An MS-CASPT2 Calculation of the Excited Electronic States of an Axial Difluoroborondipyrromethene (BODIPY) Dimer

Investigation of excited states of BODIPY derivatives and non-orthogonal dimers from the perspective of singlet fission

We report state of the art electronic structure calculations RICC2 and XMCQDPT of BODIPY nonorthogonal dimers to understand the photophysical processes from the intramolecular singlet fission (iSF) perspective. We have calculated singlet, triplet and quintet states at the XMCQDPT(8,8)/cc-pVDZ level of theory and diabatic singlet states at the XMCQDPT(4,4)/cc-pVDZ level of theory. In all the systems studied, charge transfer states (1(CA) and 1(AC)) couple strongly with locally excited (1(S1S0)) and multiexcitonic (1(T1T1)) states. The rates of formation of the multiexcitonic state from the locally excited state are very low on account of large activation energy (E(1(T1T1)) - E(1(S1S0))). A relaxed scan along the torsional angle revealed contrasting results for axial and orthogonal conformers. We proposed a probable mechanism for contrasting photophysical properties of dimers B[3,3] and B[2,8]. We also found that substitution of CN, NH2 and BH2 at meso, β and α positions reduces the energy gap (ΔSF = 2E(T1) - E(S1)) significantly, making iSF a competing process in triplet state generation. Intrigued by the success of the CN group at the meso position in reducing the energy gap, we also studied the azaBODIPY monomer and its derivatives using the same methodology. The iSF is slightly endoergic with ΔSF ∼ 0.2 eV in these systems and iSF may play an important role in their photophysical responses.

Excitation localization/delocalization induced intramolecular singlet fission in cyclopentadithiophene-based quinoidal derivatives

Two triplet excitons are generated through an ultrafast photophysical process, namely singlet fission (SF), providing a solution for efficient solar energy usage. In this work, we provide an effective guideline for designing SF materials by adjusting the planarity in cyclopentadithiophene (CPDT) derivatives. A practical strategy is proposed for tuning the quinoidal-biradical resonance structures by varying the electron push-pull groups of CPDTs for SF. The localized, delocalized, and intermediate charge-transfer excited configurations are predicted in the singlet excited state via computational simulations, which is further confirmed by ultrafast spectroscopy. Deduced from the potential energy surfaces in the low-lying excited states and transient absorption, the delocalized excited state is formed in 2.1 ps via postulated intramolecular SF in a polar solvent, followed by the ultrafast formation of the free triplet state with a lifetime of 6.8 ps. In comparison with different cross-conjugated chromophores, it is found that the increase in the charge separation could enhance the triplet-pair generation for iSF. We expect that by introducing symmetry-breaking modifications in the electronic configurations and adjusting the separation between the push-pull groups of CPDTs, it should be possible to prolong the duration of the free triplet state by preventing recombination within the triplet-pair excited configuration.

Singlet fission initiating triplet generations of BODIPY derivatives through [Formula: see text]-stacking: a theoretical study

The role of singlet fission (SF) in the triplet-state generation mechanism of 1,3,5,7-tetramethyl-boron-dipyrromethene derivatives is revealed by exploring the cause for the solvent dependence of the generation rate. Comparing the adsorption energy calculations of solvent molecules, i.e., cyclohexane, chloroform and acetonitrile molecules, to the derivatives with the [Formula: see text]-stacking energies of these derivatives surprisingly show that the hierarchy of the solvation energies and [Formula: see text]-stacking energies strongly correlates with the experimentally-suggested solvent dependence of the triplet-state generation of these derivatives for five and more adsorbing solvent molecules. Following this finding, the excitation spectra of these derivatives in acetonitrile solvent are explored using the proprietary spin-flip long-range corrected time-dependent density functional theory. It is, consequently, confirmed that the [Formula: see text]-stacking activates the second lowest singlet excitation to trigger the spin-allowed transition to the singlet doubly-excited tetraradical (TT)[Formula: see text] state, which generates the long-lived quintet (TT)[Formula: see text] state causing the SF. However, it is also found that the [Formula: see text]-stacking also get a slow intersystem crossing active around the intersections of the lowest singlet excitations with the lowest triplet T[Formula: see text] excitations in parallel with the SF due to the charge transfer characters of the lowest singlet excitations. These results suggest that SF initiates the triplet-state generations through near-degenerate low-lying singlet and (TT) excitations with a considerable singlet-triplet energy gap after the [Formula: see text]-stacking of chromophores stronger than but not far from the solvation. Since these derivatives are organic photosensitizers, this study proposes that SF should be taken into consideration in developing novel heavy atom-free organic photosensitizers, which will contribute to a variety of research fields such as medical care, photobiology, energy science, and synthetic chemistry.

