Multiconfigurational Self-Consistent Field Calculations of the Magnetically Induced Current Density Using Gauge-Including Atomic Orbitals

On the aromaticity of actinide compounds

The chemistry of actinides has flourished since the late 2010s with the synthesis of new actinide complexes and clusters. On the theoretical side, a range of tools is available for the characterization of these heavy element-containing compounds, but discrepancies in the assessment of aromaticity using different tools have led to controversies. In this Perspective, we examine the origin of controversies relating to the aromaticity of metallic compounds, with a focus on actinides. The aromaticity of actinides is important, not because these molecules are numerous or have a special role in catalysis or reactivity, but because this topic pushes theories of aromaticity to their limits. Owing to its reference independence, the magnetic criterion of aromaticity has been the most popular choice for the characterization of the aromaticity of metallic compounds, including actinide compounds. Through examination of several case studies, we show why this criterion might be misleading for metallic species and explain how findings relating to actinide compounds could reshape theories of aromaticity, not just for actinides but perhaps also for well-known hydrocarbons.

Magnetic Antiaromaticity─Paratropicity─Does Not Necessarily Imply Instability

Magnetically induced ring currents are a conventional tool for the characterization of aromaticity. Dia- and paratropic currents are thought to be associated with stabilization (aromaticity) and destabilization (antiaromaticity), respectively. In the present work, I have questioned the validity of the paratropic currents as a measure of antiaromaticity among monocyclic hydrocarbons. I have shown that while reduced/oxidized radical ions of hydrocarbons sustain strong paratropic currents, they often gain extra stabilization via cyclic conjugation compared to their acyclic counterparts.

Excited-State (Anti)Aromaticity Explains Why Azulene Disobeys Kasha's Rule

Fluorescence exclusively occurs from the lowest excited state of a given multiplicity according to Kasha's rule. However, this rule is not obeyed by a handful of anti-Kasha fluorophores whose underlying mechanism is still understood merely on a phenomenological basis. This lack of understanding prevents the rational design and property-tuning of anti-Kasha fluorophores. Here, we propose a model explaining the photophysical properties of an archetypal anti-Kasha fluorophore, azulene, based on its ground- and excited-state (anti)aromaticity. We derived our model from a detailed analysis of the electronic structure of the ground singlet, first excited triplet, and quintet states and of the first and second excited singlet states using the perturbational molecular orbital theory and quantum-chemical aromaticity indices. Our model reveals that the anti-Kasha properties of azulene and its derivatives result from (i) the contrasting (anti)aromaticity of its first and second singlet excited states (S1 and S2, respectively) and (ii) an easily accessible antiaromaticity relief pathway of the S1 state. This explanation of the fundamental cause of anti-Kasha behavior may pave the way for new classes of anti-Kasha fluorophores and materials with long-lived, high-energy excited states.

How Different are the Diamagnetic and Paramagnetic Contributions to Off-Nucleus Shielding in Aromatic and Antiaromatic Rings?

The spatial variations in the diamagnetic and paramagnetic contributions to the off-nucleus isotropic shielding, σ i s o r = σ i s o d r + σ i s o p r ${\ {{\sigma }_{{\rm i}{\rm s}{\rm o}}\left({\bf r}\right)=\ \sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm d}}\left({\bf r}\right)+{\sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm p}}\left({\bf r}\right)}$ , and to the zz component of the off-nucleus shielding tensor, σ z z r = σ z z d r + σ z z p r ${{{\sigma }_{zz}\left({\bf r}\right)=\sigma }_{zz}^{{\rm d}}\left({\bf r}\right)+{\sigma }_{zz}^{{\rm p}}\left({\bf r}\right)}$ , around benzene (C₆ H₆ ) and cyclobutadiene (C₄ H₄ ) are investigated using complete-active-space self-consistent field wavefunctions. Despite the substantial differences between σ i s o r ${{\sigma }_{{\rm i}{\rm s}{\rm o}}\left({\bf r}\right)}$ and σ z z r ${{\sigma }_{zz}\left({\bf r}\right)}$ around the aromatic C₆ H₆ and the antiaromatic C₄ H₄ , the diamagnetic and paramagnetic contributions to these quantities, σ i s o d r ${{\sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm d}}\left({\bf r}\right)}$ and σ z z d r ${{\sigma }_{zz}^{{\rm d}}\left({\bf r}\right)}$ , and σ i s o p r ${{\sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm p}}\left({\bf r}\right)}$ and σ z z P r ${{\sigma }_{zz}^{{\rm P}}\left({\bf r}\right)}$ , are found to behave similarly in the two molecules, shielding and deshielding, respectively, each ring and its surroundings. The different signs of the most popular aromaticity criterion, the nucleus-independent chemical shift (NICS), in C₆ H₆ and C₄ H₄ are shown to follow from a change in the balance between the respective diamagnetic and paramagnetic contributions. Thus, the different NICS values for antiaromatic and antiaromatic molecules cannot be attributed to differences in the ease of access to excited states only; differences in the electron density, which determines the overall bonding picture, also play an important role.

