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We present a new benchmark set of metalloenzyme model reaction energies and barrier heights, which we call MME55. The set contains eleven different enzymes, representing eight transition metals, both open and closed shell systems, and system sizes of up to 116 atoms. We use three 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. While Jacob’s Ladder is reproduced for the whole set based on averaged mean absolute deviations, hybrid DFT is preferred over double hybrids for copper- dependent enzymes, where MP2 correlation seriously adversely affects the results. Despite the popularity of B3LYP in computational enzymology, it is not a strong per- former on our benchmark set, and we discourage its use for enzyme energetics. Instead, we recommend the range-separated hybrids ωB97M-V and ωB97X-V combined with the def2-TZVPP basis set for applications, as they are a great compromise between accuracy and efficiency and have al- ready been shown to be robust across many other types of chemical problems.

The metastable trilacunary heteropolyoxomolybdate [PMo9O31(py)3]3−; 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−.

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.

We present a proof-of-concept study of the suitability of Kruse and Grimme’s geometric counterpoise correction (gCP) for basis set superposition errors (BSSEs) in double-hybrid density functional calculations with a double-ζ basis set. The gCP approach only requires geometrical information as an input and no orbital/density information is needed. Therefore, this correction is practically free of any additional cost. gCP is trained against the Boys and Bernardi counterpoise correction across a set of 528 noncovalently bound dimers. We investigate the suitability of the approach for the B2PLYP/def2-SVP level of theory, and reveal error compensation effects—missing London dispersion and the BSSE—associated with B2PLYP/def2-SVP calculations, and present B2PLYP-gCP-D3(BJ)/def2-SVP with the reparametrised DFT-D3(BJ) and gCP corrections as a more balanced alternative. Benchmarking results on the S66x8 benchmark set for noncovalent interactions and the GMTKN55 database for main-group thermochemistry, kinetics, and noncovalent interactions show a statistical improvement of the B2PLYP-gCP-D3(BJ) scheme over plain B2PLYP and B2PLYP-D3(BJ). B2PLYP-D3(BJ) shows significant overestimation of interaction energies, barrier heights with larger deviations from the reference values, and wrong relative stabilities in conformers, all of which can be associated with BSSE. We find that the gCP-corrected method represents a significant improvement over B2PLYP-D3(BJ), particularly for intramolecular noncovalent interactions. These findings encourage future developments of efficient double-hybrid DFT strategies that can be applied when double-hybrid calculations with large basis sets are not feasible due to system size.

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.

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.

The synthesis, structure and properties of a 2D FeIII network material of composition [Fe(O-bipy)2Cl](TCNQ)2 (O-bipy = 4,4'-bipyridyl N,N'-dioxide; TCNQ = 7,7,8,8-tetracyanoquinodimethane) are presented. The structure consists of a square grid in which square pyramidal FeIII centers are linked to four equivalent centers through O-bipy ligands. Pairs of TCNQ radical anions are located within rectangular cavities of the 2D network. The apical position on each Fe center is occupied by a chloride ion. Magnetic studies are indicative of weak antiferromagnetic coupling. Electrical conductivity measurements reveal that the compound is a semiconductor and on the basis of DFT calculations it is proposed that electrical conduction occurs via charge hopping between interlayer TCNQ anions. Mossbauer spectra indicate a rare example of the Goldanskii–Karyagin effect and are suggestive of unusual dynamic processes.

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.

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.

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; 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 unique 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 show 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 functional 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 ωB88PP86 as the best unscaled method in this work.

We present steps toward the construction of a quantum-chemical benchmark set for enzymatically catalyzed reactions comprising different-quite sizable-model systems for five reactions. Our work is inspired by a study of semiempirical molecular-orbital theory methods against B3LYP-based structures and energies [ Kromann et al.

Double-hybrid density functionals are currently the most accurate density functionals for ground-state properties and electronic excitations. Nevertheless, the lack of a long-range correction scheme makes them unreliable when it comes to long-range excitations. For this reason, we propose the first two time-dependent double-hybrid functionals with correct asymptotic long-range behavior named ωB2PLYP and ωB2GPPLYP. Herein, we demonstrate their excellent performance and show that they are the most accurate and robust time-dependent density functional theory methods for electronic excitation energies. They provide a balanced description of local-valence, Rydberg, and charge-transfer states. They are also able to tackle the difficult first two transitions in polycyclic aromatic hydrocarbons and show very promising results in a preliminary study on transition-metal compounds, exemplified for titanium dioxide clusters. This work shows that double hybrids can be systematically improved also for excitation energies, and further work in this field is warranted.

