Application to nonlinear optical properties of the RSX-QIDH double-hybrid range-separated functional.

The effective calculation of static nonlinear optical properties requires a considerably high accuracy at a reasonable computational cost, to tackle challenging organic and inorganic systems acting as precursors and/or active layers of materials in (nano-)devices. That trade-off implies to obtain very accurate electronic energies in the presence of externally applied electric fields to consequently obtain static polarizabilities ( α i j ) and hyper-polarizabilities ( ß i j k and γ i j k l ). Density functional theory is known to provide an excellent compromise between accuracy and computational cost, which is however largely impeded for these properties without introducing range-separation techniques. We thus explore here the ability of a modern (double-hybrid and range-separated) Range-Separated eXchange Quadratic Integrand Double-Hybrid exchange-correlation functional to compete in accuracy with more costly and/or tuned methods, thanks to its robust and parameter-free nature.

Assessment of the nonempirical r2SCAN-QIDH double-hybrid density functional against large and diverse datasets.

We update the Quadratic Integrand Double-Hybrid (QIDH) model [J. Chem. Phys. 141, 031101 (2014)] by incorporating the nonempirical restored-regularized Strongly Constrained and Appropriately Normed (r2SCAN) meta-generalized gradient approximation exchange-correlation functional, thus devising a robust density functional approximation free of any empirical parameter and incorporating all the constraints so far known for the exchange-correlation kernel. We assessed the new r2SCAN-QIDH expression on the GMTKN55 database and further extend its application to various types of non-covalent interactions (e.g., S66 × 8, O24 × 5). The assessment done shows that the model becomes very competitive in accuracy with respect to parent exchange-correlation functionals of any type, but without relying on any fitted parameter or numerical training.

Correlation vs. exchange competition drives the singlet-triplet excited-state inversion in non-alternant hydrocarbons.

In this work, we focus on the understanding of the driving force behind the S1-T1 excited-state energy inversion (which would thus violate Hund's rule, making the S1 state lower in energy than the T1 state) of two non-benzenoid non-alternant hydrocarbons, composed of odd-membered rings. The molecules considered here have identical chemical composition but different atomic configuration in space. The delicate interplay between structural and electronic factors that might induce inversion and its energy extension, only by a few meV, is systematically investigated here by state-of-the-art calculations. Qualitative and quantitative accurate predictions are obtained employing post-HF methods, thanks to the balanced and careful inclusion of electron correlation effects. The obtained results might guide and rationalize new searches for molecules violating Hund's rule, concomitantly demonstrating the importance of key contributions from the theoretical method of choice.

Electronic structure of rhombus-shaped nanographenes: system size evolution from closed- to open-shell ground states.

We theoretically study and characterize a set of rhombus-shaped nanographenes of increasing size, or n-rhombenes, where n = 2-6, displaying zigzag edges leading to an enhancement of the (poly)radicaloid nature and the appearance of intrinsic magnetism as a function of n. Due to that system-dependent radicaloid nature, we employ spin-flip methods able to capture the challenging physics of the problem, thus providing accurate energy differences between high- and low-spin solutions. The theoretical predictions agree with the experimentally available magnetic exchange coupling for the recently synthesized 5-rhombene, as well as with the size at which the transition from a closed-shell to an open-shell ground-state solution occurs. We also investigate if standard DFT methods are able to reproduce the trend disclosed by spin-flip methods and if the results are highly dependent on the functional choice and/or the intrinsic spin contamination.

Excitation energies of polycylic aromatic hydrocarbons by double-hybrid functionals: Assessing the PBE0-DH and PBE-QIDH models and their range-separated versions.

