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

Ultrafast photochemistry and electron diffraction for cyclobutanone in the S2 state: Surface hopping with time-dependent density functional theory

We simulate the photodynamics of gas-phase cyclobutanone excited to the S2 state using fewest switches surface hopping (FSSH) dynamics powered by time-dependent density functional theory (TDDFT). We predict a total photoproduct yield of 8%, with a C3:C2 product ratio of 0 trajectories to 8 trajectories. One primary S2 → S1 conical intersection is identified involving the compression of an α-carbon-carbon-hydrogen bond angle. Excited state lifetimes computed with respect to electronic state populations were found to be 3.96 ps (S2 → S1) and 498 fs (S1 → S0). We also generate time-resolved difference pair distribution functions (ΔPDFs) from our TDDFT-FSSH dynamics results in order to generate direct comparisons with ultrafast electron diffraction experiment observables. Global and target analysis of time-resolved ΔPDFs produced a distinct set of lifetimes: (i) a 0.548 ps decay and (ii) a 1.69 ps decay, both resembling the S2 minimum, as well as (iii) a long decay that resembles the S1 minimum geometry and the fully separated C2 products. Finally, we contextualize our results by considering the impact of the most likely sources of significant errors.

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.

Monitoring Density Redistribution at the Excited State in a Dual Emitting Molecule: An Analysis Based on Real-Time Density Functional Theory and Density Descriptors

In this work, we computed and analyzed, by means of density-based descriptors, the real-time evolution of both the locally excited (LE) and charge-transfer (CT) excited states for the planar and twisted conformations of the DMABN (4-(N,N-dimethylamino)benzonitrile) molecule using real-time time-dependent density functional theory (DFT) and three different exchange-correlation energy functionals (EXC) belonging to the same family (the PBE one). Our results based on the analysis of density-based descriptors show that the underlying EXC modifies the evolution in time of the density. In particular, comparing the frequency of density reorganization computed with the three functionals (PBE, PBE0, and LC-PBE), we found that the frequency of electronic interconversion of the individual determinants involved during the dynamics increases from PBE to PBE0 and to LC-PBE. This allows us to show that there is a correlation between the delocalization of the electronic density and the frequency of reorganization. In particular, the greater the mean hole-electron distance during the dynamics, the lower is the frequency of density reorganization.

Artificial design of organic emitters via a genetic algorithm enhanced by a deep neural network

The design of molecules requires multi-objective optimizations in high-dimensional chemical space with often conflicting target properties. To navigate this space, classical workflows rely on the domain knowledge and creativity of human experts, which can be the bottleneck in high-throughput approaches. Herein, we present an artificial molecular design workflow relying on a genetic algorithm and a deep neural network to find a new family of organic emitters with inverted singlet-triplet gaps and appreciable fluorescence rates. We combine high-throughput virtual screening and inverse design infused with domain knowledge and artificial intelligence to accelerate molecular generation significantly. This enabled us to explore more than 800 000 potential emitter molecules and find more than 10 000 candidates estimated to have inverted singlet-triplet gaps (INVEST) and appreciable fluorescence rates, many of which likely emit blue light. This class of molecules has the potential to realize a new generation of organic light-emitting diodes.

Toward Accurate Two-Photon Absorption Spectrum Simulations: Exploring the Landscape beyond the Generalized Gradient Approximation

In this Letter, we present a pioneering analysis of the density functional approximations (DFAs) beyond the generalized gradient approximation (GGA) for predicting two-photon absorption (2PA) strengths of a set of push-pull π-conjugated molecules. In more detail, we have employed a variety of meta-generalized gradient approximation (meta-GGA) functionals, including SCAN, MN15, and M06-2X, to assess their accuracy in describing the 2PA properties of a chosen set of 48 organic molecules. Analytic quadratic response theory is employed for these functionals, and their performance is compared against the previously studied DFAs and reference data obtained at the coupled-cluster CC2 level combined with the resolution-of-identity approximation (RI-CC2). A detailed analysis of the meta-GGA functional performance is provided, demonstrating that they improve upon their predecessors in capturing the key electronic features of the π-conjugated two-photon absorbers. In particular, the Minnesota functional MN15 shows very promising results as it delivers pleasingly accurate chemical rankings for two-photon transition strengths and excited-state dipole moments.

