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

Correlated shapeshifting and configurational isomerization

Herein we demonstrate that the rapid 'shapeshifting' constitutional isomerization of a substituted bullvalene is influenced by the E-to-Z configurational isomerization of a remote carbamate group, giving rise to correlated motion. We find that, while the E-configurational isomer of a bulky carbamate favors the β-bullvalene constitutional isomer, a noncovalent bonding interaction within the Z-carbamate tips the equilibrium toward the γ-bullvalene form. Using DFT modelling and NMR spectroscopy, this long-range interaction is identified as being between the bullvalene core and a pendant phenyl group connected to the carbamate. Coupling the constitutional changes of a bullvalene to a reciprocal configurational isomerization through a long-range interaction in this way will allow shapeshifting rearrangements to be exploited as part of collective motion in extended structures.

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.

Employing neural density functionals to generate potential energy surfaces

CONTEXT

With the union of machine learning (ML) and quantum chemistry, amid the debate between machine-learned functionals and human-designed functionals in density functional theory (DFT), this paper aims to demonstrate the generation of potential energy surfaces using computations with machine-learned density functional approximation (ML-DFA). A recent research trend is the application of ML in quantum sciences in the design of density functionals such as DeepMind's Deep Learning model (DeepMind21, DM21). Though science reported the state-of-the-art performance of DM21, the opportunity to utilize DeepMind's pretrained DM21 neural networks in computations in quantum chemistry has not yet been tapped. So far in the literature, the Deep Learning density functionals (DM21) have not been applied to generate potential energy surfaces. While the superior accuracy of DM21 has been reported, there is still a scarcity of publications that apply DM21 in calculations in the field. In this context, for the first time in literature, neural density functionals inferring 2D potential energy surfaces (ML-DFA-PES) based on machine-learned DFA-based computational method is contributed in this paper. This paper reports the ML-DFA-generated PES for C4H8, H2O, H2, and H2+ by employing a pretrained DM21m TensorFlow model with cc-pVDZ basis set. In addition, we also analyze the long-range behavior of DM21 based PES to investigate the ability to describe a system at long ranges. Furthermore, we compare PES diagrams from DM21 with popular DFT functionals (b3lyp/ PW6B95) and CCSD(T).

METHODS

In this method, 2D potential energy surfaces are obtained using a method that relies upon the neural network's ability to accurately learn the mapping between 3D electron density and exchange-correlation potential. By inserting Deep Learning inference in DFT with a pretrained neural network, self-consistent field (SCF) energy at different geometries along the coordinates of interest is computed, and then, potential energy surfaces are plotted. In this method, first, the electron density is computed mathematically, and this computed 3D electron density is used as a ML feature vector to predict the exchange correlation potential as a ML inference computed by a forward pass of pre-trained DM21 TensorFlow computational graph, followed by the computation of self-consistent field energy at multiple geometries, and then, SCF energies at different bond lengths/angles are plotted as 2D PES. We implement this in a python source code using frameworks such as PySCF and DM21. This paper contributes this implementation in open source. The source code and DM21-DFA-based PES are contributed at https://sites.google.com/view/MLfunctionals-DeepMind-PES .

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.

Correlated proton dynamics in hydrogen bonding networks: the benchmark case of 3-hydroxyglutaric acid

Proton and hydrogen-bonded networks sustain a broad range of structural and charge transfer processes in supramolecular materials. The modelling of proton dynamics is however challenging and demands insights from prototypical benchmark systems. The intramolecular H-bonding networks induced by either protonation or deprotonation of 3-hydroxyglutaric acid provide intriguing case studies of correlated proton dynamics. The vibrational signatures associated with the fluxional proton bonding and its coupling with the hydroxyglutaric backbone are investigated here with infrared action ion spectroscopy experiments and Born-Oppenheimer molecular dynamics (BOMD) computations. Despite the formally similar symmetry of protonated and deprotonated hydroxyglutaric acid, the relative proton affinities of the oxygen centers of the carboxylic and carboxylate groups with respect to that of the central hydroxyl group lead to distinct proton dynamics. In the protonated acid, a tautomeric arrangement of the type HOCO·[HOH]+·OCOH is preferred with the proton binding tighter to the central hydroxyl moiety and the electronic density being shared between the two nearly symmetric H-bonds with the carboxylic end groups. In the deprotonated acid, the asymmetric [OCO]-·HO·HOCO configuration is more stable, with a stronger H-bonding on the bare carboxylate end. Both systems display active backbone dynamics and concerted Grothuss-like proton motions, leading to diffuse band structures in their vibrational spectra. These features are accurately reproduced by the BOMD computations.

