Axial-equatorial equilibrium in substituted cyclohexanes: a DFT perspective on a small but complex problem.

In Chemistry, complexity is not necessarily associated to large systems, as illustrated by the textbook example of axial-equatorial equilibrium in mono-substituted cyclohexanes. The difficulty in modelling such a simple isomerization is related to the need for reproducing the delicate balance between two forces, with opposite effects, namely the attractive London dispersion and the repulsive steric interactions. Such balance is a stimulating challenge for density-functional approximations and it is systematically explored here by considering 20 mono-substituted cyclohexanes. In comparison to highly accurate CCSD(T) reference calculations, their axial-equatorial equilibrium is studied with a large set of 48 exchange-correlation approximations, spanning from semilocal to hybrid to more recent double hybrid functionals. This dataset, called SAV20 (as Steric A-values for 20 molecules), allows to highlight the difficulties encountered by common and more original DFT approaches, including those corrected for dispersion with empirical potentials, the 6-31G*-ACP model, and our cost-effective PBE-QIDH/DH-SVPD protocol, in modeling these challenging interactions. Interestingly, the performance of the approaches considered in this contribution on the SAV20 dataset does not correlate with that obtained with other more standard datasets, such as S66, IDISP or NC15, thus indicating that SAV20 covers physicochemical features not already considered in previous noncovalent interaction benchmarks.

Modeling Multi-Step Organic Reactions: Can Density Functional Theory Deliver Misleading Chemistry?

Many organic reactions are characterized by a complex mechanism with a variety of transition states and intermediates of different chemical natures. Their correct and accurate theoretical characterization critically depends on the accuracy of the computational method used. In this work, we study a complex ambimodal cycloaddition with five transition states, two intermediates, and three products, and we ask whether density functional theory (DFT) can provide a correct description of this type of complex and multifaceted reaction. Our work fills a gap in that most systematic benchmarks of DFT for chemical reactions have considered much simpler reactions. Our results show that many density functionals not only lead to seriously large errors but also differ from one another in predicting whether the reaction is ambimodal. Only a few of the available functionals provide a balanced description of the complex and multifaceted reactions. The parameters varied in the tested functionals are the ingredients, the treatment of medium-range and nonlocal correlation energy, and the inclusion of Hartree-Fock exchange. These results show a clear need for more benchmarks on the mechanisms of large molecules in complex reactions.

SOS1-RSX-QIDH: A spin-opposite-scaled range-separated-exchange quadratic-integrand double-hybrid density functional.

We develop and validate the SOS1-RSX-QIDH density functional, a one-parameter spin-opposite-scaled variant of the range-separated-exchange quadratic-integrand double-hybrid (RSX-QIDH) model. By entering into the family of spin-biased double hybrids, this new density functional benefits from an improved computational scaling that rivals with the one of hybrids, still conserving the accuracy of its RSX-QIDH version. As part of the latter family, this density functional is well-adapted to treat molecular systems that are particularly prone to self-interaction errors in their ground and excited states. In particular, we show that the SOS1-RSX-QIDH model is a good compromise to treat ground-state problems dealing with kinetics and has a real added value when applied to the evaluation of the excited-state properties of equilibrium and out-of-equilibrium molecular complexes. Even if spin-biased double hybrids are recognized to strongly underestimate noncovalent interactions, we notice and recommend coupling SOS1-RSX-QIDH with a nonlocal van der Waals potential, a combination that is here proved to compete with the best density-functional approximations currently in use.

Effect of Polymer Composition on the Optical Properties of a New Aggregation-Induced Emission Fluorophore: A Combined Experimental and Computational Approach.