Contrasting the excited state properties of different conformers of trans- and cis-2,2'-bipyridine oligomers in the gas phase

In this article, we present conformation-dependent photophysical and excited state properties of trans- and cis- BPY oligomers. Oligomers up to tetramers for three conformers, namely, o-, m-, and p-, are constructed and optimized at the B3LYP-D3/def2-SVPD level. The photophysical and excited state properties are interpreted in terms of UV and CD spectra at the RI-ADC(2)/def2-TZVPD level. The UV spectra of oligomers of the m-conformer show high-intensity and red-shifted UV bands compared to o- and p-oligomers. The CD spectra of p-oligomers show intense CD bands compared to o- and p-oligomers in the case of trans-structures. In contrast, oligomers of each conformer of cis-structures show high-intensity CD bands. The excited states of (BPY)2 and (BPY)4 are also characterized by analysis of one-electron transition density matrix considering three descriptors: ωCT, dexc, and PRNTO. The ωCT values of dimers are in the range of 0.06-0.32, which indicates the excited states are mainly LE states, whereas, for (BPY)4, the ωCT values range from 0.17 to 0.53, indicating the possibility of partial CT in the excited states. These observations are also explained using the NTOs and e-h correlation plots.

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.

Inverted Lowest Singlet and Triplet Excitation Energy Ordering of Graphitic Carbon Nitride Flakes

In organic light-emitting diodes (OLEDs), only 25% of electrically generated excitons are in a singlet state, S1, and the remaining 75% are in a triplet state, T1. In thermally activated delayed fluorescence (TADF) chromophores the transition from the nonradiative T1 state to the radiative S1 state can be thermally activated, which improves the efficiency of OLEDs. Chromophores with inverted energy ordering of S1 and T1 states, S1 < T1, are superior to TADF chromophores, thanks to the absence of an energy barrier for the transition from T1 to S1. We benchmark the performance of time-dependent density functional theory using different exchange-correlation functionals and find that scaled long-range corrected double-hybrid functionals correctly predict the inverted singlet-triplet gaps of N-substituted phenalene derivatives. We then show that the inverted energy ordering of S1 and T1 is an intrinsic property of graphitic carbon nitride flakes. A design strategy of new chromophores with inverted singlet-triplet gaps is proposed. The color of emitted light can be fine-tuned through flake size and amine substitution on flake vertices.

Reference Vertical Excitation Energies for Transition Metal Compounds

To enrich and enhance the diversity of the quest database of highly accurate excitation energies [Véril, M.; et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], we report vertical transition energies in transition metal compounds. Eleven diatomic molecules with a singlet or doublet ground state containing a fourth-row transition metal (CuCl, CuF, CuH, ScF, ScH, ScO, ScS, TiN, ZnH, ZnO, and ZnS) are considered, and the corresponding excitation energies are computed using high-level coupled-cluster (CC) methods, namely, CC3, CCSDT, CC4, and CCSDTQ, as well as multiconfigurational methods such as CASPT2 and NEVPT2. In many cases, to provide more comprehensive benchmark data, we also provide full configuration interaction estimates computed with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. Based on these calculations, theoretical best estimates of the transition energies are established in both the aug-cc-pVDZ and aug-cc-pVTZ basis sets. This allows us to accurately assess the performance of the CC and multiconfigurational methods for this specific set of challenging transitions. Furthermore, comparisons with experimental data and previous theoretical results are also reported.

Pitfall in simulations of vibronic TD-DFT spectra: diagnosis and assessment

In this Communication, we study the effect of spurious oscillations in the profiles of energy derivatives with respect to nuclear coordinates calculated with density functional approximations (DFAs) for formaldehyde, pyridine, and furan in their ground and electronic excited states. These spurious oscillations, which can only be removed using extensive integration grids that increase enormously the CPU cost of DFA calculations, are significant in the case of third- and fourth-order energy derivatives of the ground and excited states computed by M06-2X and ωB97X functionals. The errors in question propagate to anharmonic vibronic spectra computed under the Franck-Condon approximation, i.e., positions and intensities of vibronic transitions are affected to a large extent (shifts as significant as hundreds of cm-1 were observed). On the other hand, the LC-BLYP and CAM-B3LYP functionals show a much less pronounced effect due to spurious oscillations. Based on the results presented herein, we recommend either LC-BLYP or CAM-B3LYP with integration grids (250, 974) (or larger) for numerically stable simulations of vibronic spectra including anharmonic effects.

Theoretical Insights into a Near-Infrared Fluorescent Probe NI-VIS Based on the Organic Molecule for Monitoring Intracellular Viscosity

So many biological functional disorders and diseases, such as atherosclerosis, hypertension, diabetes, Alzheimer's disease, as well as cell malignancy are closely related with the intracellular viscosity. A safe and effective intracellular viscosity detecting method is desired by the biomedical community. Recently, a novel near-infrared fluorescent probe NI-VIS with a twisting intramolecular charge transfer mechanism was developed. The capability of this probe to visualize the viscosity variation in cirrhotic liver tissues and map the micro viscosity in vivo were testified using an experiment. In this work, the twisting intramolecular charge transfer mechanism and fluorescent properties of the probe NI-VIS were studied in detail under quantum mechanical method. The low energy barrier among the different conformations of the probe indicated the occurrence of twisting intramolecular charge transfer due to the rotation of the aryl group in the probe molecule while within the low viscosity environment. The electronic structure analysis on different probe conformations revealed the electron transfer process of the probe under optical excitation. All these theoretical results could provide insights into understand in greater depth the principles and build highly effective fluorescent probe to monitor the viscosity in biological samples.

