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.

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.

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.

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.

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.

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.

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.

Assessing the Tamm-Dancoff approximation, singlet-singlet, and singlet-triplet excitations with the latest long-range corrected double-hybrid density functionals.

We continue our work on the long-range corrected double-hybrid density functionals (LC-DHDFs) ωB2PLYP and ωB2GP-PLYP that we developed in the context of time-dependent (TD) Density Functional Theory (DFT) to enable the robust description of singlet-singlet excitations [M. Casanova-Páez, M. B. Dardis, and L. Goerigk, J. Chem. Theory Comput. 15, 4735 (2019)]. In our initial study, we only assessed the impact of a 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, ωB2PLYP and ωB2GP-PLYP as well as the global DHDF PBE-QIDH can be recommended. If a transition exhibits charge-transfer character, ωB2PLYP and ωB2GP-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 ωB2PLYP and ωB2GP-PLYP as some of the currently best TDA-DFT methods.

Toward a Quantum-Chemical Benchmark Set for Enzymatically Catalyzed Reactions: Important Steps and Insights.

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.

Visible-Light-Driven "On"/"Off" Photochromism of a Polyoxometalate Diarylethene Coordination Complex.

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 the molecular switch in both directions measured using a custom-built quantum yield determination setup in addition to fatigue resistance on prolonged irradiation.

Semi-empirical or non-empirical double-hybrid density functionals: which are more robust?

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.

A Comprehensive Assessment of the Effectiveness of Orbital Optimization in Double-Hybrid Density Functionals in the Treatment of Thermochemistry, Kinetics, and Noncovalent Interactions.

Orbital optimization (OO) has been suggested as a way to solve some shortcomings of second-order Møller-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.

A priori calculations of the free energy of formation from solution of polymorphic self-assembled monolayers.

Modern quantum chemical electronic structure methods typically applied to localized chemical bonding are developed to predict atomic structures and free energies for meso-tetraalkylporphyrin self-assembled monolayer (SAM) polymorph formation from organic solution on highly ordered pyrolytic graphite surfaces. Large polymorph-dependent dispersion-induced substrate-molecule interactions (e.g., -100 kcal mol(-1) to -150 kcal mol(-1) for tetratrisdecylporphyrin) are found to drive SAM formation, opposed nearly completely by large polymorph-dependent dispersion-induced solvent interactions (70-110 kcal mol(-1)) and entropy effects (25-40 kcal mol(-1) at 298 K) favoring dissolution. Dielectric continuum models of the solvent are used, facilitating consideration of many possible SAM polymorphs, along with quantum mechanical/molecular mechanical and dispersion-corrected density functional theory calculations. These predict and interpret newly measured and existing high-resolution scanning tunnelling microscopy images of SAM structure, rationalizing polymorph formation conditions. A wide range of molecular condensed matter properties at room temperature now appear suitable for prediction and analysis using electronic structure calculations.

Structure-reactivity correlations of the abnormal Beckmann reaction of dihydrolevoglucosenone oxime.

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.

A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions.

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.

Highly Fluorescent Pyridinium Betaines for Light Harvesting.

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.

Non-Aqueous Microwave-Assisted Syntheses of Deca- and Hexa-Molybdovanadates.

We report a new approach for the synthesis of heterohexa- and heterodecametalates via the use of non-aqueous, microwave-assisted reaction conditions. The two novel molybdovanadates have been isolated and characterized in the solid and solution states using single-crystal X-ray diffraction, FT-IR, UV/Vis, multinuclear NMR spectroscopy, and ESI-MS. The relative stabilities of the possible structural isomers were probed using dispersion-corrected DFT calculations for both polyoxometalate systems.