A Practicable Real-Space Measure and Visualization of Static Electron-Correlation Effects

Assessment of the applicability of DFT methods to [Cp*Rh]-catalyzed hydrogen evolution processes

The present computational study provides a benchmark of density functional theory (DFT) methods in describing hydrogen evolution processes catalyzed by [Cp*Rh]-containing organometallic complexes. A test set was composed of 26 elementary reactions featuring chemical transformations and bonding situations essential for the field, including the emerging concept of non-innocent Cp* behavior. Reference values were obtained from a highly accurate 3/4 complete basis set and 6/7 complete PNO space extrapolated DLPNO-CCSD(T) energies. The performance of lower-level extrapolation procedures was also assessed. We considered 84 density functionals (DF) (including 13 generalized gradient approximations (GGA), nine meta-GGAs, 33 hybrids, and 29 double-hybrids) and three composite methods (HF-3c, PBEh-3c, and r2SCAN-3c), combined with different types of dispersion corrections (D3(0), D3BJ, D4, and VV10). The most accurate approach is the PBE0-DH-D3BJ (MAD of 1.36 kcal mol-1) followed by TPSS0-D3BJ (MAD of 1.60 kcal mol-1). Low-cost r2SCAN-3c composite provides a less accurate but much faster alternative (MAD of 2.39 kcal mol-1). The widely used Minnesota-family M06-L, M06, and M06-2X DFs should be avoided (MADs of 3.70, 3.94, and 4.01 kcal mol-1, respectively).

Classification and quantitative characterisation of the excited states of π-conjugated diradicals

Diradicals are of high current interest as emerging materials for next generation optoelectronic applications. To tune their excited-state properties it would be greatly beneficial to have a detailed understanding of the wave functions of the different states involved but this endeavour is hampered by formal and practical barriers. To tackle these challenges, we present a formal analysis as well as concrete results on diradical excited states. We start with a detailed investigation of the available states of a two-orbital two-electron model viewed from both the valence-bond and molecular orbital perspectives. We highlight the presence of diradical and zwitterionic states and illustrate their connections to the states found in closed-shell molecules. Subsequently, we introduce practical protocols for analysing states from realistic multireference computations applying these to the para-quinodimethane (pQDM) molecule. The analysis reveals four different categories of states - diradical, zwitterionic, HOMO-SOMO as well as biexciton - while also providing insight into their energetics and optical properties. Twisting the CH2 groups allows us to interconvert between the closed- and open-shell forms of pQDM illustrating the connection between the states in both forms. More generally, we hope that this work will lay the foundations for a more powerful rational design approach to diradicals for photophysical applications.

Design of Anti-Hund Organic Emitters Based on Heptazine

Hund's rule, which is powerful in governing the first excited states of closed-shell organic materials, can hardly be violated to get inverted singlet-triplet gap (INVEST) molecules with negative singlet-triplet energy gaps (ΔEST), although INVEST materials have shown extraordinary photophysical properties and promising device performance especially in light-emitting diodes. Here, we propose a facile strategy to construct emissive INVEST molecules by introducing different types of substituents to heptazine in various modes, which can effectively tune the ΔEST to be negative with the enlarged oscillator strength (f) for the high fluorescence rate of the heptazine derivatives. Systematic computational studies show that the double substitution of electron-donating units with another nonconjugated substituent in hybrid substitution mode is the most favorable way in achieving slightly negative ΔEST and large f values; the conjugated substituent will compete with heptazine to make the molecule deviate from the INVEST feature. Especially, a series of high-performance heptazine-based INVEST emitters were constructed, exhibiting ΔEST low to -0.362 eV, f up to 0.0436, as well as a wide range emission color from 339 to 716 nm. Also, the designed molecules were predicted to have fluorescence radiative rates up to 106 s-1, along with efficient reverse intersystem crossing rates reaching 108 s-1. Importantly, the figure of merit (FM) was first proposed as a parameter to wholly evaluate the performance of INVEST emitters, and the highest FM of 0.198 was found in the triazine and double nonconjugated amine-substituted heptazine. These results highlight the great potential of the heptazine chromophore in constructing INVEST emitters, revealing fundamental structure-property understandings for the material design of efficient anti-Hund organic molecules with improved emission properties.

Tuneable stimuli-responsive behaviour, spectroscopic signatures and redox properties of indolo[3,2-b]carbazole-based diradicals

During the last decade, there has been an increasing interest in the rationalisation of how structural changes stabilise (or destabilise) diradical systems. Demonstrated herein is that indolocarbazole (ICz) diradicals, substituted with dicyanomethylene (DCM) groups, are useful motifs for dynamic covalent chemistry by self-assembling from isolated monomers to cyclophane structures. The comparison of ICz-based systems substituted with DCM groups in para- or meta-positions (p-ICz-CN and m-ICz-CN) and their short-chain carbazole analogues (p-Cz-CN and m-Cz-CN) may identify new potential design strategies for stimuli-responsive materials. The principal objectives of this investigation are the elucidation of (i) the connection between diradical character and the cyclophane stability, (ii) the spatial disposition of the cyclophane structures, (iii) the monomer/cyclophane interconversion both in solution and solid state in response to external stimuli and (iv) the impact that the different π-conjugation and electronic communication between the DCM terminals exerts on the electronic adsorption of the diradicals and their redox behavior. The spontaneous nature of the cyclophane structure is supported by the negative relative Gibbs free energies calculated at 298 K and experimentally by UV-Vis and Raman spectroscopy of the initial yellow solid powder. The conversion to monomeric species having diradical character was demonstrated by variable-temperature (VT) EPR, UV-Vis, Raman and IR measurements, resulting in appreciable chromic changes. In addition, electrochemical oxidation and reduction convert the cyclophane dimer (m-ICz-CN)2 to the monomer monocations and dianions, respectively. This research demonstrates how the chemical reactivity and physical properties of π-conjugated diradicals can be effectively tuned by subtle changes in their chemical structures.

Theoretical design of phosphorus-doped perylene derivatives as efficient singlet fission chromophores

Singlet fission (SF) is considered as a promising strategy to overcome the Shockley-Queisser limit of single-junction solar cells. However, only a handful of chromophores were observed to undergo SF to date. To broaden the number of SF chromophores, we designed a series of phosphorus-doped perylenes based on the diradical character strategy and examined their SF feasibility using theoretical calculations. By analysis of frontier orbitals, diradical character and aromaticity, SF-capable candidates were prescreened. These analyses reveal that the diradical character of perylene is effectively enhanced by P-doping at bay- and peri-positions of perylene, making SF more thermodynamically feasible. However, the diradical character remains nearly unchanged when P atoms are doped at ortho-positions because the spin center cannot be stabilized, leading to a more endothermic SF. This study shows how SF-related energies and diradical character of SF chromophores are altered by P doping, and extends the SF-capable molecular library.

