Extensive Time-Dependent Density Functional Theory (TD-DFT) calculations have been carried out in order to obtain a statistically meaningful analysis of the merits of a large number of functionals. To reach this goal, a very extended set of molecules (∼500 compounds, >700 excited states) covering a broad range of (bio)organic molecules and dyes have been investigated. Likewise, 29 functionals including LDA, GGA, meta-GGA, global hybrids, and long-range-corrected hybrids have been considered. Comparisons with both theoretical references and experimental measurements have been carried out. On average, the functionals providing the best match with reference data are, one the one hand, global hybrids containing between 22% and 25% of exact exchange (X3LYP, B98, PBE0, and mPW1PW91) and, on the other hand, a long-range-corrected hybrid with a less-rapidly increasing HF ratio, namely LC-ωPBE(20). Pure functionals tend to be less consistent, whereas functionals incorporating a larger fraction of exact exchange tend to underestimate significantly the transition energies. For most treated cases, the M05 and CAM-B3LYP schemes deliver fairly small deviations but do not outperform standard hybrids such as X3LYP or PBE0, at least within the vertical approximation. With the optimal functionals, one obtains mean absolute deviations smaller than 0.25 eV, though the errors significantly depend on the subset of molecules or states considered. As an illustration, PBE0 and LC-ωPBE(20) provide a mean absolute error of only 0.14 eV for the 228 states related to neutral organic dyes but are completely off target for cyanine-like derivatives. On the basis of comparisons with theoretical estimates, it also turned out that CC2 and TD-DFT errors are of the same order of magnitude, once the above-mentioned hybrids are selected.

The π → π* transitions of more than 100 organic dyes from the major classes of chromophores (quinones, diazo, ...) have been investigated using a Time-Dependent Density Functional Theory (TD-DFT) procedure relying on large atomic basis sets and the systematic modeling of solvent effects. These calculations have been performed with pure (PBE) as well as conventional (PBE0) and long-range (LR) corrected hybrid functionals (LC-PBE, LC-ωPBE, and CAM-B3LYP). The computed wavelengths are systematically guided by the percentage of exact exchange included at intermediate interelectronic distance, i.e., the λmax value always follows the PBE > PBE0 > CAM-B3LYP > LC-PBE > LC-ωPBE > HF sequence. The functional giving the best estimates of the experimental transition energies may vary, but PBE0 and CAM-B3LYP tend to outperform all other approaches. The latter functional is shown to be especially adequate to treat molecules with delocalized excited states. The mean absolute error provided by PBE0 is 22 nm (0.14 eV) with no deviation exceeding 100 nm (0.50 eV):  PBE0 is able to deliver reasonable estimates of the color of most organic dyes of practical or industrial interest. By using a calibration curve, we found that the LR functionals systematically allow an even more consistent description of the low-lying excited-state energies than the conventional hybrids. Indeed, linearly corrected LR approaches yield an average error of 10 nm for each dye family. Therefore, when such statistical treatments can be designed for given sets of dyes, a simple and rapid theoretical procedure allows both a chemically sound and a numerically accurate description of the absorption wavelengths.

Since Antiquity, humans have produced and commercialized dyes. To this day, extraction of natural dyes often requires lengthy and costly procedures. In the 19th century, global markets and new industrial products drove a significant effort to synthesize artificial dyes, characterized by low production costs, huge quantities, and new optical properties (colors). Dyes that encompass classes of molecules absorbing in the UV-visible part of the electromagnetic spectrum now have a wider range of applications, including coloring (textiles, food, paintings), energy production (photovoltaic cells, OLEDs), or pharmaceuticals (diagnostics, drugs). Parallel to the growth in dye applications, researchers have increased their efforts to design and synthesize new dyes to customize absorption and emission properties. In particular, dyes containing one or more metallic centers allow for the construction of fairly sophisticated systems capable of selectively reacting to light of a given wavelength and behaving as molecular devices (photochemical molecular devices, PMDs).Theoretical tools able to predict and interpret the excited-state properties of organic and inorganic dyes allow for an efficient screening of photochemical centers. In this Account, we report recent developments defining a quantitative ab initio protocol (based on time-dependent density functional theory) for modeling dye spectral properties. In particular, we discuss the importance of several parameters, such as the methods used for electronic structure calculations, solvent effects, and statistical treatments. In addition, we illustrate the performance of such simulation tools through case studies. We also comment on current weak points of these methods and ways to improve them.

