applications at the scale of single molecules up to bulk materials. One type of molecular switch comprises cobalt-dioxolene compounds that exhibit thermally-induced valence tautomerism (VT) interconversions between low spin Co(iii)-catecholate (LS-CoIII-cat) and high spin Co(ii)-semiquinonate (HS-CoII-sq) forms. Two families of these compounds have been investigated for decades but have generally been considered separately: neutral [Co(diox)(sq)(N2L)] and cationic [Co(diox)(N4L)]+ complexes (diox = generic dioxolene, N2L/N4L = bidentate/tetradentate N-donor ancillary ligand). Computational identification of promising new candidate compounds prior to experimental exploration is beneficial for environmental and cost considerations but requires a thorough understanding of the underlying thermochemical parameters that influence the switching. Herein, we report a robust approach for the analysis of both cobalt-dioxolene families, which involved a quantitative density functional theory-based study benchmarked with reliable quasi-experimental references. The best-performing M06L-D4/def2-TZVPP level of theory has subsequently been verified by the synthesis and experimental investigation of three new complexes, two of which exhibit thermally-induced VT, while the third remains in the LS-CoIII-cat form across all temperatures, in agreement with prediction. Valence tautomerism in solution is markedly solvent-dependent, but the origin of this has not been definitively established. We have extended our computational approach to elucidate the correlation of VT transition temperature with solvent stabilisation energy and change in dipole moment. This new understanding may inform the development of VT compounds for applications in soft materials including films, gels, and polymers.

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.

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.

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

[This retracts the article DOI: 10.1039/D2RA01703B.].

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.

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.

One-electron self-interaction error and its relationship to geometry and higher orbital occupation.

Density Functional Theory (DFT) sees prominent use in computational chemistry and physics; however, problems due to the self-interaction error (SIE) pose additional challenges to obtaining qualitatively correct results. As an unphysical energy an electron exerts on itself, the SIE impacts most practical DFT calculations. We conduct an in-depth analysis of the one-electron SIE in which we replicate delocalization effects for simple geometries. We present a simple visualization of such effects, which may help in future qualitative analysis of the one-electron SIE. By increasing the number of nuclei in a linear arrangement, the SIE increases dramatically. We also show how molecular shape impacts the SIE. Two- and three-dimensional shapes show an even greater SIE stemming mainly from the exchange functional with some error compensation from the one-electron error, which we previously defined [D. R. Lonsdale and L. Goerigk, Phys. Chem. Chem. Phys. 22, 15805 (2020)]. Most tested geometries are affected by the functional error, while some suffer from the density error. For the latter, we establish a potential connection with electrons being unequally delocalized by the DFT methods. We also show how the SIE increases if electrons occupy higher-lying atomic orbitals; seemingly one-electron SIE free methods in a ground are no longer SIE free in excited states, which is an important insight for some popular, non-empirical density functional approximations (DFAs). We conclude that the erratic behavior of the SIE in even the simplest geometries shows that robust DFAs are needed. Our test systems can be used as a future benchmark or contribute toward DFT development.

A photo-switchable molecular capsule: sequential photoinduced processes.

The metastable trilacunary heteropolyoxomolybdate [PMo9O31(py)3]3- - {PMo9}; py = pyridine) and the ditopic pyridyl bearing diarylethene (DAE) (C25H16N2F6S2) self-assemble via a facile ligand replacement methodology to yield the photo-active molecular capsule [(PMo9O31)2(DAE)3]6-. The spatial arrangement and conformation of the three DAE ligands are directed by the surface chemistry of the molecular metal oxide precursor with exclusive ligation of the photo-active antiparallel rotamer to the polyoxometalate (POM) while the integrity of the assembly in solution has been verified by a suite of spectroscopic techniques. Electrocyclisation of the three DAEs occurs sequentially and has been investigated using a combination of steady-state and time-resolved spectroscopies with the discovery of a photochemical cascade whereby rapid photoinduced ring closure is followed by electron transfer from the ring-closed DAE to the POM in the latent donor-acceptor system on subsequent excitation. This interpretation is also supported by computational and detailed spectroelectrochemical analysis. Ring-closing quantum yields were also determined using a custom quantum yield determination setup (QYDS), providing insight into the impact of POM coordination on these processes.

