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

Localized Orbital Scaling Correction to Linear-Response Time-Dependent Density Functional Approximations

The localized orbital scaling correction (LOSC) method, which was developed for eliminating the delocalization error in density functional approximations (DFAs), is extended to the linear-response regime for calculating excitation energies with time-dependent density functional theory (TDDFT). Corrections to the exchange-correlation kernel are derived within the frozen-orbitalet approximation. Extensive numerical tests on various data sets show that LOSC-DFAs are able to maintain the good performance of parent DFAs for valence excitations while systematically improving the excitation energies for Rydberg and charge-transfer excitations by reducing the delocalization error. For charge-transfer excitations, LOSC can produce correct asymptotic behaviors with the donor-acceptor separation R as well as the excitation energy at the infinite separation limit. Moreover, through the example of trans-polyacetylene oligomers, we demonstrate that the performance of LOSC does not deteriorate with increasing system size, holding promise for application in bulk systems.

Enantioselective Photochemical Generation of a Short-Lived, Twisted Cycloheptenone Isomer: Catalytic Formation, Detection, and Consecutive Chemistry

Cyclohept-2-enone-3-carboxylic acid undergoes a photochemical isomerization from its cis- to its trans-form either upon direct irradiation (λ = 366 nm) or in the presence of a triplet sensitizer (λ = 459 nm). The intermediate chiral trans-isomer was detected by step-scan FTIR, displaying a lifetime of 130 µs (r.t., CH2Cl2). Ensuing Diels-Alder reactions of the trans-isomer occurred smoothly and produced chiral trans-fused cycloaddition products (14 examples, 24%-98% yield). Benzylation led to esters, which were separated by chiral HPLC and which were employed to evaluate a possible enantioselective reaction course. It was discovered that a chiral phosphoric acid with a pendant sensitizing group induces a notable enantioselectivity in the photoisomerization step. The planar chirality of the trans-cycloheptene translates into point chirality in the Diels-Alder reaction (seven examples, up to 38% ee). Computational studies suggest that the chiral conformation of the cis-isomer adopted within the assembly to the chiral phosphoric acid induces the enantioselectivity in a one-bond flip (OBF) toward the trans-isomer. Trajectory surface hopping (TSH) simulations showed exemplarily how a chiral trans-cyclohept-2-enone is formed from a chiral cis-conformer. For the Diels-Alder reaction, a weak ground state selectivity was found to attenuate the enantioselectivity achieved in the photochemical step.

Benzazole-Based ESIPT Fluorophores: Proton Transfer from the Chalcogen Perspective. A Combined Theoretical and Experimental Study

In this study, we present a comprehensive photophysical investigation of ESIPT-reactive benzazole derivatives in both solution and the solid state. These derivatives incorporate different chalcogen atoms (O, S, and Se) into their structures, and we explore how these variations impact their electronic properties in both ground and excited states. Changes in the UV-Vis absorption and fluorescence emission spectra were analyzed and correlated with the chalcogen atom and solvent polarity. In general, the spectral band of the benzazole derivative containing selenium was redshifted in both the ground and excited states compared to that of its oxygen and sulfur counterparts. Furthermore, we observed that the solvent played a distinctive role in influencing the ESIPT process within these compounds, underscoring once again the significant influence of the chalcogen atom on their photophysical behavior. Theoretical calculations provided a deeper understanding of the molecular dynamics, electronic structures, and photophysical properties of these compounds. These calculations highlighted the effect of chalcogen atoms on the molecular geometry, absorption and emission characteristics, and intramolecular hydrogen bonding, revealing intricate details of the ESIPT mechanism. The integration of experimental and computational data offers a detailed view of the structural and electronic factors governing the photophysical behavior of benzazole derivatives.

Prediction of 57Fe Mössbauer Nuclear Quadrupole Splittings with Hybrid and Double-Hybrid Density Functionals

As a crucial parameter in Mössbauer spectroscopy, nuclear quadrupole splitting (NQS) exhibits a strong dependence on quantum chemistry methods, which makes accurate theoretical predictions challenging. Meanwhile, the continuous emergence of new density functionals presents opportunities to advance current NQS research. In this study, we evaluate the performance of eleven hybrid density functionals and twelve double-hybrid density functionals, selected from widely used functionals and newly developed functionals, in predicting the NQS values of the 57Fe nuclide for 32 iron-containing molecules within about 70 atoms. The calculations have incorporated scalar relativistic effects using the exact two-component (X2C) Hamiltonian. In general, the double-hybrid functional PBE-0DH demonstrates superior performance compared to the experimental values, achieving a mean absolute error (MAE) of 0.20 mm/s. Meanwhile, rSCAN38 is the best hybrid functional for our database with an MAE = 0.25 mm/s, and it offers a significant advantage in computational efficiency over PBE-0DH. The +/- sign of NQS has also been considered in our error statistics when it has a clear physical meaning; if neglected, the errors of many functionals decrease, but PBE-0DH and rSCAN38 remain unaffected. Notably, when calculating ferrocene [Fe(C5H5)2], which involves strong static correlations, all hybrid functionals that incorporate more than 10% exact exchange fail, while several double-hybrid functionals continue to deliver reliable results. In addition, we encountered two particularly challenging species characterized by strong static correlations: [Fe(H2O)5NO]2+ and FeO2--porphyrin. Unfortunately, none of the density functionals tested in our study yielded satisfactory results for the two cases since the density functional theory (DFT) is a single-determinant approach, and it is imperative to explore large-scale multi-configurational methods for these species. This research offers valuable guidance for selecting density functionals in Mössbauer NQS calculations and serves as a reference point for the future development of new density functionals.

