Ilaria Ciofini

TD-DFT Performance for the Visible Absorption Spectra of Organic Dyes: Conventional versus Long-Range Hybrids.

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.

A Qualitative Index of Spatial Extent in Charge-Transfer Excitations

With the aim of defining the spatial extent associated to an electronic transition, of particular relevance in the case of charge-transfer (CT) excitations, a new index, evaluated only from the computed density for the ground and excited state, is here derived and tested on a family of molecules that can be considered as prototypes of push-pull chromophores.The index (DCT) allows to define the spatial extent associated to a given transition as well as the associated fraction of electron transferred. By definition of centroids of charges associated to the density increase and depletion zones upon excitation, a qualitative and easy to visualize measure of the spatial extent of the donor and the acceptor moieties within a given molecular system is also given. Finally, an index (t) allowing to define the presence eventually pathologic CT transitions for time-dependent density functional theory treatment in conjunction with standard generalized gradient approximation or hybrid functional, that is through space CT, is disclosed.

Accurate simulation of optical properties in dyes.

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.

On the Performances of the M06 Family of Density Functionals for Electronic Excitation Energies

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.

First-Principles Modeling of Dye-Sensitized Solar Cells: Challenges and Perspectives

Since dye-sensitized solar cells (DSSCs) appeared as a promising inexpensive alternative to the traditional silicon-based solar cells, DSSCs have attracted a considerable amount of experimental and theoretical interest. In contrast with silicon-based solar cells, DSSCs use different components for the light-harvesting and transport functions, which allow researchers to fine-tune each material and, under ideal conditions, to optimize their overall performance in assembled devices. Because of the variety of elementary components present in these cells and their multiple possible combinations, this task presents experimental challenges. The photoconversion efficiencies obtained up to this point are still low, despite the significant experimental efforts spent in their optimization. The development of a low-cost and efficient computational protocol that could qualitatively (or even quantitatively) identify the promising semiconductors, dyes, and electrolytes, as well as their assembly, could save substantial experimental time and resources. In this Account, we describe our computational approach that allows us to understand and predict the different elementary mechanisms involved in DSSC working principles. We use this computational framework to propose an in silico route for the ab initio design of these materials. Our approach relies on a unique density functional theory (DFT) based model, which allows for an accurate and balanced treatment of electronic and spectroscopic properties in different phases (such as gas, solution, or interfaces) and avoids or minimizes spurious computational effects. Using this tool, we reproduced and predicted the properties of the isolated components of the DSSC assemblies. We accessed the microscopic measurable characteristics of the cells such as the short circuit current (J(sc)) or the open circuit voltage (V(oc)), which define the overall photoconversion efficiency of the cell. The absence of empirical or material-related parameters in our approach should allow for its wide application to the optimization of existing devices or the design of new ones.

DFT calculations of molecular magnetic properties of coordination compounds

Abstract An overview of density functional theory (DFT) based techniques for the calculation of the magnetic properties of molecular and supramolecular assemblies is presented. Three different approaches to compute the exchange coupling constant (Jex) are reviewed, i.e. the broken symmetry (BS) technique, the single determinant (SD) approach, and the spin projection method. The first one (BS), developed by Noodleman, is undoubtedly most commonly applied, e.g. to clusters containing several paramagnetic metal centres or to paramagnetic organic radical species. The second approach (SD) was originally developed to compute the electronic spectra of transition metal complexes, but was more recently applied to the computation of spin manifold of molecular magnets. The last method, developed by Ovchinnikov and Labanowsky, is mainly an extension of the Hartree–Fock (HF) concept of spin de-contamination to DFT. The performance of the three methods has been evaluated for model systems (HHeH, [Cu2Cl6]2−) and for more complex molecules (Ti(CatNSQ)2 and Sn(CatNSQ)2, Bis-verdazyl diradical (BVD), [Fe2(OH)3(tmtacn)2]2+ and [[Cu3O2L3]3+, L=N-Permethylated (1R,2R)-cyclohexanediamine). A comparison of these results with experimental values and with post-HF results if available is presented as well. In the case of the last two complexes, i.e. mixed valence systems, computation of the vibronic potential energy surfaces is also briefly discussed.

Assessment of Functionals for TD-DFT Calculations of Singlet−Triplet Transitions

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.

First Principles Modeling of Eosin-Loaded ZnO Films: A Step toward the Understanding of Dye-Sensitized Solar Cell Performances

A theoretical investigation of eosin-Y (EY) loaded ZnO thin films, the basic components of a dye-sensitized solar cell (DSSC), is presented. The EY/ZnO wurtzite (10-10) system has been fully described within a periodic approach using density functional theory (DFT) and a hybrid exchange-correlation functional. Reduced systems were also analyzed to simulate an electron transfer from the dye to the substrate. Injection times from dye to the semiconductor were calculated using the Newns-Anderson approach. Finally, the UV-visible spectra of EY/ZnO films were simulated using a time-dependent DFT approach and compared to that of the EY molecule computed in solution. The results obtained highlight that EY strongly adsorbs on the ZnO substrate contributing significantly to the electronic structure of the adsorbed system. The UV-visible spectral signature of the isolated EY molecule is still found when adsorbed on ZnO but the analysis of Gamma-point crystalline orbitals reveals that a direct HOMO-->LUMO excitation cannot lead to a direct electron injection into the semiconductor, the first unoccupied orbital with contributions from the ZnO substrate being the LUMO + 1. As a consequence, a two photon injection mechanism is proposed explaining the low efficiency of the EY/ZnO solar cells. On this basis, possible strategies for enhancing the cell efficiency are presented and discussed.

Time-dependent density functional theory investigation of the absorption, fluorescence, and phosphorescence spectra of solvated coumarins

Using time-dependent density functional theory (TD-DFT) and the polarizable continuum model, we have computed the electronic transitions of a large panel of coumarin dyes in their enol, keto, cationic, and anionic forms. Several processes have been studied: absorption, fluorescence, 0-0 phosphorescence, and triplet-triplet excitations. For each process, detailed comparison with experimental data has been carried out. Using the PBE06-31+G(d) scheme, it turns out that for a given electronic transition the experimental shifts resulting from the substitution of the coumarin core are nicely reproduced. Indeed, once a simple statistical correction is applied, the mean absolute errors on the absorption and fluorescence wavelengths are limited to 8 nm (0.09 eV) and 9 nm (0.07 eV), respectively. A valuable correlation between the experimental and theoretical phosphorescence auxochromic displacements has also been unravelled. The differences between the wavelengths of the various electronic processes of a given dye tend to be fairly predicted, especially for the fluorescence-phosphoresence shifts that are strongly overestimated by TD-DFT.

Verdict: Time-Dependent Density Functional Theory "Not Guilty" of Large Errors for Cyanines.

We assess the accuracy of eight Minnesota density functionals (M05 through M08-SO) and two others (PBE and PBE0) for the prediction of electronic excitation energies of a family of four cyanine dyes. We find that time-dependent density functional theory (TDDFT) with the five most recent of these functionals (from M06-HF through M08-SO) is able to predict excitation energies for cyanine dyes within 0.10-0.36 eV accuracy with respect to the most accurate available Quantum Monte Carlo calculations, providing a comparable accuracy to the latest generation of CASPT2 calculations, which have errors of 0.16-0.34 eV. Therefore previous conclusions that TDDFT cannot treat cyanine dyes reasonably accurately must be revised.