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.

Assessment of the nonempirical r2SCAN-QIDH double-hybrid density functional against large and diverse datasets

We update the Quadratic Integrand Double-Hybrid (QIDH) model [J. Chem. Phys. 141, 031101 (2014)] by incorporating the nonempirical restored-regularized Strongly Constrained and Appropriately Normed (r2SCAN) meta-generalized gradient approximation exchange-correlation functional, thus devising a robust density functional approximation free of any empirical parameter and incorporating all the constraints so far known for the exchange-correlation kernel. We assessed the new r2SCAN-QIDH expression on the GMTKN55 database and further extend its application to various types of non-covalent interactions (e.g., S66 × 8, O24 × 5). The assessment done shows that the model becomes very competitive in accuracy with respect to parent exchange-correlation functionals of any type, but without relying on any fitted parameter or numerical training.

Koopmans' Theorem-Compliant Long-Range Corrected (KTLC) Density Functional Mediated by Black-Box Optimization and Data-Driven Prediction for Organic Molecules

Density functional theory (DFT) is a significant computational tool that has substantially influenced chemistry, physics, and materials science. DFT necessitates parametrized approximation for determining an expected value. Hence, to predict the properties of a given molecule using DFT, appropriate parameters of the functional should be set for each molecule. Herein, we optimize the parameters of range-separated functionals (LC-BLYP and CAM-B3LYP) via Bayesian optimization (BO) to satisfy Koopmans' theorem. Our results demonstrate the effectiveness of the BO in optimizing functional parameters. Particularly, Koopmans' theorem-compliant LC-BLYP (KTLC-BLYP) shows results comparable to the experimental UV-absorption values. Furthermore, we prepared an optimized parameter dataset of KTLC-BLYP for over 3000 molecules through BO for satisfying Koopmans' theorem. We have developed a machine learning model on this dataset to predict the parameters of the LC-BLYP functional for a given molecule. The prediction model automatically predicts the appropriate parameters for a given molecule and calculates the corresponding values. The approach in this paper would be useful to develop new functionals and to update the previously developed functionals.

Assessment of DFT functionals for a minimal nitrogenase [Fe(SH)4H]- model employing state-of-the-art ab initio methods

We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (∆E) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ∆E estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree-Fock included (0%-54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ∆E is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn-Sham orbitals gives results within 4-11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ∼5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.

Molecular Understanding and Practical In Silico Catalyst Design in Computational Organocatalysis and Phase Transfer Catalysis-Challenges and Opportunities

Through the lens of organocatalysis and phase transfer catalysis, we will examine the key components to calculate or predict catalysis-performance metrics, such as turnover frequency and measurement of stereoselectivity, via computational chemistry. The state-of-the-art tools available to calculate potential energy and, consequently, free energy, together with their caveats, will be discussed via examples from the literature. Through various examples from organocatalysis and phase transfer catalysis, we will highlight the challenges related to the mechanism, transition state theory, and solvation involved in translating calculated barriers to the turnover frequency or a metric of stereoselectivity. Examples in the literature that validated their theoretical models will be showcased. Lastly, the relevance and opportunity afforded by machine learning will be discussed.

Understanding the Role of Intramolecular Ion-Pair Interactions in Conformational Stability Using an Ab Initio Thermodynamic Cycle

Intramolecular ion-pair interactions yield shape and functionality to many molecules. With proper orientation, these interactions overcome steric factors and are responsible for the compact structures of several peptides. In this study, we present a thermodynamic cycle based on isoelectronic and alchemical mutation to estimate the intramolecular ion-pair interaction energy. We determine these energies for 26 benchmark molecules with common ion-pair combinations and compare them with results obtained using intramolecular symmetry-adapted perturbation theory. For systems with long linkers, the ion-pair energies evaluated using both approaches deviate by less than 2.5% in the vacuum phase. The thermodynamic cycle based on density functional theory facilitates calculations of salt-bridge interactions in model tripeptides with continuum/microsolvation modeling and four large peptides: 1EJG (crambin), 1BDK (bradykinin), 1L2Y (a mini-protein with a tryptophan cage), and 1SCO (a toxin from the scorpion venom).

