Tetracyanoethylene as a Building Block in the π-Expansion of 1,4-Dihydropyrrolo[3,2-b]pyrroles.

The outcome of the reaction of tetracyanoethylene with 1,4-dihydropyrrolo[3,2-b]pyrroles (DHPPs) strongly depends on the character of the substituents present at positions 2 and 5. With electron-withdrawing substituents, the reaction does not occur at all, while, in contrast, the presence of electron-donating substituents yields addition-elimination products. When thiazol-2-yl substituents are located at positions 2 and 5, addition occurs at the thiazole ring, rather than of the DHPP core. In cases where very electron-rich heterocycles are present at positions 2 and 5, a second addition occurs followed by aromatization, leading to the formation of an additional benzene ring bridging two heterocyclic scaffolds. The reaction occurs only at one site since the presence of the strongly electron-withdrawing tricyanoethylene group has a profound impact on electron density at the remaining free position 6. The DHPPs possessing a tricyanoethylene group are strongly polarized and thus enable a push-pull system showing red-shifted absorption and negligible fluorescence. In contrast, dyes possessing a 1,2-dicyanobenzene moiety exhibit strong emission bathochromically shifted by over 100 nm compared to parent 1,4-dihydrotetraarylpyrroles[3,2-b]pyrroles (TAPPs). Computational studies shed light on the evolution of the photophysical properties as a function of the substitution pattern of the final systems.

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(N5) and O(N6) 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.

Assessing the accuracy of TD-DFT excited-state geometries through optimal tuning with GW energy levels.

We study the accuracy of excited state (ES) geometries using optimally tuned LC-PBE functionals with tuning based on GW quasiparticle energies. We compare the results obtained with the PBE, PBE0, non-tuned, and tuned LC-PBE functionals with available high-level CC reference values as well as experimental data. First, we compare ES geometrical parameters obtained for three different types of systems: molecules composed of a few atoms, 4-(dimethylamino)benzonitrile (DMABN), and conjugated dyes. To this end, we used wave-function results as benchmarks. Next, we evaluate the accuracy of the theoretically simulated spectra as compared to the experimental ones for five large dyes. Our results show that, besides small compact molecules for which tuning LC-PBE does not allow obtaining geometries more accurate than those computed with standard functionals, tuned range-separated functionals are clearly to be favored, not only for ES geometries but also for 0-0 energies, band shapes, and intensities for absorption and emission spectra. In particular, the results indicate that GW-tuned LC-PBE functionals provide improved matching with experimental spectra as compared to conventionally tuned functionals. It is an open question whether TD-DFT with GW-tuned functionals can qualitatively mimic the actual many-body Bethe-Salpeter (BSE/GW) formalism for which analytic ionic gradients remain to be developed.

Phospha-cyanines in Their Ideal Polymethine State: Synthesis and Structure-Property Relationships.

We report the synthesis and full characterization of a family of phosphorus-containing polymethine cyanines (phospha-cyanines). The compounds are easily prepared in two steps, starting from readily available phosphanes. The impact of the P-substituents and the counterions on the structural and optical properties is investigated through a joint experimental/theoretical approach. Based on the study of the single-crystal X-ray diffraction structures, all phospha-cyanines present a bond length alternation close to zero, independently of the substituents and counterions, which indicates an ideal polymethine state. All these compounds display the typical cyanine-like UV-vis absorption with an intense and sharp transition with a vibronic shoulder despite possessing a reverse electronic configuration compared to "classical" cyanines. Time-dependent density-functional theory calculations allowed us to fully rationalize the optical properties (absorption/emission wavelengths, luminescence quantum yields). Interestingly, due to the tetrahedral shape of the P atom, the optical properties are independent of the counterion, which is in marked contrast with N-analogues, which enables predictive engineering of the phospha-cyanines regardless of the medium in which they are used.

Gold-Catalyzed 1,2-Aryl Shift and Double Alkyne Benzannulation.

The tandem intramolecular hydroarylation of alkynes accompanied by a 1,2-aryl shift is described. Harnessing the unique electron-rich character of 1,4-dihydropyrrolo[3,2-b]pyrrole scaffold, we demonstrate that the hydroarylation of alkynes proceeds at the already occupied positions 2 and 5 leading to a 1,2-aryl shift. Remarkably, the reaction proceeds only in the presence of cationic gold catalyst, and it leads to heretofore unknown π-expanded, centrosymmetric pyrrolo[3,2-b]pyrroles. The utility is verified in the preparation of 13 products that bear six conjugated rings. The observed compatibility with various functional groups allows for increased tunability with regard to the photophysical properties as well as providing sites for further functionalization. Computational studies of the reaction mechanism revealed that the formation of the six-membered rings accompanied with a 1,2-aryl shift is both kinetically and thermodynamically favourable over plausible formation of products containing 7-membered rings. Steady-state UV/Visible spectroscopy reveals that upon photoexcitation, the prepared S-shaped N-doped nanographenes undergo mostly radiative relaxation leading to large fluorescence quantum yields. Their optical properties are rationalized through time-dependent density functional theory calculations. We anticipate that this chemistry will empower the creation of new materials with various functionalities.

Excess and excited-state dipole moments of real-life dyes: a comparison between wave-function, BSE/GW, and TD-DFT values.