Assessment of Charge Transfer Energies of Noncovalently Bounded Ar-TCNE Complexes Using Range-Separated Density Functionals and Double-hybrid Density Functionals

Charge Transfer (CT) molecular complexes have recently received much attention in a broad variety of fields. The time-dependent density functional theory (TDDFT), which is essential for studying CT complexes, is a well-established tool to study the excited states of relatively large molecular systems. However, when dealing with donor-acceptor molecules with CT characteristics, TDDFT calculations based on standard functionals can severely underestimate the excitation energies. The TDDFT methodology, combined with range-separated DFT and range-separated double-hybrid DFT functionals, had previously been used by different research groups to reliably predict the excitation energies of different charge transfer molecular complexes. We follow the same path to calculate the excited state charge transfer energy of some selected molecular complexes, such as, Ar-TCNE (TCNE=tetracyanoethylene; Ar= benzene, naphthalene, anthracene, etc.). The interactions between the donor-acceptor moieties of these molecular complexes are also studied and the relationship between the interaction and the charge transfer energies are shown here.

Overview of Developments in the MRCC Program System

mrcc is a versatile suite of quantum chemistry programs designed for accurate ab initio and density functional theory (DFT) calculations. This contribution outlines the general features and recent developments of the package. The most popular features include the open-ended coupled-cluster (CC) code, state-of-the-art CC singles and doubles with perturbative triples [CCSD(T)], second-order algebraic-diagrammatic construction, and combined wave function theory-DFT approaches. Cost-reduction techniques are implemented, such as natural orbital (NO), local NO (LNO), and natural auxiliary function approximations, which significantly decrease the computational demands of these methods. This paper also details the method developments made over the past five years, including efficient schemes to approach the complete basis set limit for CCSD(T) and the extension of our LNO-CCSD(T) method to open-shell systems. Additionally, we discuss the new approximations introduced to accelerate the self-consistent field procedure and the cost-reduction techniques elaborated for analytic gradient calculations at various levels. Furthermore, embedding techniques and novel range-separated double-hybrid functionals are presented for excited-state calculations, while the extension of the theories established to describe core excitations and ionized states is also discussed. For academic purposes, the program and its source code are available free of charge, and its commercial use is also facilitated.

On the performance of QTP functionals applied to second-order response properties

Correlated orbital theory (COT) is an exact one-particle treatment that adds essential electron correlation into its molecular orbitals, potentially reducing correlated treatments of response properties to one-particle coupled-perturbed Hartree-Fock- or Kohn-Sham-like calculations. Such a computation is vastly simpler than the usual ab initio correlated approach that would add correlation typically with EOM-CC after a perturbed mean-field solution. The question then is, how well can this be accomplished via the Quantum Theory Project (QTP) exchange-correlation (XC) functionals that are meant to emulate the rigorous COT framework? This paper addresses this question for response properties by making comparisons between such orbital-specific calculations and those from well-correlated EOM-CC solutions for static polarizabilities, nuclear magnetic resonance coupling constants, and chemical shifts. The simple orbital-specific version provides an accurate realization of the correlated EOM-CC results, but now in a mode that facilitates an orbital-by-orbital interpretation. Here, we compare 33 XC functionals from the different Jacob's ladder rungs always against the EOM-CCSD results. Thus, the smallest mean absolute deviation for the static polarizability comes from LC-QTP XC, 0.28 a.u. Regarding the total nuclear spin-spin coupling constants, QTP01 performs best, %Error = 10.63% (QTP02 and LC-QTP are second and third best). Finally, the XC that stood out in the chemical shift analysis was TPSS0, which presented the best result for the majority of the chemical shifts. However, considering the overall performances based on linear fitting of all isotope data points, five functionals are recommended for a chemical shift study: TPSS0, ωB97X, QTP00, QTP01, and QTP02, all presenting R2 = 0.96.

Insight into the Excited States in Monomers and π-Stacked Dimers of Azulene-Fused Acenes: ADC(2) and TD-DFT Studies

Charge transfer (CT) states in polycyclic aromatic hydrocarbons play crucial roles in determining their electronic properties and their potential applications in organic electronics. In this work, we investigate the nature of the excited states in monomers and π-stacked dimers of azulene-fused naphthalene and anthracene systems, focusing on the interplay between structure and excited-state properties. Four different isomers for azulene-fused naphthalene (NapAz-A, NapAz-B, NapAz-C, and NapAz-D) and anthracene (AntAz-A, AntAz-B, AntAz-C, and AntAz-D) are considered. The excited-state studies are performed at the SCS-ADC(2) level and at the TD-DFT level using CAM-B3LYP, SCS-ωB2GP-PLYP, and SCS-RSX-QIDH functionals. For the monomers, the SCS-ADC(2) results reveal that states with CT characters are different in naphthalene- and anthracene-based systems. In π-stacked dimers, a few of the excited states are of the charge resonance (CR) type in NapAz-A, NapAz-B, and NapAz-C and the intermolecular CT type in NapAz-D. Similarly, AntAz-A, AntAz-B, and AntAz-D have some CR type excited states, whereas the AntAz-C isomer has intramolecular CT type excited states. Overall, among the three DFT functionals considered, CAM-B3LYP has been found to reproduce well the SCS-ADC(2) excited results in both monomers and π-stacked dimers.

