An electron density based analysis to establish the electronic adiabaticity of proton coupled electron transfer reactions.

Electrons and protons are the main actors in play in proton coupled electron transfer (PCET) reactions, which are fundamental in many biological (i.e., photosynthesis and enzymatic reactions) and electrochemical processes. The mechanism, energetics and kinetics of PCET reactions are strongly controlled by the coupling between the transferred electrons and protons. Concerted PCET reactions are classified according to the electronical adiabaticity degree of the process. To discriminate among different mechanisms, we propose a new analysis based on the use of electron density based indexes. We choose, as test case, the 3-Methylphenoxyl/phenol system in two different conformations to show how the proposed analysis is a suitable tool to discriminate between the different degree of adiabaticity of PCET processes. The very low computational cost of this procedure is extremely promising to analyze and provide evidences of PCET mechanisms ruling the reactivity of many biological and catalytic systems.

Studies on the Enantioselective Iminium Ion Trapping of Radicals Triggered by an Electron-Relay Mechanism.

A combination of electrochemical, spectroscopic, computational, and kinetic studies has been used to elucidate the key mechanistic aspects of the previously reported enantioselective iminium ion trapping of photochemically generated carbon-centered radicals. The process, which provides a direct way to forge quaternary stereocenters with high fidelity, relies on the interplay of two distinct catalytic cycles: the aminocatalytic electron-relay system, which triggers the stereoselective radical trap upon iminium ion formation, and the photoredox cycle, which generates radicals under mild conditions. Critical to reaction development was the use of a chiral amine catalyst, bearing a redox-active carbazole unit, which could rapidly reduce the highly reactive and unstable intermediate generated upon radical interception. The carbazole unit, however, is also involved in another step of the electron-relay mechanism: the transiently generated carbazole radical cation acts as an oxidant to return the photocatalyst into the original state. By means of kinetic and spectroscopic studies, we have identified the last redox event as being the turnover-limiting step of the overall process. This mechanistic framework is corroborated by the linear correlation between the reaction rate and the reduction potential of the carbazole unit tethered to the aminocatalyst. The redox properties of the carbazole unit can thus be rationally tuned to improve catalytic activity. This knowledge may open a path for the mechanistically driven design of the next generation of electron-relay catalysts.

Determining the role of the underlying orbital-dependence of PBE0-DH and PBE-QIDH double-hybrid density functionals.

We study the orbital-dependence of three (parameter-free) double-hybrid density functionals, namely the PBE0-DH, the PBE-QIDH models, and the SOS1-PBE-QIDH spin-opposite-scaled variant of the latter. To do it, we feed all their energy terms with different sets of orbitals obtained previously from self-consistent density functional theory calculations using several exchange-correlation functionals (e.g., PBE, PBE0, PBEH&H), or directly with HF-PBE orbitals, to see their effect on selected datasets for atomization and reaction energies, the latter proned to marked self-interaction errors. We find that the PBE-QIDH double-hybrid model shows a great consistency, as the best results are always obtained for the set of orbitals corresponding to its hybrid scheme, which prompts us to recommend this model without any other fitting or reparameterization. © 2017 Wiley Periodicals, Inc.

Comparing the performance of TD-DFT and SAC-CI methods in the description of excited states potential energy surfaces: An excited state proton transfer reaction as case study.

The performances, in the description of excited state potential energy surfaces, of several density functional approximations representative of the currently most applied exchange correlation functionals' families have been tested with respect to post Hartree-Fock references (here Symmetry Adapted Cluster-Configuration Interaction results). An experimentally well-characterized intermolecular proton transfer reaction has been considered as test case. The computed potential energy profiles were analyzed both in the gas phase and in toluene solution, here represented as a polarizable continuum model. The presence of intermolecular (dark) and intramolecular (bright) charge transfer excited states, whose polarity strongly differs along the reaction pathway, makes clear that only subtle compensation between spurious electronic effects-related to the incorrect asymptotic behavior of the functional-and solvent stabilization of polar states leads to the overall correct description of this excited state reaction when using global hybrids with low percentage of Hartree Fock exchange. © 2017 Wiley Periodicals, Inc.

Metrics for Molecular Electronic Excitations: A Comparison between Orbital- and Density-Based Descriptors.

This study proposes a quantitative and qualitative comparison of two popular metrics used for time-dependent density functional simulations of chromophores when describing absorption and emission processes, with high discrimination power between short- and long-range character of involved electronic excitations and functional performances. To this end, a total of 160 absorption and emission electronic excitations of 80 molecular systems belonging to the "Real-Life Molecules" data set, recently introduced in literature, have been considered a relevant data set. The two selected indexes are based on density (the DCT one) and natural transition orbitals (the ΔrNTO one), respectively. For comparison purposes, an extension of the DCT index, in line with what exists for ΔrNTO, enabling to discriminate electronic transitions occurring in symmetric systems is also proposed. The results show that, independently of the exchange and correlation functional used, a good correlation between the natural transition orbital and density based descriptors is found, thus cross validating their use for the quantification of a large variety of transitions in chemically relevant molecular systems.