Self-Assembly Determines Sign of Seebeck Coefficient in Tunneling Junctions Comprising Monolayers and Bilayers of Fullerenes

We measured the Seebeck coefficient for junctions comprising self-assembled monolayers and bilayers of the fullerene moiety PTEG-1 on Au using eutectic Ga-In in a controlled anhydrous atmosphere by varying the temperature gradient from -12 to 12 °C, observing a linear response in thermovoltage across the range. The sign of the coefficient was positive for monolayers of PTEG-1, (195 ± 8) μV K-1 and negative for bilayers of PTEG-1, (-209 ± 14) μV K-1, indicating a change from HOMO-mediated to LUMO-mediated charge-transport. Charge-transport is nonresonant tunneling for both monolayers and bilayers, but the former self-assembles with the fullerene cage at the chemisorbed interface while the latter includes a fullerene cage at the physisorbed interface, demonstrating that the physical position of the fullerene cage determines the energetic position of the frontier molecular orbitals of PTEG-1.

Prediction of the ground state for indenofluorene-type systems with Clar's π-sextet model

This study introduces the Ground State Stability (GSS) rule that allows predicting the nature of the ground state of indenofluorene (IF)-type systems from the simple counting of the Clar's π-sextets in the closed- and open-shell configurations. The IF-type system exhibits a triplet ground state when acquiring double or more the number of Clar's π-sextets in the open-shell form relative to the closed-shell form; otherwise, it assumes an open-shell singlet ground state. Performed state-of-the-art DFT calculations and analysis of aromaticity for the systems of interest validate the effectiveness of the proposed rule. We demonstrate that aromaticity plays the most crucial role in determining the ground electronic state for such polycyclic hydrocarbons. The simplicity of the GSS rule makes it a robust strategy for identifying promising systems in the development of indenofluorene-type materials.

Non-Kekulé meta-Quinodimethane Singlet Diradicals Based on Classical N-Heterocyclic Carbenes

Diradicals based on a meta-quinodimethane (m-QDM) scaffold generally have a triplet ground state and are rather scarce. Herein, m-QDM-based non-Kekulé diradicals [3,3'-(NHC)2BP] (3-NHC) (NHC = SIPr = C{N(Dipp)CH2}2; IPr = C{N(Dipp)CH}2, Me-IPr = C{N(Dipp)CMe}2; Dipp = 2,6-iPr2C6H3; BP = 1,1'-C6H4C6H4) featuring N-heterocyclic carbene (NHC) pendants are reported as crystalline solids. The EPR spectra of 3-NHC show both allowed (Δms = 1) and forbidden (Δms = 2; 'half-field') transitions characteristic for triplet diradicals. Variable temperature EPR studies however reveal a singlet ground state for 3-SIPr. Consistent with the EPR spectra, calculations predict a remarkably small singlet-triplet energy gap (ΔEST ≤ 0.26 kcal/mol) for the 3-NHC compounds. The calculated singlet diradical character for the ground states of the 3-NHC compounds amounts to ~99 %.

Potential energy curves for F2, Cl2, and Br2 with the i-DMFT method

The potential energy curves for dihalogens (F2, Cl2, and Br2) are calculated with the i-DMFT method proposed recently [Wang and Baerends, Phys. Rev. Lett. 128, 013001]. All electrons are correlated in a set of self-consistent-field eigenvalue equations, with the orbital occupation numbers obeying the Fermi-Dirac distribution. The only input is the dissociation energies of the molecules, which are usually available from an experimental database. The quality of the computed potential energy curve is examined by extracting spectroscopic parameters and rotation-vibration energy levels, which are compared with experiment data and other theoretical calculations.

Regulation of quantum spin conversions in a single molecular radical

Free radicals, generally formed through the cleavage of covalent electron-pair bonds, play an important role in diverse fields ranging from synthetic chemistry to spintronics and nonlinear optics. However, the characterization and regulation of the radical state at a single-molecule level face formidable challenges. Here we present the detection and sophisticated tuning of the open-shell character of individual diradicals with a donor-acceptor structure via a sensitive single-molecule electrical approach. The radical is sandwiched between nanogapped graphene electrodes via covalent amide bonds to construct stable graphene-molecule-graphene single-molecule junctions. We measure the electrical conductance as a function of temperature and track the evolution of the closed-shell and open-shell electronic structures in real time, the open-shell triplet state being stabilized with increasing temperature. Furthermore, we tune the spin states by external stimuli, such as electrical and magnetic fields, and extract thermodynamic and kinetic parameters of the transition between closed-shell and open-shell states. Our findings provide insights into the evolution of single-molecule radicals under external stimuli, which may proof instrumental for the development of functional quantum spin-based molecular devices.

Enhancing Molecular Energy Predictions with Physically Constrained Modifications to the Neural Network Potential

Exclusively prioritizing the precision of energy prediction frequently proves inadequate in satisfying multifaceted requirements. A heightened focus is warranted on assessing the rationality of potential energy curves predicted by machine learning-based force fields (MLFFs), alongside evaluating the pragmatic utility of these MLFFs. This study introduces SWANI, an optimized neural network potential stemming from the ANI framework. Through the incorporation of supplementary physical constraints, SWANI aligns more cohesively with chemical expectations, yielding rational potential energy profiles. It also exhibits superior predictive precision compared with that of the ANI model. Additionally, a comprehensive comparison is conducted between SWANI and a prominent graph neural network-based model. The findings indicate that SWANI outperforms the latter, particularly for molecules exceeding the dimensions of the training set. This outcome underscores SWANI's exceptional capacity for generalization and its proficiency in handling larger molecular systems.

Comments on "Planar Tetracoordinate Hydrogen: Pushing the Limit of Multicentre Bonding"

In a recent communication (Angew. Chem. Int. Ed. 2024, 63, e202317312), Kalita et al. studied In4H+ system within the frame of single-reference approximation (SRA) and found that the global energy minimum (1 a) adopted the singlet state and a planar tetracoordinate hydrogen (ptH), while the second lowest isomer (1 b) located 3.0 kcal/mol above 1 a and adopted the triplet state as well as non-planar structure with a quasi-ptH. They assessed the reliability of SRA by checking the T1-diagnostic values of coupled cluster calculations. However, according to our multi-configurational second-order perturbation theory calculations at the CASPT2(12,13)/aug-cc-pVQZ (aug-cc-pVQZ-PP for In) level, both 1 a and 1 b exhibit obvious multi-referential characters, as reflected by their largest reference coefficients of 0.928 (86.1 %) and 0.938 (88.0 %), respectively. Moreover, 1 b is 5.05 kcal/mol lower than 1 a at this level, that is, what can be observed in In4H+ system is the quasi-ptH.

Reply to the Comments on Planar Tetracoordinate Hydrogen: Pushing the Limit of Multicentre Bonding

Recently, Huo et al. has commented on our communication (Angew. Chem. Int. Ed. 2024, 63, e202317312, DOI: 10.1002/anie.202317312), regarding the multireference character (MRC) of our proposed cluster. Their argument is based on small HOMO-LUMO gap, fractional occupation density (FOD) and CASPT2(12,13) calculations. They also proposed that the singlet planar In4H+ cluster cannot be observed. We present our calculations which reveals that some of their arguments are based on wrong interpretation of data and inadequate use of methodology. While we certainly agree with the strong physical ground of FOD, CASSF and CASPT2 methodology, we believe that such analysis for clusters is not adequate.

