Benchmarking Density Functional Approximations for Excited-State Properties of Fluorescent Dyes

Why does the orientation of azulene affect the two-photon activity of a porphyrinoid-azulene system?

Attaching a dipolar molecule in a symmetric system induces a major change in the electronic structure, which may be reflected as the enhancement of the optical and charge-transfer properties of the combined system as compared to the pristine ones. Furthermore, the orientation of the dipolar molecule may also affect the said properties. This idea is explored in this work by taking porphyrinoid molecules as the pristine systems. We attached azulene, a dipolar molecule, at various positions of five porphyrinoid cores and studied the effect on charge-transfer and one- and two-photon absorption properties using the state-of-the-art RICC2 method. The attachment of azulene produces two major effects - firstly it introduces asymmetry in the system and, secondly, being dipolar, it makes the resultant molecule dipolar/quadrupolar. Porphyrin, N-confused porphyrin, sub-porphyrin, sapphyrin, and hexaphyrin are used as core porphyrinoid systems. The change in charge-transfer has been studied using the orbital analysis and charge-transfer distance parameter for the first five singlet states of the systems. The effect of orientation of azulene on the said properties is also explored. The insights gained from our observations are explored further at the dipole and transition dipole moment levels using a three-state model.

Synthesis and Regioselective Functionalization of Tetrafluorobenzo-[α]-Fused BOPYPY Dyes

The synthesis of a new bis-BF2 tetrafluorobenzo-[α]-fused BOPYPY dye from 4,5,6,7-tetrafluoroisoindole and 2-hydrazinopyrazine is reported. The regioselectivity of nucleophilic substitution reactions at the periphery of the tetrafluorinated BOPYPY and its α-bromo derivative were investigated using N-, O-, S-, and C-based nucleophiles. Among the aromatic fluorine atoms, the F2 atom is consistently regioselectively substituted, except when the α-position contains a thiophenol group; in this case, F4 is substituted instead due to stabilizing π-π-stacking between the two aromatic groups. The α-bromo BOPYPY derivative also reacts under Stille cross-coupling reaction conditions to produce the corresponding α-substituted product. The spectroscopic properties of these new fluorinated BOPYPYs were investigated and compared with nonfluorinated analogs.

Beyond Explored Functionals: A Computational Journey of Two-Photon Absorption

We present a thorough investigation into the efficacy of 19 density functional theory (DFT) functionals, relative to RI-CC2 results, for computing two-photon absorption (2PA) cross sections (σ2PA) and key dipole moments (|μ00|, |μ11|, |Δμ|, |μ01|) for a series of coumarin dyes in the gas-phase. The functionals include different categories, including local density approximation (LDA), generalized gradient approximation (GGA), hybrid-GGA (H-GGA), range-separated hybrid-GGA (RSH-GGA), meta-GGA (M-GGA), and hybrid M-GGA (HM-GGA), with 14 of them being subjected to analysis for the first time with respect to predicting σ2PA values. Analysis reveals that functionals integrating both short-range (SR) and long-range (LR) corrections, particularly those within the RSH-GGA and HM-GGA classes, outperform the others. Furthermore, the range-separation approach was found more impactful compared to the varying percentages of Hartree-Fock exchange (HF Ex) within different functionals. The functionals traditionally recommended for 2PA do not appear among the top 9 in our study, which is particularly interesting, as these top-performing functionals have not been previously investigated in this context. This list is dominated by M11, QTP variants, ωB97X, ωB97X-V, and M06-2X, surpassing the performance of other functionals, including the commonly used CAM-B3LYP.