Reassessing the role and lifetime of Q x in the energy transfer dynamics of chlorophyll a

Chlorophylls are photoactive molecular building blocks essential to most photosynthetic systems. They have comparatively simple optical spectra defined by states with near-orthogonal transition dipole moments, referred to as B x and B y in the blue/green spectral region, and Q x and Q y in the red. Underlying these spectra is a surprisingly complex electronic structure, where strong electronic-vibrational interactions are crucial to the description of state characters. Following photoexcitation, energy-relaxation between these states is extremely fast and connected to only modest changes in spectral shapes. This has pushed conventional theoretical and experimental methods to their limits and left the energy transfer pathway under debate. In this work, we address the electronic structure and photodynamics of chlorophyll a using polarization-controlled static - and ultrafast - optical spectroscopies. We support the experimental data analysis with quantum dynamical simulations and effective heat dissipation models. We find clear evidence for B → Q transfer on a timescale of ∼100 fs and identify Q x signatures within fluorescence excitation and transient spectra. However, Q x is populated only fleetingly, with a lifetime well below our ∼30 fs experimental time resolution. Outside of these timescales, the kinetics are determined by vibrational relaxation and cooling. Despite its ultrashort lifetime, our theoretical analysis suggests that Q x plays a crucial role as a bridging state in B → Q energy transfer. In summary, our findings present a unified and consistent picture of chlorophyll relaxation dynamics based on ultrafast and polarization-resolved spectroscopic techniques supported by extensive theoretical models; they clarify the role of Q x in the energy deactivation network of chlorophyll a.

Assessing Computational Methods to Calculate the Binding Energies of Dimers of Five-Membered Heterocyclic Molecules

Computational electronic structure methods, including ab initio and density functional theory (DFT), have been assessed in calculating the binding energies of 14 five-membered heterocyclic dimers. The configurations were generated using classical molecular dynamics before optimization at the MP2/aug-cc-pVTZ. Benchmark binding energies are calculated at the CCSD(T)/CBS level of theory. Among the ab initio methods, the DLPNO-CCSD(T)/CBS method has the best performance, reproducing CCSD(T)/CBS with a mean absolute deviation (MAD) of 0.17 kcal/mol. In addition, a schematic CCSD(T)/CBS approach perfectly reproduces the canonical CCSD(T)/CBS with a mean absolute error of 0.08 kcal/mol. Regarding DFT functionals, it has been found that counterpoise corrections have negligible effects on the accuracy of the functionals. Furthermore, including the D3 empirical dispersion considerably enhances the accuracy of the DFT functionals. As a result, outstanding performance is noted for the double hybrid functional B2K-PLYP, with a mean absolute error of 0.25 kcal/mol. In addition to the B2K-PLYP double hybrid functional, M05-D3, B97D, M05-2X-D3, M05-2X, M06-HF, M08-HX, M11, TPSSh-D3, and RSX-0DH-D3(BJ) have MAD values lower than 0.5 kcal/mol. These functionals are recommended for further investigations of five-membered heterocyclic clusters.

Assessment of the applicability of DFT methods to [Cp*Rh]-catalyzed hydrogen evolution processes

The present computational study provides a benchmark of density functional theory (DFT) methods in describing hydrogen evolution processes catalyzed by [Cp*Rh]-containing organometallic complexes. A test set was composed of 26 elementary reactions featuring chemical transformations and bonding situations essential for the field, including the emerging concept of non-innocent Cp* behavior. Reference values were obtained from a highly accurate 3/4 complete basis set and 6/7 complete PNO space extrapolated DLPNO-CCSD(T) energies. The performance of lower-level extrapolation procedures was also assessed. We considered 84 density functionals (DF) (including 13 generalized gradient approximations (GGA), nine meta-GGAs, 33 hybrids, and 29 double-hybrids) and three composite methods (HF-3c, PBEh-3c, and r2SCAN-3c), combined with different types of dispersion corrections (D3(0), D3BJ, D4, and VV10). The most accurate approach is the PBE0-DH-D3BJ (MAD of 1.36 kcal mol-1) followed by TPSS0-D3BJ (MAD of 1.60 kcal mol-1). Low-cost r2SCAN-3c composite provides a less accurate but much faster alternative (MAD of 2.39 kcal mol-1). The widely used Minnesota-family M06-L, M06, and M06-2X DFs should be avoided (MADs of 3.70, 3.94, and 4.01 kcal mol-1, respectively).

Design of Anti-Hund Organic Emitters Based on Heptazine

Hund's rule, which is powerful in governing the first excited states of closed-shell organic materials, can hardly be violated to get inverted singlet-triplet gap (INVEST) molecules with negative singlet-triplet energy gaps (ΔEST), although INVEST materials have shown extraordinary photophysical properties and promising device performance especially in light-emitting diodes. Here, we propose a facile strategy to construct emissive INVEST molecules by introducing different types of substituents to heptazine in various modes, which can effectively tune the ΔEST to be negative with the enlarged oscillator strength (f) for the high fluorescence rate of the heptazine derivatives. Systematic computational studies show that the double substitution of electron-donating units with another nonconjugated substituent in hybrid substitution mode is the most favorable way in achieving slightly negative ΔEST and large f values; the conjugated substituent will compete with heptazine to make the molecule deviate from the INVEST feature. Especially, a series of high-performance heptazine-based INVEST emitters were constructed, exhibiting ΔEST low to -0.362 eV, f up to 0.0436, as well as a wide range emission color from 339 to 716 nm. Also, the designed molecules were predicted to have fluorescence radiative rates up to 106 s-1, along with efficient reverse intersystem crossing rates reaching 108 s-1. Importantly, the figure of merit (FM) was first proposed as a parameter to wholly evaluate the performance of INVEST emitters, and the highest FM of 0.198 was found in the triazine and double nonconjugated amine-substituted heptazine. These results highlight the great potential of the heptazine chromophore in constructing INVEST emitters, revealing fundamental structure-property understandings for the material design of efficient anti-Hund organic molecules with improved emission properties.