Nowadays, fluorophores with a tetraphenylethylene (TPE) core are considered interesting due to the aggregation-induced emission (AIE) behavior that enables their effective use in polymer films. We propose a novel TPE fluorophore (TPE-BPAN) bearing two dimethylamino push and a 4-biphenylacetonitrile pull moieties with the typical AIE characteristics in solution and in the solid state, as rationalized by DFT calculations. Five different host polymer matrices with different polarity have been selected: two homopolymers of poly(methylmethacrylate) (PMMA) and poly(cyclohexyl methacrylate) (PCHMA) and three copolymers at different compositions (P(MMA-co-CHMA) 75:25, 50:50, and 25:75 mol%). The less polar comonomer of CHMA appeared to enhance TPE-BPAN emission with the highest quantum yield (QY) of about 40% measured in P(MMA-co-CHMA) 75:25. Further reduction in polymer polarity lowered QY and decreased the film stability and adhesion to the glass surface. LSC performances were not significantly affected by the matrix's polarity and resulted in around one-third of the state-of-the-art due to the reduced QY of TPE-BPAN. The theoretical investigation based on density functional theory (DFT) calculations clarified the origin of the observed AIE and the role played by the environment in modulating the photophysical behavior.

Concerted versus stepwise proton transfer reactions in the [2, 2'-bipyridyl]-3-3'-diol molecule: A static and dynamic ab-initio investigation.

The double proton transfer (PT) reaction has been investigated in the [2,2'-bipyridyl]-3-3'-diol, a complex molecule where the proton movements is coupled to significant rearrangement of the electronic structure. Moreover, the reaction could be concerted, that is the two protons are exchanged simultaneously, or stepwise, where the two protons are transferred sequentially. To this end, a static exploration of the potential energy surface (PES) was carried together with the analysis of the free-energy surface (FES), both surfaces being evaluated at density functional theory level and different exchange-correlation functionals. While the concerted mechanism has been clearly discharged, the characteristics of the stepwise PT significantly depends on the chosen functionals, some suggesting a clear stepwise mechanism characterized by a stable reaction intermediates and two transitions states, whereas other approaches propend for a asynchronous PT, with a single TS. These features appear on both PES and FES, albeit some differences appears due to their different nature.

Barrier Heights for Diels-Alder Transition States Leading to Pentacyclic Adducts: A Benchmark Study of Crowded, Strained Transition States of Large Molecules.

Theoretical characterization of reactions of complex molecules depends on providing consistent accuracy for the relative energies of intermediates and transition states. Here we employ the DLPNO-CCSD(T) method with core-valence correlation, large basis sets, and extrapolation to the CBS limit to provide benchmark values for Diels-Alder transition states leading to competitive strained pentacyclic adducts. We then used those benchmarks to test a diverse set of wave function and density functional methods for the absolute and relative barrier heights of these transition states. Our results show that only a few of the tested density functionals can predict the absolute barrier heights satisfactorily, although relative barrier heights are more accurate. The most accurate functionals tested are ωB97M-V, M11plus, ωB97X-V, PBE-D3(0), M11, and MN15 with MUDs from best estimates less than 3.0 kcal. These findings can guide selection of density functionals for future studies of crowded, strained transition states of large molecules.

Organic compounds for solid state luminescence enhancement/aggregation induced emission: a theoretical perspective.

Organic luminophores displaying one or more forms of luminescence enhancement in solid state are extremely promising for the development and performance optimization of functional materials essential to many modern key technologies. Yet, the effort to harness their huge potential is riddled with hurdles that ultimately come down to a limited understanding of the interactions that result in the diverse molecular environments responsible for the macroscopic response. In this context, the benefits of a theoretical framework able to provide mechanistic explanations to observations, supported by quantitative predictions of the phenomenon, are rather apparent. In this perspective, we review some of the established facts and recent developments about the current theoretical understanding of solid-state luminescence enhancement (SLE) with an accent on aggregation-induced emission (AIE). A description of the macroscopic phenomenon and the questions it raises is accompanied by a discussion of the approaches and quantum chemistry methods that are more apt to model these molecular systems with the inclusion of an accurate yet efficient simulation of the local environment. A sketch of a general framework, building from the current available knowledge, is then attempted via the analysis of a few varied SLE/AIE molecular systems from literature. A number of fundamental elements are identified offering the basis for outlining design rules for molecular architectures exhibiting SLE that involve specific structural features with the double role of modulating the optical response of the luminophores and defining the environment they experience in solid state.

Tuning the Photophysical Properties of Ru(II) Photosensitizers for PDT by Protonation and Metallation: A DFT Study.

