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 (D CT) 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.
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.
We have computed the bond length alternation (BLA) in a series of π-conjugated quasilinear chains containing from two to six unit cells. Several structures (eight oligomeric sets including three ...conformers of polyacetylene, polymethineimine, polysilaacetylene, etc.) have been considered to cover the possible evolutions of the BLA with increasing chain length. Three objectives have been tackled: (1) the computation of accurate reference values using the CCSD(T) theory; (2) an evaluation of the performances of other electron correlated wave function approaches (MPn, SCS-MP2, CCSD, etc.); (3) the benchmarking of several DFT functionals, including global, range-separated, and double hybrids. It turns out that the SCS-MP2 approach is, on average, an efficient scheme in terms of its accuracy/cost ratio. Among the selected DFT approaches, no single functional emerges as uniformly accurate for all oligomeric series and chain lengths, but BHHLYP, M06-2X, and CAM-B3LYP could be reasonable choices for long oligomers.
A new index is defined with the aim of further exploring the metric of excited electronic states in the framework of the time-dependent density functional theory. This descriptor, called Δr, is based ...on the charge centroids of the orbitals involved in the excitations and can be interpreted in term of the hole–electron distance. The tests carried out on a set of molecules characterized by a significant number of charge-transfer excitations well illustrate its ability in discriminating between short (Δr ≤ 1.5 Å) and long-range (Δr ≥ 2.0 Å) excitations. On the basis of the well-known pitfalls of TD-DFT, its values can be then associated to the functional performances in reproducing different type of transitions and allow for the definition of a “trust radius” for GGA and hybrid functionals. The study of other systems, including some well-known difficult cases for other metric descriptors, gives further evidence of the high discrimination power of the proposed index. The combined use with other density or orbital-based descriptors is finally suggested to have a reliable diagnostic test of TD-DFT transitions.
We investigate the efficiency of several partial atomic charge models (Mulliken, Hirshfeld, Bader, Natural, Merz-Kollman and ChelpG) for investigating the through-space charge-transfer in push-pull ...organic compounds with Time-Dependent Density Functional Theory approaches. The results of these models are compared to benchmark values obtained by determining the difference of total densities between the ground and excited states. Both model push-pull oligomers and two classes of "real-life" organic dyes (indoline and diketopyrrolopyrrole) used as sensitisers in solar cell applications have been considered. Though the difference of dipole moments between the ground and excited states is reproduced by most approaches, no atomic charge model is fully satisfactory for reproducing the distance and amount of charge transferred that are provided by the density picture. Overall, the partitioning schemes fitting the electrostatic potential (e.g. Merz-Kollman) stand as the most consistent compromises in the framework of simulating through-space charge-transfer, whereas the other models tend to yield qualitatively inconsistent values.
Time-dependent density functional theory calculations are performed within a range-separated hybrid framework to quantify the efficiency of through-space charge transfer (CT) in organic rod-like ...push–pull compounds. Our model allows us to quantify the CT distance, the amount of transferred electron, as well as the spread of the charges. The impact of several kinds of variations has been investigated: (1) the nature and length of the π-conjugated bridge; (2) the strength of the terminal groups; (3) the presence of a central groups; and (4) the use of a polar environment. In α,ω-nitro-dimethylamino chains, we found that the charge transfer is maximized when four to six conjugated rings are separating the donor and the acceptor. The maximum CT distance is ca. 5 Å for these chains but can be improved by 1–2 Å in polar environments. Adding a stronger electron-donating group does not systematically induce an enhancement of the CT if a strong electron-accepting moiety is used, the latter tending to extract the electron from the conjugated chains rather from the donor moiety. There is indeed a fine equilibrium to respect to improve CT. This investigation is a further step toward the rational optimization of charge transfer properties.
A theoretical study elucidating the mechanism of N2 reduction in Mo nitrogenase was carried out using a QM/QM′ approach based on density functional theory/semiempirical methods. Resting on the ...consolidated Lowe–Thorneley catalytic cycle, the identified reaction mechanism corresponds to an alternating pathway where the two nitrogen atoms are alternately reduced. Furthermore, this new mechanism provides a clear mechanistic basis to most of the experimental observations, including the noninnocent role played by the carbon atom located in the center of the MoFe cofactor and by the surrounding amino acids (such as α-96ARG, α-195HIS, and α-70VAL). It also provides evidence for the presence of H2 evolution in the global reaction cycle. Our calculations indicate a large flexibility of the cofactor upon hydrogenation and subsequent N2 chemical binding, with the average Fe–C distance increasing of 0.26 Å in going from the E0 to the E4 state, in agreement with experimental evidence. Taken together, these results give new insights into the activity of Mo nitrogenase, clearly considering the most relevant experimental findings.
The performances of different functionals in the prediction of Charge Transfer excitations (CT) have been assessed, both in terms of quantitative agreement with experimental absorption data and on ...the basis of a recently developed density based diagnostic index, for a family of 18 recently synthesized push-pull compounds, containing 4-5-dicyannoimidazole (DCI) as an acceptor moiety, six different bridges and three different donor groups. The index used also allows obtaining an estimate of the charge transferred upon excitation (qCT) and of the spatial extent associated with a given electronic transition (DCT). From the computed values of these indices an estimate of the transition energy considering a purely electrostatic model (wCT) can be computed and compared to that expected for an ideal CT between the donor and the acceptor, thus enabling us to estimate the efficiency of the CT transition for the different push-pull systems.
Using a set of 40 conjugated molecules, we assess the performance of an “optimally tuned” range-separated hybrid functional in reproducing the experimental 0–0 energies. The selected protocol ...accounts for the impact of solvation using a corrected linear-response continuum approach and vibrational corrections through calculations of the zero-point energies of both ground and excited-states and provides basis set converged data thanks to the systematic use of diffuse-containing atomic basis sets at all computational steps. It turns out that an optimally tuned long-range corrected hybrid form of the Perdew–Burke–Ernzerhof functional, LC-PBE*, delivers both the smallest mean absolute error (0.20 eV) and standard deviation (0.15 eV) of all tested approaches, while the obtained correlation (0.93) is large but remains slightly smaller than its M06-2X counterpart (0.95). In addition, the efficiency of two other recently developed exchange-correlation functionals, namely SOGGA11-X and ωB97X-D, has been determined in order to allow more complete comparisons with previously published data.
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