Theoretical investigation on FRET strategy of ratio metric fluorescent probe sensing hydrogen sulfide

The level of hydrogen sulfide (H₂S) in human body is related to many diseases, such as Alzheimer's disease, Down syndrome, etc. Therefore, the detection of H₂S level in biological systems is very important and has attracted great attention from scientific and clinical researchers. Understanding the design and working mechanism of fluorescent probes for H₂S level detection is important for building new highly efficient fluorescent probe. The mechanisms of a recently reported efficient small molecule fluorescent probe based on the Fluorescence Resonance Energy Transfer (FRET) were investigated thoroughly in this work. The theoretical results would provide the insights for designing new efficient and multi-functional fluorescent probe applicable in the biological systems.

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.

Excitation energies of polycylic aromatic hydrocarbons by double-hybrid functionals: Assessing the PBE0-DH and PBE-QIDH models and their range-separated versions

A family of non-empirical double-hybrid (DH) density functionals, such as Perdew-Burke-Ernzerhof (PBE)0-DH, PBE-QIDH, and their range-separated exchange (RSX) versions RSX-0DH and RSX-QIDH, all using Perdew-Burke-Ernzerhof(PBE) exchange and correlationfunctionals, is applied here to calculate the excitation energies for increasingly longer linear and cyclic acenes as part of their intense benchmarking for excited states of all types. The energies for the two lowest-lying singlet ¹L_a and ¹L_b states of linear oligoacenes as well as the triplet ³L_a and ³L_b states, are calculated and compared with experimental results. These functionals clearly outperform the results obtained from hybrid functionals and favorably compare with other double-hybrid expressions also tested here, such as B2-PLYP, B2GP-PLYP, ωB2-PLYP, and ωB2GP-PLYP. The study is complemented by the computation of adiabatic S₀-T₁ singlet-triplet energy difference for linear acenes as well as the extension of the study to strained cyclic oligomers, showing how the family of non-empirical expressions robustly leads to competitive 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.

Thiophene and diaminobenzo- (1,2,5-thiadiazol)- based DAD-type near-infrared fluorescent probe for nitric oxide: A theoretical research

A near-infrared fluorescent probe (LS-NO) for the real-time detection of nitric oxide (NO) in inflammatory bowel disease (IBD) was developed recently. The probe used oligoglycol morpholine-functionalized thiophene as strong electron donors and diaminobenzene (1,2,5-thiadiazole) as a weak electron acceptor and NO trapping group. It could detect exogenous and endogenous NO in the lysosomes of living cells with high sensitivity and specificity. To further understand the fluorescent mechanism and character of the probes LS-NO and LS-TZ (after the reaction of the probe LS-NO with NO), the electron transfer in the excitation and emitting process within the model molecules DAD-NO and DAD-TZ was analyzed in detail under the density functional theory. The calculation results indicated the transformation from diaminobenzene (1,2,5-thiadiazole) as a weak electron acceptor to triazolo-benzo-(1,2,5-thiadiazole) as a strong electron acceptor made LS-NO an effective "off-on" near-infrared NO fluorescent probe.

Role of Exact Exchange in Difference Projected Double-Hybrid Density Functional Theory for Treatment of Local, Charge Transfer, and Rydberg Excitations

Difference approaches to the study of excited states have undergone a renaissance in recent years, with the development of a plethora of algorithms for locating self-consistent field approximations to excited states. Density functional theory is likely to offer the best balance of cost and accuracy for difference approaches, and yet there has been little investigation of how the parametrization of density functional approximations affects performance. In this work, we aim to explore the role of the global Hartree-Fock exchange parameter in tuning accuracy of different excitation types within the framework of the recently introduced difference projected double-hybrid density functional theory approach and contrast the performance with conventional time-dependent double-hybrid density functional theory. Difference projected double-hybrid density functional theory was demonstrated to give vertical excitation energies with average error and standard deviation with respect to multireference perturbation theory comparable to more expensive linear-response coupled cluster approaches ( J. Chem. Phys.2020, 153, 074103). However, despite benchmarking of local excitations, there has been no investigation of the methods performance for charge transfer or Rydberg excitations. In this work we report a new benchmark of charge transfer, Rydberg, and local excited state vertical excitation energies and examine how the exact Hartree-Fock exchange affects the benchmark performance to provide a deeper understanding of how projection and nonlocal correlation balance differing sources of error in the ground and excited states.

