The Fractional Occupation Number Weighted Density as a Versatile Analysis Tool for Molecules with a Complicated Electronic Structure

Experimental molecular structures in the gas phase at the upper size limit: The case of Si6Tip6

Currently, the largest (ramax = 19.9 Å) and by far the most complicated (234 atoms, C1 symmetry, 696 independent geometrical parameters, and 27 261 interatomic terms) experimental molecular structure of a cage-type Si6Tip6 (Tip = 2,4,6-iPr3C6H2) isomer has been investigated in the gas phase by the electron diffraction method (Tav = 645 K) supplemented with theoretical simulations. A detailed analysis of the current possibilities for experimentally investigating large molecular structures is performed. A series of density functional theory approximations and the role of dispersion interactions have been benchmarked using the obtained data. Based on the refined geometry of Si6Tip6, various quantum-chemical methods have been applied for the investigation of the electronic structure of its Si6 core. In particular, natural bond orbital, quantum theory of atoms in molecules, interacting quantum atoms, fractional occupation number weighted density, and complete active space self-consistent field (CASSCF) methods were utilized. The diradical character of the molecule has been assessed by the UHF and CASSCF approximations. The problem of bonding between the hemispheroidal silicon atoms has been investigated.

Ab initio investigation of the geometrical behavior in solution and electronic structure of the anion complexes [bis(1,3-dithiole-2-thione-4,5-dithiolate)M], for M = Bi(III), Sb(III), and Zn(II)

CONTEXT

1,3-Dithiole-2-thione-4,5-dithiolate (dmit) ligands are known for their conductive and optical properties. Dmit compounds have been assessed for use in sensor devices, information storage, spintronics, and optical material applications. Associations with various metallic centers endow dmit complexes with magnetic, optical, conductive, and antioxidant properties. Optical doping can facilitate the fabrication of magnetic conductor materials from ground-state nonmagnetic cations. While most studied complexes involve transition-metal centers due to their diverse chemistry, compounds with representative elements are less explored in the literature. This study investigated the structural and electronic properties of bisdmit complexes with representative Bi(III), Sb(III), and Zn(II) cations. AIMD calculations revealed two new geometries for Bi(III) and Zn(II) complexes, diverging from the isolated geometry typically used in quantum chemical calculations. The coordination of acetonitrile molecules to the cationic centers of the complexes resulted in unstable structures, while the dimerization of the complexes was stable. SA-CASSCF/NEVPT2 calculations were applied to the structures of the isolated complexes and stable dimers, confirming the multireference character of the electronic structure of the three systems and the multiconfigurational character of the Bi(III) complex. The electronic spectra simulated by the STEOM-DLPNO-CCSD calculations accurately reproduced the experimental UV‒Vis spectra indicating the participation of the isolated Bi(III) dmit complex and its dimeric form in solution.

METHODOLOGY

AIMD calculations of the dmit salts were conducted using the GFN2-xTB method with 60 explicit acetonitrile molecules as the solvent at 300 K for a total simulation time of 50.0 ps, with printing intervals of 0.5 fs. The final geometries were optimized employing the PBEh-3c compound method, incorporating implicit conductor-like polarizable continuum model (CPCM) solvation for acetonitrile. Local energy decomposition (LED) analysis at the DLPNO-CCSD(T)/Def2-TZVP level of theory was utilized to investigate the stability of the complex geometries identified by AIMD. The electronic structures of the complexes were assessed using the SA-CASSCF/NEVPT2/Def2-TZVP method to confirm the multiconfigurational and multireference nature of their electronic structures. Electronic spectra were analyzed using the STEOM-DLPNO-CCSD/Def2-TZVP method, with CPCM used to simulate an acetonitrile medium.

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.