A family of non-empirical double-hybrid (DH) density functionals, such as Perdew-Burke-Ernzerhof (PBE)0-DH, PBE-QIDH, and their range-separated exchange (RSX) versions RSX-0DH and RSX-QIDH, all using Perdew-Burke-Ernzerhof(PBE) exchange and correlationfunctionals, is applied here to calculate the excitation energies for increasingly longer linear and cyclic acenes as part of their intense benchmarking for excited states of all types. The energies for the two lowest-lying singlet 1La and 1Lb states of linear oligoacenes as well as the triplet 3La and 3Lb states, are calculated and compared with experimental results. These functionals clearly outperform the results obtained from hybrid functionals and favorably compare with other double-hybrid expressions also tested here, such as B2-PLYP, B2GP-PLYP, ωB2-PLYP, and ωB2GP-PLYP. The study is complemented by the computation of adiabatic S0-T1 singlet-triplet energy difference for linear acenes as well as the extension of the study to strained cyclic oligomers, showing how the family of non-empirical expressions robustly leads to competitive results.

Stability of the polyynic form of C18, C22, C26, and C30 nanorings: a challenge tackled by range-separated double-hybrid density functionals.

We calculate the relative energy between the cumulene and polyyne structures of a set of C4k+2 (k = 4-7) rings (C18, C22, C26, and C30 prompted by the recent synthesis of the cyclo[18]carbon (or simply C18) compounds. Reference results were obtained by a costly Quantum Monte-Carlo (QMC) approach, providing thus very accurate values allowing to systematically compare the performance of a variety of wavefunction methods [(i.e., MP2, SCS-MP2, SOS-MP2, DLPNO-CCSD, and DLPNO-CCSD(T)] as well as DFT approaches, applying for the latter a diversity of density functionals covering global and range-separated hybrid and double-hybrid models. The influence of the use of a range-separation scheme for density functionals, for both hybrid and double-hybrid expressions, is discussed according to its key role. Overall, range-separated double-hybrid functionals (e.g., RSX-QIDH) behave very accurately and provide competitive results compared with DLPNO-CCSD(T), at a more reasonable computational cost.

Violation of Hund's rule in molecules: Predicting the excited-state energy inversion by TD-DFT with double-hybrid methods.

The energy difference (ΔEST) between the lowest singlet (S1) state and the triplet (T1) excited state of a set of azaphenalene compounds, which is theoretically and experimentally known to violate Hund's rule, giving rise to the inversion of the order of those states, is calculated here with a family of double-hybrid density functionals. That excited-state inversion is known to be very challenging to reproduce for time-dependent density functional theory employing common functionals, e.g., hybrid or range-separated expressions, but not for wavefunction methods due to the inclusion of higher-than-single excitations. Therefore, we explore here if the last developed family of density functional expressions (i.e., double-hybrid models) is able to provide not only the right excited-state energy order but also accurate ΔEST values, thanks to the approximate inclusion of double excitations within these models. We herein employ standard double-hybrid (B2-PLYP, PBE-QIDH, and PBE0-2), range-separated (ωB2-PLYP and RSX-QIDH), spin-scaled (SCS/SOS-B2PLYP21, SCS-PBE-QIDH, and SOS-PBE-QIDH), and range-separated spin-scaled (SCS/SOS-ωB2-PLYP, SCS-RSX-QIDH, and SOS-RSX-QIDH) expressions to systematically assess the influence of the ingredients entering into the formulation while concomitantly providing insights for their accuracy.

peri-Acenoacene molecules: tuning of the singlet and triplet excitation energies by modifying their radical character.

The energy difference between singlet and triplet excitons, or ΔEST, is a key parameter for novel light-emission mechanisms (i.e., TADF or thermally activated delayed fluorescence) or other photoactivated processes. We have studied a set of conjugated molecules (peri-acenoacenes and their heteroatom-doped analogues) to observe the evolution of their excited-state properties upon increasing the system size with and without substitution with a pair of N atoms. Since these molecules exhibit a (ground-state) diradicaloid character, together with marked correlation effects influencing the excited-states formed, we have applied a variety of theoretical methods (FT-DFT, TD-DFT, SF-TD-DFT, CIS, CIS(D), SCS-CC2, SA-CASSCF, and SC-NEVPT2) to bracket the accuracy of the results while concomitantly providing insights into electronic structure. The results show how this chemical strategy (N-doping) largely modifies not only the excited-state energies but also the oscillator strengths and the ΔEST values, constituting versatile platforms for fine-tuned photophysical applications.