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.

Following the density evolution using real time density functional theory and density based indexes: Application to model push-pull molecules

Considering as test case a family of organic rod like push-pull molecules, we derived and applied density based index enabling the description and diagnostic of the electronic density evolution in real time-time dependent density functional theory (RT-TDDFT) simulations. In particular, both the charge transfer (CT) distance and a diagnostic index, the D_CT and M_AC ^RT respectively, were computed on the fly from the density distribution obtained at a given time and the reference ground state density and their mean values were compared with what obtained at Linear Response-TDDFT level. Besides giving a way of analyzing the density redistribution occurring in time, these tools allowed to show how RT-TDDFT, which is definitely a powerful method to model the evolution of the density in CT or charge separation processes, can be affected by the same artifacts known for LR-TDDFT approaches and, particularly, to those related to the use of approximate exchange correlation functionals. The analysis here performed allowed to identify and discard on fly the electronic configurations corresponding to spurious situations.

Can domain-based local pair natural orbitals approaches accurately predict phosphorescence energies?

Since the discovery of the peculiar conducting and optical properties of aromatics, many efforts have been made to characterize and predict their phosphorescence. This physical process is exploited in modern Organic Emitting Light Diodes (OLEDs), and it is also one of the processes decreasing the efficiency of Dye-sensitized solar cells (DSSCs). Herein, we propose a computational strategy for the accurate calculation of singlet-triplet gaps of aromatic compounds, which provides results that are in excellent agreement with available experimental data. Our approach relies on the domain-based local pair natural orbital (DLPNO) variant of the "gold standard" CCSD(T) method. The convergence of our results with respect to the key technical parameters of the calculation, such as the basis set used, the approximations employed in the perturbative triples correction, and the dimension of the PNOs space, was thoroughly discussed.

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.

Revisiting the Performance of Time-Dependent Density Functional Theory for Electronic Excitations: Assessment of 43 Popular and Recently Developed Functionals from Rungs One to Four

In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approximation offers a good balance between computational efficiency and accuracy. The functionals ωB97X-D and BMK are found to offer the best performance overall with a root-mean square error (RMSE) of around 0.27 eV, better than the computationally more demanding CIS(D) wave function method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for time-dependent density functional theory excitation energies, though hybrid meta generalized-gradient approximations (meta-GGAs) are not generally better than hybrid GGAs. Effects of basis set convergence, gauge invariance correction to meta-GGAs, and nonlocal correlation (VV10) are also studied, and practical basis set recommendations are provided.

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

Excimers are supramolecular systems whose binding strength is influenced by many factors that are ongoing challenges for computational methods, such as charge transfer, exciton coupling, and London dispersion interactions. Treating the various intricacies of excimer binding at an adequate level is expected to be particularly challenging for Time-Dependent Density Functional Theory (TD-DFT) methods. In addition to well-known limitations for some TD-DFT methods in the description of charge transfer or exciton coupling, the inherent London dispersion problem from ground-state DFT translates to TD-DFT. While techniques to appropriately treat dispersion in DFT are well-developed for electronic ground states, these dispersion corrections remain largely untested for excited states. Herein, we aim to shed light on current TD-DFT methods, including some of the newest developments. The binding of four model excimers is studied across nine density functionals with and without the application of additive dispersion corrections against a wave function reference of SCS-CC2/CBS(3,4) quality, which approximates select CCSDR(3)/CBS data adequately. To our knowledge, this is the first study that presents single-reference wave function dissociation curves at the complete basis set level for the assessed model systems. It is also the first time range-separated double-hybrid density functionals are applied to excimers. In fact, those functionals turn out to be the most promising for the description of excimer binding followed by global double hybrids. Range-separated and global hybrids-particularly with large fractions of Fock exchange-are outperformed by double hybrids and yield worse dissociation energies and inter-molecular equilibrium distances. The deviation between each assessed functional and reference increases with system size, most likely due to missing dispersion interactions. Additive dispersion corrections of the DFT-D3(BJ) and DFT-D4 types reduce the average errors for TD-DFT methods but do so inconsistently and therefore do not offer a black-box solution in their ground-state parametrised form. The lack of appropriate description of dispersion effects for TD-DFT methods is likely hindering the practical application of the herein identified more efficient methods. Dispersion corrections parametrised for excited states appear to be an important next step to improve the applicability of TD-DFT methods and we hope that our work assists with the future development of such corrections.