One- and two-photon absorption spectra of organoboron complexes: vibronic and environmental effects

We synthesized a series of four parent aza-β-ketoiminate organoboron complexes and performed spectroscopic studies using both experimental and computational techniques. We studied how benzannulation influences the vibronic structure of the UV/Vis absorption bands with a focus on the bright lowest-energy π → π* electronic excitation. Theoretical simulations, accounting for inhomogeneous broadening effects using different embedding schemes, allowed gaining in-depth insights into the observed differences in band shapes induced by structural modifications. We observed huge variations in the distributions of vibronic transitions depending on the position of benzannulation. By and large, the harmonic approximation combined with the adiabatic hessian model delivers qualitatively correct band shapes for the one-photon absorption spectra, except in one case. We also assessed the importance of non-Condon effects (accounted for by the linear term in Herzberg-Teller expansion of the dipole moment) for S0 → S1 band shapes. It turned out that non-Condon contributions have no effect on the band shape in one-photon absorption spectra. In contrast, these effects significantly change the Franck-Condon band shapes of the two-photon absorption spectra. For one of the studied organoboron complexes we also performed a preliminary exploration of mechanical anharmonicity, resulting in an increase of the intensity of the 0-0 transition, which improves the agreement with the experimental data compared to the harmonic model.

A Curious Case of Two-Photon Absorption in n-Helicene and n-Phenylene, n=6-10: Why n=7 is Different?

n-Helicenes and n-Phenylenes are interesting examples of twisted molecules, where although the atoms are connected through conjugated π ${\pi }$ -bonds, the π ${\pi }$ -conjugation is largely hindered by the twisted nature of the bonds. Such structures provide a unique opportunity to study the effect of twisted π ${\pi }$ -system on non-linear optical properties. In this work, we studied the two-photon absorption in donor-acceptor substituted n-helicenes and n-phenylenes employing the state-of-the-art RI-CC2 method and reported a unique feature we observed in n=7 systems. We found that both 7-helicene and 7-phenylene systems exhibit largest two-photon absorption than other members in their respective classes. Furthermore, using generalized few-state model, we provided a detailed microscopic mechanism of this unique observation involving participation of different transition dipole moment vectors and their relative orientations.

Toward Accurate Two-Photon Absorption Spectrum Simulations: Exploring the Landscape beyond the Generalized Gradient Approximation

In this Letter, we present a pioneering analysis of the density functional approximations (DFAs) beyond the generalized gradient approximation (GGA) for predicting two-photon absorption (2PA) strengths of a set of push-pull π-conjugated molecules. In more detail, we have employed a variety of meta-generalized gradient approximation (meta-GGA) functionals, including SCAN, MN15, and M06-2X, to assess their accuracy in describing the 2PA properties of a chosen set of 48 organic molecules. Analytic quadratic response theory is employed for these functionals, and their performance is compared against the previously studied DFAs and reference data obtained at the coupled-cluster CC2 level combined with the resolution-of-identity approximation (RI-CC2). A detailed analysis of the meta-GGA functional performance is provided, demonstrating that they improve upon their predecessors in capturing the key electronic features of the π-conjugated two-photon absorbers. In particular, the Minnesota functional MN15 shows very promising results as it delivers pleasingly accurate chemical rankings for two-photon transition strengths and excited-state dipole moments.

Chromophore Planarity, -BH Bridge Effect, and Two-Photon Activity: Bi- and Ter-Phenyl Derivatives as a Case Study

In this work, we have employed electronic structure theories to explore the effect of the planarity of the chromophore on the two-photon absorption properties of bi- and ter-phenyl systems. To that end, we have considered 11 bi- and 7 ter-phenyl-based chromophores presenting a donor-π-acceptor architecture. In some cases, the planarity has been enforced by bridging the rings at ortho-positions by -CH2 and/or -BH, -O, -S, and -NH moieties. The results presented herein demonstrate that in bi- and ter-phenyl systems, the planarity achieved via a -CH2 bridge increases the 2PA activity. However, the introduction of a bridge with the -BH moiety perturbs the electronic structure to a large extent, thus diminishing the two-photon transition strength to the lowest electronic excited state. As far as two-photon absorption activity is concerned, this work hints toward avoiding -BH bridge(s) to enforce planarity in bi- and ter-phenyl systems; however, one may use -CH2 bridge(s) to achieve the enhancement of the property in question. All of these conclusions have been supported by in-depth analyses based on generalized few-state models.