N-Heterocyclic Carbene Analogues of Wittig Hydrocarbon

N-Heterocyclic carbene (NHC) analogues of Wittig hydrocarbon, [(NHC)(Stil)(NHC)] (3a-c) (NHC = SIPr (1a) = C[N(Dipp)CH2]2, Dipp = 2,6-iPr2C6H3; IPr (1b) = C[N(Dipp)CH]2; Me-IPr (1c) = C[N(Dipp)CMe]2 and Stil = C6H4CHCHC6H4) have been reported as crystalline solids. 3a-c are prepared by two-electron reductions of the corresponding bis-1,3-imidazoli(ni)um bromides [(NHC)(Stil)NHC)](Br)2 (2a-c) with KC8 in >94 % yields. 2a-c are accessible by the nickel catalyzed direct C-C coupling of NHCs (1a-c) with (E)-4,4'-dibromostilbene. One-electron oxidation of 3a,b yields the corresponding radical cations [(NHC)(Stil)NHC)]B(C6F5)4 4a,b. All compounds have been characterized by UV-Vis/NMR/EPR spectroscopy as well as 2a, 3a, and 3b by single crystal X-ray diffraction. The electronic structures of representative systems have been analyzed by quantum chemical calculations.

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

Ground and excited state charge transfer at aqueous nanodiamonds

Nanodiamonds (NDs) are unique carbonaceous materials with exceptionally high stability, hardness, and notable electronic properties. Their applications in photocatalysis, biomedicine, and energy materials are usually carried out in aqueous environments, where they interact with aqueous adsorbates. Especially, electron density may rearrange from the diamond material toward oxidative adsorbates such as oxygen, which is known as charge transfer doping. In this article, we quantify the charge transfer doping for NDs with inhomogeneous surface coverings (hydroxyl, fluorine, and amorphous carbon), as well as NDs doped with heteroatoms (B, Si, N) using hybrid density functional theory (DFT) calculations. The transfer doping magnitude is largely determined by the NDs' highest occupied molecular orbital energies, which can in turn be modified by the surface covering and doping. However, local modifications of the ND structures do not have any local effects on the magnitude of the charge transfer. We furthermore analyze the impact of aqueous adsorbates on the excited states of an aqueous ND in the context of photocatalysis via time-dependent DFT. Here, we find that the excited electrons are biased to move in the direction of the respective oxidative adsorbate. Surprisingly, we find that also unreactive species such as nitrous oxide may attract the excited electrons, which is probably due to the positive partial charge that is induced by the local N2 O solvation geometry.

A reinvestigation of the boron cluster B15+/0/-: a benchmark of density functionals and consideration of aromaticity models

This study presents a thorough reinvestigation of the B15+/0/- isomers, first employing coupled-cluster theory CCSD(T) calculations to validate the performance of different DFT functionals. The B15+ cation has two planar lowest-lying isomers, while the first 3D isomer is less stable than the global minimum by ∼10 kcal mol-1. The PBE functional, within this benchmark survey, has proved to be reliable in predicting relative energies for boron isomers. Other functionals such as the TPSSh, PBE0 and HSE06 result in good energy ordering of isomers but warrant reconsideration when distinguishing between 2D and 3D forms. Caution is needed for structures having high spin contamination, as it may lead to significant errors. The anomalously lower stability of the B15- anion with respect to its neighbours, in terms of electron detachment energy, was explained through a competition between both rectangle and disk models for its geometry. This elucidates its stability with 12 electrons in rectangle model and instability with 10 electrons in disk-shaped structure, emphasizing the value of employing such geometric models. The proximity of the σ* LUMO to the π HOMO also contributes to the weakening of the B15- stability.

Central Ring Puckering Enhances the Stokes Shift of Xanthene Dyes

Small-molecule dyes are generally designed based on well-understood electronic effects. However, steric hindrance can promote excited-state geometric relaxation, increasing the difference between the positions of absorption and emission bands (the Stokes shift). Accordingly, we hypothesized that sterically induced central ring puckering in xanthene dyes could be used to systematically increase their Stokes shift. Through a combined experimental/quantum-chemical approach, we screened a group of (9-acylimino)-pyronin dyes with a perturbed central ring geometry. Our results showed that an atom with sp3 hybridization in position 10 of (9-acylimino)-pyronins induces central ring puckering and facilitates excited-state geometric relaxation, thereby markedly enhancing their Stokes shifts (by up to ~2000 cm-1). Thus, we prepared fluorescent (9-acylimino)-pyronin pH sensors, which showed a Stokes shift disparity between acid and base forms of up to ~8700 cm-1. Moreover, the concept of ring puckering-enhanced Stokes shift can be applied to a wide range of xanthene analogues found in the literature. Therefore, central ring puckering may be reliably used as a strategy for enhancing Stokes shifts in the rational design of dyes.

Boosting the π-Acceptor Property of Mesoionic Carbenes by Carbonylation with Carbon Monoxide

We report the room temperature dimerization of carbon monoxide mediated by C4/C5-vicinal anionic dicarbenes Li(ADC) (ADC = ArC{(Dipp)NC}2 ; Dipp = 2,6-iPr2 C6 H3 ; Ar = Ph, DMP (4-Me2 NC6 H4 ), Bp (4-PhC6 H4 )) to yield (E)-ethene-1,2-bis(olate) (i.e. - O-C=C-O- = COen ) bridged mesoionic carbene (iMIC) lithium compounds COen -[(iMIC)Li]2 (COen -[iMIC]2 = [ArC{(Dipp)NC}2 (CO)]2 ) in quantitative yields. COen -[(iMIC)Li]2 are highly colored stable solids, exhibit a strikingly small HOMO-LUMO energy gap, and readily undergo 2e-oxidations with selenium, CuCl (or CuCl2 ), and AgCl to afford the dinuclear compounds COon -[(iMIC)E]2 (E = Se, CuCl, AgCl) featuring a 1,2-dione bridged neutral bis-iMIC (i.e. COon -[iMIC]2 = [ArC{(Dipp)NC}2 (C=O)]2 ). COen -[(iMIC)Li]2 undergo redox-neutral salt metathesis reactions with LiAlH4 and (Et2 O)2 BeBr2 and afford COen -[(iMIC)AlH2 ]2 and COen -[(iMIC)BeBr]2 , in which the dianionic COen -moiety remains intact. All compounds have been characterized by NMR spectroscopy, mass spectrometry, and X-ray diffraction. Stereoelectronic properties of COon -[iMIC]2 are quantified by experimental and theoretical methods.

