Range-separated Functionals Research Articles

Slope of the Delocalization Function Is Proportional to Analytical Hardness.

Conceptual Density Functional Theory (CDFT) has been extended beyond its traditional role in elucidating chemical reactivity to the development of density functional theory methods, e.g., the investigation of the delocalization error. This delocalization error causes the dependence of the energy on the number of electrons (N) to deviate from its exact piecewise linear behavior, an error which is the basis of many well-known limitations of commonly used density-functional approximations (DFAs). Following our previous work on the analytical hardness η± for pure functionals, we extend its application to hybrid and range-separated functionals. A comparison is made between the analytical hardness and the slope of the delocalization function introduced by Hait and Head-Gordon. Our results show that there is a linear relationship between its slope and the analytical hardness. An approximate scheme is presented to construct the energy vs N curve without fractional occupation number calculations. The extension to densities is discussed.

Multireference calculations on bond dissociation and biradical polycyclic aromatic hydrocarbons as guidance for fractional occupation number weighted density analysis in DFT calculations

This study explores open-shell biradical and polyradical molecular compounds based on extended multireference (MR) methods (MR-configuration interaction with singles and doubles (CISD) and MR-averaged quadratic coupled cluster (AQCC) approach) using the numbers of unpaired densities NU. These results were used to guide the analysis of the fractional occupation number weighted density (FOD) calculated within the finite temperature (FT) density functional theory (DFT) approach. As critical test examples, the dissociation of carbon–carbon (CC) single, double and triple bonds and a benchmark set of polycyclic aromatic hydrocarbons (PAHs) have been chosen. By examining single, double, and triple bond dissociations, we demonstrate the utility and accuracy but also limitations of the FOD analysis for describing these dissociation processes. In significant extension of previous work (Phys Chem Chem Phys 25: 27380–27393), the assessment of FOD applications for different classes of DFT functionals was performed examining the range-separated functionals ωB97XD, ωB97M-V, CAM-B3LYP, LC-ωPBE, and MN12-SX, the hybrid (M06-2X) functional and the double hybrid (B2P-LYP) functional. In all cases, strong correlations between NFOD and NU values are found. The major task was to develop a new linear regression formula for range-separated functionals allowing a convenient determination of the optimal electronic temperature Tel for the FT-DFT calculation. We also established an optimal temperature for the semiempirical extended tight-binding GFN2-xTB method. These findings significantly broaden the applicability of FOD analysis across various DFT functionals and semiempirical methods.

Deciphering TADF Mechanisms in Metal-Free Organic Emitters BrA-HBI: Utilizing Optimally Tuned Range-Separated Functionals for Insight

Abstract Metal-free organic emitters, characterized by their thermally activated delayed fluorescence (TADF) properties, offer considerable promise for the creation of highly efficient organic light-emitting diodes (OLEDs). Recently, Shao et al. presented a novel excited state intramolecular proton transfer (ESIPT) system BrA-HBI, demonstrating an emission quantum yield of up to 50% [Adv. Funct. Mater. 32, 2201256 (2022)]. However, many open issues cannot be answered solely by experimental means only and require detailed theoretical investigations. For instance, what causes the activation of TADF from the Keto* tautomer and leads to fluorescence quenching in the Enol* form? Herein, we provide a theoretical investigation on the TADF mechanism of the BrA-HBI molecule by optimally tuned range-separated functionals. Our findings reveal that ESIPT occurs in the BrA-HBI molecule. Moreover, we have disclosed the reason for the fluorescence quenching of the Enol* form and determined that the T 2 state plays a dominant role in the TADF phenomenon. In addition, double hybrid density functionals method was utilized to verify the reliability of optimally tuned range separation functionals on the calculation of the TADF mechanism in BrA-HBI. These findings not only provide a theoretical reference for development of highly efficient organic light-emitting diodes, but also demonstrate the effectiveness of the optimally tuned range-separated functionals in predicting the luminescence properties of TADF molecules.

Range-separated hybrid van der Waals density functionals to describe Cu[formula omitted]O[formula omitted]-complexes

Dimeric copper centers are commonly used to activate molecular oxygen in enzymatic and heterogeneous catalysis where Cu2 is embedded in porous structures. Here we evaluate the ability of recently developed range-separated hybrid van der Waals density functionals to describe activated O2 in a crystal with the Cu2O2 unit and in a ▪ complex embedded in a chabzite zeolite. The electronic and geometrical structure of the Cu2O2 unit depends sensitively on the exchange–correlation functional and a sufficiently large amount of short-ranged Fock-exchange is needed to describe the experimentally observed Cu2O2 structures.