Theoretical investigation on the functional group modulation of UV-Vis absorption profiles of triphenylamine derivatives

Understanding the functional group modulation of electronic structure and excitation is pivotal to the design of organic small molecules (OSMs) for photoelectric applications. In this study, we employed density functional theory (DFT) and time-dependent DFT (TDDFT) calculations to explore the unique absorption character of four triphenylamine photosensitizers. The various conformations were investigated given the multiple single bonds in the compounds, and the resemblance in the electronic structure of different conformations is affirmed because the coplanarity and consequent long-range conjugation is maintained regardless of the orientation of the flexible blocks. Six functionals were evaluated, and MN15 was found to successfully reproduce the intense secondary absorption peak for the double 3,4-ethylenedioxythiophene (EDOT) modified sensitizer over B3LYP, PBE0, M062X, CAM-B3LYP, and ωB97XD. The introduction of EDOT gives rise to a new excited state S4, which is a local excitation constrained in the EDOT substituent triphenylamine block. This new excited state S4, in combination with inherent S2 and S3 derived from prototype molecule TPA-Pyc, jointly contributes to the hump of the secondary absorption peak of ETE-Pyc and finally affects the light-harvesting ability of the dye-sensitized TiO2 photoanode. The current findings provide guidance toward the rational design of OSMs with good light-harvest ability.

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.

Cost-Effective Simulations of Vibrationally-Resolved Absorption Spectra of Fluorophores with Machine-Learning-Based Inhomogeneous Broadening

The results of electronic and vibrational structure simulations are an invaluable support for interpreting experimental absorption/emission spectra, which stimulates the development of reliable and cost-effective computational protocols. In this work, we contribute to these efforts and propose an efficient first-principle protocol for simulating vibrationally-resolved absorption spectra, including nonempirical estimations of the inhomogeneous broadening. To this end, we analyze three key aspects: (i) a metric-based selection of density functional approximation (DFA) so to benefit from the computational efficiency of time-dependent density function theory (TD-DFT) while safeguarding the accuracy of the vibrationally-resolved spectra, (ii) an assessment of two vibrational structure schemes (vertical gradient and adiabatic Hessian) to compute the Franck-Condon factors, and (iii) the use of machine learning to speed up nonempirical estimations of the inhomogeneous broadening. In more detail, we predict the absorption band shapes for a set of 20 medium-sized fluorescent dyes, focusing on the bright ππ^★ S₀ → S₁ transition and using experimental results as references. We demonstrate that, for the studied 20-dye set which includes structures with large structural variability, the preselection of DFAs based on an easily accessible metric ensures accurate band shapes with respect to the reference approach and that range-separated functionals show the best performance when combined with the vertical gradient model. As far as band widths are concerned, we propose a new machine-learning-based approach for determining the inhomogeneous broadening induced by the solvent microenvironment. This approach is shown to be very robust offering inhomogeneous broadenings with errors as small as 2 cm^-1 with respect to genuine electronic-structure calculations, with a total CPU time reduced by 98%.

Benchmarking DFT functionals for photophysics of pyranoflavylium cations

An intense absorption, phosphorescence, a long triplet excited state lifetime and singlet oxygen generation capabilities are characteristics of pyranoflavylium cations, analogues to pyranoanthocyanidins originated in the maturation process of red wine. Such properties make these compounds potential photosensitizers to be applied in photodynamic therapy. In this context, the photophysical processes underlying that treatment critically depend on the electronic structure of the pyranoflavylium molecules. When employing density functional theory to describe the electronic structure of molecules, the choice of the most suitable functional is not trivial, and benchmark studies are needed to orient practitioners in the field. In this work, a benchmark of seven of the most commonly used density functionals in addressing the photophysical properties of a set of eight pyranoflavylium cations is reported. Ground and excited state geometries, molecular orbitals, and absorption, fluorescence and phosphorescence transition energies were calculated using density functional theory approaches, and evaluated and compared to experimental data and monoreferential wave function-based methodologies. Statistical analysis of the results indicates that global-hybrid functionals allow an excellent description of absorption and emission energies, with errors around 0.05 eV, while range-separated variants led to somewhat larger errors in the range 0.1-0.2 eV. In contrast, range-separated functionals display excellent phosphorescence energies with errors close to 0.05 eV, in this case global-hybrids showing increased discrepancies around 0.5-0.1 eV.