COMPAS-3: a dataset of peri-condensed polybenzenoid hydrocarbons

We introduce the third installment of the COMPAS Project - a COMputational database of Polycyclic Aromatic Systems, focused on peri-condensed polybenzenoid hydrocarbons. In this installment, we develop two datasets containing the optimized ground-state structures and a selection of molecular properties of ∼39k and ∼9k peri-condensed polybenzenoid hydrocarbons (at the GFN2-xTB and CAM-B3LYP-D3BJ/cc-pvdz//CAM-B3LYP-D3BJ/def2-SVP levels, respectively). The manuscript details the enumeration and data generation processes and describes the information available within the datasets. An in-depth comparison between the two types of computation is performed, and it is found that the geometrical disagreement is maximal for slightly-distorted molecules. In addition, a data-driven analysis of the structure-property trends of peri-condensed PBHs is performed, highlighting the effect of the size of peri-condensed islands and linearly annulated rings on the HOMO-LUMO gap. The insights described herein are important for rational design of novel functional aromatic molecules for use in, e.g., organic electronics. The generated datasets provide a basis for additional data-driven machine- and deep-learning studies in chemistry.

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.

Access to a peri-Annulated Aluminium Compound via C-H Bond Activation by a Cyclic Bis-Aluminylene

Carbocyclic aluminium halides [(ADC)AlX2]2 (2-X) (X=F, Cl, and I) based on an anionic dicarbene (ADC=PhC{N(Dipp)C}2, Dipp = 2,6-iPr2C6H3) framework are prepared as crystalline solids by dehydrohalogenations of the alane [(ADC)AlH2]2 (1). KC8 reduction of 2-I affords the peri-annulated Al(III) compound [(ADCH)AlH]2 (4) (ADCH=PhC{N(Dipp)C2(DippH)N}, DippH=2-iPr,6-(Me2C)C6H3)) as a colorless crystalline solid in 76 % yield. The formation of 4 suggests intramolecular insertion of the putative bis-aluminylene species [(ADC)Al]2 (3) into the methine C-H bond of HCMe2 group. Calculations predict singlet ground state for 3, while the conversion of 3 into 4 is thermodynamically favored by 61 kcal/mol. Compounds 2-F, 2-Cl, 2-I, and 4 have been characterized by NMR spectroscopy and their solid-state molecular structures have been established by single crystal X-ray diffraction.

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.

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.

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.

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.

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.

Electronic Structure of Small Isolated and Supported Manganese Oxide Clusters

In the present work, possible molecular models of the isolated manganese oxides and supported Mn3Ox/Al2O3 structures were built based on small clusters of passivated MnOx. The support was represented as a simplified model of the alumina tetramer cluster based on small fragments of AlOxHy. Combinations of MnOxHy and AlOxHy clusters were made to form both the isolated and supported manganese oxides clusters. The electronic structure of these systems was characterized by ab initio methods (DFT and CASPT2). It was observed that the vertical excitation energy of the isolated and supported Mn3OxHy clusters is significantly lower than that of the alumina cluster model, while both the isolated and supported Mn3OxHy wave function characters are qualitatively similar with respect to the ground state and electronic transition processes, suggesting that the alumina cluster behaves as an inert support, since there is little contribution of this component in the description of the low-lying electronic states. The present study also reports for the first time the spectroscopic parameters of several clusters containing the manganese transition metal atom.

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.

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.

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.

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.

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.

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).

Analysing binding stoichiometries in NMR titration experiments using Monte Carlo simulation and resampling techniques

The application of Monte Carlo simulation and resampling techniques to analyse possible binding stoichiometries in NMR titration experiments is presented. Four simulated NMR titration experiments having complex species with 1:1, 2:1 and 1:2 stoichiometries were each analysed using a 1:1, 2:1/1:1, 1:1/1:2 and a 2:1/1:1/1:2 model as implemented in SupraFit. Each best-fit model was inspected using Monte Carlo simulation (MC), Cross Validation (CV) and a new protocol termed Reduction Analysis (RA). The results of the statistical post-processes were used to calculate characteristic descriptors that are the base of the judgment for both, the models and individual stability constants. The results indicate promising approaches to correctly identify 1:1, 2:1/1:1 and 1:1/1:2 models, however with some limitations in case of the 2:1/1:1/1:2 model. All simulations and post-processing protocols were performed with the newly presented SupraFit.

Best-Practice DFT Protocols for Basic Molecular Computational Chemistry

Nowadays, many chemical investigations are supported by routine calculations of molecular structures, reaction energies, barrier heights, and spectroscopic properties. The lion's share of these quantum-chemical calculations applies density functional theory (DFT) evaluated in atomic-orbital basis sets. This work provides best-practice guidance on the numerous methodological and technical aspects of DFT calculations in three parts: Firstly, we set the stage and introduce a step-by-step decision tree to choose a computational protocol that models the experiment as closely as possible. Secondly, we present a recommendation matrix to guide the choice of functional and basis set depending on the task at hand. A particular focus is on achieving an optimal balance between accuracy, robustness, and efficiency through multi-level approaches. Finally, we discuss selected representative examples to illustrate the recommended protocols and the effect of methodological choices.

