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.

Using a multistate mapping approach to surface hopping to predict the ultrafast electron diffraction signal of gas-phase cyclobutanone

Using the recently developed multistate mapping approach to surface hopping (multistate MASH) method combined with SA(3)-CASSCF(12,12)/aug-cc-pVDZ electronic structure calculations, the gas-phase isotropic ultrafast electron diffraction (UED) of cyclobutanone is predicted and analyzed. After excitation into the n-3s Rydberg state (S2), cyclobutanone can relax through two S2/S1 conical intersections, one characterized by compression of the CO bond and the other by dissociation of the α-CC bond. Subsequent transfer into the ground state (S0) is then achieved via two additional S1/S0 conical intersections that lead to three reaction pathways: α ring-opening, ethene/ketene production, and CO liberation. The isotropic gas-phase UED signal is predicted from the multistate MASH simulations, allowing for a direct comparison to the experimental data. This work, which is a contribution to the cyclobutanone prediction challenge, facilitates the identification of the main photoproducts in the UED signal and thereby emphasizes the importance of dynamics simulations for the interpretation of ultrafast experiments.

First-Principles Calculations of Excited-State Decay Rate Constants in Organic Fluorophores

In this Perspective, we discuss recent advances made to evaluate from first-principles the excited-state decay rate constants of organic fluorophores, focusing on the so-called static strategy. In this strategy, one essentially takes advantage of Fermi's golden rule (FGR) to evaluate rate constants at key points of the potential energy surfaces, a procedure that can be refined in a variety of ways. In this way, the radiative rate constant can be straightforwardly obtained by integrating the fluorescence line shape, itself determined from vibronic calculations. Likewise, FGR allows for a consistent calculation of the internal conversion (related to the non-adiabatic couplings) in the weak-coupling regime and intersystem crossing rates, therefore giving access to estimates of the emission yields when no complex photophysical phenomenon is at play. Beyond outlining the underlying theories, we summarize here the results of benchmarks performed for various types of rates, highlighting that both the quality of the vibronic calculations and the accuracy of the relative energies are crucial to reaching semiquantitative estimates. Finally, we illustrate the successes and challenges in determining the fluorescence quantum yields using a series of organic fluorophores.

Extensive Analysis of the Parameters Influencing Radiative Rates Obtained through Vibronic Calculations

Defining a theoretical model systematically delivering accurate ab initio predictions of the fluorescence quantum yields of organic dyes is highly desirable for designing improved fluorophores in a systematic rather than trial-and-error way. To this end, the first required step is to obtain reliable radiative rates (kr), as low kr typically precludes effective emission. In the present contribution, using a series of 10 substituted phenyls with known experimental kr, we analyze the impact of the computational protocol on the kr determined through the thermal vibration correlation function (TVCF) approach on the basis of time-dependent density functional theory (TD-DFT) calculations of the energies, structures, and vibrational parameters. Both the electronic structure (selected exchange-correlation functional, application or not of the Tamm-Dancoff approximation) and the vibronic parameters (line-shape formalism, coordinate system, potential energy surface model, and dipole expansion) are tackled. Considering all possible combinations yields more than 3500 cases, allowing to extract statistically-relevant information regarding the impact of each computational parameter on the magnitude of the estimated kr. It turns out that the selected vibronic model can have a significant impact on the computed kr, especially the potential energy surface model. This effect is of the same order of magnitude as the difference noted between B3LYP and CAM-B3LYP estimates. For the treated compounds, all evaluated functionals do deliver reasonable trends, fitting the experimental values.

De novo creation of a naked eye-detectable fluorescent molecule based on quantum chemical computation and machine learning

Designing fluorescent molecules requires considering multiple interrelated molecular properties, as opposed to properties that straightforwardly correlated with molecular structure, such as light absorption of molecules. In this study, we have used a de novo molecule generator (DNMG) coupled with quantum chemical computation (QC) to develop fluorescent molecules, which are garnering significant attention in various disciplines. Using massive parallel computation (1024 cores, 5 days), the DNMG has produced 3643 candidate molecules. We have selected an unreported molecule and seven reported molecules and synthesized them. Photoluminescence spectrum measurements demonstrated that the DNMG can successfully design fluorescent molecules with 75% accuracy (n = 6/8) and create an unreported molecule that emits fluorescence detectable by the naked eye.

Individual control of singlet lifetime and triplet yield in halogen-substituted coumarin derivatives

The photophysical properties of three 3-diethylphosphonocoumarin derivatives are studied by transient absorption spectroscopy and DFT calculations. The measured lifetime of the first excited singlet state changes upon halogen substitution at the 6-position from 40 ps for the unsubstituted compound to 100 ps for Cl and 24 ps for Br. This observation is in clear contradiction with the estimated singlet–triplet quantum yield, which increases with atomic weight of the substituted atom and is usually referred as a heavy-atom effect. The DFT calculations give evidence that the main reason for this behavior is the different composition of the HOMO, while the LUMO is similar for all three compounds. The optical excitation leads to intramolecular charge transfer from the halogen lone pairs to the π* molecular orbital and thus to a significant change in the molecular dipole moment. Hence, the latter phenomenon in combination with the heavy-atom effect enables an independent control of singlet lifetime and singlet–triplet quantum yield in the studied 3-diethylphosphonocoumarin derivatives.

The photophysical properties of three 3-diethylphosphonocoumarin derivatives are studied by transient absorption spectroscopy and DFT calculations.

The Interplay between Solvation and Stacking of Aromatic Rings Governs Bright and Dark Sites of Benzo[g]coumarins

Coumarins are classic, strongly polarized fluorophores with multiple applications, and significant efforts have been put into modifying their emission characteristics and elucidating their photophysics. Expecting that π-expansion of these donor-acceptor chromophores could modify their ground- and excited-state characteristics, the authors performed combined, detailed photophysical and computational studies of linearly π-expanded coumarins, that is, 8-dialkylamino-3-carboxyalkyl-benzo[g]coumarins. The investigation led to the conclusion that emission is only possible thanks to the stabilizing effect of the solvent and that breaking of the lactone ring leads to the conical intersection with the ground state and induces the radiationless decay of the electronic excitation. Aiming at the fine-tuning the excited state properties through the construction of covalently linked dye assemblies, the authors designed and synthesized a new bis(benzo[g]coumarin), built from two similar moieties that exhibit different degrees of polarization due to the electron donor at position 8: one possesses a dialkylamino, and the other a weaker amide donor. Comprehensive studies have shown that the observed weak fluorescence of the system is the result of the interplay between the solvation-induced separation of the benzo[g]coumarin moieties, which stabilizes the emitting locally excited singlet state and the π-stacking interactions, favoring their sandwiched orientation and leading to the non-emissive charge-transfer state.