Negative Singlet-Triplet Excitation Energy Gap in Triangle-Shaped Molecular Emitters for Efficient Triplet Harvesting.

The full harvesting of both singlet and triplet excitons can pave the way toward more efficient molecular light-emission mechanisms (i.e., TADF or thermally activated delayed fluorescence) beyond the spin statistics limit. This TADF mechanism benefits from low (but typically positive) singlet-triplet energy gaps or ΔEST. Recent research has suggested the possibility of inverting the order of the energy of lowest singlet and triplet excited states, thus opening new pathways to promote light emission without any energy barrier through triplet to singlet conversion, which is systematically investigated here by means of theoretical methods. To this end, we have selected a set of heteroatom-substituted triangle-shaped molecules (or triangulenes) for which ΔEST < 0 is predicted. We successfully rationalize the origin of that energy inversion and the reasons for which theoretical methods might produce qualitatively inconsistent predictions depending on how they treat n-tuple excitations (e.g., the large contribution of double excitations for all of the ground and excited states involved). Unfortunately, the time-dependent density functional theory method is unable to deal with the physical effects driving this behavior, which prompted us to use more sophisticated ab initio methods here such as SA-CASSCF, SC-NEVPT2, SCS-CC2, and SCS-ADC(2).

Singlet-Triplet Excited-State Inversion in Heptazine and Related Molecules: Assessment of TD-DFT and ab initio Methods.

We have investigated the origin of the S1 -T1 energy levels inversion for heptazine, and other N-doped π-conjugated hydrocarbons, leading thus to an unusually negative singlet-triplet energy gap ( ΔEST<0 ). Since this inversion might rely on substantial doubly-excited configurations to the S1 and/or T1 wavefunctions, we have systematically applied multi-configurational SA-CASSCF and SC-NEVPT2 methods, SCS-corrected CC2 and ADC(2) approaches, and linear-response TD-DFT, to analyze if the latter method could also face this challenging issue. We have also extended the study to B-doped π-conjugated systems, to see the effect of chemical composition on the results. For all the systems studied, an intricate interplay between the singlet-triplet exchange interaction, the influence of doubly-excited configurations, and the impact of dynamic correlation effects, serves to explain the ΔEST<0 values found for most of the compounds, which is not predicted by TD-DFT.

Nature (Hole or Electron) of Charge-Transfer Ability of Substituted Cyclopyrenylene Hoop-Shaped Compounds.

We theoretically investigate here by means of DFT methods how the selective substitution in cyclic organic nanorings composed of pyrene units may promote semiconducting properties, analyzing the energy needed for a hole- or electron-transfer accommodation as a function of the substitution pattern and the system size (i.e., number of pyrene units). We choose to study both [3]Cyclo-2,7-pyrenylene ([3]CPY) and [4]Cyclo-2,7-pyrenylene ([4]CPY) compounds, the latter already synthesized, with substituents other than hydrogen acting in ipso and ortho positions, as well as the effect of the per-substitution. As substituents, we selected a set of electroactive halogen atoms (F, Cl, and Br) and groups (CN) to disclose structure-property relationships allowing thus to anticipate the use of these systems as organic molecular semiconductors.

Precision Nanotube Mimics via Self-Assembly of Programmed Carbon Nanohoops.