We explore two significant factors on the outcomes of benchmark studies for enzymatically catalysed reactions, namely the level of theory of the benchmarks and the size of the model system used to represent the enzyme active site. For the benchmarks, we compare two potential alternatives to canonical coupled cluster results for situations where CCSD(T) is computationally too demanding: a strategy to estimate finite basis set coupled cluster values and the local-correlation DLPNO-CCSD(T) method at the complete basis set limit. We confirm the high accuracy of DLPNO-CCSD(T) used with tight thresholds. We also show that notable differences can be seen when using both sets of references for a benchmark study, with absolute deviations from the higher quality references generally smaller than those from lowerquality ones as well as changes in the ranking of the assessed methods. For geometries, we test three models for the active site of 4-oxalocrotonate tautomerase: one typical of the QM region that may be used in QM/MM studies, and two smaller variants that neglect the surrounding chemical environment. Benchmarking of 12 density functionals known to perform well on enzymatically catalysed reactions shows inconsistent performance of each method across the three models, contradicting the common idea that small representative systems can be used to accurately assess the applicability of low-level methods for larger biochemical applications. Our findings shall serve as a reminder on the standards that should be adhered to in benchmark studies, and as a guide for future studies, both on enzyme-related and other chemical problems.

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.

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.

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.

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 semi-empirical 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 non-empirical 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 double-hybrid density functionals for GMTKN55 are still the semi-empirical 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.

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 -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.

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.

Previously, we introduced DFT-D3(BJ) variants of the B97M-V, ωB97X-V and ωB97M-V functionals and assessed them for the GMTKN55 database [Najibi and Go- erigk, 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 catalysed and metal-organic reactions. We find that B97M-D4 is now the second-best performing meta-GGA functional for the GMTKN55 database and it can provide noticeably better organometallic reaction energies com- pared 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 analysing 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 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.

The chromium–manganese bimetallic oxide clusters CrMnO4+, CrMn2O5,6+, Cr2MnO6,7+, CrMn3O6+, Cr2Mn2O7,8+, and Cr3MnO8,9+ were synthesized in a laser ablation cluster source and characterized by infr...

We continue our work on the long-range corrected double-hybrid density functionals (LC-DHDFs) {\omega}B2PLYP and {\omega}B2GP-PLYP that we developed in the context of time-dependent (TD) Density Functional Theory (DFT) to enable the robust description of singlet-singlet excitations [J. Chem. Theory Comput. 15, 4735 (2019)]. In our initial study, we only assessed the impact of a long-range correction (LC) on BLYP-based DHDFs, and herein we extend our understanding by providing the first test of PBE-based LC-DHDFs within the established TD-DHDF scheme. Moreover, this study is one of few that provides a direct comparison between TD-DHDFs and their faster Tamm-Dancoff-Approximation variants (TDA-DHDFs). Most importantly, this is the first TDA-DHDF study since Grimme and Neese's TDA-B2PLYP [J. Chem. Phys. 127, 154116 (2007)] and the first work on TD-DHDFs that addresses singlet-triplet excitations. We show how the difference between TD-DHDFs and TDA-DHDFs is often negligible for singlet-singlet excitations, but how one has to apply TDA-DHDFs for triplet excitations. For both excitation types, the LC is beneficial to the BLYP-based DHDFs but detrimental to the PBE-based ones. For local-valence and Rydberg excitations, {\omega}B2PLYP and {\omega}B2GP-PLYP as well as the global DHDF PBE-QIDH can be recommended. If a transition exhibits charge-transfer character, {\omega}B2PLYP and {\omega}B2GP-PLYP should be applied. An analysis of the gaps between the first singlet and triplet excited states of our systems revealed that there is room for further improvements to reach better robustness. Until that goal has been achieved, we recommend {\omega}B2PLYP and {\omega}B2GP-PLYP as some of the currently best TDA-DFT methods., Comment: The following article has been submitted to The Journal of Chemical Physics. After it is published, it will be found at https://aip.scitation.org/journal/jcp?gclid=EAIaIQobChMIvpPUhd2A6gIVFn8rCh2NlQWEEAAYASAAEgJXYPD_BwE This revised version has been corrected for typos, includes more theoretical details, more details on basis-set dependence and relative timings, more references