Excited-State Proton Transfer and Intramolecular Charge Transfer in 1,3-Diketone Molecules.

The photophysical signature of the tautomeric species of the asymmetric (N,N-dimethylanilino)-1,3-diketone molecule are investigated using approaches rooted in density functional theory (DFT) and time-dependent DFT (TD-DFT). In particular, since this molecule, in the excited state, can undergo proton transfer reactions coupled to intramolecular charge transfer events, the different radiative and nonradiative channels are investigated by making use of different density-based indexes. The use of these tools, together with the analysis of both singlet and triplet potential energy surfaces, provide new insights into excited-state reactivity allowing one to rationalize the experimental findings including different behavior of the molecule as a function of solvent polarity.

Quadratic integrand double-hybrid made spin-component-scaled.

We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.

Computational Insights into Excited-State Proton-Transfer Reactions in Azo and Azomethine Dyes.

State of the art density functional theory approaches are employed to provide an accurate description of the photophysical properties of azodyes and Schiff bases displaying intramolecular hydrogen-bonding features. These compounds exist as tautomeric mixtures at the ground state and, in the case of Schiff bases, an excited-state intramolecular proton transfer (ESIPT) occurs upon excitation. The experimentally observed photophysical properties are discussed here in light of the theoretical findings. To rationalize the different experimentally observed radiative behavior of the azo and azomethine structures, a nonradiative decay pathway that is possibly active in such systems is determined. The characterization of this deactivation path, tested for two related compounds exhibiting different fluorescence quantum yields, enables us to disentangle the different and contrasting effects governing the excited-state behavior of these molecular systems.

Controlled tautomeric switching in azonaphthols tuned by substituents on the phenyl ring.

A series of new tautomeric azonaphthols are synthesized and the possibilities for molecular switching are investigated using molecular spectroscopy, X-ray analysis and density functional theory quantum chemical calculations. Two opposite effects that influence switching are studied: attaching a piperidine sidearm, and adding substituents to the phenyl ring. On the one hand, the attached piperidine moiety stabilizes the enol form leading to a controlled shift of the equilibrium upon protonation. On the other hand, the relative stability of the azonaphthol tautomers strongly depends on the effects of the substituents on the phenyl ring: electron donors tend to stabilize the enol tautomer, whereas electron acceptors lead to stabilization of the keto form. However, these effects do not shift fully the equilibrium towards either of the tautomers. Nevertheless, the effect of the substituents can be an additional tool to affect the switching between "on" and "off" states. Electron-withdrawing substituents stabilize the keto form and impede switching to the off state, whereas electron donors stabilize the enol form. The effect of the piperidine unit is dominant overall, and with strongly electron-withdrawing substituents at the phenyl ring, the enol form exists as a zwitterion.

Intermolecular proton shuttling in excited state proton transfer reactions: insights from theory.

The mechanism of base to base intermolecular proton shuttling occurring in the excited state proton transfer reaction between 7-hydroxy-4-(trifluoromethyl)coumarin (CouOH) and concentrated 1-methylimidazole base (1-MeId) in toluene solution is disclosed here by means of a computational approach based on Density Functional Theory (DFT) and Time Dependent DFT (TD-DFT). These methods allow us to characterize both the ground and excited state potential energy surfaces along the proton shuttling coordinate, and to assess the nature of the emitting species in the presence of an excess of 1-MeId. As a result, the tautomerism of CouOH is found to be photo-activated and, from a mechanistic point of view, the calculations clearly show that the overall driving force of the entire shuttling is the coumarin photoacidity, which is responsible for both the first proton transfer event and the strengthening of the following chain mechanism of base to base proton hopping.

Non-radiative decay paths in rhodamines: new theoretical insights.

We individuate a photoinduced electron transfer (PeT) as a quenching mechanism affecting rhodamine B photophysics in solvent. The PeT involves an electron transfer from the carboxylate group to the xanthene ring of rhodamine B. This is finely modulated by the subtle balance of coulombic and non-classical interactions between the carboxyphenyl and xanthene rings, also mediated by the solvent. We propose the use of an electronic density based index, the so called DCT index, as a new tool to assess and quantify the nature of the excited states involved in non-radiative decays near the region of their intersection. In the present case, this analysis allows us to gain insight on the interconversion process from the bright state to the dark state responsible for the quenching of rhodamine B fluorescence. Our findings encourage the use of density based indices to study the processes affecting excited state reactions that are characterized by a drastic change in the excitation nature, in order to rationalize the photophysical behavior of complex molecular systems.