Due to their activity, photosensitizers with the Ru(II)-polypyridyl complex structure represent an intriguing class of photodynamic therapy agents used to treat neoplasms. However, their solubility is poor, intensifying experimental research into improving this property. One recently proposed solution is to attach a polyamine macrocycle ring. In this paper, the density functional theory (DFT) and time-dependent DFT (TD-DFT) studies on such derivative were performed to assess the impact of the protonation-capable macrocycle and its ability to chelate transition state metals, as illustrated by the Cu(II) ion, on the expected photophysical activity. These properties were determined by examining ultraviolet-visible (UV-vis) spectra, intersystem conversion, and type I and II photoreactions of all species possibly present in a tumor cell. For comparison purposes the structure devoid of the macrocycle was also examined. The results show that the subsequent protonation of amine groups improves the reactivity, with [H2L]4+/[H3L]5+ being borderline, whereas complexation appears to weaken the desired photoactivity.

Absorption Spectra of Flexible Fluorescent Probes by a Combined Computational Approach: Molecular Dynamics Simulations and Time-Dependent Density Functional Theory.

A detailed understanding and interpretation of absorption spectra of molecular systems, especially in condensed phases, requires computational models that allow their structural and electronic features to be connected to the observed macroscopic spectra. This work is focused on modeling the electronic absorption spectrum of a fluorescent probe, namely, the 9-(4-((bis(2-((2-(ethylthio)ethyl)thio)ethyl)amino)methyl)phenyl)-6-(pyrrolidin-1-yl)-3H-xanthen-3-one molecule, depicted by a combined classical-quantum chemical approach. Particularly, first classical molecular dynamics (MD) has been used to explore the configurational space, and next, the absorption spectrum has been reconstructed by averaging the results of time-dependent density functional theory (TD-DFT) calculations performed on equispaced molecular conformations extracted from MD to properly sample the configurational space explored at finite temperature. To verify the effect of molecular conformation on the spectral profile, the generated electronic absorption spectra were compared with those obtained considering a single structure corresponding to the optimized one, an approach also referred to as static. This comparison allows one to highlight a sizable though small shift between the maxima of the corresponding reconstructed absorption spectra, highlighting the importance of conformational sampling in the case of this rather flexible molecule. Four different exchange and correlation functionals (PBE, BLYP, PBE0, B3LYP) were considered to compute vertical transition via TD-DFT calculations. From the results obtained in gas and in condensed, here solution, phases, it appears that the magnitude of the shift is actually more affected by the phase in which the system is found than by the functional used. This fact underlines the central importance of conformational mobility, that is flexibility, of this molecule. From a more quantitative point of view, a comparison with available experimental data shows that hybrid functionals, such as PBE0 and B3LYP, enable one to faithfully reproduce the observed absorption maxima.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Double Hybrids and Noncovalent Interactions: How Far Can We Go?

The accurate evaluation of weak noncovalent interactions in large, that is those containing up to thousand atoms, molecular systems represents a difficult challenge for any quantum chemical method. Indeed, some approximations are often introduced to render affordable these calculations. Here, we consider the PBE-QIDH/DH-SVPD protocol, combining a nonempirical double hybrid functional (PBE-QIDH) with a small basis set (DH-SVPD) tailored for noncovalent interactions with a double aim: (i) explore the robustness and accuracy of this protocol with respect to other Density Functional Approximations; (ii) illustrate how its performances are affected by the computational parameters underlying the calculation of the exact exchange and the Coulomb contribution, as well as the perturbative term. To this end, we consider three data sets, namely S66, L7, and CiM13, incorporating molecules of increasing size. On the bright side, our results suggest that the PBE-QIDH/DH-SVPD protocol is particularly accurate for large systems such as those contained in the CiM13 set (up to more than 1000 atoms and 14 000 basis functions), for which the DLPNO approximation leads to a significant speed-up for the evaluation of the perturbative correlation term. However, our analysis also points out the limit of this statistical exercise, when the quality of the reference data cannot be easily assessed, due to the size of the molecular complexes involved, and when the number of molecules is limited.

Tackling an accurate description of molecular reactivity with double-hybrid density functionals.