The scalable production of homogeneous, uniform carbon nanomaterials represents a key synthetic challenge for contemporary organic synthesis as nearly all current fabrication methods provide heterogeneous mixtures of various carbonized products. For carbon nanotubes (CNTs) in particular, the inability to access structures with specific diameters or chiralities severely limits their potential applications. Here, we present a general approach to access solid-state CNT mimic structures via the self-assembly of fluorinated nanohoops, which can be synthesized in a scalable, size-selective fashion. X-ray crystallography reveals that these CNT mimics exhibit uniform channel diameters that are precisely defined by the diameter of their nanohoop constituents, which self-assemble in a tubular fashion via a combination of arene-pefluoroarene and C-H-F interactions. The nanotube-like assembly of these systems results in capabilities such as linear guest alignment and accessible channels, both of which are observed in CNTs but not in the analogous all-hydrocarbon nanohoop systems. Calculations suggest that the organofluorine interactions observed in the crystal structure are indeed critical in the self-assembly and robustness of the CNT mimic systems. This work establishes the self-assembly of carbon nanohoops via weak interactions as an attractive means to generate solid-state materials that mimic carbon nanotubes, importantly with the unparalleled tunability enabled by organic synthesis.

From cyclic nanorings to single-walled carbon nanotubes: disclosing the evolution of their electronic structure with the help of theoretical methods.

We systematically investigate the relationships between structural and electronic effects of finite size zigzag or armchair carbon nanotubes of various diameters and lengths, starting from a molecular template of varying shape and diameter, i.e. cyclic oligoacene or oligophenacene molecules, and disclosing how adding layers and/or end-caps (i.e. hemifullerenes) can modify their (poly)radicaloid nature. We mostly used tight-binding and finite-temperature density-based methods, the former providing a simple but intuitive picture about their electronic structure, and the latter dealing effectively with strong correlation effects by relying on a fractional occupation number weighted electron density (ρFOD), with additional RAS-SF calculations backing up the latter results. We also explore how minor structural modifications of nanotube end-caps might influence the results, showing that topology, together with the chemical nature of the systems, is pivotal for the understanding of the electronic properties of these and other related systems.

Computational Design of Thermally Activated Delayed Fluorescence Materials: The Challenges Ahead.

Thermally activated delayed fluorescence (TADF) offers promise for all-organic light-emitting diodes with quantum efficiencies competing with those of transition-metal-based phosphorescent devices. While computational efforts have so far largely focused on gas-phase calculations of singlet and triplet excitation energies, the design of TADF materials requires multiple methodological developments targeting among others a quantitative description of electronic excitation energetics, fully accounting for environmental electrostatics and molecular conformational effects, the accurate assessment of the quantum mechanical interactions that trigger the elementary electronic processes involved in TADF, and a robust picture for the dynamics of these fundamental processes. In this Perspective, we describe some recent progress along those lines and highlight the main challenges ahead for modeling, which we hope will be useful to the whole TADF community.

Communication: Accurate description of interaction energies and three-body effects in weakly bound molecular complexes by PBE-QIDH models.

We apply a recently developed parameter-free double-hybrid density functional belonging to the quadratic-integrand double-hybrid model to calculate association energies (ΔE) and three-body effects (Δ3E) arising from intermolecular interactions in weakly bound supramolecular complexes (i.e., the dataset 3B-69). The model behaves very accurately for trimer association energies and is found to outperform widely used density functional approximations while approaching the accuracy of more costly ab initio methods for three-body effects. The results are further improved when we add some specific corrections for the remaining dispersion interactions, D3(BJ) or VV10 for two-body effects and Axilrod-Teller-Muto for three-body effects, leading to marginal deviations (less than 1 kcal/mol for ΔE and around 0.03-0.04 kcal/mol for Δ3E) with respect to benchmark results.

The role of topology in organic molecules: origin and comparison of the radical character in linear and cyclic oligoacenes and related oligomers.