Implementation and First Evaluation of Strong-Correlation-Corrected Local Hybrid Functionals for the Calculation of NMR Shieldings and Shifts

Local hybrid functionals containing strong-correlation factors (scLHs) and range-separated local hybrids (RSLHs) have been integrated into an efficient coupled-perturbed Kohn-Sham implementation for the calculation of nuclear shielding constants. Several scLHs and the ωLH22t RSLH have then been evaluated for the first time for the extended NS372 benchmark set of main-group shieldings and shifts and the TM70 benchmark of 3d transition-metal shifts. The effects of the strong-correlation corrections have been analyzed with respect to the spatial distribution of the sc-factors, which locally diminish exact-exchange admixture at certain regions in a molecule. The scLH22t, scLH23t-mBR, and scLH23t-mBR-P functionals, which contain a "damped" strong-correlation factor to retain the excellent performance of the underlying LH20t functional for weakly correlated situations, tend to make smaller corrections to shieldings and shifts than the "undamped" scLH22ta functional. While the latter functional can also deteriorate agreement with the reference data in certain weakly correlated cases, it provides overall better performance, in particular for systems where static correlation is appreciable. This pertains only to a minority of systems in the NS372 main-group test set but to many more systems in the TM70 transition-metal test set, in particular for high-oxidation-state complexes, e.g., Cr(+VI) complexes and other systems with stretched bonds. Another undamped scLH, the simpler LDA-based scLH21ct-SVWN-m, also tends to provide significant improvements in many cases. The differences between the functionals and species can be rationalized on the basis of one-dimensional plots of the strong-correlation factors, augmented by isosurface plots of the fractional orbital density (FOD). Position-dependent exact-exchange admixture is thus shown to provide substantial flexibility in treating response properties like NMR shifts for both weakly and strongly correlated systems.

To Split or Not to Split: [AsCCAs]-Coordinated Mo, W, and Re Complexes and Their Reactivity toward Molecular Dinitrogen

Molybdenum, tungsten, and rhenium halides bearing a 2,2'-(iPr2As)2-substituted diphenylacetylene ([AsCCAs], 1-As) were prepared and reduced under an atmosphere of dinitrogen in order to activate the latter substrate. In the case of molybdenum, a diiodo (2-As) and a triiodo molybdenum precursor (5) were equally suited for reductive N2 splitting, which led to the isolation of [AsCCAs]Mo≡N(I) (3-As) in each case. For tungsten, [AsCCAs]WCl3 (6) was reduced under N2 to afford {[AsCCAs]WCl2}2(N2) (7), which is best described as a dinuclear π8δ4-configured μ-(η1: η1)-N2-bridged dimer. Attempts to reductively cleave the N2 unit in 7 did not lead to the expected tungsten nitride (8), which had to be prepared independently via the treatment of 7 with sodium azide. To arrive at a π10δ4-configured N2-bridged dimer in a tetragonally distorted ligand environment, [AsCCAs]ReCl3 (9) was reduced in the presence of N2. As expected, a μ-(η1: η1)-N2-bridged dirhenium species, namely, {[AsCCAs]ReCl2}2(N2) (10), was formed, but found to very quickly decompose (presumably via loss of N2), not only under reduced pressure, but also upon irradiation or heating. Hence, an alternative synthetic route to the originally envisioned nitride, [AsCCAs]Re≡N(Cl)2 (11), was developed. While all the aforementioned nitrides (3-As, 8, and 11) were found to be fairly robust, significantly different stabilities were noticed for {[AsCCAs]MCl2}2(N2) (7 for M = W, 10 for M = Re), which is ascribed to the electronically different MN2M cores (π8δ4 for 7 vs π10δ4 for 10) in these μ-(η1: η1)-N2-bridged dimers.

First-principles theory of the nitrogen interstitial in hBN: a plausible model for the blue emitter

Color centers in hexagonal boron nitride (hBN) have attracted considerable attention due to their remarkable optical properties enabling robust room temperature photonics and quantum optics applications in the visible spectral range. On the other hand, identification of the microscopic origin of color centers in hBN has turned out to be a great challenge that hinders the in-depth theoretical characterization, on-demand fabrication, and development of integrated photonic devices. This is also true for the blue emitter, which is a result of irradiation damage in hBN, emitting at 436 nm wavelength with desirable properties. Here, we propose the negatively charged nitrogen split interstitial defect in hBN as a plausible microscopic model for the blue emitter. To this end, we carried out a comprehensive first-principles theoretical study of the nitrogen interstitial. We carefully analyzed the accuracy of first-principles methods and showed that the commonly used HSE hybrid exchange-correlation functional fails to describe the electronic structure of this defect. Using the generalized Koopman's theorem, we fine-tuned the functional and obtained a zero-phonon photoluminescence (ZPL) energy in the blue spectral range. We showed that the defect exhibits a high emission rate in the ZPL line and features a characteristic phonon side band that resembles the blue emitter's spectrum. Furthermore, we studied the electric field dependence of the ZPL and numerically showed that the defect exhibits a quadratic Stark shift that is perpendicular to plane electric fields, making the emitter insensitive to electric field fluctuations in the first order. Our work emphasizes the need for assessing the accuracy of common first-principles methods in hBN and exemplifies a workaround methodology. Furthermore, our work is a step towards understanding the structure of the blue emitter and utilizing it in photonics applications.

Positivity preserving density matrix minimization at finite temperatures via square root

We present a Wave Operator Minimization (WOM) method for calculating the Fermi-Dirac density matrix for electronic structure problems at finite temperature while preserving physicality by construction using the wave operator, i.e., the square root of the density matrix. WOM models cooling a state initially at infinite temperature down to the desired finite temperature. We consider both the grand canonical (constant chemical potential) and canonical (constant number of electrons) ensembles. Additionally, we show that the number of steps required for convergence is independent of the number of atoms in the system. We hope that the discussion and results presented in this article reinvigorate interest in density matrix minimization methods.

Isolation of an Anionic Dicarbene Embedded Sn2 P2 Cluster and Reversible CO2 Uptake

Decarbonylation of a cyclic bis-phosphaethynolatostannylene [(ADC)Sn(PCO)]2 based on an anionic dicarbene framework (ADC = PhC{N(Dipp)C}2 ; Dipp = 2,6-iPr2 C6 H3 ) under UV light results in the formation of a Sn2 P2 cluster compound [(ADC)SnP]2 as a green crystalline solid. The electronic structure of [(ADC)SnP]2 is analyzed by quantum-chemical calculations. At room temperature, [(ADC)SnP]2 reversibly binds with CO2 and forms [(ADC)2 {SnOC(O)P}SnP]. [(ADC)SnP]2 enables catalytic hydroboration of CO2 and reacts with elemental selenium and Fe2 (CO)9 to afford [(ADC)2 {Sn(Se)P2 }SnSe] and [(ADC)Sn{Fe(CO)4 }P]2 , respectively. All compounds are characterized by multinuclear NMR spectroscopy and their solid-state molecular structures are determined by single-crystal X-ray diffraction.