Accurate and efficient evaluation of the ionization potentials of extreme ultraviolet photoresists using density functionals and semi-empirical methods

Extreme ultraviolet (EUV) photoresists have become the core materials in lithography with nanometer-sized patterns and are actively explored on the path to realizing smaller critical dimensions. These photoresists can be small molecule-, polymer-, or organic–inorganic hybrid-based, with the full molecular working mechanism under investigation. For the rational design of EUV photoresists, theoretical guidance using tools like first-principle calculations and multi-scale simulations can be of great help. Considering the extremely high standard of accuracy in EUV lithography, it is critical to ensure the adoption of the appropriate methodologies in the theoretical evaluation of EUV photoresists. However, it is known that density functionals and semi-empirical methods differ in accuracy and efficiency, without a universal rule across materials. This poses a challenge in developing a reliable theoretical framework for calculating EUV photoresists. Here, we present a benchmark investigation of density functionals and semi-empirical methods on the three main types of EUV photoresists, focusing on the ionization potential, a key parameter in their microscopic molecular reactions. The vertical detachment energies (VDE) and adiabatic detachment energies (ADE) were calculated using 12 functionals, including pure functionals, hybrid functionals, Minnesota functionals, and the recently developed optimally tuned range-separated (OTRS) functionals. Several efficient semi-empirical methods were also chosen, including AM1, PM6, PM7, and GFN1-xTB in the extended tight-binding theoretical framework. These results guide the accurate and efficient calculation of EUV photoresists and are valuable for the development of multi-scale lithography protocols.Graphical

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.

The performance and efficiency of twelve range-separated hybrid DFT functionals for calculation of the magnetic exchange coupling constants of di-nuclear first row transition metal complexes

The performance and efficiency of twelve range-separated hybrid functionals are compared with each other in calculating magnetic exchange coupling constant (J) data on eleven di-nuclear first-row transition metal complexes having di-copper (Cu) and di-vanadium (V) as their central atoms. The J values are then compared with the experimental findings. In addition to that we also computed the B3LYP results of these complexes. We compared them with the results obtained from range-separated functionals as well as with the experimental results to understand their performances in predicting the magnetic exchange coupling constant. When computing, we reoptimized all the structures of the complexes taken from the crystal data, and then the values of Js were determined. The performances are predicted in terms of four statistical error matrices, namely, the mean absolute error (MAE), mean fractional error (MFE), mean signed error (MSE), root mean square error (RMSE) in cm−1.

Accurate Electronic and Optical Properties of Organic Doublet Radicals Using Machine Learned Range-Separated Functionals.

Luminescent organic semiconducting doublet-spin radicals are unique and emergent optical materials because their fluorescent quantum yields (Φfl) are not compromised by the spin-flipping intersystem crossing (ISC) into a dark high-spin state. The multiconfigurational nature of these radicals challenges their electronic structure calculations in the framework of single-reference density functional theory (DFT) and introduces room for method improvement. In the present study, we extended our earlier development of ML-ωPBE [J. Phys. Chem. Lett., 2021, 12, 9516-9524], a range-separated hybrid (RSH) exchange-correlation (XC) functional constructed using the stacked ensemble machine learning (SEML) algorithm, from closed-shell organic semiconducting molecules to doublet-spin organic semiconducting radicals. We assessed its performance for a new test set of 64 doublet-spin radicals from five categories while placing all previously compiled 3926 closed-shell molecules in the new training set. Interestingly, ML-ωPBE agrees with the nonempirical OT-ωPBE functional regarding the prediction of the molecule-dependent range-separation parameter (ω), with a small mean absolute error (MAE) of 0.0197 a0-1, but saves the computational cost by 2.46 orders of magnitude. This result demonstrates an outstanding domain adaptation capacity of ML-ωPBE for diverse organic semiconducting species. To further assess the predictive power of ML-ωPBE in experimental observables, we also applied it to evaluate absorption and fluorescence energies (Eabs and Efl) using linear-response time-dependent DFT (TDDFT), and we compared its behavior with nine popular XC functionals. For most radicals, ML-ωPBE reproduces experimental measurements of Eabs and Efl with small MAEs of 0.299 and 0.254 eV, only marginally different from those of OT-ωPBE. Our work illustrates a successful extension of the SEML framework from closed-shell molecules to doublet-spin radicals and will open the venue for calculating optical properties for organic semiconductors using single-reference TDDFT.

Cross-over from pyrene to acene optical and electronic properties: a theoretical investigation of a series of pyrene derivatives fused with N-, S, and O-containing heterocycles.

