Predicting redox potentials by graph-based machine learning methods.

The evaluation of oxidation and reduction potentials is a pivotal task in various chemical fields. However, their accurate prediction by theoretical computations, which is a complementary task and sometimes the only alternative to experimental measurement, may be often resource-intensive and time-consuming. This paper addresses this challenge through the application of machine learning techniques, with a particular focus on graph-based methods (such as graph edit distances, graph kernels, and graph neural networks) that are reviewed to enlighten their deep links with theoretical chemistry. To this aim, we establish the ORedOx159 database, a comprehensive, homogeneous (with reference values stemming from density functional theory calculations), and reliable resource containing 318 one-electron reduction and oxidation reactions and featuring 159 large organic compounds. Subsequently, we provide an instructive overview of the good practice in machine learning and of commonly utilized machine learning models. We then assess their predictive performances on the ORedOx159 dataset through extensive analyses. Our simulations using descriptors that are computed in an almost instantaneous way result in a notable improvement in prediction accuracy, with mean absolute error (MAE) values equal to 5.6 kcal mol - 1 $$ {}^{-1} $$ for reduction and 7.2 kcal mol - 1 $$ {}^{-1} $$ for oxidation potentials, which paves a way toward efficient in silico design of new electrochemical systems.

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.

Are Redox-Active Centers Bridged by Saturated Flexible Linkers Systematically Electrochemically Independent?

The extent to which electrophores covalently bridged by a saturated linker are electrochemically independent was investigated considering the charge/spin duality of the electron and functionality of the electrophore as a spin carrier upon reduction. By combining computational modeling with electrochemical experiments, we investigated the mechanism by which tethered electrophores react together within 4,4'-oligo[n]methylene-bipyridinium assemblies (with n=2 to 5). We show that native dicationic electrophores (redox state Z=+2) are folded prior to electron injection into the system, allowing the emergence of supra-molecular orbitals (supra-MOs) likely to support the process of the reductive σ bond formation giving cyclomers. Indeed, for Z=+2, London Dispersion (LD) forces contribute to flatten the potential energy surface such that all-trans and folded conformers are approximately isoenergetic. Then, upon one-electron injection, for radical cations (Z=+1), LD forces significantly stabilize the folded conformers, except for the ethylene derivative deprived of supra-MOs. For radical cations equipped with supra-MOs, the unpaired electron is delocalized over both heterocycles through space. Cyclomer completion (Z=0) upon the second electron transfer occurs according to the inversion of redox potentials. This mechanism explains why intramolecular reactivity is favored and why pyridinium electrophores are not independent.

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.

DockSurf: A Molecular Modeling Software for the Prediction of Protein/Surface Adhesion.

The elucidation of structural interfaces between proteins and inorganic surfaces is a crucial aspect of bionanotechnology development. Despite its significance, the interfacial structures between proteins and metallic surfaces are yet to be fully understood, and the lack of experimental investigation has impeded the development of many devices. To overcome this limitation, we suggest considering the generation of protein/surface structures as a molecular docking problem with a homogenous plan as the target. To this extent, we propose a new software, DockSurf, which aims to quickly propose reliable protein/surface structures. Our approach considers the conformational exploration with Euler's angles, which provide a cartography instead of a unique structure. Interaction energies were derived from quantum mechanics computations for a set of small molecules that describe protein atom types and implemented in a Derjaguin, Landau, Verwey, and Overbeek potential for the consideration of large systems such as proteins. The validation of DockSurf software was conducted with molecular dynamics for corona proteins with gold surfaces and provided enthusiastic results. This software is implemented in the RPBS platform to facilitate widespread access to the scientific community.

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.

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.

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.

On the Supra-LUMO Interaction: Case Study of a Sudden Change of Electronic Structure as a Functional Emergence.