In this Communication, we assess a panel of 18 double-hybrid density functionals for the modeling of the thermochemical and kinetic properties of an extended dataset of 449 organic chemistry reactions belonging to the BH9 database. We show that most of DHs provide a statistically robust performance to model barrier height and reaction energies in reaching the "chemical accuracy." In particular, we show that nonempirical DHs, such as PBE0-DH and PBE-QIDH, or minimally parameterized alternatives, such as ωB2PLYP and B2K-PLYP, succeed to accurately model both properties in a balanced fashion. We demonstrate, however, that parameterized approaches, such as ωB97X-2 or DSD-like DHs, are more biased to only one of both properties.

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.

Electronic Energy and Local Property Errors at QTAIM Critical Points while Climbing Perdew's Ladder of Density-Functional Approximations.

We investigate the relationships between electron-density and electronic-energy errors produced by modern exchange-correlation density-functional approximations belonging to all of the rungs of Perdew's ladder. To this aim, a panel of relevant (semi)local properties evaluated at critical points of the electron-density field (as defined within the framework of Bader's atoms-in-molecules theory) are computed on a large selection of molecular systems involved in thermodynamic, kinetic, and noncovalent interaction chemical databases using density functionals developed in a nonempirical and minimally and highly parametrized fashion. The comparison of their density- and energy-based performance, also discussed in terms of density-driven errors, casts light on the strengths and weaknesses of the most recent and efficient density-functional approximations.

Chasing unphysical TD-DFT excited states in transition metal complexes with a simple diagnostic tool.

Transition Metal Complexes (TMCs) are known for the rich variety of their excited states showing different nature and degrees of locality. Describing the energies of these excited states with the same degree of accuracy is still problematic when using time-dependent density functional theory in conjunction with the most current density functional approximations. In particular, the presence of unphysically low lying excited states possessing a relevant Charge Transfer (CT) character may significantly affect the spectra computed at such a level of theory and, more relevantly, the interpretation of their photophysical behavior. In this work, we propose an improved version of the MAC index, recently proposed by the authors and collaborators, as a simple and computationally inexpensive diagnostic tool that can be used for the detection and correction of the unphysically predicted low lying excited states. The analysis, performed on five prototype TMCs, shows that spurious and ghost states can appear in a wide spectral range and that it is difficult to detect them only on the basis of their CT extent. Indeed, both delocalization of the excited state and CT extent are criteria that must be combined, as in the MAC index, to detect unphysical states.

Aggregation-Induced Emission: A Challenge for Computational Chemistry Taking TPA-BMO as an Example*.

A multi-environment computational approach is proposed to study the modulation of the emission behavior of the triphenylamine (Z)-4-benzylidene-2-methyloxazol-5(4H)-one (TPA-BMO) molecule [Tang et al., J. Phys. Chem. C 119, 21875 (2015)]. We aim at (1) proposing a realistic description of the molecule in several environments (solution, aggregate, polymer matrix), (2) modelling its absorption and emission properties, and (3) providing a qualitative understanding of the experimental observations by highlighting the photophysical phenomena leading to the emission modulation. To this purpose, we rely on (TD-)DFT calculations and classical Molecular Dynamics simulations, but also on the hybrid ONIOM QM/QM' approach and the in situ chemical polymerization methodology. In low-polar solvents, the investigation of the potential energy surfaces and the modulation of the emission quantum yield can be attributed to possible photophysical energy dissipation caused by low-frequency vibrational modes. In the aggregate and in the polymer matrix, the emission modulation can be qualitatively interpreted in terms of the possible restriction of the intramolecular vibrations. For these two systems, our study highlights that a careful modelling of the environment is far from trivial but is fundamental to model the optical properties of the fluorophore.

A combined Monte Carlo/DFT approach to simulate UV-vis spectra of molecules and aggregates: Merocyanine dyes as a case study.