Singlet and triplet excited states of a series of BODIPY dyes as calculated by TDDFT and DLPNO-STEOM-CCSD methods

The singlet and triplet excited states of three iodine substituted BODIPY dyes differing by their substituents (-phenyl, -phenylOH and -phenylNO2) at the meso position of the BODIPY core (BOD) are investigated using (TDA)-TDDFT and DLPNO-STEOM-CCSD calculations. An assessment of hybrid (B3LYP and MN15) and double hybrid (SOS-PBE-QIDH and SOS-ωPBEPP86) exchange-correlation functionals is performed with respect to the DLPNO-STEOM-CCSD method for four types of transitions, namely , , and . It is found that MN15 and SOS-PBE-QIDH provide a balanced description of the excited state energies when compared to the DLPNO-STEOM-CCSD results. An investigation of the effects of the solvent (dichloromethane), of the substituent and of geometrical relaxation in the excited states is then performed. In particular, the study discusses the possibility of populating charge transfer states ( and ) following photoexcitation in the first and second absorption bands in these systems.

Assessment of the similarity-transformed equation of motion (STEOM) for open-shell organic and transition metal molecules

This study benchmarks the newly re-implemented single-reference excited-state methods, IP-EOM-CCSD, EA-EOM-CCSD, and STEOM-CCSD, in ORCA6.0, with a focus on open-shell systems. We compare STEOM against EOM-CCSD, CC3, and CCSDT across a range of systems, including small organic radicals, hydrated transition metal (TM) ions, and TM diatomic systems with both closed and open-shell configurations. For organic radicals, STEOM and EOM-CCSD show comparable performance, aligning closely with CC3 and CCSDT results. In the case of hydrated TM ions, IP-EOM closely matches DLPNO-CCSD results, while deviations from DLPNO-CCSD(T) are consistent. For open-shell TM systems, IP-EOM exhibits a blueshift relative to both the DLPNO-CCSD methods, while EA-EOM-CCSD shows better agreement. When comparing STEOM and CC3 to CCSDT, STEOM shows slightly larger deviations in closed-shell systems but shows excellent agreement in open-shell systems. Computational efficiency is also assessed, revealing a significant speedup in ORCA 6.0 compared to ORCA 5.0, with optimizations improving computation times. This study provides valuable insights into the performance and efficiency of STEOM in various chemical environments, highlighting its strengths and limitations.

Exploring non-covalent interactions in excited states: beyond aromatic excimer models

Time-dependent density functional theory (TD-DFT) offers a relatively accurate and inexpensive approach for excited state calculations. However, conventional TD-DFT may suffer from the same poor description of non-covalent interactions (NCIs) which is known from ground-state DFT. In this work we present a comprehensive benchmark study of TD-DFT for excited-state NCIs. This is achieved by calculating dissociation curves for excited complexes ('exciplexes'), whose binding strength depends on excited-state NCIs including electrostatics, Pauli repulsion, charge-transfer, and London dispersion. Reference dissociation curves are calculated with the reasonably accurate wave function method SCS-CC2/CBS(3,4) which is used to benchmark a range of TD-DFT methods. Additionally, we test the effect of ground-state dispersion corrections, DFT-D3(BJ) and VV10, for exciplex binding. Overall, we find that TD-DFT methods generally under-bind exciplexes which can be explained by the missing dispersion forces. Underbinding errors reduce going up the rungs of Jacob's ladder. Further, the D3(BJ) dispersion correction is essential for good accuracy in most cases. Likewise, the VV10-type non-local kernel yields relatively low errors and has comparable performance in either its fully self-consistent implementation or as a post-SCF additive correction, but its impact is solely on ground-state energies and not on excitation energies. From our analysis, the most robust TD-DFT methods for exciplexes with localised excitations in their equilibrium and non-equilibrium geometries are the double hybrids B2GP-PLYP-D3(BJ) and B2PLYP-D3(BJ). Their range-separated versions ωB2(GP-)PLYP-D3(BJ) or the spin-opposite scaled, range-separated double hybrid SOS-ωB88PP86 can be recommended when charge transfer plays a role in the excitations. We also identify the need for a state-specific dispersion correction as the next step for improved TD-DFT performance.

Molecular interactions of photosystem I and ZIF-8 in bio-nanohybrid materials

Bio-nanohybrid devices featuring natural photocatalysts bound to a nanostructure hold great promise in the search for sustainable energy conversion. One of the major challenges of integrating biological systems is protecting them against harsh environmental conditions while retaining, or ideally enhancing their photophysical properties. In this mainly computational work we investigate an assembly of cyanobacterial photosystem I (PS I) embedded in a metal-organic framework (MOF), namely the zeolitic imidazolate framework ZIF-8. This complex has been reported experimentally [Bennett et al., Nanoscale Adv., 2019, 1, 94] but so far the molecular interactions between PS I and the MOF remained elusive. We show via absorption spectroscopy that PS I remains intact throughout the encapsulation-release cycle. Molecular dynamics (MD) simulations further confirm that the encapsulation has no noticeable structural impact on the photosystem. However, the MOF building blocks frequently coordinate to the Mg2+ ions of chlorophylls in the periphery of the antenna complex. High-level quantum mechanical calculations reveal charge-transfer interactions, which affect the excitonic network and thereby may reversibly change the fluorescence properties of PS I. Nevertheless, our results highlight the stability of PS I in the MOF, as the reaction center remains unimpeded by the heterogeneous environment, paving the way for applications in the foreseeable future.