TEMPO as a Hydrogen Atom Transfer Catalyst for Aerobic Dehydrogenation of Activated Alkanes to Alkenes

2,2,6,6-Tetramethylpiperidine-N-oxyl (TEMPO) has been extensively utilized as a radical scavenger or an oxidation catalyst. In contrast, TEMPO as a hydrogen atom transfer (HAT) catalyst has rarely been studied. Here, we report that TEMPO, as the HAT catalyst, homolytically cleaves benzylic or allylic C-H bonds to give the corresponding alkyl radicals. Benefiting from the dual roles played by TEMPO as the HAT catalyst and the radical scavenger, the highly challenging aerobic dehydrogenation of activated alkanes to alkenes is successfully developed.

Tuning the Diradical Character of Indolocarbazoles: Impact of Structural Isomerism and Substitution Position

In this study, a set of 10 positional indolocarbazole (ICz) isomers substituted with dicyanomethylene groups connected via para or meta positions are computationally investigated with the aim of exploring the efficiency of structural isomerism and substitution position in controlling their optical and electronic properties. Unrestricted density functional theory (DFT), a spin-flip time-dependent DFT approach, and the multireference CASSCF/NEVPT2 method have been applied to correlate the diradical character with the energetic trends (i.e., singlet-triplet energy gaps). In addition, the nucleus-independent chemical shift together with ACID plots and Raman intensity calculations were used to strengthen the relationship between the diradical character and (anti)aromaticity. Our study reveals that the substitution pattern and structural isomerism represent a very effective way to tune the diradical properties in ICz-based systems with meta-substituted systems with a V-shaped structure displaying the largest diradical character. Thus, this work contributes to the elucidation of the challenging chemical reactivity and physical properties of diradicaloid systems, guiding experimental chemists to produce new molecules with desirable properties.

Ultrafast bandgap narrowing and cohesion loss of photoexcited fused silica

Coupling and spatial localization of energy on ultrafast timescales and particularly on the timescale of the excitation pulse in ultrashort laser irradiated dielectric materials are key elements for enabling processing precision beyond the optical limit. Transforming matter on mesoscopic scales facilitates the definition of nanoscale photonic functions in optical glasses. On these timescales, quantum interactions induced by charge non-equilibrium become the main channel for energy uptake and transfer as well as for the material structural change. We apply a first-principles model to determine dynamic distortions of energy bands following the rapid increase in the free-carrier population in an amorphous dielectric excited by an ultrashort laser pulse. Fused silica glass is reproduced using a system of (SiO₄)^4- tetrahedra, where density functional theory extended to finite-temperature fractional occupation reproduces ground and photoexcited states. Triggered by electronic charge redistribution, a bandgap narrowing of more than 2 eV is shown to occur in fused silica under geometry relaxation. Calculations reveal that the bandgap decrease results from the rearrangement of atoms altering the bonding strength. Despite an atomic movement impacting strongly the structural stability, the observed change of geometry remains limited to 7% of the interatomic distance and occurs on the femtosecond timescale. This structural relaxation is thus expected to take place quasi-instantly following the photon energy flux. Moreover, under intense laser pulse excitation, fused silica loses its stability when an electron temperature of around 2.8 eV is reached. A further increase in the excitation energy leads to the collapse of both the structure and bandgap.

Assessing Alkene Reactivity toward Cytochrome P450-Mediated Epoxidation through Localized Descriptors and Regression Modeling

The prediction of sites of epoxidation by cytochrome P450s during metabolism is particularly important in drug design, as epoxides are capable of alkylating biological macromolecules. Reliable methods are needed to quantitatively predict P450-mediated epoxidation barriers for inclusion in high-throughput screening campaigns alongside protein-ligand docking. Utilizing the fractional occupation number weighted density (FOD) and orbital-weighted Fukui index (f_w⁺) as descriptors of local reactivity and a data set of 36 alkene epoxidation barriers computed with density functional theory (DFT), we developed and validated a multiple linear regression model for the reliable estimation of epoxidation barriers using only substrate structures as input. Using our recommended level of theory (GFN2-xTB//GFN-FF), mean absolute errors in the training and test sets were found to be 0.66 and 0.70 kcal/mol, respectively, with coefficients of determination of ca. 0.80. We demonstrate the utility of this approach on three known substrates of CYP101A1 and further show that this approach is inappropriate for particularly electron-rich alkenes. By employing a modern semiempirical method on force-field-generated geometries, the required descriptors can be calculated on the millisecond timescale per structure, making the approach well suited for incorporation into high-throughput methodologies alongside docking.