The synergistic functioning of redox-active components that emerges from prototypical 2,2'-di(N-methylpyrid-4-ylium)-1,1'-biphenyl is described. Interestingly, even if a trans conformation of the native assembly is expected, due to electrostatic repulsion between cationic pyridinium units, we demonstrate that cis conformation is equally energy-stabilized on account of a peculiar LUMO (SupLUMO) that develops through space, encompassing the two pyridiniums in a single, made-in-one-piece, electronic entity (superelectrophoric behavior). This SupLUMO emergence, with the cis species as superelectrophore embodiment, originates in a sudden change of electronic structure. This finding is substantiated by insights from solid state (single-crystal X-ray diffraction) and solution (NOE NMR and UV-vis-NIR spectroelectrochemistry) studies, combined with electronic structure computations. Electrochemistry shows that electron transfers are so strongly correlated that two-electron reduction manifests itself as a single-step process with a large potential inversion consistent with inner creation of a carbon-carbon bond (digital simulation). Besides, absence of reductive formation of dimers is a further indication of a preferential intramolecular reactivity determined by the SupLUMO interaction (cis isomer pre-organization). The redox-gated covalent bond, serving as electron reservoir, was studied via atropisomerism of the reduction product (VT NMR study). The overall picture derived from this in-depth study of 2,2'-di(N-methylpyrid-4-ylium)-1,1'-biphenyl proves that trans and cis species are worth considered as intrinsically sharply different, that is, as doubly-electrophoric and singly-superelectrophoric switchable assemblies, beyond conformational isomerism. Most importantly, the through-space-mediated SupLUMO may come in complement of other weak interactions encountered in Supramolecular Chemistry as a tool for the design of electroactive architectures.

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.

Triangulenium dyes: the comprehensive photo-absorption and emission story of a versatile family of chromophores.

The triangulenium dyes constitute a family of versatile chromophores whose impressive photo-absorption and emission properties are currently highlighted in numerous novel experimental applications. In this investigation, we provide a comprehensive TDDFT characterization of their spectroscopic properties elucidating the origin of their large and complex absorption and emission vibronic spectra spread over the (whole) visible region. More precisely, by benchmarking the performance of 10 commonly-used exchange-correlation density functionals belonging to different classes of approximation, we develop and validate a computational protocol allowing the accurate modeling of both the position and optical line-shape of their vibrationally-resolved absorption and emission band structures. We find that semilocal approximations provide the best estimate of the structure of the vibronic spectra, however they spuriously and strongly underestimate their position. We finally show that global-hybrid density functionals mixing between 20 and 30% of exact-like exchange are an excellent compromise to get a satisfactory estimate of both of these properties.

Range-separated hybrid and double-hybrid density functionals: A quest for the determination of the range-separation parameter.

We recently derived a new and simple route to the determination of the range-separation parameter in range-separated exchange hybrid and double-hybrid density functionals by imposing an additional constraint to the exchange-correlation energy to recover the total energy of the hydrogen atom [Brémond et al., J. Chem. Phys. 15, 201102 (2019)]. Here, we thoroughly assess this choice by statistically comparing the derived values of the range-separation parameters to the ones obtained using the optimal tuning (OT) approach. We show that both approaches closely agree, thus, confirming the reliability of ours. We demonstrate that it provides very close performances in the computation of properties particularly prone to the one- and many-electron self-interaction errors (i.e., ionization potentials). Our approach arises as an alternative to the OT procedure, conserving the accuracy and efficiency of a standard Kohn-Sham approach to density-functional theory computation.

Cooperativity in a cycloalkane-1,2/1,3-polyol corona: Topological hydrogen bonding in 1,2-diol motifs.

A corona, consisting of 18 carbon atoms bearing 12 hydroxy groups in a continuous hydrogen-bonded chain, is built up by alternating degenerate conformations of alternating alkane-1,2-diol and 1,3-diol motifs. Geometries, proton nuclear magnetic resonance shifts and interaction energies for the dodecahydroxycyclo-octadecane and selected fragments are determined by density functional calculations at the B3LYP/6-311+G(d,p) level. Cooperative effects of O-H⋯O-H bonding are evident from the simple juxtaposition of these two motifs with a common OH group in butane-1,2,4-triol conformers. Bracketing a 1,2-diol motif with two 1,3-diol motifs in hexane-1,3,4,6-tetrol leads to a structure in which the 1,2-diol motif displays a bond critical point for hydrogen bonding. This is associated with enhancement of the shift of the hydrogen-bonded OH proton and of the corresponding H⋯O interaction energy. The full corona has a complete outer ring of O-H⋯O-H bond paths, and an inner ring of bond paths, due to C-H⋯H-C hydrogen-hydrogen bonding, which result in a central ring critical point. The topological O-H⋯O-H hydrogen bond, never seen in simple alkane-1,2-diols, is associated with cooperative enhancement of the H⋯O interaction energy, but this is not a necessary condition for a bond path: values for topological C-H⋯H-C hydrogen-hydrogen bonds can be as low as -0.4 kcal mol-1 .