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.

Assessing Recent Time-Dependent Double-Hybrid Density Functionals on Doublet-Doublet Excitations.

This work is the first thorough investigation of time-dependent double-hybrid density functionals (DHDFs) for the calculation of doublet-doublet excitation energies. It sheds light on the current state-of-the-art techniques in the field and clarifies if there is still room for future improvements. Overall, 29 hybrid functionals and DHDFs are investigated. We separately analyze the individual impacts of the Tamm-Dancoff approximation (TDA), range separation, and spin-component/opposite scaling (SCS/SOS) on 45 doublet-doublet excitations in 23 radicals before concluding with an overarching analysis that includes and excludes challenging excitations with double-excitation or multireference character. Our results show again that so-called "nonempirical" DHDFs are outperformed by semiempirical ones. While the best assessed functionals are DHDFs, some of the worst are also DHDFs and outperformed by all assessed hybrids. SCS/SOS is particularly beneficial for range-separated DHDFs. Spin-scaled, range-separated DHDFs paired with the TDA belong to the best tested methods here, and we particularly highlight SCS-ωB2GP-PLYP, SOS-ωB2PLYP, SOS-ωB2GP-PLYP, SOS-ωB88PP86, SOS-RSX-QIDH, and SOS-ωPBEPP86. When comparing our functional rankings with previous studies on singlet-singlet and singlet-triplet excitations, we recommend TDA-SOS-ωB88PP86 and TDA-SOS-ωPBEPP86 as robust methods for excitation energies in general until further improvements have been achieved that surpass the chemical accuracy threshold for challenging open-shell excitations without increasing the computational effort.

A Convenient DFT-Based Strategy for Predicting Transition Temperatures of Valence Tautomeric Molecular Switches.

The ability to identify promising candidate switchable molecules computationally, prior to synthesis, represents a considerable advance in the development of switchable molecular materials. Even more useful would be the possibility of predicting the switching temperature. Cobalt-dioxolene complexes can exhibit thermally induced valence tautomeric switching between low-spin CoIII-catecholate and high-spin CoII-semiquinonate forms, where the half-temperature (T1/2) is the temperature at which there are equal amounts of the two tautomers. We report the first simple computational strategy for accurately predicting T1/2 values for valence tautomeric complexes. Dispersion-corrected density functional theory (DFT) methods have been applied to the [Co(dbdiox)(dbsq)(N2L)] (dbdiox/dbsq•- = 3,5-di-tert-butyldioxolene/semiquinonate; N2L = diimine) family of valence tautomeric complexes, including the newly reported [Co(dbdiox)(dbsq)(MeO-bpy)] (1) (MeO-bpy = 4,4'-dimethoxy-2,2'-bipyridine). The DFT strategy has been thoroughly benchmarked to experimental data, affording highly accurate spin-distributions and an excellent energy match between experimental and calculated spin-states. Detailed orbital analysis of the [Co(dbdiox)(dbsq)(N2L)] complexes has revealed that the diimine ligand tunes the T1/2 value primarily through π-acceptance. We have established an excellent correlation between experimental T1/2(toluene) values for [Co(dbdiox)(dbsq)(N2L)] complexes and the calculated lowest unoccupied molecular orbital energy of the corresponding diimine ligand. The model affords accurate T1/2(toluene) values for [Co(dbdiox)(dbsq)(N2L)] complexes, with an average error of only 3.7%. This quantitative and simple DFT strategy allows experimentalists to not only rapidly identify proposed VT complexes but also predict the transition temperature. This study lays the groundwork for future in silico screening of candidate switchable molecules prior to experimental investigation, with associated time, cost, and environmental benefits.

Multifunctional Coordination Polymer Exhibiting Reversible Mechanical Motion Allowing Selective Uptake of Guests and Leading to Enhanced Electrical Conductivity.

