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.

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.

Computational Design of Multiple Resonance-Type BN Molecules for Inverted Singlet and Triplet Excited States.

A computational design of linearly extended multiple resonance (MR)-type BN molecules based on DABNA-1 is proposed herein in the quest to find potential candidates that exhibit a negative singlet-triplet gap (ΔEST) and a large oscillator strength value. The impact of a proper account of the electron correlation in the lowest singlet and triplet excited states is systematically investigated by using double-hybrid functionals within the TD-DFT framework, as well as wavefunction-based methods (EOM-CCSD and SCS-CC2), since this contribution plays an essential role in driving the magnitude of the ΔEST in MR-TADF and inverted singlet-triplet gap compounds. Our results point out a gradual reduction of the ΔEST gap with respect to the increasing sum of the number of B and N atoms, reaching negative ΔEST values for some molecules as a function of their size. The double-hybrid functionals reproduce the gap with only slight deviation compared to available experimental data for DABNA-1, ν-DABNA, and mDBCz and nicely agree with high-level quantum mechanical methods (e.g., EOM-CCSD and SCS-CC2). Larger oscillator strengths are found compared to the azaphenalene-type molecules, also exhibiting the inversion of their singlet and triplet excited states. We hope this study can serve as a motivation for further design of the molecules showing negative ΔEST based on boron- and nitrogen-doped polyaromatic hydrocarbons.

RPA, an Accurate and Fast Method for the Computation of Static Nonlinear Optical Properties.

The accurate computation of static nonlinear optical properties (SNLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic connection fluctuation theorem is known to be a reliable and cost-effective method to render electronic correlation effects when combined with density-fitting techniques and integration over imaginary frequencies. We explore the ability of the RPA energy expression to predict SNLOPs by evaluating RPA electronic energies in the presence of finite electric fields to obtain (using the finite difference method) static polarizabilities and hyperpolarizabilities. We show that the RPA based on hybrid functional self-consistent field calculations yields accurate SNLOPs as the best-tuned double-hybrid functionals developed today, with the additional advantage that the RPA avoids any system-specific adjustment.

Design Strategies for Diradical Boron/Nitrogen Doped Carbon-Based Materials.

New heterocyclic diradicaloids based on boron and nitrogen-doped polycyclic systems with open-shell ground-states are obtained via concomitant structural and quinoidal extensions, thus allowing to merge the best of both design strategies. A combination of experimental characterization and theoretical calculations have helped disclose their electronic structure, as well as rationalize their associated magnetic and photophysical properties, spanning the chemical space of available molecular templates for cutting-edge applications in organic electronics and spintronics.

Benchmarking DFT Functionals for Excited-State Calculations of Donor-Acceptor TADF Emitters: Insights on the Key Parameters Determining Reverse Inter-System Crossing.

The importance of intermediate triplet states and the nature of excited states has gained interest in recent years for the thermally activated delayed fluorescence (TADF) mechanism. It is widely accepted that simple conversion between charge transfer (CT) triplet and singlet excited states is too crude, and a more complex route involving higher-lying locally excited triplet excited states has to be invoked to witness the magnitude of the rate of reverse inter-system crossing (RISC) rates. The increased complexity has challenged the reliability of computational methods to accurately predict the relative energy between excited states as well as their nature. Here, we compare the results of widely used density functional theory (DFT) functionals, CAM-B3LYP, LC-ωPBE, LC-ω*PBE, LC-ω*HPBE, B3LYP, PBE0, and M06-2X, against a wavefunction-based reference method, Spin-Component Scaling second-order approximate Coupled Cluster (SCS-CC2), in 14 known TADF emitters possessing a diversity of chemical structures. Overall, the use of the Tamm-Dancoff Approximation (TDA) together with CAM-B3LYP, M06-2X, and the two ω-tuned range-separated functionals LC-ω*PBE and LC-ω*HPBE demonstrated the best agreement with SCS-CC2 calculations in predicting the absolute energy of the singlet S1, and triplet T1 and T2 excited states and their energy differences. However, consistently across the series and irrespective of the functional or the use of TDA, the nature of T1 and T2 is not as accurately captured as compared to S1. We also investigated the impact of the optimization of S1 and T1 excited states on ΔEST and the nature of these states for three different functionals (PBE0, CAM-B3LYP, and M06-2X). We observed large changes in ΔEST using CAM-B3LYP and PBE0 functionals associated with a large stabilization of T1 with CAM-B3LYP and a large stabilization of S1 with PBE0, while ΔEST is much less affected considering the M06-2X functional. The nature of the S1 state barely evolves after geometry optimization essentially because this state is CT by nature for the three functionals tested. However, the prediction of the T1 nature is more problematic since these functionals for some compounds interpret the nature of T1 very differently. SCS-CC2 calculations on top of the TDA-DFT optimized geometries lead to a large variation in terms of ΔEST and the excited-state nature depending on the chosen functionals, further stressing the large dependence of the excited-state features on the excited-state geometries. The presented work highlights that despite good agreement of energies, the description of the exact nature of the triplet states should be undertaken with caution.