The Adsorption of Small Molecules on the Copper Paddle-Wheel: Influence of the Multi-Reference Ground State

We report a theoretical study of the adsorption of a set of small molecules (C₂H₂, CO, CO₂, O₂, H₂O, CH₃OH, C₂H₅OH) on the metal centers of the “copper paddle-wheel”—a key structural motif of many MOFs. A systematic comparison between DFT of different rungs, single-reference post-HF methods (MP2, SOS–MP2, MP3, DLPNO–CCSD(T)), and multi-reference approaches (CASSCF, DCD–CAS(2), NEVPT2) is performed in order to find a methodology that correctly describes the complicated electronic structure of paddle-wheel structure together with a reasonable description of non-covalent interactions. Apart from comparison with literature data (experimental values wherever possible), benchmark calculations with DLPNO–MR–CCSD were also performed. Despite tested methods show qualitative agreement in the majority of cases, we showed and discussed reasons for quantitative differences as well as more fundamental problems of specific cases.

Crystalline phosphino-functionalized mesoionic olefins (p-MIOs)

Phosphino-functionalized mesoionic olefins (p-MIOs), (iMIC)CHR (iMIC = PhC{N(Dipp)}2C(PPh2)C, Dipp = 2,6-iPr2C6H3; R = H 4a or Ph 4b) derived from a 1,3-imidazole based mesoionic carbene (iMIC) are reported. The p-MIOs...

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 ΔE_ST, 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 ΔE_ST values, constituting versatile platforms for fine-tuned photophysical applications.

Assessing Density Functional Theory for Chemically Relevant Open-Shell Transition Metal Reactions

Due to the principle lack of systematic improvement possibilities of density functional theory, careful assessment of the performance of density functional approximations (DFAs) on well-designed benchmark sets, for example, for reaction energies and barrier heights, is crucial. While main-group chemistry is well covered by several available sets, benchmark data for transition metal chemistry is sparse. This is especially the case for larger, chemically relevant molecules. Addressing this issue, we recently introduced the MOR41 benchmark which covers chemically relevant reactions of closed-shell complexes. In this work, we extend these efforts to single-reference open-shell systems and introduce the "reactions of open-shell single-reference transition metal complexes" (ROST61) benchmark set. ROST61 includes accurate coupled-cluster reference values for 61 reaction energies with a mean reaction energy of -42.8 kcal mol^-1. Complexes with 13-93 atoms covering 20 d-block elements are included, but due to the restriction to single-reference open-shell systems, important elements such as iron or platinum could not be taken into account, or only to a small extent. We assess the performance of 31 DFAs in combination with three London dispersion (LD) correction schemes. Further, DFT-based composite methods, MP2, and a few semiempirical quantum chemical methods are evaluated. Consistent with the results for the MOR41 closed-shell benchmark, we find that the ordering of DFAs according to Jacob's ladder is preserved and that adding an LD correction is crucial, clearly improving almost all tested methods. The recently introduced r²SCAN-3c composite method stands out with a remarkable mean absolute deviation (MAD) of only 2.9 kcal mol^-1, which is surpassed only by hybrid DFAs with low amounts of Fock exchange (e.g., 2.3 kcal mol^-1 for TPSS0-D4/def2-QZVPP) and double-hybrid (DH) DFAs but at a significantly higher computational cost. The lowest MAD of only 1.6 kcal mol^-1 is obtained with the DH DFA PWPB95-D4 in the def2-QZVPP basis set approaching the estimated accuracy of the reference method. Overall, the ROST61 set adds important reference data to a sparsely sampled but practically relevant area of chemistry. At this point, it provides valuable orientation for the application and development of new DFAs and electronic structure methods in general.