Magnetic Aromaticity of Cycloporphyrin Nanorings

The ascertainment of magnetic aromaticity is not necessarily straightforward, especially for large and bent systems, such as the cycloporphyrin nanorings recently synthesized by the group of Anderson. Six of these cycloporphyrin nanorings were studied here computationally. Indirect methods, based on nuclear shielding and magnetizabilities, and direct methods, based on standard quantum mechanics, were both used effectively to determine their magnetically induced current strength, which mostly confirmed Anderson’s classification. However, in the case of hexanions, and in particular for cyclohexaporphyrin hexacations, a significant cancellation of delocalized diatropic and paratropic flow occurred, showing that the resultant faint aromatic character was a result of competing aromatic and antiaromatic contributions, as also evidenced by the ipsocentric method. A warning is renewed on the use of isotropic shielding to determine the tropicity of the magnetically induced current.

Unraveling the stability of cyclobutadiene complexes using aromaticity markers

Cyclobutadiene (CBD) is the paradigmatic antiaromatic molecule but is known to form highly stable aromatic complexes, e.g. CBD-Fe(CO)3. This intriguing reversal of aromaticity from antiaromatic to aromatic terrain during the complexation process cannot be appropriately handled with single-reference-based theoretical techniques. We explore this aromaticity reversal, for the first time, by a detailed aromaticity analysis using magnetically induced current densities (MICD) and nucleus independent chemical shifts (NICS) using genuine ab initio multi-reference wavefunction-based theory. We trace the dramatic change of aromaticity for a prototypical cyclobutadiene complex, CBD-CH+ (CH+Fe(CO)3), considering a 3D potential energy surface for two independent parameters, namely the approach of CH+ and the automerization cross-section of cyclobutadiene. The 3D potential energy surfaces indicate the presence of a conical intersection/avoided crossing between the ground and the first excited state. The plot of aromaticity indices and the corresponding numerical values show that the change of aromaticity indices is drastic around the conical intersection/avoided crossing and automerization of cyclobutadiene plays a crucial role in the formation of cyclobutadiene complexes. Computations on analogous CBD-Be and CBD-CO systems (Be/COFe(CO)3) emphasize the generality of the conclusions drawn from the CBD-CH+ system.

Visualisation of Chemical Shielding Tensors (VIST) to Elucidate Aromaticity and Antiaromaticity

Aromaticity is a central concept in chemistry, pervading areas from biochemistry to materials science. Recently, chemists also started to exploit intricate phenomena such as the interplay of local and global (anti)aromaticity or aromaticity in non-planar systems and three dimensions. These phenomena pose new challenges in terms of our fundamental understanding and the practical visualisation of aromaticity. To overcome these challenges, a method for the visualisation of chemical shielding tensors (VIST) is developed here that allows for a 3D visualisation with quantitative information about the local variations and anisotropy of the chemical shielding. After exemplifying the method in different planar hydrocarbons, we study two non-planar macrocycles to show the unique benefits of the VIST method for molecules with competing π-conjugated systems and conclude with a norcorrole dimer showing clear evidence of through-space aromaticity. We believe that the VIST method will be a highly valuable addition to the computational toolbox.

Exploitation of Baird Aromaticity and Clar’s Rule for Tuning the Triplet Energies of Polycyclic Aromatic Hydrocarbons

Polycyclic aromatic hydrocarbons (PAH) are a prominent substance class with a variety of applications in molecular materials science. Their electronic properties crucially depend on the bond topology in ways that are often highly non-intuitive. Here, we study, using density functional theory, the triplet states of four biphenylene-derived PAHs finding dramatically different triplet excitation energies for closely related isomeric structures. These differences are rationalised using a qualitative description of Clar sextets and Baird quartets, quantified in terms of nucleus independent chemical shifts, and represented graphically through a recently developed method for visualising chemical shielding tensors (VIST). The results are further interpreted in terms of a 2D rigid rotor model of aromaticity and through an analysis of the natural transition orbitals involved in the triplet excited states showing good consistency between the different viewpoints. We believe that this work constitutes an important step in consolidating these varying viewpoints of electronically excited states.

Norcorrole: Aromaticity and Antiaromaticity in Contest

Magnetic shielding studies demonstrate that nickel norcorrole (NiNc) and norcorrole (H₂Nc) provide unusual examples of stable molecules with high antagonistic levels of antiaromaticity and aromaticity: Both incorporate an antiaromatic "core", a 14-membered cyclic conjugated subsystem with 16 π electrons, surrounded by an aromatic "halo" in the form of a ring of either 14 atoms and 14 π electrons with a new type of homoconjugation (NiNc), or 18 atoms with 18 π electrons (H₂Nc).

Understanding the Role of Aromaticity and Conformational Changes in Bond Dissociation Processes of Photo-Protecting Groups

Photoremovable protecting groups (PPGs) provide spatial and temporal control over the release of various chemicals. Using surface hopping studies with multireference electronic structure methods we have unravelled the nuclear and the electronic events at play. Furthermore, the electronic changes along the reaction path were probed using excited state aromaticity quantifiers and orbital analysis. We find that upon irradiation with light of appropriate wavelength on the substituted coumarin system a π-π* electronic excitation occurs which is followed by an electron loss from the aromatic ring on gaining proper alignment between the π* and the C-LG (LG = leaving group) σ*. This alignment is brought about by a critical dihedral angle change in the molecule, which subsequently triggers C-LG bond cleavage. The sequence of events is indicative of an intramolecular electron catalyzed process which is established through investigations of changes in aromaticity of the phenyl ring which acts as an electron reservoir.