Reference CC3 Excitation Energies for Organic Chromophores: Benchmarking TD-DFT, BSE/GW, and Wave Function Methods

To expand the QUEST database of highly accurate vertical transition energies, we consider a series of large organic chromogens ubiquitous in dye chemistry, such as anthraquinone, azobenzene, BODIPY, and naphthalimide. We compute, at the CC3 level of theory, the singlet and triplet vertical transition energies associated with the low-lying excited states. This leads to a collection of more than 120 new highly accurate excitation energies. For several singlet transitions, we have been able to determine CCSDT transition energies with a compact basis set, finding minimal deviations from the CC3 values for most states. Subsequently, we employ these reference values to benchmark a series of lower-order wave function approaches, including the popular ADC(2) and CC2 schemes, as well as time-dependent density-functional theory (TD-DFT), both with and without applying the Tamm-Dancoff approximation (TDA). At the TD-DFT level, we evaluate a large panel of global, range-separated, local, and double hybrid functionals. Additionally, we assess the performance of the Bethe-Salpeter equation (BSE) formalism relying on both G0W0 and evGW quasiparticle energies evaluated from various starting points. It turns out that CC2 and ADC(2.5) are the most accurate models among those with respective O ( N 5 ) and O ( N 6 ) scalings with system size. In contrast, CCSD does not outperform CC2. The best performing exchange-correlation functionals include BMK, M06-2X, M06-SX, CAM-B3LYP, ωB97X-D, and LH20t, with average deviations of approximately 0.20 eV or slightly below. Errors on vertical excitation energies can be further reduced by considering double hybrids. Both SOS-ωB88PP86 and SOS-ωPBEPP86 exhibit particularly attractive performances with overall quality on par with CC2, whereas PBE0-DH and PBE-QIDH are only slightly less efficient. BSE/evGW calculations based on Kohn-Sham starting points have been found to be particularly effective for singlet transitions, but much less for their triplet counterparts.

Benchmarking DFT-based excited-state methods for intermolecular charge-transfer excitations

Intermolecular charge-transfer is a highly important process in biology and energy-conversion applications where generated charges need to be transported over several moieties. However, its theoretical description is challenging since the high accuracy required to describe these excited states must be accessible for calculations on large molecular systems. In this benchmark study, we identify reliable low-scaling computational methods for this task. Our reference results were obtained from highly accurate wavefunction calculations that restrict the size of the benchmark systems. However, the density-functional theory based methods that we identify as accurate can be applied to much larger systems. Since targeting charge-transfer states requires the unambiguous classification of an excited state, we first analyze several charge-transfer descriptors for their reliability concerning intermolecular charge-transfer and single out the charge-transfer distance calculated based on the variation of electron density upon excitation (DCT) as an optimal choice for our purposes. In general, best results are obtained for orbital-optimized methods and among those, the maximum overlap method proved to be the most numerically stable variant when using the initial MOs as reference orbitals. Favorable error cancellation with optimally-tuned range-separated hybrid functionals and a rather small basis set can provide an economical yet reasonable wavefunction when using time-dependent density functional theory, which provides relevant information about the excited-state character to be used in the orbital-optimized methods. The qualitative agreement makes these fast calculations attractive for high-throughput screening applications.

Deciphering the doublet luminescence mechanism in neutral organic radicals: spin-exchange coupling, reversed-quartet mechanism, excited-state dynamics

Neutral organic radical molecules have recently attracted considerable attention as promising luminescent and quantum-information materials. However, the presence of a radical often shortens their excited-state lifetime and results in fluorescence quenching due to enhanced intersystem crossing (EISC). Recently, an experimental report introduced an efficient luminescent radical molecule, tris(2,4,6-trichlorophenyl)methyl-carbazole-anthracene (TTM-1Cz-An). In this study, we systematically performed quantum theoretical calculations combined with the path integral approach to quantitatively calculate the excited-state dynamics processes and spectral characteristics. Our theoretical findings suggest that the sing-doublet D1 state, originating from the anthracene excited singlet state, is quickly converted to the doublet (trip-doublet) state via EISC, facilitated by a significant nonequivalence exchange interaction, with ΔJ ST = 0.174 cm-1. The formation of the quartet state (Q1, trip-quartet) was predominantly dependent on the exchange coupling 3/2J TR = 0.086 cm-1 between the triplet spin electrons of anthracene and the TTM-1Cz radical. Direct spin-orbit coupling ISC to the Q1 state was minimal due to the nearly identical spatial wavefunctions of the and Q1 levels. The effective occurrence of reverse intersystem crossing (RISC) from the Q1 to D1 state is a critical step in controlling the luminescence of TTM-1Cz-An. The calculated RISC rate k RISC, including the Herzberg-Teller effect, was 3.64 × 105 s-1 at 298 K, significantly exceeding the phosphorescence and nonradiative rates of the Q1 state, thus enabling the D1 repopulation. Subsequently, a strong electronic coupling of 37.4 meV was observed between the D1 and D2 states, along with a dense manifold of doublet states near the D1 state energy, resulting in a larger reverse internal conversion rate k RIC of 9.26 × 1010 s-1. Distributed to the D2 state, the obtained emission rate of k f = 2.98-3.18 × 107 s-1 was in quite good agreement with the experimental value of 1.28 × 107 s-1, and its temperature effect was not remarkable. Our study not only provides strong support for the experimental findings but also offers valuable insights for the molecular design of high-efficiency radical emitters.

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.

Cobalt-Mediated Photochemical C-H Arylation of Pyrroles

Precious metal complexes remain ubiquitous in photoredox catalysis (PRC) despite concerted efforts to find more earth-abundant catalysts and replacements based on 3d metals in particular. Most otherwise plausible 3d metal complexes are assumed to be unsuitable due to short-lived excited states, which has led researchers to prioritize the pursuit of longer excited-state lifetimes through careful molecular design. However, we report herein that the C-H arylation of pyrroles and related substrates (which are benchmark reactions for assessing the efficacy of photoredox catalysts) can be achieved using a simple and readily accessible octahedral bis(diiminopyridine) cobalt complex, [1-Co](PF6)2. Notably, [1-Co]2+ efficiently functionalizes both chloro- and bromoarene substrates despite the short excited-state lifetime of the key photoexcited intermediate *[1-Co]2+ (8 ps). We present herein the scope of this C-H arylation protocol and provide mechanistic insights derived from detailed spectroscopic and computational studies. These indicate that, despite its transient existence, reduction of *[1-Co]2+ is facilitated via pre-assembly with the NEt3 reductant, highlighting an alternative strategy for the future development of 3d metal-catalyzed PRC.