Accurate Vertical Excitation Energies of BODIPY/Aza-BODIPY Derivatives from Excited-State Mean-Field Calculations

We report a benchmark study of vertical excitation energies and oscillator strengths for the HOMO → LUMO transitions of 17 boron–dipyrromethene (BODIPY) structures, showing a large variety of ring sizes and substituents. Results obtained at the time-dependent density functional theory (TDDFT) and at the delta-self-consistent-field (ΔSCF) by using 13 different exchange correlation kernels (within LDA, GGA, hybrid, and range-separated approximations) are benchmarked against the experimental excitation energies when available. It is found that the time-independent ΔSCF DFT method, when used in combination with hybrid PBE0 and B3LYP functionals, largely outperforms TDDFT and can be quite competitive, in terms of accuracy, with computationally more costly wave function based methods such as CC2 and CASPT2.

Semi-Empirical Calculation of Bodipy Aggregate Spectroscopic Properties through Direct Sampling of Configurational Ensembles

Efficient prediction of the aggregation-induced callback of organic chromophores for utilization in molecular sensorics is a desirable development goal in modern computational chemistry. Dye aggregates are complicated to study when utilizing conventional quantum chemistry approaches, since they are usually composed of too many atoms to be effectively analyzed, even with high-throughput parallel systems. Here, we present a successful attempt to develop a protocol to assess the spectroscopic changes happening in BODIPY dyes upon aggregation from the first principles utilizing extended tight-binding (XTB) and Zerner's intermediate neglect of differential overlap (ZINDO) Hamiltonians. The developed sampling technique for aggregate configurational space scanning was found to be sufficient to both reproduce peculiarities and justify experimental data on the spectroscopic behavior of chromophore aggregates. The sTDA, sTD-DFT (GFN2-XTB) and CIS (ZINDO) approaches were assessed, and then sources of errors and benefits were outlined. Importantly, our goal was to keep any of the mentioned calculations within a computational cost feasible for a single workstation, whereas scaling was possible at any point in time. Finally, several aggregate structures were investigated in the external field to try to achieve distributions similar to the ones observed in the electrostatic potential of the air-water interface to assess the borderlines of practical applicability of the suggested scheme.

A local pair-natural orbital-based complete-active space perturbation theory using orthogonal localized virtual molecular orbitals

The multireference second-order perturbation theory (CASPT2) is known to deliver a quantitative description of various complex electronic states. Despite its near-size-consistent nature, the applicability of the CASPT2 method to large, real-life systems is mostly hindered by large computational and storage costs for the two-external tensors, such as two-electron integrals, amplitudes, and residuum. To this end, Menezes and co-workers developed a reduced-scaling CASPT2 scheme by incorporating the local pair-natural orbital (PNO) representation of the many-body wave functions using non-orthonormal projected atomic orbitals (PAOs) into the CASPT theory [F. Menezes et al., J. Chem. Phys. 145, 124115 (2016)]. Alternatively, in this paper, we develop a new PNO-based CASPT2 scheme using the orthonormal localized virtual molecular orbitals (LVMOs) and assess its performance and accuracy in comparison with the conventional PAO-based counterpart. Albeit the compactness, the LVMOs were considered to perform somewhat poorly compared to PAOs in the local correlation framework because they caused enormously large orbital domains. In this work, we show that the size of LVMO domains can be rendered comparable to or even smaller than that of PAOs by the use of the differential overlap integrals for domain construction. Optimality of the MOs from the CASSCF treatment is a key to reducing the LVMO domain size for the multireference case. Due to the augmented Hessian-based localization algorithm, an additional computational cost for obtaining the LVMOs is relatively minor. We demonstrate that the LVMO-based PNO-CASPT2 method is routinely applicable to large, real-life molecules such as Menshutkin SN2 reaction in a single-walled carbon nanotube reaction field.

Benchmarking CASPT3 Vertical Excitation Energies

Based on 280 reference vertical transition energies of various natures (singlet, triplet, valence, Rydberg, n → π∗, π → π∗, and double excitations) extracted from the QUEST database, we assess the accuracy of third-order multireference perturbation theory, CASPT3, in the context of molecular excited states. When one applies the disputable ionization- potential-electron-affinity (IPEA) shift, we show that CASPT3 provides a similar accuracy as its second-order counterpart, CASPT2, with the same mean absolute error of 0.11 eV. However, as already reported, we also observe that the accuracy of CASPT3 is almost insensitive to the IPEA shift, irrespective of the transition type and system size, with a small reduction of the mean absolute error to 0.09 eV when the IPEA shift is switched off.

Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies

Methods able to simultaneously account for both static and dynamic electron correlations have often been employed, not only to model photochemical events but also to provide reference values for vertical transition energies, hence allowing benchmarking of lower-order models. In this category, both the complete-active-space second-order perturbation theory (CASPT2) and the N-electron valence state second-order perturbation theory (NEVPT2) are certainly popular, the latter presenting the advantage of not requiring the application of the empirical ionization-potential-electron-affinity (IPEA) and level shifts. However, the actual accuracy of these multiconfigurational approaches is not settled yet. In this context, to assess the performances of these approaches, the present work relies on highly accurate (±0.03 eV) aug-cc-pVTZ vertical transition energies for 284 excited states of diverse character (174 singlet, 110 triplet, 206 valence, 78 Rydberg, 78 n → π*, 119 π → π*, and 9 double excitations) determined in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. The CASPT2 calculations are performed with and without IPEA shift and compared to the partially contracted (PC) and strongly contracted (SC) variants of NEVPT2. We find that both CASPT2 with IPEA shift and PC-NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of 0.11 and 0.13 eV, respectively. These values are found to be rather uniform for the various subgroups of transitions. The present work completes our previous benchmarks focused on single-reference wave function methods ( J. Chem. Theory Comput. 2018, 14, 4360; J. Chem. Theory Comput. 2020, 16, 1711), hence allowing for a fair comparison between various families of electronic structure methods. In particular, we show that ADC(2), CCSD, and CASPT2 deliver similar accuracies for excited states with a dominant single-excitation character.

Generation of multiple triplet states in an orthogonal bodipy dimer: a breakthrough spectroscopic and theoretical approach

Generation of triplet states in assemblies of organic chromophores is extremely appealing for their potential use in optoelectronic applications. In this work, we investigate the intricacies of triplet state generation in an orthogonal BODIPY dimer by combining delayed photoemission techniques with electronic structure calculations. Our analysis provides a deep understanding of the electronic states involved, and describes different competing deactivation channels beyond prompt radiative decay. In particular, we identify charge-transfer (CT) mediated intersystem crossing (ISC) as the most likely mechanism for the triplet state generation in this system. The different emission bands at long times can be associated with delayed fluorescence, CT emission and phosphorescence from multiple low-energy triplets. Interestingly, the dependence of the yield of triplet state population and emission profiles with the solvent polarity evidences the decisive role of the CT configuration in the fate of the photoactivated dimer, controlling the relative ISC, reverse ISC, and internal conversion efficiencies. Overall, the present results provide a rather complete description of the delayed photophysics in the BODIPY dimer, but are not able to fully rationalize the unexpected photoluminescence recorded at long wavelengths (≥ 900 nm). We hypothesize that the origin of this emission, not present in BODIPY monomers, emerges from intermonomer interactions triggered by intramolecular distortions opening up a new vision in the controverted mechanism driving the photophysical behavior from orthogonally linked organic monomers.

Dye-sensitized solar cells strike back

Dye-sensitized solar cells (DSCs) are celebrating their 30th birthday and they are attracting a wealth of research efforts aimed at unleashing their full potential. In recent years, DSCs and dye-sensitized photoelectrochemical cells (DSPECs) have experienced a renaissance as the best technology for several niche applications that take advantage of DSCs' unique combination of properties: at low cost, they are composed of non-toxic materials, are colorful, transparent, and very efficient in low light conditions. This review summarizes the advancements in the field over the last decade, encompassing all aspects of the DSC technology: theoretical studies, characterization techniques, materials, applications as solar cells and as drivers for the synthesis of solar fuels, and commercialization efforts from various companies.

Mild Open-Shell Character of BODIPY and Its Impact on Singlet and Triplet Excitation Energies

This study describes and rationalizes the electronic structure of BODIPY combining a large variety of quantum chemistry methods and computational tools. Examination of the obtained results using state-of-the-art electronic structure analyses provides a new and complete interpretation of the nature of low-lying electronic states in BODIPY and elucidates the limitations of excited-state methods in the computation of T₁ and S₁ energies, that is, systematic under- and overestimation of time-dependent density functional theory energies, respectively, and a large overestimation of the T₁/S₁ energy gap. Our analysis identifies the important role and physical origin of the mild open-shell character in the BODIPY ground state, that is, strong highest occupied and lowest unoccupied molecular orbital exchange interactions. The study provides guidelines for the accurate quantification of the T₁/S₁ gap, which is extremely relevant for the computational investigation of the photophysical properties of BODIPY and its derivatives. These conclusions should be taken into consideration in order to predict and interpret conspicuous photoactivated phenomena such as intersystem crossing, singlet fission, and triplet-triplet annihilation. Moreover, we believe that our study might provide new ideas and strategies for the analysis of other molecular chromophores.