Pyrene and acene derivatives are an important source of materials for optoelectronic device applications both as emitters and organic semiconductors. The mobility of major charge carriers is correlated with the coupling constants of the respective major charge carrier as well as the relaxation energies. Herein, we have applied range-separated density functionals for the estimation of said values. A series of five alkylated derivatives of pyrene laterally extended by heteroaromatic or phenyl groups were explored and contrasted to nascent pyrene, alkylated pyrene and tetracene. The ground state geometries along with absorption properties and relaxation energies are presented as well as a discussion of the suitability of the material toward hole and electron transport materials.

How does theory compare to experiment for oscillator strengths in electronic spectra? Proposing range-separated hybrids with reliable accountability.

As an important quantity in atomic and molecular spectroscopy, oscillator strength should be mentioned. Oscillator strength is linked to the transition dipole moment and consequently to the transition probability between two states, where its magnitude is directly connected to the intensity of the peaks in ultraviolet-visible spectra. However, accurately accounting for oscillator strengths still remains one of the greatest challenges in theory and experiment. Given previous efforts in the context of investigations into oscillator strengths, the related theoretical treatments are relatively limited and have proven to be challenging. In this work, the oscillator strengths in the electronic spectra of organic compounds have thoroughly been investigated with the help of optimally tuned range-separated hybrids (OT-RSHs). In particular, variants of the OT-RSHs combined with the polarizable continuum model (PCM), OT-RSHs-PCM, as well as their screened versions accounting for the screening effects by the electron correlation through the dielectric constant, OT-SRSHs-PCM, are proposed for reliable prediction of the oscillator strengths. The role of the involved ingredients in the proposed methods, namely the underlying density functional approximations, short-range and long-range Hartree-Fock (HF) exchange, as well as the range-separation parameter, has been examined in detail. It is shown that any combination of the parameters in the proposed approximations does not render the reliable oscillator strengths, but a particular compromise among them is needed to describe the experimental data well. Perusing all the results of our developed methods, the best ones are found to be the generalized gradient approximation-based OT-RSHs-PCM, coupled with the linear response theory in the non-equilibrium solvation regime, with the correct asymptotic behavior and incorporating no (low) HF exchange contributions in the short-range part. The best proposed approximations also reveal superior performances not only with respect to their standard counterparts with the default parameters but also as compared to earlier range-separated functionals. Finally, the applicability of the best approximation is also put into broader perspective, where it is used for predicting the oscillator strengths in other sets of compounds not included in the process of developing the approximations. Hopefully, our proposed method can function as an affordable alternative to the expensive wave function-based methods for both theoretical modeling and confirming the experimental observations in the field of electronic spectroscopy.

Performance of point charge embedding schemes for excited states in molecular organic crystals.

Modeling excited state processes in molecular crystals is relevant for several applications. A popular approach for studying excited state molecular crystals is to use cluster models embedded in point charges. In this paper, we compare the performance of several embedding models in predicting excited states and S1-S0 optical gaps for a set of crystals from the X23 molecular crystal database. The performance of atomic charges based on ground or excited states was examined for cluster models, Ewald embedding, and self-consistent approaches. We investigated the impact of various factors, such as the level of theory, basis sets, embedding models, and the level of localization of the excitation. We consider different levels of theory, including time-dependent density functional theory and Tamm-Dancoff approximation (TDA) (DFT functionals: ωB97X-D and PBE0), CC2, complete active space self-consistent field, and CASPT2. We also explore the impact of selection of the QM region, charge leakage, and level of theory for the description of different kinds of excited states. We implemented three schemes based on distance thresholds to overcome overpolarization and charge leakage in molecular crystals. Our findings are compared against experimental data, G0W0-BSE, periodic TDA, and optimally tuned screened range-separated functionals.

Improved Description of Intra- and Intermolecular Interactions through Dispersion-Corrected Second-Order Møller-Plesset Perturbation Theory.