Do Double-Hybrid Functionals Benefit from Regularization in the PT2 Term? Observations from an Extensive Benchmark

We put to the test a recent suggestion [Shee, J., et al. J. Phys. Chem. Lett. 2021, 12 (50), 12084-12097] that MP2 regularization might improve the performance of double-hybrid density functionals. Using the very large and chemically diverse GMTKN55 benchmark, we find that κ-regularization is indeed beneficial at lower percentages of Hartree-Fock exchange, especially if spin-component scaling is not applied [such as in B2GP-PLYP or ωB97M(2)]. This benefit dwindles for DSD and DOD functionals and vanishes entirely in the ∼70% HF exchange region optimal for them.

Optimal Tuning Perspective of Range-Separated Double Hybrid Functionals

We study the optimal tuning of the free parameters in range-separated double hybrid functionals, based on enforcing the exact conditions of piecewise linearity and spin constancy. We find that introducing the range separation in both the exchange and the correlation terms allows for the minimization of both fractional charge and fractional spin errors for singlet atoms. The optimal set of parameters is system specific, underlining the importance of the tuning procedure. We test the performance of the resulting optimally tuned functionals for the dissociation curves of diatomic molecules. We find that they recover the correct dissociation curve for the one-electron system, H2+, and improve the dissociation curves of many-electron molecules such as H2 and Li2, but they also yield a nonphysical maximum and only converge to the correct dissociation limit at very large distances.

Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

The performance of the most recent density functionals is assessed for charge-transfer (CT) excitations using comprehensive intra- and intermolecular CT benchmark sets with high-quality reference values. For this comparison, the state-of-the-art range-separated (RS) and long-range-corrected (LC) double hybrid (DH) approaches are selected, and global DH and LC hybrid functionals are also inspected. The correct long-range behavior of the exchange-correlation (XC) energy is extensively studied, and various CT descriptors are compared as well. Our results show that the most robust performance is attained by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types of CT excitations with outstanding accuracy. Furthermore, concerning the intramolecular transitions, unexpectedly excellent results are obtained for most of the global DHs, but their limitations are also demonstrated for bimolecular complexes. Despite the outstanding performance of the LC-DH methods for common intramolecular excitations, serious deficiencies are pointed out for intermolecular CT transitions, and the wrong long-range behavior of the XC energy is revealed. The application of LC hybrids to such transitions is not recommended in any respect.

Origin of the Failure of Density Functional Theories in Predicting Inverted Singlet-Triplet Gaps

Recent experimental and theoretical studies have shown several new organic molecules that violate Hund's rule and have the first singlet excited state lower in energy than the first triplet excited state. While many correlated single reference wave function methods have successfully predicted excited-state energetics of these low-lying states, conventional linear-response time-dependent density functional theory (TDDFT) fails to predict the correct excited-state energy ordering. In this article, we have explored the performance of combined DFT and wave function methods like doubles-corrected TDDFT and multiconfiguration pair-density functional theory for the calculation of inverted singlet-triplet gaps. We have also tested the performance of the excited-state DFT (eDFT) method for this problem. Our results have shown that it is possible to obtain inverted singlet-triplet gaps both by using doubles-corrected TDDFT with a proper choice of double-hybrid functionals or by using eDFT.

Accurate Spectral Properties within Double-Hybrid Density Functional Theory: A Spin-Scaled Range-Separated Second-Order Algebraic-Diagrammatic Construction-Based Approach

Our second-order algebraic-diagrammatic construction [ADC(2)]-based double-hybrid (DH) ansatz (J. Chem. Theory Comput. 2019, 15, 4440. DOI: 10.1021/acs.jctc.9b00391) is combined with range-separation techniques. In the present scheme, both the exchange and the correlation contributions are range-separated, while spin-scaling approaches are also applied. The new methods are thoroughly tested for the most popular benchmark sets including 250 singlet and 156 triplet excitations, as well as 80 oscillator strengths. It is demonstrated that the range separation for the correlation contributions is highly recommended for both the genuine and the ADC(2)-based DH approaches. Our results show that the latter scheme slightly but consistently outperforms the former one for single excitation dominated transitions. Furthermore, states with larger fractions of double excitations are assessed as well, and challenging charge-transfer excitations are also discussed, where the recently proposed spin-scaled long-range corrected DHs fail. The suggested iterative fourth-power scaling RS-PBE-P86/SOS-ADC(2) method, using only three adjustable parameters, provides the most robust and accurate excitation energies within the DH theory. In addition, the relative error of the oscillator strengths is reduced by 65% compared to the best genuine DH functionals.