From photosensitizers to light harvesters adapting the molecular structure in all-BODIPY assemblies

Herein we detail a protocol to design dyads and triads based solely on BODIPY dyes as halogen-free singlet oxygen photosensitizers or energy transfer molecular cassettes. The conducted photonic characterization reveals the key role of the BODIPY-BODIPY linkage to finely modulate the balance between the triplet state population and fluorescence decay.

Women in the Singlet Fission World: Pearls in a Semi-Open Shell

Singlet fission, a multiple exciton generation process, can revolutionize existing solar cell technologies. Offering the possibility to double photocurrent, the process has become a focal point for physicists, chemists, software developers, and engineers. The following review is dedicated to the female investigators, predominantly theorists, who have contributed to the field of singlet fission. We highlight their most significant advances in the subject, from deciphering the mechanism of the process to designing coveted singlet fission materials.

Assessment of local coupled cluster methods for excited states of BODIPY/Aza-BODIPY families

It was previously reported that Laplace transformed local CC2 (LCC2*) provided the best agreement (MAE = 0.145 eV) when comparing vertical excitation energies to experimental λ_max for a benchmark set of 17 BODIPY/Aza-BODIPY molecules. However, these energies did not agree with values obtained from canonical CC2. Here we report LCC2* computations of vertical excitation energies on the same benchmark set of molecules using a newly implemented treatment of the ground state. Comparison with resolution-of-identity approximate coupled cluster to second-order (RI-CC2) results demonstrate that the new LCC2* results agree quantitatively. Furthermore, these values can easily be corrected empirically to also provide excellent agreement with the experiment. We show that the local algebraic diagrammatic construction to second-order (LADC(2)) method exhibits the same differences between implementations as seen for LCC2. The source of the difference is traced to an improved treatment of the ground state in the local methods, which decreases agreement with the experiment (as attributed to a fortuitous cancellation of errors) but significantly improves agreement with RI-CC2. While the absolute vertical excitation energies now show larger deviations, there remains a strong linear correlation between the LCC2* results and the experiment. For the 17 BODIPY/Aza-BODIPY molecules vertical excitation energies are determined using DLPNO-STEOM-CCSD and shown to have excellent agreement with experimental λ_max (MAE = 0.145 eV), which is the best of all the single-reference methods. The vertical excitation energies are determined using LCC2*, empirically corrected LCC2*, and RI-CC2 for a series of eight large BODIPYs and Aza-BODIPYs.

A hybrid approach to excited-state-specific variational Monte Carlo and doubly excited states

We extend our hybrid linear-method/accelerated-descent variational Monte Carlo optimization approach to excited states and investigate its efficacy in double excitations. In addition to showing a superior statistical efficiency when compared to the linear method, our tests on small molecules show good energetic agreement with benchmark methods. We also demonstrate the ability to treat double excitations in systems that are too large for a full treatment by using selected configuration interaction methods via an application to 4-aminobenzonitrile. Finally, we investigate the stability of state-specific variance optimization against collapse to other states' variance minima and find that symmetry, Ansatz quality, and sample size all have roles to play in achieving stability.

Toward Quantitative Prediction of Fluorescence Quantum Efficiency by Combining Direct Vibrational Conversion and Surface Crossing: BODIPYs as an Example

Accurate theoretical description of the electronic structure of boron dipyrromethene (BODIPY) molecules has been a challenge, let alone the prediction of fluorescence quantum efficiency. In this Letter, we show that the electronic structures of BODIPYs can be accurately evaluated via the spin-flip time-dependent density functional theory with the B3LYP functional. With the resulting electronic structures, the experimental spectral line shapes of representative BODIPYs are successfully reproduced by our previously developed thermal vibration correlation function method. Most importantly, a two-channel scheme is proposed to describe the internal conversion of S₁ to S₀ in BODIPYs: channel I via direct vibrational relaxation within the harmonic region and channel II via a distorted S₀/S₁ minimum energy crossing point well away from the harmonic region. The fluorescence quantum yields are accurately predicted within this two-channel scheme, which can therefore serve as a generalized method for predicting the photophysical parameters of organic fluorescent compounds.

Boron-Doped Polycyclic Aromatic Hydrocarbons: A Molecular Set Revealing the Interplay between Topology and Singlet Fission Propensity

We demonstrate the relationship between the topology (the way in which the atoms are connected), open-shell character, and singlet fission (SF) propensity in a series of diboron-doped anthracenes and phenanthrenes. The study is performed by using high-level wave-function-based quantum-chemical calculations. The results show that the molecular topology plays a crucial role for the optical properties and, respectively, for the SF propensity of the studied compounds. The topology-derived correlations between the structure and properties are interpreted in the light of the Kekulé hydrocarbons concept and serve as molecular design guidelines for the discovery of new SF materials. Finally, several boron-doped polycyclic aromatic hydrocarbons are proposed as SF chromophores for organic solar cells.