The development of van der Waals density functional approximations (vdW-DFAs) has gained considerable interest over the past decade. While in a strictest sense, energy calculations with vdW-DFAs should be carried out fully self-consistently, we demonstrate conclusively for a total of 11 methods that such a strategy only increases the computational time effort without having any significant effect on energetic properties, electron densities, or orbital-energy differences. The strategy to apply a nonlocal vdW-DFA kernel as an additive correction to a fully converged conventional DFA result is therefore justified and more efficient. As part of our study, we utilize the extensive GMTKN55 database for general main-group thermochemistry, kinetics, and noncovalent interactions [ Phys. Chem. Chem. Phys. 2017, 19, 32184], which allows us to analyze the very promising B97M-V [ J. Chem. Phys. 2015, 142, 074111] and ωB97M-V [ J. Chem. Phys. 2016, 144, 214110] DFAs. We also present new DFT-D3(BJ) based counterparts of these two methods and of ωB97X-V [ J. Chem. Theory Comput 2013, 9, 263], which are faster variants with similar accuracy. Our study concludes with updated recommendations for the general method user, based on our current overview of 325 dispersion-corrected and -uncorrected DFA variants analyzed for GMTKN55. vdW-DFAs are the best representatives of the three highest rungs of Jacob's Ladder, namely, B97M-V, ωB97M-V, and DSD-PBEP86-NL.

For the first time, we combine time-dependent double-hybrid density functional approximations (TD-DHDFAs) for the calculation of electronic excitation energies with the concepts of spin-component and spin-opposite scaling (SCS/SOS) of electron-pair contributions to their nonlocal correlation components. Different flavors of this idea, ranging from standard SCS parameters to fully fitted parameter sets, are presented and tested on six different parent DHDFAs. For cross-validation, we assess those methods on three benchmark sets that cover small- to medium-sized chromophores (up to 78 atoms) and different excitation types. For this purpose, we also introduce new CC3 reference values for the popular Gordon benchmark set that we recommend using in future studies. Our results confirm that already the (unscaled) parent TD-DHDFAs are accurate and outperform some wave function methods. Further introduction of SCS/SOS eliminates extreme outliers, reduces deviation spans from reference values by up to 0.5 eV, aligns the performance of the Tamm-Dancoff approximation (TDA) to that of full TD calculations, and also enables a more balanced description of different excitation types. The best-performing TD-based methods in our cross validation have mean absolute deviations as low as 0.14 eV compared to the time- and resource-intensive CC3 approach. A very important finding is that we also obtained SOS variants with excellent performance, contrary to wave function based methods. This opens a future pathway to highly efficient methods for the optimization of excited-state geometries, particularly when paired with computing strategies such as the Laplace transform. We recommend our SCS- and SOS-based variants for further testing and subsequent applications.

Ein neuer Ansatz zur Synthese von Heterohexa- und Heterodecametallaten unter nichtwassrigen, mikrowellengestutzten Reaktionsbedingungen wurde entwickelt. Die zwei neuartigen Molybdovanadate wurden isoliert und im festen sowie gelosten Zustand mittels Einkristall-Rontgenbeugung, FT-IR-, UV/Vis- und multinuklearer NMR-Spektroskopie sowie ESI-MS charakterisiert. Die relativen Stabilitaten der moglichen Strukturisomere beider Polyoxometallatsysteme wurden mithilfe von dispersionskorrigierten DFT-Rechnungen untersucht.