A remarkably flexible, multifunctional, 2D coordination polymer exhibiting an unprecedented mode of reversible mechanical motion, enabling pores to open and close, is reported. Such multifunctional materials are highly sought after, owing to the potential to exploit coexisting electronic and mechanical functionalities that underpin useful technological applications such as actuators and ultrasensitive detectors. The coordination polymer, of composition Mn(F4TCNQ)(py)2 (F4TCNQ = 2,3,5,6-tetrafluoro-7,7,8,8-tetracycanoquinodimethane; py = pyridine), consists of Mn(II) centers bridged by F4TCNQ dianions and coordinated by py molecules that extend above and below the 2D network. Exposure of Mn(F4TCNQ)(py)2, in its collapsed state, to carbon dioxide results in a pore-opening process at a threshold pressure for a given temperature. In addition to carbon dioxide, a variety of volatile guests may be incorporated into the pores, which are lined with electron-rich F4TCNQ dianions. The inclusion of electron-deficient guests such as 1,4-benzoquinone, nitrobenzene, maleic anhydride, and iodine into the pores is accompanied by a striking color change associated with a new host-guest charge-transfer interaction and an improvement in the semiconductor behavior, with the iodine adduct showing an increase in conductivity of almost 5 orders of magnitude. Experimental and density functional theory calculations on this remarkable multifunctional material demonstrate a reduction in the optical band gap with increasing electron affinity of the guest.

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.

Analysis of Recent BLYP- and PBE-Based Range-Separated Double-Hybrid Density Functional Approximations for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions.

We investigate the effects of range separation of the exchange energy on electronic ground-state properties for recently published double-hybrid density functionals (DHDFs) with the extensive GMTKN55 database for general main-group thermochemistry, kinetics, and noncovalent interactions. We include the semiempirical range-separated DHDFs ωB2PLYP and ωB2GP-PLYP developed by our group for excitation energies, together with their ground-state-parametrized variants, which we denote herein as ωB2PLYP18 and ωB2GP-PLYP18. We also include the nonempirical range-separated DHDFs RSX-0DH and RSX-QIDH. For all six DHDFs, damping parameters for the DFT-D3 dispersion correction (and for its DFT-D4 variant) are presented. We comment on when the range-separated functionals can be more beneficial than their global counterparts and conclude that range separation alone is no guarantee for overall improved results. We observe that the BLYP-based functionals generally outperform the PBE-based functionals. We finally note that the best-performing DHDFs for GMTKN55 are still the semiempirical range-separated double hybrids ωDSD3-PBEP86-D4 and ωDSD72-PBEP86-D4, the former of which includes a third-order perturbative correlation term in addition to the more conventional second-order perturbation that DHDFs are based upon.

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.

The role of conformational heterogeneity in the excited state dynamics of linked diketopyrrolopyrrole dimers.

Diketopyrrolopyrrole (DPP) derivatives have been proposed for both singlet fission and energy upconversion as they meet the energetic requirements and exhibit superior photostability compared to many other chromophores. In this study, both time-resolved electronic and IR spectroscopy have been applied to investigate excited state relaxation processes competing with fission in dimers of DPP derivatives with varying linker structures. A charge-separated (CS) state is shown to be an important intermediate with dynamics that are both solvent and linker dependent. The CS state is found for a subset of the total population of excited molecules and it is proposed that CS state formation requires suitably aligned dimers within a broader distribution of conformations available in solution. No long-lived triplet signatures indicative of singlet fission were detected, with the CS state likely acting as an alternative relaxation pathway for the excitation energy. This study provides insight into the role of molecular conformation in determining excited state relaxation pathways in DPP dimer systems.

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.

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

Previously, we introduced DFT-D3(BJ)ωB97X-V and ωB97M-V functionals and assessed them for the GMTKN55 database [Najibi and Goerigk, J Chem. Theory Comput. 2018, 14, 5725]. In this study, we present DFT-D4 damping parameters to build the DFT-D4 counterparts of these functionals and assess these in comparison. We extend our analysis beyond GMTKN55 and especially turn our attention to enzymatically catalyzed and metal-organic reactions. We find that B97M-D4 is now the second-best performing meta-generalized-gradient approximation functional for the GMTKN55 database and it can provide noticeably better organometallic reaction energies compared to B97M-D3(BJ). Moreover, the aforementioned DFT-D3(BJ)-based functionals have not been thoroughly assessed for geometries and herein we close this gap by analyzing geometries of noncovalently bound dimers and trimers, peptide conformers, water hexamers and transition-metal complexes. We find that several of the B97(M)-based methods-particularly the DFT-D4 versions-surpass the accuracy of previously studied methods for peptide conformer, water hexamer, and transition-metal complex geometries, making them safe-to-use, cost-efficient alternatives to the original methods. The DFT-D4 variants can be easily used with ORCA4.1 and above.