Modeling of Multiresonant Thermally Activated Delayed Fluorescence Emitters─Properly Accounting for Electron Correlation Is Key!

With the surge of interest in multiresonant thermally activated delayed fluorescent (MR-TADF) materials, it is important that there exist computational methods to accurately model their excited states. Here, building on our previous work, we demonstrate how the spin-component scaling second-order approximate coupled-cluster (SCS-CC2), a wavefunction-based method, is robust at predicting the ΔEST (i.e., the energy difference between the lowest singlet S1 and triplet T1 excited states) of a large number of MR-TADF materials, with a mean average deviation (MAD) of 0.04 eV compared to experimental data. Time-dependent density functional theory calculations with the most common DFT functionals as well as the consideration of the Tamm-Dancoff approximation (TDA) consistently predict a much larger ΔEST as a result of a poorer account of Coulomb correlation as compared to SCS-CC2. Very interestingly, the use of a metric to assess the importance of higher order excitations in the SCS-CC2 wavefunctions shows that Coulomb correlation effects are substantially larger in the lowest singlet compared to the corresponding triplet and need to be accounted for a balanced description of the relevant electronic excited states. This is further highlighted with coupled cluster singles-only calculations, which predict very different S1 energies as compared to SCS-CC2 while T1 energies remain similar, leading to very large ΔEST, in complete disagreement with the experiments. We compared our SCS-CC2/cc-pVDZ with other wavefunction approaches, namely, CC2/cc-pVDZ and SOS-CC2/cc-pVDZ leading to similar performances. Using SCS-CC2, we investigate the excited-state properties of MR-TADF emitters showcasing large ΔET2T1 for the majority of emitters, while π-electron extension emerges as the best strategy to minimize ΔEST. We also employed SCS-CC2 to evaluate donor-acceptor systems that contain a MR-TADF moiety acting as the acceptor and show that the broad emission observed for some of these compounds arises from the solvent-promoted stabilization of a higher-lying charge-transfer singlet state (S2). This work highlights the importance of using wavefunction methods in relation to MR-TADF emitter design and associated photophysics.

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.

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.

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.

Large magnetic exchange coupling in rhombus-shaped nanographenes with zigzag periphery.

Nanographenes with zigzag edges are predicted to manifest non-trivial π-magnetism resulting from the interplay of concurrent electronic effects, such as hybridization of localized frontier states and Coulomb repulsion between valence electrons. This provides a chemically tunable platform to explore quantum magnetism at the nanoscale and opens avenues towards organic spintronics. The magnetic stability in nanographenes is thus far greatly limited by the weak magnetic exchange coupling, which remains below the room-temperature thermal energy. Here, we report the synthesis of large rhombus-shaped nanographenes with zigzag peripheries on gold and copper surfaces. Single-molecule scanning probe measurements show an emergent magnetic spin singlet ground state with increasing nanographene size. The magnetic exchange coupling in the largest nanographene (C70H22, containing five benzenoid rings along each edge), determined by inelastic electron tunnelling spectroscopy, exceeds 100 meV or 1,160 K, which outclasses most inorganic nanomaterials and survives on a metal electrode.

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.

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.

Investigating the (Poly)Radicaloid Nature of Real-World Organic Compounds with DFT-Based Methods.

Recent advances in the synthesis of stable organic (open-shell) polyradicaloids have opened their application as active compounds for emerging technologies. These systems typically exhibit small energy differences between states with different spin multiplicities, which are intrinsically difficult to calculate by theoretical methods. We thus apply here some DFT-based variants (FT-DFT, SF-DFT, and SF-TDDFT) on a test set of large and real-world molecules, as test systems for which such energy differences are experimentally available, also comparing systematically with RAS-SF results to infer if shortcomings of previous DFT applications are corrected. Additionally, we explore the spin-spin contribution to the ZFS tensor, of high interest for EPR spectroscopy, and derive the spatial extent of the corresponding (photoexcited) triplet state.

Computational Studies of Molecular Materials for Unconventional Energy Conversion: The Challenge of Light Emission by Thermally Activated Delayed Fluorescence.

In this paper we describe the mechanism of light emission through thermally activated delayed fluorescence (TADF)-a process able to ideally achieve 100% quantum efficiencies upon fully harvesting the energy of triplet excitons, and thus minimizing the energy loss of common (i.e., fluorescence and phosphorescence) luminescence processes. If successful, this technology could be exploited for the manufacture of more efficient organic light-emitting diodes (OLEDs) made of only light elements for multiple daily applications, thus contributing to the rise of a sustainable electronic industry and energy savings worldwide. Computational and theoretical studies have fostered the design of these all-organic molecular emitters by disclosing helpful structure-property relationships and/or analyzing the physical origin of this mechanism. However, as the field advances further, some limitations have also appeared, particularly affecting TD-DFT calculations, which have prompted the use of a variety of methods at the molecular scale in recent years. Herein we try to provide a guide for beginners, after summarizing the current state-of-the-art of the most employed theoretical methods focusing on the singlet-triplet energy difference, with the additional aim of motivating complementary studies revealing the stronger and weaker aspects of computational modelling for this cutting-edge technology.

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).

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.