We assessed the accuracy of the four members of the M06 family of functionals (M06-L, M06, M06-2X, and M06-HF) for the prediction of electronic excitation energies of main-group compounds by time-dependent density functional theory. This is accomplished by comparing the predictions both to high-level theoretical benchmark calculations and some experimental data for gas-phase excitation energies of small molecules and to experimental data for midsize and large chromogens in liquid-phase solutions. The latter comparisons are carried out using implicit solvation models to include the electrostatic effects of solvation. We find that M06-L is one of the most accurate local functionals for evaluating electronic excitation energies, that M06-2X outperforms BHHLYP, and that M06-HF outperforms HF, although in each case, the compared functionals have the same or a similar amount of Hartree-Fock exchange. For the majority of investigated excited states, M06 emerges as the most accurate functional among the four tested, and it provides an accuracy similar to the best of the other global hybrids such as B3LYP, B98, and PBE0. For 190 valence excited states, 20 Rydberg states, and 16 charge transfer states, we try to provide an overall assessment by comparing the quality of the predictions to those of time-dependent Hartree-Fock theory and nine other density functionals. For the valence excited states, M06 yields a mean absolute deviation (MAD) of 0.23 eV, whereas B3LYP, B98, and PBE0 have MADs in the range 0.19-0.22 eV. Of the functionals tested, M05-2X, M06-2X, and BMK are found to perform best for Rydberg states, and M06-HF performs best for charge transfer states, but no single functional performs satisfactorily for all three kinds of excitation. The performance of functionals with no Hartree-Fock exchange is of great practical interest because of their high computational efficiency, and we find that M06-L predicts more accurate excitation energies than other such functionals.

Assessment of conventional density functional schemes for computing the polarizabilities and hyperpolarizabilities of conjugated oligomers: An ab initio investigation of polyacetylene chains.

Using the long-range correction (LC) density functional theory (DFT) scheme introduced by Iikura et al. [J. Chem. Phys. 115, 3540 (2001)] and the Coulomb-attenuating model (CAM-B3LYP) of Yanai et al. [Chem. Phys. Lett. 393, 51 (2004)], we have calculated a series of properties that are known to be poorly reproduced by standard functionals: Bond length alternation of pi-conjugated polymers, polarizabilities of delocalized chains, and electronic spectra of extended dyes. For each of these properties, we present cases in which traditional hybrid functionals do provide accurate results and cases in which they fail to reproduce the correct trends. The quality of the results is assessed with regard to experimental values and/or data arising from electron-correlated wave function approaches. It turns out that (i) both LC-DFT and CAM-B3LYP provide an accurate bond length alternation for polyacetylene and polymethineimine, although for the latter they decrease slightly too rapidly with chain length. (ii) The LC generalized gradient approximation and MP2 polarizabilities of long polyphosphazene and polymethineimine oligomers agree almost perfectly. In the same way, CAM-B3LYP corrects the major part of the B3LYP faults. (iii) LC and CAM techniques do not help in correcting the nonrealistic evolution with chain length of the absorption wavelengths of cyanine derivatives. In addition, though both schemes significantly overestimate the ground to excited state transition energy of substituted anthraquinone dyes, they provide a more consistent picture once a statistical treatment is performed than do traditional hybrid functionals.

A general TDDFT procedure has been set up that accurately evaluates the UV/vis absorption spectra of a series of new conjugated metal-free organic dyes based on the triphenylamine (TPA) moiety, which have recently been developed for dye-sensitized solar cells (DSSCs). It turns out that the BHandH functional, combined with the 6-311+G(2d,2p) basis set, gives reliable auxochromic shifts when the bulk solvation effects are included in the model. Indeed, the theoretical procedure provides λmax with a mean absolute deviation limited to ∼0.1 eV only. In addition, we give insights into the geometrical and electronic structures of the dyes, and we unravel the structural modifications allowing to optimize the properties of TPA-based DSSCs. This investigation aims at improving the electron-injection process, as well as the light-harvesting efficiency (LHE) of the dyes. To this purpose, we considered a set of about 20 new dyes, and starting from the TPC-1 structure, the following modifications help to get better electron injection and light-harvesting properties: (i) the extension of the bridging group by addition of an ethylene subunit between the two phenyl groups (TPC-14); (ii) the 16-COOH, 15-OMe, 1a,6-diCN functionalization (TPC-18); (iii) moving the terminal cyano acceptor from the 16 to the 15 position, while introducing two −OMe functions in 11 and 13 positions and/or grafting two −CN groups in 1a and 6 positions on the TPA moiety (TPC-20). These specific modifications induce a maximal increase of the LHE and a more exoenergic free enthalpy of injection (−2.20 eV compared to −1.84 eV for TPC-1). Finally, TPC-23 (which results from the TPC-14/TPC-20 combination) shows an improvement of both the spectroscopic and energetic parameters. Moreover, the molecular topology analysis demonstrates that the coplanarity between the anchoring and the bridging unit is broken, that is, the positive charge is not directly in contact with the TiO2 surface, and the recombination reaction is therefore inhibited.

The calculation of transition energies for electronically excited states remains a challenge in quantum chemistry, for which time-dependent density functional theory (TD-DFT) is often viewed as a balanced (computational effort/obtained accuracy) technique. In this study, we benchmark 34 DFT functionals in the specific framework of TD-DFT calculations for singlet-triplet transitions. The results are compared to accurate wave function data reported for the same set of 63 excited-states, and it turns out that, within the selected TD-DFT framework, BMK and M06-2X emerge as the most efficient hybrids. This investigation clearly illustrates that the conclusions drawn for singlet excited states do not necessarily hold for triplet states, even for similar molecular structures.