We present the GMTKN55 benchmark database for general main group thermochemistry, kinetics and noncovalent interactions. Compared to its popular predecessor GMTKN30 [Goerigk and Grimme J. Chem. Theory Comput., 2011, 7, 291], it allows assessment across a larger variety of chemical problems-with 13 new benchmark sets being presented for the first time-and it also provides reference values of significantly higher quality for most sets. GMTKN55 comprises 1505 relative energies based on 2462 single-point calculations and it is accessible to the user community via a dedicated website. Herein, we demonstrate the importance of better reference values, and we re-emphasise the need for London-dispersion corrections in density functional theory (DFT) treatments of thermochemical problems, including Minnesota methods. We assessed 217 variations of dispersion-corrected and -uncorrected density functional approximations, and carried out a detailed analysis of 83 of them to identify robust and reliable approaches. Double-hybrid functionals are the most reliable approaches for thermochemistry and noncovalent interactions, and they should be used whenever technically feasible. These are, in particular, DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), and B2GPPLYP-D3(BJ). The best hybrids are ωB97X-V, M052X-D3(0), and ωB97X-D3, but we also recommend PW6B95-D3(BJ) as the best conventional global hybrid. At the meta-generalised-gradient (meta-GGA) level, the SCAN-D3(BJ) method can be recommended. Other meta-GGAs are outperformed by the GGA functionals revPBE-D3(BJ), B97-D3(BJ), and OLYP-D3(BJ). We note that many popular methods, such as B3LYP, are not part of our recommendations. In fact, with our results we hope to inspire a change in the user community's perception of common DFT methods. We also encourage method developers to use GMTKN55 for cross-validation studies of new methodologies.

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

For years, there has been ongoing interest in experimentally and theoretically understanding inversion and racemization processes. However, to the best of our knowledge, there has been no computational study that systematically investigated how well low-level quantum-chemical methods predict inversion barriers. Herein, we provide an answer to this question and we present the INV24 benchmark set of 24 high-level, ab initio inversion barriers. INV24 covers inversion in triatomics, in pyramidal molecules, in one cyclic system, and in various helical and bowl-shaped compounds. Our results indicate that previously applied DFT approximations combined with small basis sets are not reliable enough and that at least a triple-ζ basis is needed for meaningful results. Moreover, we show that intramolecular London dispersion influences the barriers by 2 kcal/mol or more and that dispersion corrections should always be applied to DFT results. With our analysis of 34 DFT approximations, we can reproduce the well-known Jacob’s Ladder scheme with (meta-)generalized-gradient-approximation methods underestimating barriers and global-hybrid DFT functionals performing better. Range-separated hybrids or Minnesota-type hybrids are not particularly superior to more conventional methods, such as B3LYP-D3. The by far best results are achieved with dispersion-corrected double hybrids, which give results below the chemical accuracy target of 1 kcal/mol. They also outperform wave-function second-order perturbation theory approaches and we recommend using them whenever possible. Given that our systematic study of INV24 is the first of its kind, our findings have the potential to change common practice in this field and they will guide future investigations of inversion processes.

We present steps toward the construction of a quantum-chemical benchmark set for enzymatically catalyzed reactions comprising different-quite sizable-model systems for five reactions. Our work is inspired by a study of semiempirical molecular-orbital theory methods against B3LYP-based structures and energies [ Kromann et al. PeerJ 2016 , 4 , e1994 ]. Taking the same model systems, we herein demonstrate first how adequate treatments of London dispersion and basis-set superposition error lead to structural differences compared to structures obtained at the popular B3LYP/6-31G(d,p) level. The changes observed by us have a significant influence on the final reaction barrier heights (BHs) and energies (REs), which are our main focus herein. We then proceed and carefully investigate different strategies to obtain either exact or estimated complete-basis-set BHs and REs with the help of the DLPNO-CCSD(T) approach, which offers an exciting path into exploring larger biochemically relevant structures at the coupled cluster level. On the basis of our analysis, we present three strategies for obtaining reliable values. While these recommendations constitute our main findings and are meant to be used as useful guidelines for others in the field, we demonstrate their applicability in a preliminary benchmark set comprising 16 BHs and 12 REs on which we assess 35 density functional theory (DFT) approximations. This preliminary benchmark study was used as an indicator for the validity of our approach toward generating such a benchmark set, based on the fact that we were able to reproduce major recommendations in the field of modern DFT, such as the reproduction of the famous Jacob's Ladder scheme, while also pointing out subtle differences to previous benchmark studies. We end our study by critically assessing the still popular choice to gauge the accuracy of low-level methods against B3LYP data, and we show the risks of such a strategy, adding to the ever-growing list of calls to move away from B3LYP as a standard black-box approach.