Mild Open-Shell Character of BODIPY and Its Impact on Singlet and Triplet Excitation Energies

This study describes and rationalizes the electronic structure of BODIPY combining a large variety of quantum chemistry methods and computational tools. Examination of the obtained results using state-of-the-art electronic structure analyses provides a new and complete interpretation of the nature of low-lying electronic states in BODIPY and elucidates the limitations of excited-state methods in the computation of T₁ and S₁ energies, that is, systematic under- and overestimation of time-dependent density functional theory energies, respectively, and a large overestimation of the T₁/S₁ energy gap. Our analysis identifies the important role and physical origin of the mild open-shell character in the BODIPY ground state, that is, strong highest occupied and lowest unoccupied molecular orbital exchange interactions. The study provides guidelines for the accurate quantification of the T₁/S₁ gap, which is extremely relevant for the computational investigation of the photophysical properties of BODIPY and its derivatives. These conclusions should be taken into consideration in order to predict and interpret conspicuous photoactivated phenomena such as intersystem crossing, singlet fission, and triplet-triplet annihilation. Moreover, we believe that our study might provide new ideas and strategies for the analysis of other molecular chromophores.

Modern multireference methods and their application in transition metal chemistry

Transition metal chemistry is a challenging playground for quantum chemical methods owing to the simultaneous presence of static and dynamic electron correlation effects in many systems. Wavefunction based multireference (MR) methods constitute a physically sound and systematically improvable Ansatz to deal with this complexity but suffer from some conceptual difficulties and high computational costs. The latter problem partially arises from the unfavorable scaling of the Full Configuration Interaction (Full-CI) problem which in the majority of MR methods is solved for a subset of the molecular orbital space, the so-called active space. In the last years multiple methods such as modern variants of selected CI, Full-CI Quantum Monte Carlo (FCIQMC) and the density matrix renormalization group (DMRG) have been developed that solve the Full-CI problem approximately for a fraction of the computational cost required by conventional techniques thereby significantly extending the range of applicability of modern MR methods. This perspective review outlines recent advancements in the field of MR electronic structure methods together with the resulting chances and challenges for theoretical studies in the field of transition metal chemistry. In light of its emerging importance a special focus is put on the selection of adequate active spaces and the concomitant development of numerous selection aides in recent years.

Adsorption of lindane (γ-hexachlorocyclohexane) on nickel modified graphitic carbon nitride: a theoretical study

Adsorption of lindane (HCH) on nickel modified graphitic carbon nitride (Ni-gCN) was investigated using a novel, accurate and broadly parametrized self-consistent tight-binding quantum chemical (GFN2-xTB) method. Two graphitic carbon nitride (gCN) models were used: corrugated and planar, which represent the material with different thicknesses. Electronic properties of the adsorbates and adsorbent were estimated via vertical ionization potential, vertical electron affinity, global electrophilicity index and the HOMO and LUMO. Adsorption energy and population analyses were carried out to figure out the nature of the adsorption process. The results reveal that the introduction of the nickel atom significantly influences the electronic properties of gCN, and results in the improvement of adsorption ability of gCN for lindane. Lindane adsorption on Ni-gCN is considered as chemisorption, which is primarily supported by the interaction of the nickel atom and chlorine atoms of HCH. The effect of solvents (water, ethanol, acetonitrile) was investigated via the analytical linearized Poisson-Boltzmann model. Due to the strong chemisorption, Ni-gCN can collect lindane from different solvents. The adsorption configurations of HCH on Ni-gCN were also shown to be thermally stable at 298 K, 323 K, 373 K, 473 K, and 573 K via molecular simulation calculations. The obtained results are useful for a better understanding of lindane adsorption on Ni-gCN and for the design of materials with high efficiency for lindane treatment based on adsorption-photocatalytic technology.