Surprisingly Good Performance of XYG3 Family Functionals Using a Scaled KS-MP3 Correlation

By adding a GLPT3 (third-order Görling-Levy perturbation theory, or KS-MP3) term E₃ to the XYG7 form for a double hybrid, we are able to bring down WTMAD2 (weighted total mean absolute deviation) for the very large and chemically diverse GMTKN55 benchmark to an unprecedented 1.17 kcal/mol, competitive with much costlier composite wave function ab initio approaches. Intriguingly, (a) the introduction of E₃ makes an empirical dispersion correction redundant; (b) generalized gradient approximation (GGA) or meta-GGA semilocal correlation functionals offer no advantage over the local density approximation (LDA) in this framework; (c) if a dispersion correction is retained, then simple Slater exchange leads to no significant loss in accuracy. It is possible to create a six-parameter functional with WTMAD2 = 1.42 that has no post-LDA density functional theory components and no dispersion correction in the final energy.

Assessment of hybrid functionals for singlet and triplet excitations: Why do some local hybrid functionals perform so well for triplet excitation energies?

The performance of various hybrid density functionals is assessed for 105 singlet and 105 corresponding triplet vertical excitation energies from the QUEST database. The overall lowest mean absolute error is obtained with the local hybrid (LH) functional LH12ct-SsirPW92 with individual errors of 0.11 eV (0.11 eV) for singlet (triplet) n → π* excitations and 0.29 eV (0.17 eV) for π → π* excitations. This is slightly better than with the overall best performing global hybrid M06-2X [n → π*: 0.13 eV (0.17 eV), π → π*: 0.30 eV (0.20 eV)], while most other global and range-separated hybrids and some LHs suffer from the "triplet problem" of time-dependent density functional theory. This is exemplified by correlating the errors for singlet and triplet excitations on a state-by-state basis. The excellent performance of LHs based on a common local mixing function, i.e., an LMF constructed from the spin-summed rather than the spin-resolved semilocal quantities, is systematically investigated by the introduction of a spin-channel interpolation scheme that allows us to continuously modulate the fraction of opposite-spin terms used in the LMF. The correlation of triplet and singlet errors is systematically improved for the n → π* excitations when larger fractions of the opposite-spin-channel are used in the LMF, whereas this effect is limited for the π → π* excitations. This strongly supports a previously made hypothesis that attributes the excellent performance of LHs based on a common LMF to cross-spin-channel nondynamical correlation terms.

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 Co^III-catecholate and high-spin Co^II-semiquinonate forms, where the half-temperature (T_1/2) is the temperature at which there are equal amounts of the two tautomers. We report the first simple computational strategy for accurately predicting T_1/2 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 T_1/2 value primarily through π-acceptance. We have established an excellent correlation between experimental T_1/2(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 T_1/2(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.

Optical and Electronic Properties of Organic NIR-II Fluorophores by Time-Dependent Density Functional Theory and Many-Body Perturbation Theory: GW-BSE Approaches

Organic-molecule fluorophores with emission wavelengths in the second near-infrared window (NIR-II, 1000-1700 nm) have attracted substantial attention in the life sciences and in biomedical applications because of their excellent resolution and sensitivity. However, adequate theoretical levels to provide efficient and accurate estimations of the optical and electronic properties of organic NIR-II fluorophores are lacking. The standard approach for these calculations has been time-dependent density functional theory (TDDFT). However, the size and large excitonic energies of these compounds pose challenges with respect to computational cost and time. In this study, we used the GW approximation combined with the Bethe-Salpeter equation (GW-BSE) implemented in many-body perturbation theory approaches based on density functional theory. This method was used to perform calculations of the excited states of two NIR molecular fluorophores (BTC980 and BTC1070), going beyond TDDFT. In this study, the optical absorption spectra and frontier molecular orbitals of these compounds were compared using TDDFT and GW-BSE calculations. The GW-BSE estimates showed excellent agreement with previously reported experimental results.

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.

Spin-Scaled Range-Separated Double-Hybrid Density Functional Theory for Excited States

Our recently presented range-separated (RS) double-hybrid (DH) time-dependent density functional approach [J. Chem. Theory Comput. 17, 927 (2021)] is combined with spin-scaling techniques. The proposed spin-component-scaled (SCS) and scaled-opposite-spin (SOS) variants are thoroughly tested for almost 500 excitations including the most challenging types. This comprehensive study provides useful information not only about the new approaches but also about the most prominent methods in the DH class. The benchmark calculations confirm the robustness of the RS-DH ansatz, while several tendencies and deficiencies are pointed out for the existing functionals. Our results show that the SCS variant consistently improves the results, while the SOS variant preserves the benefits of the original RS-DH method reducing its computational expenses. It is also demonstrated that, besides our approaches, only the nonempirical functionals provide balanced performance for general applications, while particular methods are only suggested for certain types of excitations.