Fluorescence lifetimes and quantum yields of rhodamine derivatives: new insights from theory and experiment.

Although lifetimes and quantum yields of widely used fluorophores are often largely characterized, a systematic approach providing a rationale of their photophysical behavior on a quantitative basis is still a challenging goal. Here we combine methods rooted in the time-dependent density functional theory and fluorescence lifetime imaging microscopy to accurately determine and analyze fluorescence signatures (lifetime, quantum yield, and band peaks) of several commonly used rhodamine and pyronin dyes. We show that the radiative lifetime of rhodamines can be correlated to the charge transfer from the phenyl toward the xanthene moiety occurring upon the S(0) ← S(1) de-excitation, and to the xanthene/phenyl relative orientation assumed in the S(1) minimum structure, which in turn is variable upon the amino and the phenyl substituents. These findings encourage the synergy of experiment and theory as unique tool to design finely tuned fluorescent probes, such those conceived for modern optical sensors.

Free Energy Profiles of Proton Transfer Reactions: Density Functional Benchmark from Biased Ab Initio Dynamics.

By coupling an enhanced sampling algorithm with an orbital-localized variant of Car-Parrinello molecular dynamics, the so-called atomic centered density matrix propagation model, we reconstruct the free energy profiles along reaction pathways using different density functional approximations (DFAs) ranging from locals to hybrids. In particular, we compare the computed free energy barrier height of proton transfer (PT) reactions to those obtained by a more traditional static approach, based on the intrinsic reaction coordinate (IRC), for two case systems, namely malonaldehyde and formic acid dimer. The obtained results show that both the IRC profiles and the potentials of mean force, derived from biased dynamic trajectories, are very sensitive to the density functional approximation applied. More precisely, we observe that, with the notable exception of M06-L, local density functionals always strongly underestimate the reaction barrier heights. More generally, we find that also the shape of the free energy profile is very sensitive to the density functional choice, thus highlighting the effect, often neglected, that the choice of DFA has also in the case of dynamics simulations.

Electron Spin Densities and Density Functional Approximations: Open-Shell Polycyclic Aromatic Hydrocarbons as Case Study.

The way different density functional approximations (DFAs) are able to predict, in open-shell systems, spin density, that is the difference between the densities of electrons with spin α and those of spin ß, is investigated. Here, a large panel of functionals were tested on a set composed of seven π-radicals expected to amplify DFA errors in modeling electron delocalization and spin polarization effects due to their extended electronic conjugation coupled with their planar structures. Our results show that generally the DFA performances follow a systematic improvement in going from semilocal to hybrid functionals. More problematic is, instead, the case of double hybrid functionals, where the perturbative contribution to correlation damps the positive effect of the presence of a high percent of exact exchange. More interestingly, differences are observed in the spin delocalization and polarization patterns, thus restraining the possibility of applying some of current DFAs to study chemically relevant properties, like molecular magnetism or charge/electron transport.

Modeling the Electron Transfer Chain in an Artificial Photosynthetic Machine.

The development of efficient artificial leaves relies on the subtle combination of molecular assemblies able to absorb sunlight, converting light energy into electrochemical potential energy and finally transducing it into accessible chemical energy. The electronic design of these charge transfer molecular machines is crucial to build a complex supramolecular architecture for the light energy conversion. Here, we present an ab initio simulation of the whole decay pathways of a recently proposed artificial molecular reaction center. A complete structural and energetic characterization has been carried out with methods based on density functional theory, its time-dependent version, and a broken-symmetry approach. On the basis of our findings we provide a revision of the pathway only indirectly postulated from an experimental point of view, along with unprecedented and significant insights on the electronic and nuclear structure of intramolecular charge-separated states, which are fundamental for the application of this molecular assembly in photoelectrochemical cells. Importantly, we unravel the molecular driving forces of the various charge transfer steps, in particular those leading to the proton-coupled electron transfer final product, highlighting key elements for the future design strategies of such molecular assays.

Accuracy of TD-DFT Geometries: A Fresh Look.