Resilience of Hund's rule in the chemical space of small organic molecules

We embark on a quest to identify small molecules in the chemical space that can potentially violate Hund's rule. Utilizing twelve TDDFT approximations and the ADC(2) many-body method, we report the energies of S1 and T1 excited states of 12 880 closed-shell organic molecules within the bigQM7ω dataset with up to 7 CONF atoms. In this comprehensive dataset, none of the molecules, in their minimum energy geometry, exhibit a negative S1-T1 energy gap at the ADC(2) level while several molecules display values <0.1 eV. The spin-component-scaled double-hybrid method, SCS-PBE-QIDH, demonstrates the best agreement with ADC(2). Yet, at this level, a few molecules with a strained sp3-N center turn out as false-positives with the S1 state lower in energy than T1. We investigate a prototypical cage molecule with an energy gap <-0.2 eV, which a closer examination revealed as another false positive. We conclude that in the chemical space of small closed-shell organic molecules, it is possible to identify geometric and electronic structural features giving rise to S1-T1 degeneracy; still, there is no evidence of a negative gap. We share the dataset generated for this study as a module, to facilitate seamless molecular discovery through data mining.

Determining Excited-State Absorption Properties of a Quinoid Flavin by Polarization-Resolved Transient Spectroscopy

As important naturally occurring chromophores, photophysical/chemical properties of quinoid flavins have been extensively studied both experimentally and theoretically. However, little is known about the transition dipole moment (TDM) orientation of excited-state absorption transitions of these important compounds. This aspect is of high interest in the fields of photocatalysis and quantum control studies. In this work, we employ polarization-associated spectra (PAS) to study the excited-state absorption transitions and the underlying TDM directions of a standard quinoid flavin compound. As compared to transient absorption anisotropy (TAA), an analysis based on PAS not only avoids diverging signals but also retrieves the relative angle for ESA transitions with respect to known TDM directions. Quantum chemical calculations of excited-state properties lead to good agreement with TA signals measured in magic angle configuration. Only when comparing experiment and theory for TAA spectra and PAS, do we find deviations when and only when the S0 → S1 of flavin is used as a reference. We attribute this to the vibronic coupling of this transition to a dark state. This effect is only observed in the employed polarization-controlled spectroscopy and would have gone unnoticed in conventional TA.

Tris-Azo Triangular Paraphenylenes: Synthesis and Reversible Interconversion into Radial π-Conjugated Macrocycles

We report the synthesis of cycloparaphenylene derivatives featuring tris-azo groups. The smaller derivative, [3]cycloazobenzene, adopts a triangular all-cis form and exhibits thermally and photochemically stable characteristics due to significant ring strain as well as symmetric Kagome-patterned crystal packing. In contrast, the as-synthesized [3]cycloazobenzene with three biphenylene bridges adopts a triangular all-cis form, which undergoes photoinduced isomerization, leading to a photostationary state. Interestingly, the addition of an excess of acid selectively leads to the formation of an all-trans form. DFT calculations reveal that the interconversion from a triangular to a circular shape correlates with an increase in HOMO and a decrease in LUMO, characteristics intrinsic to radial π-conjugated systems.

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.

Heptazine, Cyclazine, and Related Compounds: Chemically-Accurate Estimates of the Inverted Singlet-Triplet Gap

Molecules that violate Hund's rule and exhibit an inverted gap between the lowest singlet S1 and triplet T1 excited states have attracted considerable attention due to their potential applications in optoelectronics. Among these molecules, the triangular-shaped heptazine, and its derivatives, have been in the limelight. However, conflicting reports have arisen regarding the relative energies of S1 and T1. Here, we employ highly accurate levels of theory, such as CC3, to not only resolve the debate concerning the sign but also quantify the magnitude of the S1-T1 gap. We also determined the 0-0 energies to evaluate the significance of the vertical approximation. In addition, we compute reference S1-T1 gaps for a series of 10 related molecules. This enables us to benchmark lower-order methods for future applications in larger systems within the same family of compounds. This contribution can serve as a foundation for the design of triangular-shaped molecules with enhanced photophysical properties.

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.

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.

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.

Theoretical design and evaluation of efficient small donor molecules for organic solar cells

CONTEXT

The development of high-efficiency photovoltaic devices is the need of time with increasing demand for energy. Herein, we designed seven small molecule donors (SMDs) with A-π-D-π-A backbones containing various acceptor groups for high-efficiency organic solar cells (OSCs). Molecular engineering was performed by substituting the acceptor group in the synthesized compound (BPR) with another highly efficient acceptor group to improve the photoelectric performance of the molecule.

METHOD

The photovoltaic, optoelectronic, and photophysical properties of the proposed compounds (BP1-BP7) were investigated in comparison to BPR using DFT and TD-DFT at MPW1PW91/6-311G(d,p) level of theory. All molecules we designed have red-shifted absorption spectra. The modification of the acceptor fragment of the BPR resulted in a reduced HOMO-LUMO energy gap; thus, the designed compounds (BP1-BP7) had improved optoelectronic responses as compared with the BPR molecule. Various key factors that are crucial for efficient SMDs such as exciton binding energy, frontier molecular orbitals (FMOs), absorption maximum (λmax), open circuit voltage (VOC), dipole moment (μ), excitation charge mobilities, and the transition density matrix of (BPR, BP1-BP7) have also been studied. Low reorganizational energy (holes and electrons) values provide high charge mobility, and all the designed compounds are efficient in this regard. Here, BP6 exhibits low excitation energy (1.66 eV), highest open circuit voltage (2.00 V), normalized VOC (77.23), and fill factor (0.931). Consequently, the superiority of the designed molecules advises experimenters to envision future developments in extremely effective OSC devices.