All-Purpose Measure of Electron Correlation for Multireference Diagnostics

We present an analytical relationship between two natural orbital occupancy-based indices, I N D ¯ and INDmax, and two established electron correlation metrics: the leading term of a configuration interaction expansion, c0, and the D2 diagnostic. Numerical validation revealed that I N D ¯ and INDmax can effectively substitute for c0 and D2, respectively. These indices offer three distinct advantages: (i) they are universally applicable across all electronic structure methods, (ii) their interpretation is more intuitive, and (iii) they can be readily incorporated into the development of hybrid electronic structure methods. Additionally, we draw a distinction between correlation measures and correlation diagnostics, establishing MP2 and CCSD numerical thresholds for INDmax, which are to be used as a multireference diagnostic. Our findings further demonstrate that establishing thresholds for other electronic structure methods can be easily accomplished using small data sets.

Sufficient driving force for quinoidal isoindigo-based diradicaloids with tunable diradical characters

Stable organic π-conjugated diradcialoids with tunable diradical characters can profoundly affect emerging technology. Over the past years, great efforts have been devoted to studying the structure-diradical character relationship in diradicaloids. Herein, a series of quinoidal isoindigo (IID) compounds with different attached terminal end groups were designed. Detailed analysis focuses on elucidating the driving force for evoking and enhancing the diradical character in the quinoidal IID systems. The arylene units of the IID core and the bridged aromatic units determine the contribution of the open-shell diradical form in the ground state. Diradical character y0 correlates well with bond length alternation (BLA), the total HOMA, and the total NICS(1)zz, and it is tuned by bridged aromatic units and terminal end groups in symmetric systems. The zwitterionic character weakens the diradical character in asymmetric systems to different extents. This work contributes to the deep understanding of evoking and enhancing the diradical character in quinoidal IID-based diradcialoids, providing useful guidelines to produce new molecules with desirable properties.

Benchmarking Density Functional Theory Methods for Metalloenzyme Reactions: The Introduction of the MME55 Set

We present a new benchmark set of metalloenzyme model reaction energies and barrier heights that we call MME55. The set contains 10 different enzymes, representing eight transition metals, both open and closed shell systems, and system sizes of up to 116 atoms. We use four DLPNO-CCSD(T)-based approaches to calculate reference values against which we then benchmark the performance of a range of density functional approximations with and without dispersion corrections. Dispersion corrections improve the results across the board, and triple-ζ basis sets provide the best balance of efficiency and accuracy. Jacob's ladder is reproduced for the whole set based on averaged mean absolute (percent) deviations, with the double hybrids SOS0-PBE0-2-D3(BJ) and revDOD-PBEP86-D4 standing out as the most accurate methods for the MME55 set. The range-separated hybrids ωB97M-V and ωB97X-V also perform well here and can be recommended as a reliable compromise between accuracy and efficiency; they have already been shown to be robust across many other types of chemical problems, as well. Despite the popularity of B3LYP in computational enzymology, it is not a strong performer on our benchmark set, and we discourage its use for enzyme energetics.

Theoretical Study on the Optoelectronic Properties of Merocyanine-Dyes

Merocyanines, as prototypes of highly polar π-conjugated molecules, have been intensively investigated for their self-assembly and optoelectronic properties, both experimentally and theoretically. However, an accurate description of their structural and electronic properties remains challenging for quantum-chemical methods. We assessed several theoretical approaches, TD-DFT, GW-BSE, STEOM-DLPNO-CCSD, and CASSCF/NEVPT2-FIC for their reliability in reproducing optoelectronic properties of a series of donor/acceptor (D/A) merocyanines, focusing on the first excitation energy. Additionally, we tested an all-electron perturbative method based on time-dependent coupled-perturbed density functional theory, denoted as TDCP-DFT. Particular focus was set on direct and indirect solvent effects, which affect excited-state energies by electrostatic interaction and molecular geometry. The molecular configuration space was sampled at the semiempirical tight-binding level. Our results corroborate previous investigations, showing that the S0 - S1 excitation energy strongly depends on the merocyanine molecular structure and the dielectric constant of the solvent. We found significant effects of the polar solution environment on the geometry of the merocyanines, which strongly affect the calculated excitation energies. Taking these effects into account, the best agreement between calculated and measured excitation energies was obtained with TDCP-DFT and GW-BSE. We also calculated excitation energies of molecular crystals at the TDCP-DFT level and compared the results to the corresponding monomers.

Quantification of the Ionic Character of Multiconfigurational Wave Functions: The Qat Diagnostic

The complete active space self-consistent field (CASSCF) method is a cornerstone in modern excited-state quantum chemistry providing the starting point for most common multireference computations. However, CASSCF, when used with a minimal active space, can produce significant errors (>2 eV) even for the excitation energies of simple hydrocarbons if the states of interest possess ionic character. After illustrating this problem in some detail, we present a diagnostic for ionic character, denoted as Q at, that is readily computed from the transition density. A set of 11 molecules is considered to study errors in vertical excitation energies. State-averaged CASSCF obtains a mean absolute error (MAE) of 0.87 eV for the 34 singlet states considered. We highlight a strong correlation between the obtained errors and the Q at diagnostic, illustrating its power to predict problematic cases. Conversely, using multireference configuration interaction with single and double excitations and Pople's size extensivity correction (MR-CISD+P), excellent results are obtained with an MAE of 0.11 eV. Furthermore, correlations with the Q at diagnostic disappear. In summary, we hope that the presented diagnostic will facilitate reliable and user-friendly multireference computations on conjugated organic molecules.

A theoretical study on π-stacking and ferromagnetism of the perylene diimide radical anion dimer and tetramer

Ferromagnetism is rare in pure organic materials. Recently, the perylene diimide radical anion (PDI-) salt prepared through solvothermal reduction by hydrazine hydrate has shown room-temperature ferromagnetism in our work [Jiang et al., Adv. Mater., 2022, 34, 2108103]. Based on this, herein we conduct a theoretical study based on density functional theory (DFT) to reveal the stacked geometries between two NH4PDI monomers for low-spin (LS) and high-spin (HS) states and their magnetic exchange interactions (JAB) using Yamaguchi's approximate spin projection. It is observed that the pancake-bonded dimer of NH4PDI is the most stable pimer compared to others on both LS and HS potential energy surfaces. A transition of magnetic properties from strong antiferromagnetic (-1333.9 cm-1) to moderate ferromagnetic (67.0 cm-1) appears after increasing the interplanar distance between monomers and their relative rotation angle to access the HS state. According to energy decomposition analysis, the enhanced hydrogen bond formation and decrease of Pauli repulsion is able to counteract the decrease of attraction induced by electron correlation after accessing the HS state. Stacking patterns of exchange-coupled chain consisting of the NH4PDI tetramer are obtained for the HS state after geometry optimization of the structure constructed by two most stable HS pimers. The exchange interactions (51.8 cm-1, 381.2 cm-1 and 53.2 cm-1) between adjacent NH4PDI monomers are ferromagnetic in the HS state, which is in accordance with the experimentally observed room-temperature ferromagnetism.

Imidazolyl-Substituted Benzo- and Naphthodithiophenes as Precursors for the Synthesis of Transient Open-Shell Quinoids

The synthesis of three novel imidazolyl-substituted sulfur-containing heteroacenes is reported. These heteroacenes consisting of annelated benzo- and naphthothiophenes serve as precursors for the generation of open-shell quinoid heteroacenes by oxidation with alkaline ferric cyanide. Spectroscopic and computational experiments support the formation of reactive open-shell quinoids, which, however, quickly produce paramagnetic polymeric material.