We benchmark a panel of 48 DFT exchange-correlation functionals in the framework of TD-DFT optimizations of the geometry of valence singlet excited states. To this end, we use a set of 41 small- and medium-sized organic molecules for which reference geometries were obtained at high level of theory, typically, CC3 or CCSDR(3), with the aug-cc-pVTZ atomic basis set. For the ground-state parameters, the tested functionals provide average deviations that are small (0.010 Å and 0.5° for bond lengths and valence angles) and not very sensitive to the selected (hybrid) functional, but the errors are larger for the most polarized bonds (CO, CN, and so on). Nevertheless, DFT has a tendency to provide too compact distances, a trend slightly enhanced for functionals including a large amount of exact exchange. The average errors largely increase when going to the excited-state for most bond types, that is, TD-DFT delivers less accurate excited-state distances than DFT for ground state. In particular TD-DFT combined with hybrid functionals provides significantly too short CO and CS/CSe bonds with respective average errors in the -0.026/-0.052 Å and -0.015/-0.082 Å ranges, depending on the selected hybrid functional. For the carbonyl bonds, the sizes of the TD-DFT deviations obtained when selecting standard hybrid functionals are of the same order of magnitude as the EOM-CCSD ones.

Range-Separated Double-Hybrid Functional from Nonempirical Constraints.

On the basis of our previous developments in the field of nonempirical double hybrids, we present here a new exchange-correlation functional based on a range-separated model for the exchange part and integrating a nonlocal perturbative correction to the electron correlation contribution. Named RSX-QIDH, the functional is free from any kind of empirical parametrization. Its range-separation parameter is set to recover the total energy of the hydrogen atom, thus eliminating the self-interaction error for this one-electron system. Subsequent tests on some relevant benchmark data sets confirm that the self-interaction error is particularly low for RSX-QIDH. This new functional provides also correct dissociation profiles for charged rare-gas dimers and very accurate ionization potentials directly from Kohn-Sham orbital energies. Above all, these good results are not obtained at the expense of other properties. Indeed, further tests on standard benchmarks show that RSX-QIDH is competitive with the more empirical ωB97X-2 double hybrid and outperforms the parent LC-PBE long-range corrected hybrid, thus underlining the important role of the nonlocal perturbative correlation.

Speed-Up of the Excited-State Benchmarking: Double-Hybrid Density Functionals as Test Cases.

The EX6-0, EX7-0, and EX7-1 representative benchmark sets are developed for the fast evaluation of the performance of a density functional, or more generally of a computational protocol, in modeling low-lying valence singlet-singlet excitation energies of organic dyes within the range of 1.5 to 4.5 eV. All sets share the advantage of being small (a maximum of 7 molecules) but providing statistical errors representative of larger and extended databases. To that extent, the EX7-1 benchmark set goes a step further and is composed of systems as small as possible in order to alleviate the associated computational cost. The reliability of all the sets is assessed through the benchmarking of 15 modern double-hybrid density functionals. The investigation shows not only that the 3 benchmark sets provide close error metrics for each density functional but also that when taking advantage of the Resolution-of-the-Identity and a balanced triple-ζ basis set (e.g., def2-TZVP), double hybrids overperform the "popular" hybrids in modeling vertical absorption, emission, and adiabatic energies.

Benchmarking Density Functionals on Structural Parameters of Small-/Medium-Sized Organic Molecules.

In this Letter we report the error analysis of 59 exchange-correlation functionals in evaluating the structural parameters of small- and medium-sized organic molecules. From this analysis, recently developed double hybrids, such as xDH-PBE0, emerge as the most reliable methods, while global hybrids confirm their robustness in reproducing molecular structures. Notably the M06-L density functional is the only semilocal method reaching an accuracy comparable to hybrids'. A comparison with errors obtained on energetic databases (including thermochemistry, reaction barriers, and interaction energies) indicate that most of the functionals have a coherent behavior, showing low (or high) deviations on both energy and structure data sets. Only a few of them are more prone toward one of these two properties.

Describing excited state intramolecular proton transfer in dual emissive systems: a density functional theory based analysis.

The excited state intramolecular proton transfer (ESIPT) reaction taking place within 2-(2-hydroxyphenyl)benzoxazole (HBT) and two recently experimentally characterized napthalimide derivatives-known as N-1 and N-4-has been investigated in order to identify and test a possible protocol for the description and complete mechanistic and electronic characterization of the reaction at the excited state. This protocol is based on density functional theory, time-dependent density functional theory, and a recently proposed electron density based index (DCT). This method is able to identify all stable species involved in the reaction, discriminate between possible reaction pathways over potential energy surfaces (PES), which are intrinsically very flat and difficult to characterize, and quantitatively measure the excited state charge transfer character throughout the reaction. The photophysical properties of the molecules (i.e., absorption and emission wavelength) are also quantitatively determined via the implicit inclusion of solvent effects in the case of toluene and, the more polar, tetrahydrofuran. The accuracy obtained with this protocol then opens up the possibility of the ab initio design of molecules exhibiting ESIPT for tailored applications such as highly selective molecular sensors.