Quantum Chemistry Calculations for Metabolomics

A primary goal of metabolomics studies is to fully characterize the small-molecule composition of complex biological and environmental samples. However, despite advances in analytical technologies over the past two decades, the majority of small molecules in complex samples are not readily identifiable due to the immense structural and chemical diversity present within the metabolome. Current gold-standard identification methods rely on reference libraries built using authentic chemical materials ("standards"), which are not available for most molecules. Computational quantum chemistry methods, which can be used to calculate chemical properties that are then measured by analytical platforms, offer an alternative route for building reference libraries, i.e., in silico libraries for "standards-free" identification. In this review, we cover the major roadblocks currently facing metabolomics and discuss applications where quantum chemistry calculations offer a solution. Several successful examples for nuclear magnetic resonance spectroscopy, ion mobility spectrometry, infrared spectroscopy, and mass spectrometry methods are reviewed. Finally, we consider current best practices, sources of error, and provide an outlook for quantum chemistry calculations in metabolomics studies. We expect this review will inspire researchers in the field of small-molecule identification to accelerate adoption of in silico methods for generation of reference libraries and to add quantum chemistry calculations as another tool at their disposal to characterize complex samples.

Multidimensional Lewis Acidity: A Consistent Data Set of Chloride, Hydride, Methide, Water and Ammonia Affinities for 183 p-Block Element Lewis Acids

The computed fluoride ion affinity (FIA) is a widely applied descriptor to gauge Lewis acidity. Like every other single-parameter Lewis acidity scale, the FIA metric suffers from the one-dimensionality, that prohibits addressing Lewis acidity by the multidimensionality it inherently requires (i. e., reference Lewis base dependency). However, a systematic screening of computed affinities other than the FIA is much less developed. Herein, we extended our CCSD(T)/CBS benchmark of different density functionals and the DLPNO-CCSD(T) method for chloride (CIA), methide (MIA), hydride (HIA), water (WA), and ammonia (AA) affinities. The best performing methods are subsequently applied to yield nearly 800 affinities for 183 p-block element compounds of group 13-16 with an estimated accuracy of <10 kJ mol-1 . The study's output serves as a consistent library for qualitative analyses and a training set for future statistical approaches. A first holistic correlation analysis underscores the need for a multidimensional description of Lewis acidity.

Whether planar or corrugated graphitic carbon nitride combined with titanium dioxide exhibits better photocatalytic performance?

The density functional theory method was performed to study the electronic structures of planar (pGN), corrugated (cGN) graphitic carbon nitride and their interactions with titanium dioxide cluster (TiO₂)₇. The transfer of photoinduced electrons was analyzed and electronic excitations were calculated. The obtained results show that cGN is thermodynamically more stable than pGN. cGN chemically interacts with titanium dioxide clusters, while the interaction between pGN and the cluster is assigned to physical nature. The combination of cGN and pGN with (TiO₂)₇ reduces the energy of the first excited states compared to that of the pure substances. The photocatalytic activities were estimated based on hypotheses on the location of the reduction and oxidation sites, the distance between the photoinduced holes and electrons and the electron density of molecular orbitals involved in the excitation. cGN/TiO₂ is predicted to have a higher photocatalytic activity than pGN/TiO₂.

Dynamic Covalent Properties of a Novel Indolo[3,2-b]carbazole Diradical

This work describes the synthesis and properties of a dicyanomethylene-substituted indolo[3,2-b]carbazole diradical ICz-CN. This quinoidal system dimerises almost completely to (ICz-CN)₂ , which contains two long C(sp³ )-C(sp³ ) σ-bonds between the dicyanomethylene units. The minor open-shell ICz-CN component in the solid-state mixture was identified by EPR spectroscopy. Cyclic voltammetry and UV-visible spectroelectrochemical data, as well as comparison with reference monomer ICz-Br reveal that the nature of the one-electron oxidation of (ICz-CN)₂ at ambient temperature and ICz-CN at elevated temperature is very similar in all these compounds due to the prevailing localization of their HOMO on the ICz backbone. The peculiar cathodic behaviour reflects the co-existence of (ICz-CN)₂ and ICz-CN. The involvement of the dicyanomethylene groups stabilizes the close-lying LUMO and LUMO+1 of (ICz-CN)₂ and especially ICz-CN compared to ICz-Br, resulting in a distinctive cathodic response at low overpotentials. Differently from neutral ICz-CN, its radical anion and dianion are remarkably stable under ambient conditions. The UV/Vis(-NIR) electronic transitions in parent (ICz-CN)₂ and ICz-CN and their different redox forms have been assigned convincingly with the aid of TD-DFT calculations. The σ-bond in neutral (ICz-CN)₂ is cleaved in solution and in the solid-state upon soft external stimuli (temperature, pressure), showing a strong chromism from light yellow to blue-green. Notably, in the solid state, the monomeric diradical species is predominantly formed under high hydrostatic pressure (>1 GPa).

