Denis Jacquemin

Extensive TD-DFT Benchmark: Singlet-Excited States of Organic Molecules

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.

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.

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.

TD-DFT Assessment of Functionals for Optical 0-0 Transitions in Solvated Dyes.

Using TD-DFT, we performed simulations of the adiabatic energies of 40 fluorescent molecules for which the experimental 0-0 energies in condensed phase are available. We used six hybrid functionals (B3LYP, PBE0, M06, M06-2X, CAM-B3LYP, and LC-PBE) that have been shown to provide accurate transition energies in previous TD-DFT assessments, selected two diffuse-containing basis sets, and applied the most recent models for estimating bulk solvation effects. In each case, the correction arising from the difference of zero-point vibrational energies between the ground and the excited states has been consistently determined. Basis set effects have also been carefully studied. It turned out that PBE0 and M06 are the most effective functionals in terms of average deviation (mean absolute error of 0.22-0.23 eV). However, both the M06-2X global hybrid that contains more exact exchange and the CAM-B3LYP range-separated hybrid significantly improve the consistency of the prediction for a relatively negligible degradation of the average error. In addition, we assessed (1) the cross-structure/spectra relationships, (2) the importance of solvent effects, and (3) the differences between adiabatic and vertical energies.

Assessment of the efficiency of long-range corrected functionals for some properties of large compounds

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.

Choosing a Functional for Computing Absorption and Fluorescence Band Shapes with TD-DFT

The band shapes corresponding to both the absorption and emission spectra of a set of 20 representative conjugated molecules, including recently synthesized structures, have been simulated with a Time-Dependent Density Functional Theory model including diffuse atomic orbitals and accounting for bulk solvent effects. Six hybrid functionals, including two range-separated hybrids (B3LYP, PBE0, M06, M06-2X, CAM-B3LYP, and LC-PBE) have been assessed in light of the experimental band shapes obtained for these conjugated compounds. Basis set and integration grid effects have also been evaluated. It turned out that all tested functionals but LC-PBE reproduce the main experimental features for both absorption and fluorescence, though the average errors are significantly larger for the latter phenomena. No single functional stands out as the most accurate for all aspects, but B3LYP yields the smallest mean absolute deviation. On the other hand, M06-2X could be a valuable compromise for excited-states as it reproduces the 0-0 energies and also gives reasonable band shapes. The typical mean absolute deviations between the relative positions of the experimental and theoretical peaks in the vibrationally resolved spectra are ca. 100 cm(-1) for absorption and 250 cm(-1) for emission. In the same time, the relative intensities of the different maxima are reproduced by TD-DFT with a ca. 10-15% accuracy.

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 hyperpolarizability of polymethineimine with long-range corrected functionals

Using the long-range corrected (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 the longitudinal dipole moments and static electronic first hyperpolarizabilities of increasingly long polymehtineimine oligomers. For comparison purposes Hartree-Fock (HF), Moller-Plesset perturbation theory (MP2), and conventional pure and hybrid functionals have been considered as well. HF, generalized gradient approximation (GGA), and conventional hybrids provide too large dipole moments for long oligomers, while LC-DFT allows to reduce the discrepancy with respect to MP2 by a factor of 3. For the first hyperpolarizability, the incorrect evolution with the chain length predicted by HF is strongly worsened by BLYP, Perdew-Burke-Ernzerhof (PBE), and also by B3LYP and PBE0. On the reverse, LC-BLYP and LC-PBE hyperpolarizabilities are correctly predicted to be positive (but for the two smallest chains). Indeed, for medium and long oligomers LC hyperpolarizabilities are slightly smaller than MP2 hyperpolarizabilities, as it should be. CAM-B3LYP also strongly improves the B3LYP results, though a bit less impressively for small chain lengths. The present study demonstrates the efficiency of long-range DFT, even in very pathological cases.

Single Molecule Multiphotochromism with Diarylethenes

In single photochromes, the two isomers that are interconverted in photoinduced reactions can serve as on and off states in a molecular switching device. The addition of several photochromic moieties onto a single molecule can allow the processing of more complex logical patterns. For example, an asymmetric triad could, in principle, store a byte, rather than a bit, of data. Because of the potential impact of multiphotochromic molecules in many research areas, over the past decade several groups have synthesized these coupled structures. The targets are easily addressable molecules that display increased contrast between the on and off states and in which all isomers have significantly distinguishable optical signatures. In this Account, we provide an overview of the multiswitchable molecular systems that incorporate at least one diarylethene group, which is the most successful thermally stable (P-type) organic photochrome. Up to this point, most systems have presented significant limitations. First of all, the reversibility of the processes is hindered by several side reactions more frequently than for single photochromes. Second, switching one part of the compound impedes the photoreactivity of other fragments in approximately 50% of the cases, and maximizing the electronic communication increases the probability of partial activity. In addition, most of the few synthesized operative systems only demonstrate cumulative absorption spectra rather than new features. Finally, it is impossible to selectively induce a chosen conversion because one wavelength might trigger several processes. We also emphasize the promising successes of asymmetric diarylethene dimers and trimers and molecules that combine two families of photochromes, such as diarylethene added to fulgimide or phenoxy-naphthacenequinone. In that framework, theoretical simulations offer complementary tools to investigate these structures, both to obtain structure/property relationships and to propose paths for the design of more efficient molecules. However, due to the size of the systems, researchers can only apply semiquantitative models. The investigation of the absorption spectra of the photochromes with time-dependent density functional theory (TD-DFT), the analysis of the topology of the LUMO + n (typically n = 1) of the closed-open hybrid, and an estimate of the steric stress in the hypothetical (ground-state) closed-closed structure serve as a useful combination of parameters to obtain initial insights regarding the photocyclization of the different open diarylethene groups. Nevertheless, because a first-order qualitative approach does not explore the potential energy surface of the photoexcited states, it remains inadequate for the investigation of some molecules.