Design of annulene-within-an-annulene systems by the altanisation approach. A study of altan-[n]annulenes

Computations on neutral and charged [n]annulenes confirm the general effectiveness of altanisation to design paratropic perimeter circulations. An extension of the design strategy is required for open-shell singlet species.

Main-Group-Element Isophlorin Complexes Revisited: The Question of a Subvalent Central Atom

A careful density functional theory reexamination of the geometric and electronic structures of reduced main-group porphyrin complexes E(Por)L₂ (E = Si or Ge; L = pyridine or tetrahydrofuran), B₂(Por), and C₂(Por) has confirmed these as pure isophlorin derivatives with normal-valent coordinated central atoms. Only axially unligated Ge(Por) and the dications [B₂(Por)]²⁺ and [C₂(Por)]²⁺ feature aromatic porphyrin ligands. The calculations faithfully reproduce the strong bond-length alternation along the outer rim of the macrocycle in the reduced complexes, consistent with antiaromatic character, as well as much stronger ruffling in the reduced group 14 complexes relative to their nonreduced counterparts such as E(Por)X₂ (E = Si or Ge; X = F or Cl). The latter is thought to reflect the lower barrier to nonplanar deformation for the antiaromatic systems. In addition, unlike B₂(Por) and its dication, which are planar, C₂(Por) and its dication are predicted to be strongly ruffled, reflecting the smaller size of the central C₂ unit. The calculations also predict characteristically low ionization potentials and singlet-triplet gaps for the antiaromatic complexes. A brief exploratory study of the as-yet-unknown group 15 complexes E(TPP)(Ph)(py), where E = P and As, also indicated an antiaromatic isophlorin macrocycle coordinated to a pentavalent group 15 center.

Deciphering the cryptic role of a catalytic electron in a photochemical bond dissociation using excited state aromaticity markers

Upon photoexcitation of 5-phenyltetrazole, an electron is injected from the phenyl ring to the tetrazole ring, which performs a catalytic role in the photolytic dissociation of N₂. The footprints of the “mercenary” electron are captured via dramatic changes in excited state aromaticity of the associated rings.

Analysis of the magnetically induced current density of molecules consisting of annelated aromatic and antiaromatic hydrocarbon rings

The aromatic pathway of molecules with annelated aromatic and antiaromatic rings has been studied by calculating magnetically induced current densities.

A Serendipitous Rendezvous with a Four-Center Two-Electron Bonded Intermediate in the Aerial Oxidation of Hydrazine

Oxidation by dioxygen has a rich repertoire of mechanistic intricacies. Herein, we report a hitherto unknown paradigm of dioxygen activation reaction which propagates through a four center two electron (4c-2e) bound species. Using static DFT and ab initio quantum chemical techniques we have unraveled the oxidation pathway for hydrazine and its methylated analogues by dioxygen which involves formation of this unconventional 4c-2e bonded species en route to the oxidation products. Inconvertible evidence in favor of such an unprecedented dioxygen activation route is provided by capturing the events of formation of the 4c-2e species in aqueous phase for hydrazine and its congeners and the experimentally observed products from the respective 4c-2e species, like H2O2 and N2H2 , diazene in the case of hydrazine using Car-Parrinello molecular dynamics simulations.

Revisiting Aromaticity and Chemical Bonding of Fluorinated Benzene Derivatives

The electron delocalization of benzene (C6H6) and hexafluorobenzene (C6F6) was analyzed in terms of the induced magnetic field, nucleus-independent chemical shift (NICS), and ring current strength (RCS). The computed out-of-plane component of the induced magnetic field at a distance (r) greater than or equal to 1.0 Å above the ring center correlates well (R (2)>0.99) with the RCS value. According to these criteria, fluorination has two effects on the C6 skeleton; concomitantly, the resonant effects diminish the π electron delocalization and the inductive effects decrease the charge density at the ring center and therefore reduce the magnitude of the paratropic current generated in this region. The equilibrium between both effects decreases aromaticity in the fluorinated benzene derivatives. These results can be extrapolated to determine the aromaticity of any derivative within the series of fluorinated benzene derivatives (C6H(6-n)F n , where n=1-5).

On the diatropic perimeter of iterated altan-molecules

Ab initio calculations confirm that the design of large paratropic circuits through altanisation fails in altan-[10,5]coronene. This molecule is predicted to be an open-shell singlet biradical, like the cycloacene that it contains.

How does relativity affect magnetically induced currents?

Relativity contributes via induced spin-density to magnetically induced currents (j_B) in closed-shell systems and in general enhances curvature in j_B.

Theoretical and experimental investigations on mono-substituted and multi-substituted functional polyhedral oligomeric silsesquioxanes

Theoretical and experimental investigations on substituted functional polyhedral oligomeric silsesquioxanes.