In this work, we assess the accuracy of the Bethe-Salpeter equation (BSE) many-body Green's function formalism, adopting the eigenvalue-self-consistent evGW exchange-correlation kernel, for the calculation of the excited-state (µES) and excess dipole moments (Δµ), the latter ones being the changes of dipole amplitude between the ground and excited states (ES), in organic dyes. We compare the results obtained with wave-function methods [ADC(2), CC2, and CCSD], time-dependent density functional theory (TD-DFT), and BSE/evGW levels of theory. First, we compute the evolution of the dipole moments of the two lowest singlet excited states of 4-(dimethylamino)benzonitrile (DMABN) upon twisting of the amino group. Next, we use a set of 25 dyes having ES characters ranging from locally excited to charge transfer to determine both µES and Δµ. For DMABN our results show that BSE/evGW provides Δµ values closer to the CCSD reference and more consistent trends than TD-DFT. Moreover, a statistical analysis of both Δµ and µES for the set of 25 dyes shows that the BSE/evGW accuracy is comparable or sometimes slightly better than that of TD-M06-2X and TD-CAM-B3LYP, BSE/evGW outperforming TD-DFT in challenging cases (zwitterionic and cyanine transitions). Finally, the starting point dependency of BSE/evGW seems to be larger for Δµ, ES dipoles, and oscillator strengths than for transition energies.

Lagrangian Z-vector approach to Bethe-Salpeter analytic gradients: Assessing approximations.

We present an implementation of excited-state analytic gradients within the Bethe-Salpeter equation formalism using an adapted Lagrangian Z-vector approach with a cost independent of the number of perturbations. We focus on excited-state electronic dipole moments associated with the derivatives of the excited-state energy with respect to an electric field. In this framework, we assess the accuracy of neglecting the screened Coulomb potential derivatives, a common approximation in the Bethe-Salpeter community, as well as the impact of replacing the GW quasiparticle energy gradients by their Kohn-Sham analogs. The pros and cons of these approaches are benchmarked using both a set of small molecules for which very accurate reference data are available and the challenging case of increasingly extended push-pull oligomer chains. The resulting approximate Bethe-Salpeter analytic gradients are shown to compare well with the most accurate time-dependent density-functional theory (TD-DFT) data, curing in particular most of the pathological cases encountered with TD-DFT when a nonoptimal exchange-correlation functional is used.

Exploring Bethe-Salpeter Excited-State Dipoles: The Challenging Case of Increasingly Long Push-Pull Oligomers.

The change of molecular dipole moment induced by photon absorption is key to interpret the measured optical spectra. Except for compact molecules, time-dependent density functional theory (TD-DFT) remains the only theory allowing to quickly predict excited-state dipoles (µES), albeit with a strong dependency on the selected exchange-correlation functional. This Letter presents the first assessment of the performances of the many-body Green's function Bethe-Salpeter equation (BSE) formalism for the evaluation of the µES. We explore increasingly long push-pull oligomers as they present an excited-state nature evolving with system size. This work shows that BSE's µES do present the same evolution with oligomeric length as their CC2 and CCSD counterparts, with a dependency on the starting exchange-correlation functional that is strongly decreased as compared to TD-DFT. This Letter demonstrates that BSE is a valuable alternative to TD-DFT for properties related to the excited-state density and not only for transition energies and oscillator strengths.

Excited state potential energy surfaces of N-phenylpyrrole upon twisting: reference values and comparison between BSE/GW and TD-DFT.

The puzzling case of the mixing between the charge transfer (CT) and local excited (LE) characters upon twisting of the geometry of N-phenylpyrrole (N-PP) is investigated considering the six low-lying singlet excited states (ES). The theoretical calculations of the potential energy surfaces (PES) have been performed for these states using a Coupled Cluster method accounting for the impact of the contributions from the triples, many-body Green's function GW and Bethe-Salpeter equation (BSE) formalisms, as well as Time-Dependent Density Functional Theory (TD-DFT) using various exchange-correlation functionals. Our findings confirm that the BSE formalism is more reliable than TD-DFT for close-lying ES with mixed CT/LE nature. More specifically, BSE/GW yields a more accurate evolution of the excited state PES than TD-DFT when compared to the reference coupled cluster values. BSE/GW PES curves also show negligible exchange-correlation functional starting point dependency in sharp contrast with their TD-DFT counterparts.

Modeling of excited state potential energy surfaces with the Bethe-Salpeter equation formalism: The 4-(dimethylamino)benzonitrile twist.

We present a benchmark study of excited state potential energy surfaces (PES) using the many-body Green's function GW and Bethe-Salpeter equation (BSE) formalisms, coupled cluster methods, as well as Time-Dependent Density Functional Theory (TD-DFT). More specifically, we investigate the evolution of the two lowest excited states of 4-(dimethylamino)benzonitrile (DMABN) upon the twisting of the amino group, a paradigmatic system for dual fluorescence and excited-state benchmarks. Our results demonstrate that the BSE/GW approach is able to reproduce the correct topology of excited state PES upon geometry changes in both gas and condensed phases. The vertical transition energies predicted by BSE/GW are indeed in good agreement with coupled cluster values, including triples. The BSE approach ability to include both linear response and state-specific solvent corrections further enables it to accurately describe the solvatochromism of both excited states during the twisting of DMABN. This contribution stands as one of the first proof-of-concept that BSE/GW PES should be accurate in cases for which TD-DFT struggles, including the central case of systems embedded in a dielectric environment.

Tuning the Charge Transfer in λ5-Phosphinines with Amino Substituents.

We report the substitution of λ5-phosphinines (2,6-dicarbonitrile diphenyl-1-λ5-phosphinine) with an amino group. The impact of these modifications on both the optical and redox properties is investigated using a joint experimental/theoretical approach. In particular, we show that the choice of the donor diphenylamino group dramatically impacts the nature of the charge transfer. The use of di(methoxyphenyl)amine redshifts the optical properties and allows thermally activated delayed fluorescence in the solid state. Finally, we demonstrated that λ5-phosphinines with an amino group can be used as active emitters in an electroluminescent device.