The three kingdoms-Photoinduced electron transfer cascades controlled by electronic couplings

Excited states are the key species in photocatalysis, while the critical parameters that govern their applications are (i) excitation energy, (ii) accessibility, and (iii) lifetime. However, in molecular transition metal-based photosensitizers, there is a design tension between the creation of long-lived excited (triplet), e.g., metal-to-ligand charge transfer (3MLCT) states and the population of such states. Long-lived triplet states have low spin-orbit coupling (SOC) and hence their population is low. Thus, a long-lived triplet state can be populated but inefficiently. If the SOC is increased, the triplet state population efficiency is improved-coming at the cost of decreasing the lifetime. A promising strategy to isolate the triplet excited state away from the metal after intersystem crossing (ISC) involves the combination of transition metal complex and an organic donor/acceptor group. Here, we elucidate the excited state branching processes in a series of Ru(II)-terpyridyl push-pull triads by quantum chemical simulations. Scalar-relativistic time-dependent density theory simulations reveal that efficient ISC takes place along 1/3MLCT gateway states. Subsequently, competitive electron transfer (ET) pathways involving the organic chromophore, i.e., 10-methylphenothiazinyl and the terpyridyl ligands are available. The kinetics of the underlying ET processes were investigated within the semiclassical Marcus picture and along efficient internal reaction coordinates that connect the respective photoredox intermediates. The key parameter that governs the population transfer away from the metal toward the organic chromophore either by means of ligand-to-ligand (3LLCT; weakly coupled) or intra-ligand charge transfer (3ILCT; strongly coupled) states was determined to be the magnitude of the involved electronic coupling.

Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level

The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.

Enantiopure J-Aggregate of Quaterrylene Bisimides for Strong Chiroptical NIR-Response

Chiral polycyclic aromatic hydrocarbons can be tailored for next-generation photonic materials by carefully designing their molecular as well as supramolecular architectures. Hence, excitonic coupling can boost the chiroptical response in extended aggregates but is still challenging to achieve by pure self-assembly. Whereas most reports on these potential materials cover the UV and visible spectral range, systems in the near infrared (NIR) are underdeveloped. We report a new quaterrylene bisimide derivative with a conformationally stable twisted π-backbone enabled by the sterical congestion of a fourfold bay-arylation. Rendering the π-subplanes accessible by small imide substituents allows for a slip-stacked chiral arrangement by kinetic self-assembly in low polarity solvents. The well dispersed solid-state aggregate reveals a sharp optical signature of strong J-type excitonic coupling in both absorption (897 nm) and emission (912 nm) far in the NIR region and reaches absorption dissymmetry factors up to 1.1 × 10^-2. The structural elucidation was achieved by atomic force microscopy and single-crystal X-ray analysis which we combined to derive a structural model of a fourfold stranded enantiopure superhelix. We could deduce that the role of phenyl substituents is not only granting stable axial chirality but also guiding the chromophore into a chiral supramolecular arrangement needed for strong excitonic chirality.

Performance of Common Density Functionals for Excited States of Tetraphenyldibenzoperiflanthene

Time-dependent density functional theory is the method of choice to efficiently calculate excitation spectra with the functional and basis set choice allowing one to compromise between accuracy and computational cost. In this work, the performance of different functionals as well as the second-order approximate coupled cluster singles and doubles model CC2 is evaluated by comparing the results to experimental results of the example molecule tetraphenyldibenzoperiflanthene (DBP). The choice of the functional has a significant impact on the calculated spectrum of DBP. The performance of a number of different functionals was evaluated, quantified, and, where possible, discussed. The best functional, tuned-CAM-B3LYP, is used to investigate DBP on a surface of hexagonal boron nitride (h-BN). The resulting spectrum shows excellent agreement with experimental results for a monolayer of DBP on h-BN.

Thermal site energy fluctuations in photosystem I: new insights from MD/QM/MM calculations

Cyanobacterial photosystem I (PSI) is one of the most efficient photosynthetic machineries found in nature. Due to the large scale and complexity of the system, the energy transfer mechanism from the antenna complex to the reaction center is still not fully understood. A central element is the accurate evaluation of the individual chlorophyll excitation energies (site energies). Such an evaluation must include a detailed treatment of site specific environmental influences on structural and electrostatic properties, but also their evolution in the temporal domain, because of the dynamic nature of the energy transfer process. In this work, we calculate the site energies of all 96 chlorophylls in a membrane-embedded model of PSI. The employed hybrid QM/MM approach using the multireference DFT/MRCI method in the QM region allows to obtain accurate site energies under explicit consideration of the natural environment. We identify energy traps and barriers in the antenna complex and discuss their implications for energy transfer to the reaction center. Going beyond previous studies, our model also accounts for the molecular dynamics of the full trimeric PSI complex. Via statistical analysis we show that the thermal fluctuations of single chlorophylls prevent the formation of a single prominent energy funnel within the antenna complex. These findings are also supported by a dipole exciton model. We conclude that energy transfer pathways may form only transiently at physiological temperatures, as thermal fluctuations overcome energy barriers. The set of site energies provided in this work sets the stage for theoretical and experimental studies on the highly efficient energy transfer mechanisms in PSI.

Inverse molecular design and parameter optimization with Hückel theory using automatic differentiation

Semiempirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semiempirical model still in widespread use in chemistry is Hückel's π-electron molecular orbital theory. In this work, we implemented a Hückel program using differentiable programming with the JAX framework based on limited modifications of a pre-existing NumPy version. The auto-differentiable Hückel code enabled efficient gradient-based optimization of model parameters tuned for excitation energies and molecular polarizabilities, respectively, based on as few as 100 data points from density functional theory simulations. In particular, the facile computation of the polarizability, a second-order derivative, via auto-differentiation shows the potential of differentiable programming to bypass the need for numeric differentiation or derivation of analytical expressions. Finally, we employ gradient-based optimization of atom identity for inverse design of organic electronic materials with targeted orbital energy gaps and polarizabilities. Optimized structures are obtained after as little as 15 iterations using standard gradient-based optimization algorithms.