The development of non-empirical double-hybrid density functionals (DHDFs) is a very active research area with the number of approaches in this field having increased rapidly. At the same time, there is a lack of published work that provides a fair assessment and comparison between non-empirical and semi-empirical DHDFs on an equal footing. Herein, we close this gap and present a thorough analysis of both classes of DHDFs on the large GMTKN55 benchmark database for general main-group thermochemistry, kinetics, and noncovalent interactions [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184–32215]. In total, 115 variations of dispersion-corrected and -uncorrected DHDFs are tested, which will be condensed to an in-depth assessment of 31 methods: 19 non-empirical and 12 semi-empirical DHDFs. As such, our study represents the largest DHDF study ever conducted and can serve as an important benchmark informing method developers and users alike. Our results show that semi-empirical DHDFs are the most robust density functional approximations and more reliable and accurate than non-empirical ones. In fact, some non-empirical approaches are even outperformed by hybrid approaches or even dispersion-corrected and -uncorrected MP2 and SCS-MP2. SOS0-PBE0-2-D3(BJ) is the only exception and the only non-empirical DHDF that we can safely recommend for general applicability. However, it is still outperformed by six semi-empirical DHDFs, of which we would like to particularly recommend the following five: ωB97X-2-D3(BJ), DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), B2NC-PLYP-D3(BJ), and B2GPPLYP-D3(BJ). Our findings seriously question current trends in the field and they highlight that novel strategies have to be found in order to outperform the currently best density functional theory methods on the market. We hope that our study can function as an important cornerstone inspiring such a change of direction in the field.

Herein we report the first photochromic polyoxometalate (POM)-based diarylethene (DAE) coordination complex, prepared by ligation of two cobalt(III)-incorporated borotungstates [BIIIWVI11O39CoIII]6– with the ditopic pyridyl-containing diarylethene (C25H16N2F6S2). The solution-state composition, structure, and stability of the assembly were probed using 1H and 19F nuclear magnetic resonance spectroscopy (NMR), electrospray ionization quadrupolar time-of-flight mass spectrometry (ESI-QTOF-MS), ultraviolet–visible spectroscopy (UV–vis), and small-angle X-ray scattering (SAXS), revealing that the complex self-organizes to adopt a molecular dumbbell structure due to electrostatic and steric considerations. This conformation is a prerequisite for the photocyclization reaction. The assembly was found to be switchable between two states using visible light due to the perturbation of the DAE electronic structure on coordination to the POM. We present photophysical data, including the reaction quantum efficiency of...

Orbital optimization (OO) has been suggested as a way to solve some shortcomings of second-order Moller-Plesset (MP2) variants and double-hybrid density functionals (DHDFs). A closer inspection of the literature, however, shows that the only two studies on OO-DHDFs were limited to three nonempirical PBE-based functionals, which are known to be of only mediocre accuracy. Herein, we provide a more in-depth analysis of OO-DHDFs with the main focus being on main-group thermochemistry, kinetics, and noncovalent interactions. We reanalyze two PBE-based OO-DHDFs and present four new OO-DHDF variants, two of which make use of the spin-component-scaling idea in their nonlocal correlation part. We also provide a more thorough analysis of three OO-MP2 variants. After assessing more than 621 reference points, we come to the conclusion that the benefits of OO are not as straightforward as previously thought. Results heavily depend on the underlying parent method. While OO-SCS/SOS-MP2 usually provide improved results-including for noncovalently bound systems-the opposite is true for OO-MP2. OO-DHDFs, like their nonoptimized counterparts, still require London-dispersion corrections. Among the DHDFs, the largest effect of OO on thermochemical properties is seen for PBE0-2 and the smallest for PBE0-DH. However, results can both worsen and improve with OO. If the latter is the case, the resulting OO-DHDF is still outperformed by the currently most accurate conventional DHDFs, namely DSD-BLYP and DSD-PBEP86. We therefore recommend the OO technique only to be used in specialized cases. For the general method user we re-emphasize using conventional dispersion-corrected DHDFs for robust, reliable results. Our findings also indicate that entirely different strategies seem to be required in order to obtain a substantial improvement over the currently best DHDFs.