Real-Time Extension of TAO-DFT

Thermally assisted occupation density functional theory (TAO-DFT) has been an efficient electronic structure method for studying the ground-state properties of large electronic systems with multi-reference character over the past few years. To explore the time-dependent (TD) properties of electronic systems (e.g., subject to an intense laser pulse), in this work, we propose a real-time (RT) extension of TAO-DFT, denoted as RT-TAO-DFT. Moreover, we employ RT-TAO-DFT to study the high-order harmonic generation (HHG) spectra and related TD properties of molecular hydrogen H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly polarized laser pulse. The TD properties obtained with RT-TAO-DFT are compared with those obtained with the widely used time-dependent Kohn-Sham (TDKS) method. In addition, issues related to the possible spin-symmetry breaking effects in the TD properties are discussed.

Polyradical character assessment using multireference calculations and comparison with density-functional derived fractional occupation number weighted density analysis

The biradicaloid character of different types of polycyclic aromatic hydrocarbons (PAHs) based on small band gaps is an important descriptor to assess their opto-electronic properties. In this work, the unpaired electron densities and numbers of unpaired electrons (NU values) calculated at the high-level multireference averaged quadratic coupled-cluster (MR-AQCC) method are used to develop a test set to assess the capabilities of different biradical descriptors based on density functional theory. A benchmark collection of 29 different compounds has been selected. The DFT descriptors contain primarily the fractional occupation number weighted electron density (FOD) based on simplified thermally-assisted-occupation density functional theory (TAO-DFT) calculations, but the singlet-triplet energy difference and other descriptors denoted as y0 and nLUNO have been considered as well. After adjustment of the literature-recommended finite temperatures, a very good, detailed agreement between unpaired density and FOD analysis is observed which is also manifested in excellent statistical correlations. The other two descriptors also show good correlations even though the absolute scaling is not satisfactory. A new linear fit of FOD data to the MR-AQCC reference values leads to an improved regression relation for determining the recommended finite temperature value in dependence of the Hartree-Fock exchange. This provides the basis for fast and reliable assessment of the biradical character of many classes of PAHs without the need for performing computationally extended MR calculations.

Toward Benchmark-Quality Ab Initio Predictions for 3d Transition Metal Electrocatalysts: A Comparison of CCSD(T) and ph-AFQMC

Generating accurate ab initio ionization energies for transition metal complexes is an important step toward the accurate computational description of their electrocatalytic reactions. Benchmark-quality data is required for testing existing theoretical methods and developing new ones but is complicated to obtain for many transition metal compounds due to the potential presence of both strong dynamical and static electron correlation. In this regime, it is questionable whether the so-called gold standard, coupled cluster with singles, doubles, and perturbative triples (CCSD(T)), provides the desired level of accuracy─roughly 1-3 kcal/mol. In this work, we compiled a test set of 28 3d metal-containing molecules relevant to homogeneous electrocatalysis (termed 3dTMV) and computed their vertical ionization energies (ionization potentials) with CCSD(T) and phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) in the def2-SVP basis set. A substantial effort has been made to converge away the phaseless bias in the ph-AFQMC reference values. We assess a wide variety of multireference diagnostics and find that spin-symmetry breaking of the CCSD wave function and the PBE0 density functional correlate well with our analysis of multiconfigurational wave functions. We propose quantitative criteria based on symmetry breaking to delineate correlation regimes inside of which appropriately performed CCSD(T) can produce mean absolute deviations from the ph-AFQMC reference values of roughly 2 kcal/mol or less and outside of which CCSD(T) is expected to fail. We also present a preliminary assessment of density functional theory (DFT) functionals on the 3dTMV set.

Revisiting the electronic structure of N2-bound cAAC-borylene at the CASSCF level: a detailed bonding picture of borylene-N2 interaction

A base-trapped borylene species featuring a cyclic-(alkyl)(amino)carbene (cAAC) has shown unique bonding interactions with dinitrogen, thereby, opening a new avenue for N2 activation by main-group compounds. The detailed electronic structure and qualitative bonding picture between cAAC-trapped borylene and N2 remain to be fully understood. This work presents a multiconfigurational complete active space self-consistent field (CASSCF)-based electronic structure investigation on the N2-bound cAAC-borylene species (1) isolated by Braunschweig et al. Specifically, the synergistic bonding between the borylene units and N2 involving the donation from the N-N σ to the unoccupied orbital of borylene and back-donation from the occupied orbital of borylene to the N-N π* has been unequivocally established using CASSCF-derived natural orbitals and electronic configuration. Bonding interactions between the HOMO of the borylene units and the N-N π* (HOMOcAAC-B + π*NN) and the LUMO of the borylene units and the N-N σ (LUMOcAAC-B + σNN) in 1 were apparent through the CASSCF-derived natural orbitals. The unique bonding of the B-N-N-B core in 1 and the resulting geometry have also been compared with the M-N-N-M core of a prototypical transition metal(M)-N2 complex. Finally, the change in the electronic structure and geometry of the N2-bound borylene species 1 on two-electron reduction has been investigated in the context of N2 activation.

Cross-coupling by a noncanonical mechanism involving the addition of aryl halide to Cu(II)

Copper complexes are widely used in the synthesis of fine chemicals and materials to catalyze couplings of heteroatom nucleophiles with aryl halides. We show that cross-couplings catalyzed by some of the most active catalysts occur by a mechanism not previously considered. Copper(II) [Cu(II)] complexes of oxalamide ligands catalyze Ullmann coupling to form the C-O bond in aryl ethers by concerted oxidative addition of an aryl halide to Cu(II) to form a high-valent species that is stabilized by radical character on the oxalamide ligand. This mechanism diverges from those involving Cu(I) and Cu(III) intermediates that have been posited for other Ullmann-type couplings. The stability of the Cu(II) state leads to high turnover numbers, >1000 for the coupling of phenoxide with aryl chloride electrophiles, as well as an ability to run the reactions in air.

Heteroatom-Based Diradical(oid)s

Heteroatom-centered diradical(oid)s have been in the focus of molecular main group chemistry for nearly 30 years. During this time, the diradical concept has evolved and the focus has shifted to the rational design of diradical(oid)s for specific applications. This review article begins with some important theoretical considerations of the diradical and tetraradical concept. Based on these theoretical considerations, the design of diradical(oid)s in terms of ligand choice, steric, symmetry, electronic situation, element choice, and reactivity is highlighted with examples. In particular, heteroatom-centered diradical reactions are discussed and compared with closed-shell reactions such as pericyclic additions. The comparison between closed-shell reactivity, which proceeds in a concerted manner, and open-shell reactivity, which proceeds in a stepwise fashion, along with considerations of diradical(oid) design, provides a rational understanding of this interesting and unusual class of compounds. The application of diradical(oid)s, for example in small molecule activation or as molecular switches, is also highlighted. The final part of this review begins with application-related details of the spectroscopy of diradical(oid)s, followed by an update of the heteroatom-centered diradical(oid)s and tetraradical(oid)s published in the last 10 years since 2013.