The one-electron self-interaction error in 74 density functional approximations: a case study on hydrogenic mono- and dinuclear systems.

The self-interaction error (SIE), i.e. unphysical interactions of electrons with themselves, has plagued developers and users of Density Functional Approximations (DFAs) since the inception of Density Functional Theory (DFT). Formally, it can be separated into the one-electron and many-electron SIE; herein we present one of the most comprehensive studies of the first. While we focus mostly on the total SIE, we also make use of two different decompositions. The first is a separation into functional and density-driven errors as championed by Sim, Burke and co-workers [J. Phys. Chem. Lett., 2018, 9, 6385-6392]; the second separates the error into exchange, correlation, and one-electron components, with the latter being a density error that has not been discussed in this form before. After investigating the familiar hydrogen atom and dihydrogen cation, we establish a relationship between the SIE and the nuclear charge with the help of a series of heavier hydrogenic analogues. For the mononuclear systems and the diatomics at the dissociation limit, this relationship is linear in nature with prominent exceptions, mostly belonging to the Minnesota and range-separated (double-)hybrid DFAs. For the first time, we also show how the magnitude of the SIE depends on the underlying atomic-orbital basis set and how DFAs that rely on a popular van-der-Waals DFT type London-dispersion term exhibit "self-dispersion". We find that range separation is not a panacea for solving the one-electron SIE. DFAs that have been developed to be one-electron SIE free for one system, such as the hydrogen atom, show larger errors for heavier hydrogenic systems. Often, one-electron SIE-free DFAs rely on fortuitous error cancellation between their exchange and correlation components. An analysis of the most robust methods for general applications to date reveals that they suffer moderately from the one-electron SIE, while DFAs that are nearly SIE-free do not perform well in applications. Implicit in the continued existence of the one-electron SIE is that well-performing DFAs continue to suffer insufficiencies at their fundamental levels that are being compensated for by the SIE. Our analysis includes more than 250 000 datapoints, resulting in multiple insights that may drive future developments of new DFAs or SIE corrections.

Clam-like Cyclotricatechylene-based Capsules: Identifying the Roles of Protonation State and Guests as well as the Drivers for Stability and (Anti-)Cooperativity.

Cyclotricatechylene (ctcH6 ) is a bowl-shaped macrocyclic compound that can be used as a building block for self-assembled capsules. ctcH6 and its derivatives in various protonation states - here collectively labeled as CTC - form dimers that resemble the shape of a clam. These clam-shaped entities have been studied experimentally by Abrahams, Robson, and co-workers [B. F. Abrahams, N. J. FitzGerald, T. A. Hudson, R. Robson and T. Waters, Angew. Chem. Int. Ed. 2009, 48, 3129-3132] where the capsules acted as an excellent host for large alkali-metal cations. In this study, we present a detailed analysis based on accurate dispersion-corrected Density Functional Theory approaches that reveals the factors that stabilise such CTC-based capsules at different protonation states and their interaction with various encapsulated guests. Our results show that the capsules' overall stability results as an interplay of hydrogen bonding, London dispersion, and electrostatic effects. The most stable capsules with group-1 and group-2 cations as guests contain only six phenolic hydrogens, as opposed to the maximum possible number of twelve. Inclusion of larger alkali-metal cations is favoured due to larger London-dispersion contributions. Cations are favoured as guests over isoelectronic neutral species, as the resulting host-guest complexes experience additional stability due to cooperative effects. In fact, using the latter to drive the formation of specific capsules could be used in future strategies aimed at synthesising similar aggregates; our results provide an insightful understanding and useful guidance for such future endeavours.