Unconventional singlet fission materials

Singlet fission (SF) is a photophysical downconversion pathway, in which a singlet excitation transforms into two triplet excited states. As such, it constitutes an exciton multiplication generation process, which is currently at the focal point for future integration into solar energy conversion devices. Beyond this, various other exciting applications were proposed, including quantum cryptography or organic light emitting diodes. Also, the mechanistic understanding evolved rapidly during the last year. Unfortunately, the number of suitable SF-chromophores is still limited. This is per se problematic, considering the wide range of envisaged applicability. With that in mind, we emphasize uncommon SF-scaffolds and outline requirements as well as strategies to expand the chromophore pool of SF-materials.

Theoretical study on conformational energies of transition metal complexes

Conformational energies are an important chemical property for which a performance assessment of theoretical methods is mandatory. Existing benchmark sets are often limited to biochemical or main group element containing molecules, while organometallic systems are generally less studied. A key problem herein is to routinely generate conformers for these molecules due to their complexity and manifold of possible coordination patterns. In this study we used our recently published CREST protocol [Pracht et al., Phys. Chem. Chem. Phys., 2020, 22, 7169-7192] to generate conformer ensembles for a variety of 40 challenging transition metal containing molecules, which were then used to form a comprehensive conformational energy benchmark set termed TMCONF40. Several low-cost semiempirical, density functional theory (DFT) and force-field methods were compared to high level DLPNO-CCSD(T1) and double-hybrid DFT reference values. Close attention was paid to the energetic ordering of the conformers in the statistical evaluation. With respect to the double-hybrid references, both tested low-cost composite DFT methods produce high Pearson correlation coefficients of rp,mean,B97-3c//B97-3c = 0.922 and rp,mean,PBEh-3c//B97-3c = 0.890, with mean absolute deviations close to or below 1 kcal mol-1. This good performance also holds for a comparison to DLPNO-CCSD(T1) reference energies for a smaller subset termed TMCONF5. Based on DFT geometries, the GFNn-xTB methods yield reasonable Pearson correlation coefficients of rp,mean,GFN1-xTB//B97-3c = 0.617 (MADmean = 2.15 kcal mol-1) and rp,mean,GFN2-xTB//B97-3c = 0.567 (MADmean = 2.68 kcal mol-1), outperforming the widely used PMx methods on the TMCONF40 test set. Employing the low-cost composite DFT method B97-3c on GFN2-xTB geometries yields an slightly improved correlation of rp,mean,B97-3c//GFN2-xTB = 0.632. Furthermore, for 68% of the investigated complexes at least one low-energy conformer was found that is more stable than the respective crystal structure conformation, which signals the importance of conformational studies. General recommendations for the application of the CREST protocol and DFT methods for transition metal conformational energies are given.

Comparison of Methods for Active Orbital Selection in Multiconfigurational Calculations

Several methods of constructing the active orbital space for multiconfigurational wave functions are compared on typical moderately strongly or strongly correlated ground-state molecules. The relative merits of these methods and problems inherent in multiconfigurational calculations are discussed. Strong correlation in the ground electronic state is found typically in larger conjugated and in antiaromatic systems, transition states which involve bond breaking or formation, and transition metal complexes. Our examples include polyenes, polyacenes, the reactant, product and transition state of the Bergman cyclization, and two transition metal complexes: Hieber's anion [(CO)3FeNO]- and ferrocene. For the systems investigated, the simplest and oldest selection method, based on the fractional occupancy of unrestricted Hartree-Fock natural orbitals (the UNO criterion), yields the same active space as much more expensive approximate full CI methods. A disadvantage of this method used to be the difficulty of finding broken spin symmetry UHF solutions. However, our analytical method, accurate to fourth order in the orbital rotation angles (Tóth and Pulay J. Chem. Phys. 2016, 145, 164102.), has solved this problem. Two further advantages of the UNO criterion are that, unlike most other methods, it measures not only the energetic proximity to the Fermi level but also the magnitude of the exchange interaction with strongly occupied orbitals and therefore allows the estimation of the correlation strength for orbital selection in Restricted Active Space methods.