Highly Soluble Cyclic Organoalanes Based on Anionic Dicarbenes

Cyclic organoalane compounds [(ADCAr )AlH2 ]2 (ADCAr = ArC{(DippN)C}2 ; Dipp = 2,6-iPr2 C6 H3 ; Ar = Ph or 4-PhC6 H4 (Bp)) based on anionic dicarbene (ADC) frameworks have been reported as crystalline solids. Treatments of Li(ADCAr ) with LiAlH4 at room temperature afford [(ADCAr )AlH2 ]2 with the concomitant release of LiH. Compounds [(ADCAr )AlH2 ]2 are stable crystalline solids and are freely soluble in common organic solvents. They are annulated tricyclic compounds with an almost planar central C4 Al2 -core embedded between two peripheral 1,3-imidazole (C3 N2 ) rings. At room temperature, [(ADCPh )AlH2 ]2 readily reacts with CO2 to form two- and four-fold hydroalumination products [(ADCPh )AlH(OCHO)]2 and [(ADCPh )Al(OCHO)2 ]2 , respectively. Further hydroalumination reactivity of [(ADCPh )AlH2 ]2 has been shown with isocyanate (RNCO) and isothiocyanate (RNCS) species (R=alkyl or aryl group). All compounds have been characterized by NMR spectroscopy, mass spectrometry, and single-crystal X-ray diffraction.

Assessment of Density Functional Theory Methods for the Structural Prediction of Transition and Post-Transition Metal-Nucleic Acid Complexes

Understanding the structure of metal-nucleic acid systems is important for many applications such as the design of new pharmaceuticals, metal detection platforms, and nanomaterials. Herein, we explore the ability of 20 density functional theory (DFT) functionals to reproduce the crystal structure geometry of transition and post-transition metal-nucleic acid complexes identified in the Protein Data Bank and Cambridge Structural Database. The environmental extremes of the gas phase and implicit water were considered, and analysis focused on the global and inner coordination geometry, including the coordination distances. Although gas-phase calculations were unable to describe the structure of 12 out of the 53 complexes in our test set regardless of the DFT functional considered, accounting for the broader environment through implicit solvation or constraining the model truncation points to crystallographic coordinates generally afforded agreement with the experimental structure, suggesting that functional performance for these systems is likely due to the models rather than the methods. For the remaining 41 complexes, our results show that the reliability of functionals depends on the metal identity, with the magnitude of error varying across the periodic table. Furthermore, minimal changes in the geometries of these metal-nucleic acid complexes occur upon use of the Stuttgart-Dresden effective core potential and/or inclusion of an implicit water environment. The overall top three performing functionals are ωB97X-V, ωB97X-D3(BJ), and MN15, which reliably describe the structure of a broad range of metal-nucleic acid systems. Other suitable functionals include MN15-L, which is a cheaper alternative to MN15, and PBEh-3c, which is commonly used in QM/MM calculations of biomolecules. In fact, these five methods were the only functionals tested to reproduce the coordination sphere of Cu²⁺-containing complexes. For metal-nucleic acid systems that do not contain Cu²⁺, ωB97X and ωB97X-D are also suitable choices. These top-performing methods can be utilized in future investigations of diverse metal-nucleic acid complexes of relevance to biology and material science.

Phenylalanine Residues in the Active Site of CYP2E1 Participate in Determining the Binding Orientation and Metabolism-Dependent Genotoxicity of Aromatic Compounds

The composition of amino acids forming the active site of a CYP enzyme is impactful in its substrate selectivity. For CYP2E1, the role of PHE residues in the formation of effective binding orientations for its aromatic substrates remains unclear. In this study, molecular docking and molecular dynamics analysis were performed to reflect the interactions between PHEs in the active site of human CYP2E1 and various aromatic compounds known as its substrates. The results indicated that the orientation of 1-methylpyrene (1-MP) in the active site was highly determined by the presence of PHEs, PHE478 contributing to the binding free energy most significantly. Moreover, by building a random forest model the relationship between each of 19 molecular descriptors of polychlorinated biphenyl (PCB) compounds (from molecular docking, quantum mechanics, and physicochemical properties) and their human CYP2E1-dependent mutagenicityas established mostly in our lab, was investigated. The presence of PHEs did not appear to significantly modify the electronic or structural feature of each bound ligand (PCB), instead, the flexibility of the conformation of PHEs contributed substantially to the effective binding energy and orientation. It is supposed that PHE residues adjust their own conformation to permit a suitablly shaped cavity for holding the ligand and forming its orientation as favorable for a biochemical reaction. This study has provided some insights into the role of PHEs in guiding the interactive adaptation of the active site of human CYP2E1 for the binding and metabolism of aromatic substrates.

Extremely Long C-C Bonds Predicted beyond 2.0 Å

A number of conjugated molecules are designed with extremely long single C-C bonds beyond 2.0 Å. Some of the investigated molecules are based on analogues to the recently discovered molecule by Kubo et al. These bonds are analyzed by a variety of indices in addition to their equilibrium bond length including the Wiberg bond index, bond dissociation energy (BDE), and measures of diradicaloid character. All unrestricted DFT calculations indicate no diradical character supported by high-level multireference calculations. Finally, NFOD was computed through fractional orbital density (FOD) calculations and used to compare relative differences of diradicaloid character across twisted molecules without central C-C bonding and those with extremely elongated C-C bonds using a comparison with the C-C bond breaking in ethane. No example of direct C-C bonds beyond 2.4 Å are seen in the computational modeling; however, extremely stretched C-C bonds in the vicinity of 2.2 Å are predicted to be achievable with a BDE of 15-25 kcal mol-1.

Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations

In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.

TAO-DFT with the Polarizable Continuum Model

For the ground-state properties of gas-phase nanomolecules with multi-reference character, thermally assisted occupation (TAO) density functional theory (DFT) has recently been found to outperform the widely used Kohn-Sham DFT when traditional exchange-correlation energy functionals are employed. Aiming to explore solvation effects on the ground-state properties of nanomolecules with multi-reference character at a minimal computational cost, we combined TAO-DFT with the PCM (polarizable continuum model). In order to show its usefulness, TAO-DFT-based PCM (TAO-PCM) was used to predict the electronic properties of linear acenes in three different solvents (toluene, chlorobenzene, and water). According to TAO-PCM, in the presence of these solvents, the smaller acenes should have nonradical character, and the larger ones should have increasing polyradical character, revealing striking similarities to the past findings in the gas phase.