Double-Hybrid Density Functional Theory for Core Excitations: Theory and Benchmark Calculations

The double-hybrid (DH) time-dependent density functional theory is extended to core excitations. Two different DH formalisms are presented utilizing the core-valence separation (CVS) approximation. First, a CVS-DH variant is introduced relying on the genuine perturbative second-order correction, while an iterative analogue is also presented using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH ansatz. The performance of the new approaches is tested for the most popular DH functionals using the recently proposed XABOOM [J. Chem. Theory Comput.2021, 17, 1618] benchmark set. In order to make a careful comparison, the accuracy and precision of the methods are also inspected. Our results show that the genuine approaches are highly competitive with the more advanced CVS-ADC(2)-based methods if only excitation energies are required. In contrast, as expected, significant differences are observed in oscillator strengths; however, the precision is acceptable for the genuine functionals as well. Concerning the performance of the CVS-DH approaches, the PBE0-2/CVS-ADC(2) functional is superior, while its spin-opposite-scaled variant is also recommended as a cost-effective alternative. For these approaches, significant improvements are realized in the error measures compared with the popular CVS-ADC(2) method.

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

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

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.

Inversion Theory Leveling as a New Methodological Approach to Antioxidant Thermodynamics: A Case Study on Phenol

Antioxidants are various types of compounds that represent a link between biology and chemistry. With the development of theoretical and computational methods, antioxidants are now being studied theoretically. Here, a novel method is presented that aims to reduce the estimated wall times for DFT calculations that result in the same or higher degree of accuracy in the second derivatives over energy than is the case with the regular computational route (i.e., optimizing the reaction system at a lower model and then recalculating the energies at a higher level of theory) by applying the inversion of theory level to the universal chemical scavenger model, i.e., phenol. The resulting accuracy and wall time obtained with such a methodological setup strongly suggest that this methodology could be generally applied to antioxidant thermodynamics for some costly DFT methods with relative absolute deviation.

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.

Double Hybrid Density Functionals for the Electronic Excitation Energies of Linear Cyanines

The lowest bright electronic excitations of seven model linear cyanines (CN3-CN15) using 28 double-hybrid (DH) density functionals are benchmarked against accurate and recent CC3 results. Some of these DH functionals are recently designed specifically for excited electronic state calculations. In addition, CIS, CIS(D), SCS-CIS(D), and SOS-CIS(D) were also tested. Four different basis sets were used for the vertical electronic excitation calculations: cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis. Augmented basis sets (e.g. aug-cc-pVDZ and aug-cc-pVTZ) are found to be required for accurate and consistent results using DH functionals. The DH functionals tested in this work are classified into four main groups: global double-hybrids (GDH), range-separated double-hybrids (RSDH), spin-component and spin-opposite scaling global double-hybrids (SCS/SOS-GDH), and spin-component and spin-opposite scaling range-separated double-hybrids (SCS/SOS-RSDH). Within these groups, the SCS/SOS-RSDH group of functionals is found to provide the lowest mean absolute error (MAE) values (in the range 0.020-0.148 eV) in comparison with the GDH group (0.195-0.441 eV), the RSDH group (0.186-0.511 eV), and the SCS/SOS-GDH group (0.079-0.461 eV). Of all the DH functionals and ab initio methods investigated in the present contribution, the following functionals are found to be the most accurate and consistent: SCS-ωB2GPPLYP (MAE = 0.036 eV), SOS-ωB2GPPLYP (MAE = 0.020 eV), SOS-ωB88PP86 (MAE = 0.035 eV), and SOS-ωPBEPP86 (MAE = 0.037 eV). In general, the ab initio methods tested here show mediocre performance as compared to many DH functionals.

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

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.

A Mountaineering Strategy to Excited States: Revising Reference Values with EOM-CC4

In the framework of the computational determination of highly accurate vertical excitation energies in small organic compounds, we explore the possibilities offered by the equation-of-motion formalism relying on the approximate fourth-order coupled-cluster (CC) method, CC4. We demonstrate, using an extended set of more than 200 reference values based on CC including up to quadruples excitations (CCSDTQ), that CC4 is an excellent approximation to CCSDTQ for excited states with a dominant contribution from single excitations with an average deviation as small as 0.003 eV. We next assess the accuracy of several additive basis set correction schemes, in which vertical excitation energies obtained with a compact basis set and a high-order CC method are corrected with lower-order CC calculations performed in a larger basis set. Such strategies are found to be overall very beneficial, though their accuracy depends significantly on the actual scheme. Finally, CC4 is employed to improve several theoretical best estimates of the QUEST database for molecules containing between four and six (nonhydrogen) atoms, for which previous estimates were computed at the CCSDT level.

Activity-Based Photosensitizers with Optimized Triplet State Characteristics Toward Cancer Cell Selective and Image Guided Photodynamic Therapy

Activity-based theranostic photosensitizers are highly attractive in photodynamic therapy as they offer enhanced therapeutic outcome on cancer cells with an imaging opportunity at the same time. However, photosensitizers (PS) cores that can be easily converted to activity-based photosensitizers (aPSs) are still quite limited in the literature. In this study, we modified the dicyanomethylene-4H-chromene (DCM) core with a heavy iodine atom to get two different PSs (DCMO-I, I-DCMO-Cl) that can be further converted to aPS after simple modifications. The effect of iodine positioning on singlet oxygen generation capacity was also evaluated through computational studies. DCMO-I showed better performance in solution experiments and further proved to be a promising phototheranostic scaffold via cell culture studies. Later, a cysteine (Cys) activatable PS based on the DCMO-I core (DCMO-I-Cys) was developed, which induced selective photocytotoxicity along with a fluorescence turn-on response in Cys rich cancer cells.

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.