© 2015 Taylor & Francis. The recent advent of dispersion-corrected density-functional theory (DFT) methods allows for quantitative modelling of molecular self-assembly processes, and we consider what is required to develop applications to the formation of large self-assembled monolayers (SAMs) on hydrophobic surfaces from organic solution. Focus is on application of the D3 dispersion correction of Grimme combined with the solvent dispersion model of Floris, Tomasi and Pascual-Ahuir to simulate observed scanning-tunnelling microscopy (STM) images of various polymorphs of tetraalkylporphyrin SAMs on highly oriented pyrolytic graphite surfaces. The most significant problem is identified as the need to treat SAM structures that are incommensurate with those of the substrate, providing a challenge to the use of traditional periodic-imaging boundary techniques. Using nearby commensurate lattices introduces non-systematic errors into calculated lattice constants and free energies of SAM formation that are larger than experimental uncertainties and polymorph differences. Developing non-periodic methods for polymorph interface simulation also remains a challenge. Despite these problems, existing methods can be used to interpret STM images and SAM atomic structures, distinguishing between multiple feasible polymorph types. They also provide critical insight into the factors controlling polymorphism. All this stems from a delicate balance that the intermolecular D3 and solvent Floris, Tomasi and Pascual-Ahuir corrections provide. Combined optimised treatments should yield fully quantitative approaches in the future.

In this study, we explore the effect of supplementing the DuT spin-component-scaled double-hybrid density functional method with post-second-order Møller-Plesset-type theory (MP2) correlation terms. We find that the inclusion of additional MP3 correlation energies has almost no effect on the performance. Further addition of correlation effects from MP4 generally leads to a small improvement in the performance. However, we find that the inclusion of the higher-order perturbative correlation effects does not rectify some major shortcomings of DuT for more challenging systems, and the use of MP4, in fact, leads to a significant deterioration in the performance in some cases. We also find that the use of correlation energies from CCSD(T) instead of those from MP3 and MP4 does not lead to a substantial improvement over the MP4-based method, both in general and in some difficult cases that we have examined. An additional observation is that, for large systems that are dominated by noncovalent interactions, DuT and the two MPn-based post-MP2 double-hybrid density functional theory (DFT) procedures all benefit from the inclusion of dispersion corrections. Overall, our investigation suggests that the current generation of MP2-based double-hybrid DFT methods may already be providing close to the optimal performance that can be achieved with the double-hybrid methodology paired with spin-component-scaling. Development of even better double hybrids is an active research field, and we hope that our study provides valuable insights. We recommend the continuing use of existing MP2-based double-hybrid methods as a bridging level between hybrid density functional procedures and high-level wave-function-based procedures.

A new heteroaromatic thiophene containing organoimido functionalized hexamolybdate has been synthesized and characterized in both solid form and solution. Structural analysis shows successful introduction of the organoimido ligand through replacement of one terminal oxo site on [Mo6O19]2− to yield the singly functionalized hexamolybdate. Spectroscopic and theoretical analysis indicates charge transfer between the inorganic and organic components, with a significantly red-shifted lowest lying transition of 399 nm vs. the parent Lindqvist ion of 325 nm. Additional characterization includes, thermal gravimetric analysis (TGA), infrared (IR), cyclic voltammetry (CV), nuclear magnetic resonance (NMR) and time-dependent density functional theory (TD-DFT) studies.

A structural, spectroscopic and computational study of a series of oximes was undertaken to investigate how geometric and structural changes relevant to the reaction coordinate for the Beckmann reaction (normal Beckmann) and Beckmann fragmentation (abnormal Beckmann) manifest in the ground state. X-ray structures of a range of oximes derived from dihydrolevoglucosan (Cyrene™; which undergoes the abnormal Beckmann reaction), in which the oxygen substituent was systematically varied were determined. As the electron demand of the OR group increased, the major structural changes included lengthening of the N-OR bond distance, and a decrease in the magnitude of the C2[double bond, length as m-dash]N-O bond angle, consistent with the changes seen for cyclohexanone oximes, which undergo the normal Beckmann reaction. However, unique to the Cyrene oximes, an increase in the length of the fissile C1-C2 bond was observed, which correlated with a decrease in the 13C-13C 1-bond coupling constants as the electron demand of the OR substituent increased. Computational studies of Cyrene and cyclohexanone oximes using Natural Bond Orbital analysis support an electronic structure involving n(O) → σ*C1-C2 and σC1-C2 → σ*N-O localized orbital interactions.

We report the findings of our experimental and theoretical investigations into the properties of pyridinium enolates and their potential utility in light-harvesting applications, such as in luminescent solar concentrators (LSCs). We present the synthesis, structures, photophysical characterization, and wavefunction-based quantum-chemical studies of five cyclobetaines. The performance of an LSC device incorporating one of these cyclobetaines is shown to be comparable to state-of-the-art devices.