A comprehensive benchmark investigation of quantum chemical methods for carbocations

The application of various density functional approximations (DFAs) and an emphasis on popular methods without any consensus have prevailed in computational studies dedicated to carbocations. More importantly, an extensive and rigorous benchmark investigation on density functionals for the class is still lacking. To close this gap, we present a comprehensive benchmark study of quantum chemical methods on a series of classical and nonclassical carbocations, the CARBO33 dataset. We evaluate a total of 107 DFT methods from all rungs giving particular attention to double hybrid density functionals as the potential of the class has been largely undermined in the context of carbocations. To support our findings, DLPNO-CCSD(T) at the complete basis set (CBS) limit and W1-F12 are used as reference methods. Our results indicate that the composite CBS-QB3 method performs poorly and should not be adopted for target energies. Oftentimes, the tested DFAs of a lower rung perform better than several DFAs in a higher rung of Perdew's "Jacob's ladder". Nonetheless, double hybrids DSD-PBEP86-NL and ωB97X-2-D3(BJ) stand out by showing the overall best performance. Among the hybrids evaluated, about half of them show mean absolute deviation (MAD) below 1.1 kcal mol^-1, including the popular hybrids M06-2X and mPW1PW91. In this family, MN15-D3(BJ) performs particularly well (MAD = 0.77 kcal mol^-1) displaying reliable results across various tests. Highly popular B3LYP exhibited one of the worst performances (MAD = 4.74 kcal mol^-1), and we do not recommend its application to carbocations. We also assess the 24 general-purpose basis sets of single- up to quadruple-ζ quality. The best compromise between accuracy and computational cost is achieved with cc-pVTZ followed by def2-TZVP. Computations on larger structures of general interest, including terpene carbocations, are also presented for selected DFT methods confirming general trends in the results.

Building on the strengths of a double-hybrid density functional for excitation energies and inverted singlet-triplet energy gaps

It is demonstrated that a double hybrid density functional approximation, ωB88PTPSS, that incorporates equipartition of density functional theory and the non-local correlation, however with a meta-generalized gradient approximation correlation functional, as well as with the range-separated exchange of ωB2PLYP, provides accurate excitation energies for conventional systems, as well as correct prescription of negative singlet-triplet gaps for non-conventional systems with inverted gaps, without any necessity for parametric scaling of the same-spin and opposite-spin non-local correlation energies. Examined over "safe" excitations of the QUESTDB set, ωB88PTPSS performs quite well for open-shell systems, correctly and fairly accurately [relative to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) reference] predicts negative gaps for 50 systems with inverted singlet-triplet gaps, and is one of the leading performers for intramolecular charge-transfer excitations and achieves near-second-order approximate coupled cluster (CC2) and second-order algebraic diagrammatic construction quality for the Q1 and Q2 subsets. Subsequently, we tested ωB88PTPSS on two sets of real-life examples from recent computational chemistry literature-the low energy bands of chlorophyll a (Chl a) and a set of thermally activated delayed fluorescence (TADF) systems. For Chl a, ωB88PTPSS qualitatively and quantitatively achieves DLPNO-STEOM-CCSD-level performance and provides excellent agreement with experiment. For TADF systems, ωB88PTPSS agrees quite well with spin-component-scaled CC2 (SCS-CC2) excitation energies, as well as experimental values, for the gaps between the S₁ and T₁ excited states.

Explicitly Correlated Double-Hybrid DFT: A Comprehensive Analysis of the Basis Set Convergence on the GMTKN55 Database

Double-hybrid density functional theory (DHDFT) offers a pathway to accuracy approaching composite wavefunction approaches such as G4 theory. However, the Görling-Levy second-order perturbation theory (GLPT2) term causes them to partially inherit the slow ∝L-3 (with L the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied by introducing F12 explicit correlation: we investigate the basis set convergence of both DHDFT and DHDFT-F12 (where GLPT2 is replaced by GLPT2-F12) for the large and chemically diverse general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 DHDFs are investigated as test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12 basis sets as large as cc-pVQZ-F12. We show that F12 greatly accelerates basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12 basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPPD in orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z. Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set convergence in both the development and applications of double-hybrid functionals. Mass storage and I/O bottlenecks for larger systems can be circumvented by localized pair natural orbital approximations, which also exhibit much gentler system size scaling.