Chasing unphysical TD-DFT excited states in transition metal complexes with a simple diagnostic tool

Transition Metal Complexes (TMCs) are known for the rich variety of their excited states showing different nature and degrees of locality. Describing the energies of these excited states with the same degree of accuracy is still problematic when using time-dependent density functional theory in conjunction with the most current density functional approximations. In particular, the presence of unphysically low lying excited states possessing a relevant Charge Transfer (CT) character may significantly affect the spectra computed at such a level of theory and, more relevantly, the interpretation of their photophysical behavior. In this work, we propose an improved version of the M_AC index, recently proposed by the authors and collaborators, as a simple and computationally inexpensive diagnostic tool that can be used for the detection and correction of the unphysically predicted low lying excited states. The analysis, performed on five prototype TMCs, shows that spurious and ghost states can appear in a wide spectral range and that it is difficult to detect them only on the basis of their CT extent. Indeed, both delocalization of the excited state and CT extent are criteria that must be combined, as in the M_AC index, to detect unphysical states.

Spin-Opposite-Scaled Range-Separated Exchange Double-Hybrid Models (SOS-RSX-DHs): Marriage Between DH and RSX/SOS-RSX Is Not Always a Happy Match

The range-separated version of double-hybrid density functional theory (DH-DFT) with a remarkable efficiency for both ground-state and excited-state characteristics has recently come into spotlight. In this work, based on theoretical arguments, several variants of spin-opposite-scaled range-separated exchange double-hybrid models (SOS-RSX-DHs) have been proposed and validated. More specifically, we first extend the RSX-DHs to design some other related models. Next, the SOS version of the resulting approximations is constructed and thoroughly evaluated using standard benchmark compilations of various properties. It is shown that although there are properties for which the RSX-DH and SOS-RSX-DH frameworks are rival, there are still some problems particularly prone to the self-interaction error issues where our proposed models seem to be beneficial. Furthermore, some of the presented models devoid of any additional corrections can also surpass the recently proposed approximations from different rungs of "Jacob's Ladder". Nonetheless, perusing the results of different methods and detailed comparisons with the predecessors discloses that all things may not necessarily be well with the RSX and SOS-RSX schemes, where the parent DHs as well as their SOS counterparts can still come into play.

Copper-Oxo Active Sites for Methane C-H Activation in Zeolites: Molecular Understanding of Impact of Methane Hydroxylation on UV-Vis Spectra

Here, we analyze changes in the optical spectra of activated copper-exchanged zeolites during methane activation with the Tamm-Dancoff time-dependent density functional theory, TDA-DFT, while using the ωB2PLYP functional. Two active sites, [Cu₂O]²⁺ and [Cu₃O₃]²⁺, were studied. For [Cu₂O]⁺, the 22 700 cm^-1 peak is associated with μ-oxo 2p → Cu 3d/4s charge transfer. Of the [Cu₂O]²⁺ methane C-H activation intermediates that we examined, only [Cu-O(H)(H)-Cu] and [Cu-O(H)(CH₃)-Cu] have spectra that match experimental observations. After methane activation, the μ-oxo 2p orbitals lose two electrons and become hybridized with methanol C 2p orbitals and/or H 1s orbitals. The frontier unoccupied orbitals become more Cu 4s/4p Rydberg-like, reducing overlap with occupied orbitals. These effects cause the disappearance of the 22 700 cm^-1 peak. For [Cu₃O₃]²⁺, the exact structures of the species formed after methane activation are unknown. Thus, we considered eight possible structures. Several of these provide a significant decrease in intensity near 23 000-38 000 cm^-1, as seen experimentally. Notably, these species involve either rebound of the separated methyl to a μ-oxo atom or its remote stabilization at a Brønsted acid site in exchange for the acidic proton. These spectral changes are caused by the same mechanism seen in [Cu₂O]²⁺ and are likely responsible for the observed reduced intensities near 23 000-38 000 cm^-1. Thus, TDA-DFT calculations with ωB2PLYP provide a molecular-level understanding of the evolution of copper-oxo active sites during methane-to-methanol conversion.

Methane C-H Activation by [Cu2O]2+ and [Cu3O3]2+ in Copper-Exchanged Zeolites: Computational Analysis of Redox Chemistry and X-ray Absorption Spectroscopy