The combination of a Monte Carlo (MC) sampling of the configurational space with time dependent-density functional theory (TD-DFT) to estimate vertical excitations energies has been applied to compute the absorption spectra of a family of merocyanine dyes in both their monomeric and dimeric forms. These results have been compared to those obtained using a static DFT/TD-DFT approach as well as to the available experimental spectra. Though suffering of the limitations related to the use of DFT and TD-DFT for this type of systems, our data clearly show that the classical MC sampling provides a suitable alternative to classical molecular dynamics to explore the structural flexibility of these donor-acceptor (D-π-A) chromophores enabling a realistic description of the potential energy surface of both their monomers and aggregates (here dimers) and thus of their spectra. Overall, the combination of MC sampling with quantum mechanics (TD-DFT) calculations, carried out in implicit dioxane solvent on random snapshots, provides a workable compromise to solve the combined challenge of accuracy and time-consuming problem not only for merocyanines momers, but also for their dimers, up to now less investigated. Indeed, the simulated absorption spectra fairly agree with the experimental ones, suggesting the general reliability of the method.

Beyond Chemical Accuracy for Alkane Thermochemistry: The DHthermo Approach.

The so-called protobranching phenomenon, that is the greater stability of branched alkanes with respect to their linear isomers, represents an interesting challenge for approaches based on density functional theory (DFT), since it requires a balanced description of several electronic effects, including (intramolecular) dispersion forces. Here, we investigate this problem using a protocol recently developed based on double-hybrid functionals and a small basis set, DH-SVPD, suited for noncovalent interactions. The energies of bond separation reactions (BSR), defined on the basis of an isodesmic principle, are taken as reference properties for the evaluation of 15 DFT approaches. The obtained results show that error lower than the so-called "chemical accuracy" (<1.0 kcal/mol) can be obtained by the proposed protocol on both relative reaction energies and enthalpies. These results are then verified on the standard BSR36 data set and support the proposition of our computational protocol, named DHthermo, where any DH functional, such as PBE-QIDH or B2PLYP, provides accurate results when coupled to an empirical dispersion correction and the DH-SVPD basis set. This protocol not only gives subchemical accuracy on the thermochemistry of alkanes but it is extremely easy to use with common quantum-chemistry codes.

Assessing challenging intra- and inter-molecular charge-transfer excitations energies with double-hybrid density functionals.

We investigate the performance of a set of recently introduced range-separated double-hybrid functionals, namely ωB2-PLYP, ωB2GP-PLYP, RSX-0DH, and RSX-QIDH models for hard-to-calculate excitation energies. We compare with the parent (B2-PLYP, B2GP-PLYP, PBE0-DH, and PBE-QIDH) and other (DSD-PBEP86) double-hybrid models as well as with some of the most widely employed hybrid functionals (B3LYP, PBE0, M06-2X, and ωB97X). For this purpose, we select a number of medium-sized intra- and inter-molecular charge-transfer excitations, which are known to be challenging to calculate using time-dependent density-functional theory (TD-DFT) and for which accurate reference values are available. We assess whether the high accuracy shown by the newest double-hybrid models is also confirmed for those cases too. We find that asymptotically corrected double-hybrid models yield a superior performance, especially for the inter-molecular charge-transfer excitation energies, as compared to standard double-hybrid models. Overall, the PBE-QIDH and its corresponding range-separated RSX-QIDH functional are recommended for general-purpose TD-DFT applications, depending on whether long-range effects are expected to play a significant role.

Pairing double hybrid functionals with a tailored basis set for an accurate thermochemistry of hydrocarbons.

A collection of five challenging datasets, including noncovalent interactions, reaction barriers and electronic rearrangements of medium-sized hydrocarbons, has been selected to verify the robustness of double-hybrid functionals used in conjunction with the small DH-SVPD basis set, especially developed for noncovalent interactions. The analysis is completed by other, more standard functionals, for a total of 17 models, including also empirical corrections for dispersion. The obtained results show that the chemical accuracy threshold, that is an error lower than 1.0 kcal mol-1, can be obtained by pairing the nonempirical PBE-QIDH functional with the DH-SVPD basis set, as well as by other semi-empirical functionals, such as DSD-PBEP86, using larger basis sets and empirical corrections. More in general, a significant improvement can be obtained using the DH-SVPD basis set with DHs, without resorting to any empirical corrections. This choice leads to a fast computational protocol that, avoiding any empirical potential, remains on a fully quantum ground.