We discuss the nature of electron-correlation effects in carbon nanorings and nanobelts using an analysis tool known as fractional occupation number weighted electron density (ρFOD) and the RAS-SF method, revealing for the first time significant differences in static correlation effects depending on how the rings (i.e. chemical units) are fused and/or connected until closing the loop. We choose to study in detail linear and cyclic oligoacene molecules of increasing size, and relate the emerging differences with the difficulties for the synthesis of the latter due to their radicaloid character. We finally explore how minor structural modifications of the cyclic forms can alter these results, showing the potential use of these systems as molecular templates for the growth of well-shaped carbon nanotubes as well as the usefulness of theoretical tools for molecular design.

Partnering dispersion corrections with modern parameter-free double-hybrid density functionals.

The PBE-QIDH and SOS1-PBE-QIDH double-hybrid density functionals are merged with a pair of dispersion corrections, namely the pairwise additive D3(BJ) and the non-local correlation functional VV10, leading to the corresponding dispersion-corrected models. The parameters adjusting each of the dispersion corrections to the functionals are obtained by fitting to well-established energy datasets (e.g. S130) used as a benchmark, giving rise to functionals spanning covalent and non-covalent binding forces. The application of the models to challenging systems out of the training set, like those comprising the L7 database of large supramolecular complexes, or the S66x8 dataset of stretched and elongated intermolecular distances, reveals the high accuracy of the coupling.

Importance of Orbital Optimization for Double-Hybrid Density Functionals: Application of the OO-PBE-QIDH Model for Closed- and Open-Shell Systems.

We assess here the reliability of orbital optimization for modern double-hybrid density functionals such as the parameter-free PBE-QIDH model. We select for that purpose a set of closed- and open-shell strongly and weakly bound systems, including some standard and widely used data sets, to show that orbital optimization improves the results with respect to standard models, notably for electronically complicated systems, and through first-order properties obtained as derivatives of the energy.

Theoretical rationalization of the singlet-triplet gap in OLEDs materials: impact of charge-transfer character.

New materials for OLED applications with low singlet-triplet energy splitting have been recently synthesized in order to allow for the conversion of triplet into singlet excitons (emitting light) via a Thermally Activated Delayed Fluorescence (TADF) process, which involves excited-states with a non-negligible amount of Charge-Transfer (CT). The accurate modeling of these states with Time-Dependent Density Functional Theory (TD-DFT), the most used method so far because of the favorable trade-off between accuracy and computational cost, is however particularly challenging. We carefully address this issue here by considering materials with small (high) singlet-triplet gap acting as emitter (host) in OLEDs and by comparing the accuracy of TD-DFT and the corresponding Tamm-Dancoff Approximation (TDA), which is found to greatly reduce error bars with respect to experiments thanks to better estimates for the lowest singlet-triplet transition. Finally, we quantitatively correlate the singlet-triplet splitting values with the extent of CT, using for it a simple metric extracted from calculations with double-hybrid functionals, that might be applied in further molecular engineering studies.

Cost-Effective Force Field Tailored for Solid-Phase Simulations of OLED Materials.

A united atom force field is empirically derived by minimizing the difference between experimental and simulated crystal cells and melting temperatures for eight compounds representative of organic electronic materials used in OLEDs and other devices: biphenyl, carbazole, fluorene, 9,9'-(1,3-phenylene)bis(9H-carbazole)-1,3-bis(N-carbazolyl)benzene (mCP), 4,4'-bis(N-carbazolyl)-1,1'-biphenyl (pCBP), phenazine, phenylcarbazole, and triphenylamine. The force field is verified against dispersion-corrected DFT calculations and shown to also successfully reproduce the crystal structure for two larger compounds employed as hosts in phosphorescent and thermally activated delayed fluorescence OLEDs: N,N'-di(1-naphthyl)-N,N'-diphenyl-(1,1'-biphenyl)-4,4'-diamine (NPD), and 1,3,5-tri(1-phenyl-1H-benzo[d]imidazol-2-yl)phenyl (TPBI). The good performances of the force field coupled to the large computational savings granted by the united atom approximation make it an ideal choice for the simulation of the morphology of emissive layers for OLED materials in crystalline or glassy phases.