Double-Hybrid Functionals and Tailored Basis Set: Fullerene (C60) Dimer and Isomers as Test Cases.

A computational protocol making use of double hybrid functionals in conjunction with a recently developed basis set tailored to reproduce noncovalent interactions (hereafter named DH-SVPD) is here applied and tested for the evaluation of the properties of C60 fullerenes, namely intermolecular interactions in the weakly bound C60 dimer and relative stabilities of C60 isomers (as described by the C60ISO and iso-C60 data sets). The obtained results suggest that the DH-SVPD performance is very close to that obtained with empirical corrections and larger quadruple-ζ basis for the C60 dimer. In contrast, both approaches (tailored basis set and larger basis with empirical potential) do not reach the envisaged accuracy for the relative stabilities of C60 isomers. Nevertheless, this test well underlined how the DH-SVPD basis set is able to recover the performance obtained by coupling the DH functionals with empirical dispersion corrections and larger basis set, significantly reducing the computational effort for double hybrids and thus enabling expansion of their application domain to larger molecular systems.

sp-hybridized carbon allotrope molecular structures: An ongoing challenge for density-functional approximations.

The recent synthesis of a C18 monocyclic ring constitutes a major breakthrough as a new all-carbon disclosed form. However, modern density functional theory approaches do not lead to the correct experimental polyynic structure and favor the cumulenic one instead. We demonstrate here that this serious drawback can be solved by recently developed range-separated nonempirical schemes, independently of which kind of functional is being applied (i.e., semilocal, hybrid, or double-hybrid).

Range-separated hybrid density functionals made simple.

In this communication, we present a new and simple route to derive range-separated exchange (RSX) hybrid and double hybrid density functionals in a nonempirical fashion. In line with our previous developments [Brémond et al., J. Chem. Theory Comput. 14, 4052 (2018)], we show that by imposing an additional physical constraint to the exchange-correlation energy, i.e., by enforcing to reproduce the total energy of the hydrogen atom, we are able to generalize the nonempirical determination of the range-separation parameter to a family of RSX hybrid density functionals. The success of the resulting models is illustrated by an accurate modeling of several molecular systems and properties, like ionization potentials, particularly prone to the one- and many-electron self-interaction errors.

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.

Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists.

Density functional theory (DFT) emerged in the last two decades as the most reliable tool for the description and prediction of properties of molecular systems and extended materials, coupling in an unprecedented way high accuracy and reasonable computational cost. This success rests also on the development of more and more performing density functional approximations (DFAs). Indeed, the Achilles' heel of DFT is represented by the exchange-correlation contribution to the total energy, which, being unknown, must be approximated. Since the beginning of the 1990s, global hybrids (GH) functionals, where an explicit dependence of the exchange-correlation energy on occupied Kohn-Sham orbitals is introduced thanks to a fraction of Hartree-Fock-like exchange, imposed themselves as the most reliable DFAs for chemical applications. However, if these functionals normally provide results of sufficient accuracy for most of the cases analyzed, some properties, such as thermochemistry or dispersive interactions, can still be significantly improved. A possible way out is represented by the inclusion, into the exchange-correlation functional, of an explicit dependence on virtual Kohn-Sham orbitals via perturbation theory. This leads to a new class of functionals, called double-hybrids (DHs). In this Account, we describe our nonempirical approach to DHs, which, following the line traced by the Perdew-Burke-Ernzerhof approach, allows for the definition of a GH (PBE0) and a DH (QIDH) model. In such a way, a whole family of nonempirical functionals, spanning on the highest rungs of the Perdew's quality scale, is now available and competitive with other-more empirical-DFAs. Discussion of selected cases, ranging from thermochemistry and reactions to weak interactions and excitation energies, not only show the large range of applicability of nonempirical DFAs, but also underline how increasing the number of theoretical constraints parallels with an improvement of the DFA's numerical performances. This fact further consolidates the strong theoretical framework of nonempirical DFAs. Finally, even if nonempirical DH approaches are still computationally expensive, relying on the fact that they can benefit of all technical enhancements developed for speeding up post-Hartree-Fock methods, there is substantial hope for their near future routine application to the description and prediction of complex chemical systems and reactions.