Stacking Is Favored over Hydrogen Bonding in Azaphenanthrene Dimers

N-Doped polycyclic aromatic hydrocarbons have recently emerged as potential organic electronic materials. The function of such materials is determined not only by the intrinsic electronic properties of individual molecules but also by their supramolecular interactions in the solid state. Therefore, a proper characterization of the interactions between the individual units is of interest to materials science since they ultimately govern properties such as excitons and charge transfer. Here, we report a joint experimental and computational study of two azaphenanthrene dimers to determine the structure and the nature of supramolecular interactions in the aggregates. IR/UV double-resonance experiments were carried out using far- and mid-infrared free-electron laser radiation. The experimental spectra are compared with quantum chemical calculations for the lowest-energy π-stacked and hydrogen-bonded structures. The data reveal a preference of the π-stacked structure for the benzo[f]quinoline and the phenanthridine dimer.

Benefits of Range-Separated Hybrid and Double-Hybrid Functionals for a Large and Diverse Data Set of Reaction Energies and Barrier Heights

To better understand the thermochemical kinetics and mechanism of a specific chemical reaction, an accurate estimation of barrier heights (forward and reverse) and reaction energies is vital. Because of the large size of reactants and transition state structures involved in real-life mechanistic studies (e.g., enzymatically catalyzed reactions), density functional theory remains the workhorse for such calculations. In this paper, we have assessed the performance of 91 density functionals for modeling the reaction energies and barrier heights on a large and chemically diverse data set (BH9) composed of 449 organic chemistry reactions. We have shown that range-separated hybrid functionals perform better than the global hybrids for BH9 barrier heights and reaction energies. Except for the PBE-based range-separated nonempirical double hybrids, range separation of the exchange term helps improve the performance for barrier heights and reaction energies. The 16-parameter Berkeley double hybrid, ωB97M(2), performs remarkably well for both properties. However, our minimally empirical range-separated double hybrid functionals offer marginally better accuracy than ωB97M(2) for BH9 barrier heights and reaction energies.

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.

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.

Tackling an accurate description of molecular reactivity with double-hybrid density functionals

In this Communication, we assess a panel of 18 double-hybrid density functionals for the modeling of the thermochemical and kinetic properties of an extended dataset of 449 organic chemistry reactions belonging to the BH9 database. We show that most of DHs provide a statistically robust performance to model barrier height and reaction energies in reaching the “chemical accuracy.” In particular, we show that nonempirical DHs, such as PBE0-DH and PBE-QIDH, or minimally parameterized alternatives, such as ωB2PLYP and B2K-PLYP, succeed to accurately model both properties in a balanced fashion. We demonstrate, however, that parameterized approaches, such as ωB97X-2 or DSD-like DHs, are more biased to only one of both properties.

Stability of the polyynic form of C18, C22, C26, and C30 nanorings: a challenge tackled by range-separated double-hybrid density functionals

We calculate the relative energy between the cumulene and polyyne structures of a set of C_4k+2 (k = 4-7) rings (C₁₈, C₂₂, C₂₆, and C₃₀ prompted by the recent synthesis of the cyclo[18]carbon (or simply C₁₈) compounds. Reference results were obtained by a costly Quantum Monte-Carlo (QMC) approach, providing thus very accurate values allowing to systematically compare the performance of a variety of wavefunction methods [(i.e., MP2, SCS-MP2, SOS-MP2, DLPNO-CCSD, and DLPNO-CCSD(T)] as well as DFT approaches, applying for the latter a diversity of density functionals covering global and range-separated hybrid and double-hybrid models. The influence of the use of a range-separation scheme for density functionals, for both hybrid and double-hybrid expressions, is discussed according to its key role. Overall, range-separated double-hybrid functionals (e.g., RSX-QIDH) behave very accurately and provide competitive results compared with DLPNO-CCSD(T), at a more reasonable computational cost.

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.

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.

Assessing the Applicability of the Geometric Counterpoise Correction in B2PLYP/Double-ζ Calculations for Thermochemistry, Kinetics, and Noncovalent Interactions

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.