There is an ongoing debate regarding the role of [Cu₃O₃]²⁺ in methane-to-methanol conversion by copper-exchanged zeolites. Here, we perform electronic structure analysis and localized orbital bonding analysis to probe the redox chemistry of its Cu and μ-oxo sites. Also, the X-ray absorption near-edge structure, XANES, of methane activation in [Cu₃O₃]²⁺ is compared to that of the more ubiquitous [Cu₂O]²⁺. Methane C-H activation is associated with only the Cu²⁺/Cu⁺ redox couple in [Cu₂O]²⁺. For [Cu₃O₃]²⁺, there is no basis for the Cu³⁺/Cu²⁺ couple's participation at the density functional theory ground state. In [Cu₃O₃]²⁺, there are many possible intrazeolite intermediates for methane activation. In the nine possibilities that we examined, methane activation is driven by a combination of the Cu²⁺/Cu⁺ and oxyl/O^2- redox couples. Based on this, the Cu 1s-edge XANES spectra of [Cu₂O]²⁺ and [Cu₃O₃]²⁺ should both have energy signatures of Cu²⁺ → Cu⁺ reduction during methane activation. This is indeed what we obtained from the calculated XANES spectra. [Cu₂O]²⁺ and [Cu₃O₃]²⁺ intermediates with one Cu⁺ site are shifted by 0.9-1.7 eV, while those with two Cu⁺ sites are shifted by 3.0-4.2 eV. These are near a range of 2.5-3.2 eV observed experimentally after contacting methane with activated copper-exchanged zeolites. Thus, activation of methane by [Cu₃O₃]²⁺ will lead to formation of Cu⁺ sites. Importantly, for future quantitative XANES studies, involvement of O^- + e^- → O^2- in [Cu₃O₃]²⁺ implies a disconnect between the overall reactivity and the number of electrons used in the Cu²⁺/Cu⁺ redox couple.

Assessing challenging intra- and inter-molecular charge-transfer excitations energies with double-hybrid density functionals

We investigate the performance of a set of recently introduced range-separated double-hybrid functionals, namely ωB2-PLYP, ωB2GP-PLYP, RSX-0DH, and RSX-QIDH models for hard-to-calculate excitation energies. We compare with the parent (B2-PLYP, B2GP-PLYP, PBE0-DH, and PBE-QIDH) and other (DSD-PBEP86) double-hybrid models as well as with some of the most widely employed hybrid functionals (B3LYP, PBE0, M06-2X, and ωB97X). For this purpose, we select a number of medium-sized intra- and inter-molecular charge-transfer excitations, which are known to be challenging to calculate using time-dependent density-functional theory (TD-DFT) and for which accurate reference values are available. We assess whether the high accuracy shown by the newest double-hybrid models is also confirmed for those cases too. We find that asymptotically corrected double-hybrid models yield a superior performance, especially for the inter-molecular charge-transfer excitation energies, as compared to standard double-hybrid models. Overall, the PBE-QIDH and its corresponding range-separated RSX-QIDH functional are recommended for general-purpose TD-DFT applications, depending on whether long-range effects are expected to play a significant role.

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States

A simple and robust range-separated (RS) double-hybrid (DH) time-dependent density functional approach is presented for the accurate calculation of excitation energies of molecules within the Tamm-Dancoff approximation. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decomposition of the Coulomb potential, for which both the exchange and correlation contributions are range-separated. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approximation is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on standard DHs in most cases, and it can provide a more robust and accurate alternative. In addition, on average, it noticeably surpasses the existing RS hybrid and RS DH functionals.

Time-Dependent Density Functional Theory Study of Copper(II) Oxo Active Sites for Methane-to-Methanol Conversion in Zeolites

Copper-exchanged zeolites are useful materials for step-wise methane-to-methanol conversion (MMC). However, methanol yields on copper-exchanged zeolites are often modest, spurring interest in the development of active-site species that are activated at moderate temperatures, afford greater yields, and provide excellent methanol selectivities. Ultraviolet-visible (UV-vis) spectroscopy is a major tool for characterizing the active-sites and their evolution during the step-wise MMC process. However, computation of the UV-vis spectra of the copper-oxo active sites using Tamm-Dancoff time-dependent density functional theory (TDA-DFT) can be quite problematic. This has led to utilization of expensive methods based on multireference approaches, Green functions, and the Bethe-Salpeter equation. In this work, we examined the optical spectra of [CuO]⁺, [Cu₂O]²⁺, [Cu₂O₂]²⁺, and [Cu₃O₃]²⁺ species implicated in MMC in zeolites. For the larger species, we examined how agreement with experimental data is improved with increasingly larger cluster models. For [CuO]⁺, we compared TDA-DFT against restricted active space 2nd-order perturbation theory, RASPT2. We found that signature peaks for [CuO]⁺ have multireference behavior. The excited states have many configuration state functions with a double excitation character. These effects are likely responsible for the poor utility of conventional TDA-DFT methods. Indeed, we obtain good agreement with experimental data and RASPT2 after accounting for 2h/2p excitations within TDA-DFT with a previously described configuration interaction singles and doubles, CIS(D)-style scheme. This was the case for [CuO]⁺, [Cu₂O]²⁺, as well as a [Cu₂O₂]²⁺ species. Using a long-range corrected double-hybrid, ωB2PLYP, we provide for the first time computational evidence for the experimental UV-vis spectrum of the [Cu₃O₃]²⁺ active site motif.

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.