ConspectusThe quantum chemical modeling of organic crystals and other molecular condensed-phase problems requires computationally affordable electronic structure methods which can simultaneously describe intramolecular conformational energies and intermolecular interactions accurately. To achieve this, we have developed a spin-component-scaled, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D) model. SCS-MP2D augments canonical MP2 with a dispersion correction which removes the uncoupled Hartree-Fock dispersion energy present in canonical MP2 and replaces it with a more reliable coupled Kohn-Sham treatment, all evaluated within the framework of Grimme's D3 dispersion model. The spin-component scaling is then used to improve the description of the residual (nondispersion) portion of the correlation energy.The SCS-MP2D model improves upon earlier corrected MP2 models in a few ways. Compared to the highly successful dispersion-corrected MP2C model, which is based solely on intermolecular perturbation theory, the SCS-MP2D dispersion correction improves the description of both inter- and intramolecular interactions. The dispersion correction can also be evaluated with trivial computational cost, and nuclear analytic gradients are computed readily to enable geometry optimizations. In contrast to earlier spin-component scaling MP2 models, the optimal spin-component scaling coefficients are only mildly sensitive to the choice of training data, and a single global parametrization of the model can describe both thermochemistry and noncovalent interactions.The resulting dispersion-corrected, spin-component-scaled MP2 (SCS-MP2D) model predicts conformational energies and intermolecular interactions with accuracy comparable to or better than those of many range-separated and double-hybrid density functionals, as is demonstrated on a variety of benchmark tests. Among the functionals considered here, only the revDSD-PBEP86-D3(BJ) functional gives consistently smaller errors in benchmark tests. The results presented also hint that further improvements of SCS-MP2D may be possible through a more robust fitting procedure for the seven empirical parameters.To demonstrate the performance of SCS-MP2D further, several applications to molecular crystal problems are presented. The three chosen examples all represent cases where density-driven delocalization error causes GGA or hybrid density functionals to artificially stabilize crystals exhibiting more extended π-conjugation. Our pragmatic strategy addresses the delocalization error by combining a periodic density functional theory (DFT) treatment of the infinite lattice with intramolecular/conformational energy corrections computed with SCS-MP2D. For the anticancer drug axitinib, applying the SCS-MP2D conformational energy correction produces crystal polymorph stabilities that are consistent with experiment, in contrast to earlier studies. For the crystal structure prediction of the ROY molecule, so named for its colorful red, orange, and yellow crystals, this approach leads to the first plausible crystal energy landscape, and it reveals that the lowest-energy polymorphs have already been found experimentally. Finally, in the context of photomechanical crystals, which transform light into mechanical work, these techniques are used to predict the structural transformations and extract design principles for maximizing the work performed.

Understanding Photophysical Properties of Molecules Relevant in Organic Semiconductor Laser Diodes from Electron Localization Function-Tuned and Solvent-Tuned Range-Separated Functionals.

Organic semiconductor laser diodes (OSLDs) are prevalent in optoelectronics because of their sustainable energy applications. Organic molecules used in such diodes are usually large; hence, their studies are computationally challenging with high-end benchmark methods. Computational methods with reliable accuracy and efficiency are always indispensable. In the present work, we have applied our computationally inexpensive, nonempirically tuned [electron localization function (ELF*) and solvent (Sol*)] range-separated (RS) functionals to study five molecules used in OSLDs. The emission energies in three different environments [toluene, CBP (4,4'-bis(n-carbazolyl)-1,1'-biphenyl) film, and gas] have been computed with the tuned functionals and compared with the experimental emission energies. ELF* and Sol* functionals can accurately reproduce emission energies in toluene and CBP film environments. On the other hand, both ELF* and IP-tuned functionals with excited-state geometry (IP*) perform better in the gas phase. In addition, a comparative study is performed between time-dependent density functional theory and the Tamm-Dancoff approximation. Along with the emission energy, oscillator strength values have also been reported. Different IP-tuned RS parameters were obtained with the ground- and excited-state geometries. Interestingly, it has been observed that the optimally tuned RS parameter with excited-state geometry (IP*) performs better compared to that with ground-state geometries (IP). Fractional occupation calculations show that the tuned functionals exhibit less localization and delocalization error. The study envisages that ELF* and Sol* functionals can be used to design future candidates for OSLDs.

Koopmans' Theorem-Compliant Long-Range Corrected (KTLC) Density Functional Mediated by Black-Box Optimization and Data-Driven Prediction for Organic Molecules.

Density functional theory (DFT) is a significant computational tool that has substantially influenced chemistry, physics, and materials science. DFT necessitates parametrized approximation for determining an expected value. Hence, to predict the properties of a given molecule using DFT, appropriate parameters of the functional should be set for each molecule. Herein, we optimize the parameters of range-separated functionals (LC-BLYP and CAM-B3LYP) via Bayesian optimization (BO) to satisfy Koopmans' theorem. Our results demonstrate the effectiveness of the BO in optimizing functional parameters. Particularly, Koopmans' theorem-compliant LC-BLYP (KTLC-BLYP) shows results comparable to the experimental UV-absorption values. Furthermore, we prepared an optimized parameter dataset of KTLC-BLYP for over 3000 molecules through BO for satisfying Koopmans' theorem. We have developed a machine learning model on this dataset to predict the parameters of the LC-BLYP functional for a given molecule. The prediction model automatically predicts the appropriate parameters for a given molecule and calculates the corresponding values. The approach in this paper would be useful to develop new functionals and to update the previously developed functionals.

Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level.

The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.

Benchmarking DFT Functionals for Excited-State Calculations of Donor–Acceptor TADF Emitters: Insights on the Key Parameters Determining Reverse Inter-System Crossing

The importance of intermediate triplet states and the nature of excited states has gained interest in recent years for the thermally activated delayed fluorescence (TADF) mechanism. It is widely accepted that simple conversion between charge transfer (CT) triplet and singlet excited states is too crude, and a more complex route involving higher-lying locally excited triplet excited states has to be invoked to witness the magnitude of the rate of reverse inter-system crossing (RISC) rates. The increased complexity has challenged the reliability of computational methods to accurately predict the relative energy between excited states as well as their nature. Here, we compare the results of widely used density functional theory (DFT) functionals, CAM-B3LYP, LC-ωPBE, LC-ω*PBE, LC-ω*HPBE, B3LYP, PBE0, and M06-2X, against a wavefunction-based reference method, Spin-Component Scaling second-order approximate Coupled Cluster (SCS-CC2), in 14 known TADF emitters possessing a diversity of chemical structures. Overall, the use of the Tamm-Dancoff Approximation (TDA) together with CAM-B3LYP, M06-2X, and the two ω-tuned range-separated functionals LC-ω*PBE and LC-ω*HPBE demonstrated the best agreement with SCS-CC2 calculations in predicting the absolute energy of the singlet S1, and triplet T1 and T2 excited states and their energy differences. However, consistently across the series and irrespective of the functional or the use of TDA, the nature of T1 and T2 is not as accurately captured as compared to S1. We also investigated the impact of the optimization of S1 and T1 excited states on ΔEST and the nature of these states for three different functionals (PBE0, CAM-B3LYP, and M06-2X). We observed large changes in ΔEST using CAM-B3LYP and PBE0 functionals associated with a large stabilization of T1 with CAM-B3LYP and a large stabilization of S1 with PBE0, while ΔEST is much less affected considering the M06-2X functional. The nature of the S1 state barely evolves after geometry optimization essentially because this state is CT by nature for the three functionals tested. However, the prediction of the T1 nature is more problematic since these functionals for some compounds interpret the nature of T1 very differently. SCS-CC2 calculations on top of the TDA-DFT optimized geometries lead to a large variation in terms of ΔEST and the excited-state nature depending on the chosen functionals, further stressing the large dependence of the excited-state features on the excited-state geometries. The presented work highlights that despite good agreement of energies, the description of the exact nature of the triplet states should be undertaken with caution.

Comparison of the Performance of Density Functional Methods for the Description of Spin States and Binding Energies of Porphyrins.

This work analyzes the performance of 250 electronic structure theory methods (including 240 density functional approximations) for the description of spin states and the binding properties of iron, manganese, and cobalt porphyrins. The assessment employs the Por21 database of high-level computational data (CASPT2 reference energies taken from the literature). Results show that current approximations fail to achieve the "chemical accuracy" target of 1.0 kcal/mol by a long margin. The best-performing methods achieve a mean unsigned error (MUE) <15.0 kcal/mol, but the errors are at least twice as large for most methods. Semilocal functionals and global hybrid functionals with a low percentage of exact exchange are found to be the least problematic for spin states and binding energies, in agreement with the general knowledge in transition metal computational chemistry. Approximations with high percentages of exact exchange (including range-separated and double-hybrid functionals) can lead to catastrophic failures. More modern approximations usually perform better than older functionals. An accurate statistical analysis of the results also casts doubts on some of the reference energies calculated using multireference methods. Suggestions and general guidelines for users are provided in the conclusions. These results hopefully stimulate advances for both the wave function and the density functional side of electronic structure calculations.

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.

Exact non-adiabatic coupling vectors for the time-dependent density functional based tight-binding method.

We report on non-adiabatic coupling vectors between electronic excited states for the time-dependent-density functional theory based tight-binding (TD-DFTB) method. The implementation includes orbital relaxation effects that have been previously neglected and covers also the case of range-separated exchange-correlation functionals. Benchmark calculations with respect to first principles TD-DFT highlight the large dependence of non-adiabatic couplings on the functional. Closer investigations of the topology around a conical intersection between excited states show that TD-DFTB delivers near-exact values of the Berry phase, which paves the way for consistent non-adiabatic molecular dynamics simulations for large systems.