Impact of Di- and Poly-Radical Characters on the Relative Energy of the Doubly Excited and La States of Linear Acenes and Cyclacenes

Linear and cyclic acenes are polycyclic aromatic hydrocarbons that can be viewed as building blocks of graphene nanoribbons and carbon nanotubes, respectively. While short linear acenes demonstrated remarkable efficiency in several optoelectronic applications, the longer members are unstable and difficult to synthesize as their cyclic counterparts. Recent progress in on-surface synthesis, a powerful tool to prepare highly reactive species, opens promising perspectives and motivates the computational investigations of these potentially functional molecules. Owing to their di- and poly-radical character, low-lying excited states dominated by doubly excited configurations are expected to become more important for longer members of both linear and cyclic molecules. In this work, we investigate the lowest-lying La and the doubly excited (DE) state of linear acenes and cyclacenes, with different computational approaches, to assess the influence of the di-/poly-radical characters (increasing with the molecular dimensions) on their relative order. We show that DFT/MRCI calculations correctly reproduce the crossing of the two states for longer linear acenes, while TDUDFT calculations fail to predict the correct excitation energy trend of the DE state. The study suggests a similarity in the excited electronic state pattern of long linear and cyclic acenes leading ultimately to a lowest lying dark DE state for both.

Active Learning Exploration of Transition-Metal Complexes to Discover Method-Insensitive and Synthetically Accessible Chromophores

Transition-metal chromophores with earth-abundant transition metals are an important design target for their applications in lighting and nontoxic bioimaging, but their design is challenged by the scarcity of complexes that simultaneously have well-defined ground states and optimal target absorption energies in the visible region. Machine learning (ML) accelerated discovery could overcome such challenges by enabling the screening of a larger space but is limited by the fidelity of the data used in ML model training, which is typically from a single approximate density functional. To address this limitation, we search for consensus in predictions among 23 density functional approximations across multiple rungs of "Jacob's ladder". To accelerate the discovery of complexes with absorption energies in the visible region while minimizing the effect of low-lying excited states, we use two-dimensional (2D)efficient global optimization to sample candidate low-spin chromophores from multimillion complex spaces. Despite the scarcity (i.e., ∼0.01%) of potential chromophores in this large chemical space, we identify candidates with high likelihood (i.e., >10%) of computational validation as the ML models improve during active learning, representing a 1000-fold acceleration in discovery. Absorption spectra of promising chromophores from time-dependent density functional theory verify that 2/3 of candidates have the desired excited-state properties. The observation that constituent ligands from our leads have demonstrated interesting optical properties in the literature exemplifies the effectiveness of our construction of a realistic design space and active learning approach.

Symmetry-Induced Singlet-Triplet Inversions in Non-Alternant Hydrocarbons

Molecules with inversion of the singlet and triplet excited-state energies are highly promising for the development of organic light-emitting diodes (OLEDs). To date, azaphenalenes are the only class of molecules where these inversions have been identified. Here, we screen a curated database of organic crystal structures to identify existing compounds for violations of Hund's rule in the lowest excited states. We identify two further classes with this behavior. The first, a class of zwitterions, has limited relevance to molecular emitters as the singlet-triplet inversions occur in the third excited singlet state. The second class consists of two D_2h -symmetry non-alternant hydrocarbons, a fused azulene dimer and a bicalicene, whose lowest excited singlet states violate Hund's rule. Due to the connectivity of the polycyclic structure, they achieve this symmetry through aromatic stabilization. These hydrocarbons show promise as the next generation of building blocks for OLED emitters.

Redox-active ligands as a challenge for electronic structure methods

To improve the catalytic activity of 3d transition metal catalysts, redox-active ligands are a promising tool. These ligands influence the oxidation state of the metal center as well as the ground spin-state and make the experimental determination of both properties challenging. Therefore, first-principles calculations, in particular employing density functional theory with a proper choice of exchange-correlation (xc) functional, are crucial. Common xc functionals were tested on a simple class of metal complexes: homoleptic, octahedral tris(diimine) iron(II) complexes. The spin-state energy splittings for most of these complexes showed the expected linear dependence on the amount of exact exchange included in the xc functionals. Even though varying redox-activity affects the electronic structure of the complexes considerably, the sensitivity of the spin-state energetics to the exact exchange admixture is surprisingly small. For iron(II) complexes with highly redox-active ligands and for a broad range of ligands in the reduced tris(diimine) iron(I) complexes, self-consistent field convergence to local minima was observed, which differ from the global minimum in the redox state of the ligand. This may also result in convergence to a molecular structure that corresponds to an energetically higher-lying local minimum. One criterion to detect such behavior is a change in the sign of the slope for the dependence of the spin-state energy splittings on the amount of exact exchange. We discuss possible protocols for dealing with such artifacts in cases in which a large number of calculations makes checking by hand unfeasible.

DFT-Based Multireference Diagnostics in the Solid State: Application to Metal-Organic Frameworks

When a many-body wave function of a system cannot be captured by a single determinant, high-level multireference (MR) methods are required to properly explain its electronic structure. MR diagnostics to estimate the magnitude of such static correlation have been primarily developed for molecular systems and range from low in computational cost to as costly as the full MR calculation itself. We report the first application of low-cost MR diagnostics based on the fractional occupation number calculated with finite-temperature DFT to solid-state systems. To compare the behavior of the diagnostics on solids and molecules, we select metal-organic frameworks (MOFs) as model materials because their reticular nature provides an intuitive way to identify molecular derivatives. On a series of closed-shell MOFs, we demonstrate that the DFT-based MR diagnostics are equally applicable to solids as to their molecular derivatives. The magnitude and spatial distribution of the MR character of a MOF are found to have a good correlation with those of its molecular derivatives, which can be calculated much more affordably in comparison to those of the full MOF. The additivity of MR character discussed here suggests the set of molecular derivatives to be a good representation of a MOF for both MR detection and ultimately for MR corrections, facilitating accurate and efficient high-throughput screening of MOFs and other porous solids.

Isolation of an Annulated 1,4-Distibabenzene Diradicaloid

The first 1,4-distibabenzene-1,4-diide compound [(ADC)Sb]₂ (5) based on an anionic dicarbene (ADC) (ADC=PhC{N(Dipp)C}₂ , Dipp=2,6-iPr₂ C₆ H₃ ) is reported as a bordeaux-red solid. Compound 5, featuring a central six-membered C₄ Sb₂ ring with formally Sb^I atoms may be regarded as a base-stabilized cyclic bis-stibinidene in which each of the Sb atoms bears two lone-pairs of electrons. 5 undergoes 2 e-oxidation with Ph₃ C[B(C₆ F₅ )₄ ] to afford [(ADC)Sb]₂ [B(C₆ F₅ )₄ ]₂ (6) as a brick-red solid. Each of the Sb atoms of 6 has an unpaired electron and a lone-pair. The broken-symmetry open-shell singlet diradical solution for (6)²⁺ is calculated to be 2.13 kcal mol^-1 more stable than the closed-shell singlet. The diradical character of (6)²⁺ according to SS-CASSCF (state-specific complete active space self-consistent field) and UHF (unrestricted Hartree-Fock) methods amounts to 36 % and 39 %, respectively. Treatments of 6 with (PhE)₂ yield [(ADC)Sb(EPh)]₂ [B(C₆ F₅ )₄ ]₂ (7-E) (E=S or Se). Reaction of 5 with (cod)Mo(CO)₄ affords [(ADC)Sb]₂ Mo(CO)₄ (8).

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.