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

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.

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.

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.

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.

Excited-state properties of organic semiconductor dyes as electrically pumped lasing candidates from new optimally tuned range-separated models

Even though many efforts have been devoted to optical lasing in recent years, the realization of lasing by direct electrical excitation of organic semiconductors is hampered mainly due to optical losses from electrical contacts and electrical losses induced by triplets and polarons at high current densities. Hereby, accurately accounting for the electrically pumped organic semiconductor laser diodes (OSLDs) still remains one of the greatest challenges in optoelectronics. In this work, the excited-state characteristics of the organic semiconductor dyes used in the electrically pumped OSLDs have thoroughly been investigated using optimally tuned range-separated hybrids (OT-RSHs). Considering several experimentally known compounds of the electrically pumped OSLDs as working models, several variants of OT-RSHs, their combination forms with the polarizable continuum model (PCM), OT-RSH-PCM, as well as their screened versions accounting for the screening effects by the electron correlation through the scalar dielectric constant, OT-SRSHs, have been proposed for reliable prediction of their emission energies and oscillator strengths in both the gas and solvent phases. The role of involved ingredients in the models, namely, the underlying density functional approximations, short- and long-range exact-like exchange, as well as the range-separation parameter, has been examined in detail. It is shown that the newly designed OT-RSHs with the correct behavior of asymptotic exchange-correlation potential outperform the standard RSHs and other density functionals with both fixed and interelectronic distance-dependent exact-like exchange for describing the excite-state properties of compounds of the electrically pumped OSLDs. Concerning the computational cost of the models, it is unveiled that performing both the optimal tuning procedure and subsequent excited-state computations using OT-RSHs in the gas phase can be considered as a more reliable and affordable framework. Finally, the applicability of the proposed models is also put into a broader perspective for the computational design of several compounds as promising candidates to be used in the OSLD materials. Hopefully, our recommended OT-RSHs can function as efficient models for both the related theoretical modeling and confirming the experimental observations in the field of electrically pumped OSLDs.

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.

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.