Controlling the fluorescence quantum yields of benzothiazole-difluoroborates by optimal substitution

Precise tuning of the fluorescence quantum yield, vital for countless applications of fluorophores, remains exceptionally challenging due to numerous factors affecting energy dissipation phenomena often leading to its counterintuitive behavior. In contrast to the absorption and emission wavelength which can be precisely shifted to the desired range by simple structural changes, no general strategy exists for controllable modification of the fluorescence quantum yield. The rigidification of the molecular skeleton is known to usually enhance the emission and can be practically realized via the limiting molecular vibrations by aggregation. However, the subtle balance between the abundant possible radiative and non-radiative decay pathways makes the final picture exceptionally sophisticated. In the present study, a series of nine fluorophores obtained by peripheral substitution with two relatively mild electron donating and electron withdrawing groups are reported. The obtained fluorescence quantum yields range from dark to ultra-bright and the extreme values are obtained for the isomeric molecules. These severe changes in emission efficiency have been shown to arise from the complex relationship between the Franck-Condon excited state and conical intersection position. The experimental findings are rationalized by the advanced quantum chemical calculations delivering good correlation between the measured emission parameters and theoretical radiative and internal conversion rate constants. Therefore, the described substituent exchange provides a method to rigorously adjust the properties of molecular probes structurally similar to thioflavin T.

Multi-State Second-Order Nonlinear Optical Switches Incorporating One to Three Benzazolo-Oxazolidine Units: A Quantum Chemistry Investigation

This contribution employs quantum chemistry methods to describe the variations of the second nonlinear optical responses of molecular switches based on benzazolo-oxazolidine (BOX) units, connected by π-linkers, along their successive opening/closing. Under the fully closed forms, all of them display negligible first hyperpolarizability (β) values. When one BOX is opened, which is sketched as C→O, a push–pull π-conjugated segment is formed, having the potential to enhance β and to set the depolarization ratio (DR) to its one-dimensional-like value (DR = 5). This is observed when only one BOX is open, either for the monoBOX species (C→O) or for the diBOX (CC→CO) and triBOX (CCC→CCO) compounds, i.e., when the remaining BOXs stay closed. The next BOX openings have much different effects. For the diBOXs, the second opening (CO→OO) is associated with a decrease of β, and this decrease is tuned by controlling the conformation of the π-linker, i.e., the centrosymmetry of the whole compound because β vanishes in centrosymmetric compounds. For the triBOXs, the second opening gives rise to a Λ-shape compound, with a negligible change of β, but a decrease of the DR whereas, along the third opening, β remains similar and the DR decreases to the typical value of octupolar systems (DR = 1.5).

Machine learned calibrations to high-throughput molecular excited state calculations

Understanding the excited state properties of molecules provides insight into how they interact with light. These interactions can be exploited to design compounds for photochemical applications, including enhanced spectral conversion of light to increase the efficiency of photovoltaic cells. While chemical discovery is time- and resource-intensive experimentally, computational chemistry can be used to screen large-scale databases for molecules of interest in a procedure known as high-throughput virtual screening. The first step usually involves a high-speed but low-accuracy method to screen large numbers of molecules (potentially millions), so only the best candidates are evaluated with expensive methods. However, use of a coarse first-pass screening method can potentially result in high false positive or false negative rates. Therefore, this study uses machine learning to calibrate a high-throughput technique [eXtended Tight Binding based simplified Tamm-Dancoff approximation (xTB-sTDA)] against a higher accuracy one (time-dependent density functional theory). Testing the calibration model shows an approximately sixfold decrease in the error in-domain and an approximately threefold decrease in the out-of-domain. The resulting mean absolute error of ∼0.14 eV is in line with previous work in machine learning calibrations and out-performs previous work in linear calibration of xTB-sTDA. We then apply the calibration model to screen a 250k molecule database and map inaccuracies of xTB-sTDA in chemical space. We also show generalizability of the workflow by calibrating against a higher-level technique (CC2), yielding a similarly low error. Overall, this work demonstrates that machine learning can be used to develop a cost-effective and accurate method for large-scale excited state screening, enabling accelerated molecular discovery across a variety of disciplines.