Calculations of current densities and aromatic pathways in cyclic porphyrin and isoporphyrin arrays

Tetraquinolines; four linked quinoline units or porphyrinoids

Tetraquinolines (TEQs) have been recently synthesized and proposed to be a new member of the porphyrinoid family with highly distorted, nonplanar, geometries. In this contribution by studying several molecules, closely related to TEQs, we have suggested that the origin of the nonplanarity of TEQs and their counterparts is a combination of steric strain and the propensity of the molecules to avoid antiaromaticity. The tendency of TEQs to coordinate with doubly charged metal ions can be interpreted in terms of their transition from potential antiaromaticity to nonaromaticity. Even metal-coordinated TEQs do not sustain diatropic ring currents. Although full planarization is not possible because of steric strain, doubly oxidized TEQs and their counterparts sustain moderate global diatropic ring currents and partially planarize. The nature of current density in the molecules is studied in the light of Steiner-Fowler selection rules.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

φ-Aromaticity in prismatic {Bi6}-based clusters

The occurrence of aromaticity in organic molecules is widely accepted, but its occurrence in purely metallic systems is less widespread. Molecules comprising only metal atoms (M) are known to be able to exhibit aromatic behaviour, sustaining ring currents inside an external magnetic field along M-M connection axes (σ-aromaticity) or above and below the plane (π-aromaticity) for cyclic or cage-type compounds. However, all-metal compounds provide an extension of the electrons' mobility also in other directions. Here, we show that regular {Bi₆} prisms exhibit a non-localizable molecular orbital of f-type symmetry and generate a strong ring current that leads to a behaviour referred to as φ-aromaticity. The experimentally observed heterometallic cluster [{CpRu}₃Bi₆]^-, based on a regular prismatic {Bi₆} unit, displays aromatic behaviour; according to quantum chemical calculations, the corresponding hypothetical Bi₆^2- prism shows a similar behaviour. By contrast, [{(cod)Ir}₃Bi₆] features a distorted Bi₆ moiety that inhibits φ-aromaticity.

Magnetically Induced Current Densities in Zinc Porphyrin Nanoshells

The molecular structures of porphyrinoid cages were obtained by constructing small polyhedral graphs whose vertices have degree-4. The initial structures were then fully optimized at the density functional theory (DFT) level using the generalized gradient approximation. Some of polyhedral vertices were replaced with Zn-porphyrin units and their edges were replaced with ethyne or butadiyne bridges or connected by fusing two neighboring Zn-porphyrin units. Molecule 1 is an ethyne-bridge porphyrinoid nanotube, whose ends are sealed with a Zn-porphyrin. Molecule 2 is the corresponding open porphyrinoid nanotube. Molecule 3 is a clam-like porphyrinoid cage, whose shells consist of fused Zn-porphyrins, and the two halves are connected via butadiyne bridges. Molecule 4 is a cross-belt of fused Zn-porphyrins, and molecule 5 is a cross-belt of Zn-porphyrins connected with butadiyne bridges. The magnetically induced current density of the optimized porphyrinoid cages was calculated for determining the aromatic character, the degree of aromaticity and the current-density pathways. The current-density calculations were performed at the DFT level with the gauge─including magnetically induced currents (GIMIC) method using the B3LYP hybrid functional and def2-SVP basis sets. Calculations of the current densities show that molecule 2 sustains a paratropic ring current around the nanotube, whereas sealing the ends as in molecule 1 leads to an almost nonaromatic nanotube. Fusing porphyrinoids as in molecules 3 and 4 results in complicated current-density pathways that differ from the ones usually appearing in porphyrinoids. The aromatic character of molecules 4 and 5 changes upon oxidation. The neutral molecule 4 is antiaromatic, whereas the dication is nonaromatic. Molecule 5 is nonaromatic, and its dication is aromatic.

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.

Zinc- and Cadmium meso-Aryl-Isoporphyrins: Non-Aromatic NIR Dyes with Distinct Conformational Features

A series of pyrrolyl and dipyrrinyl isoporphyrins carrying different phenyl and thienyl groups is reported. The compounds are obtained by a one-pot approach in the presence of a template reagent. Thienyl derivatives gave better yields, and were the only subclass to form with steric hindrance. The structural analyses carried out on compounds 1 and 14 revealed distinct conformational differences which are likely to result from an intramolecular NH… Cl hydrogen bridge of the pyrrolyl subclass. In addition, this hydrogen bridge strongly favors one of the two possible atropisomers. Hindered rotation of the meso-aryl groups is observed only in the cases of methylbenzothienyl derivatives 10 and 15 and leads to the observation of several diastereomers. NIR absorptions up to 923 nm are found throughout. Electrochemical investigations into the 1e- and 2e- reduced species unravel axial ligand exchange dynamics for the zinc isoporphyrin radical, and the probable formation of a zinc phlorinate.

Substantial π-aromaticity in the anionic heavy-metal cluster [Th@Bi12]4

The concept of aromaticity was originally defined as a property of unsaturated, cyclic planar organic molecules like benzene, which gain stability by the inherent delocalization of 4n + 2 π-electrons over the ring atoms. Since then, π-aromaticity has been observed for a large variety of organic and inorganic non-metal compounds, yet, for molecules consisting only of metal atoms, it has remained restricted to systems with three to five atoms. Here, we present the straightforward synthesis of a metal 12-ring that exhibits 2π-aromaticity and has a ring current much stronger than that of benzene (6π) and equivalent to that of porphine (26π), despite these organic molecules having (much) larger numbers of π-electrons. Highly reducing reaction conditions allowed access to the heterometallic anion [Th@Bi₁₂]^4-, with interstitial Th⁴⁺ stabilizing a Bi₁₂^8- moiety. Our results show that it is possible to design and generate substantial π-aromaticity in large metal rings, and we hope that such π-aromatic heavy-metal cycles will eventually find use in cluster-based reactions.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Anisotropy of the vorticity tensor as a magnetic indicator of aromaticity

The vorticity vector of the current density J^B, induced in the electron cloud of a molecule by a magnetic field B, is defined by V^B = ∇ × J^B.

Frequency-dependent current density tensors as density functions of dynamic polarizabilities

Relationships accounting for contributions to the first-order charge density ρ⁽¹⁾ and current density J⁽¹⁾, induced in the electrons of a molecule by a monochromatic plane wave, have been obtained via time-dependent quantum mechanical perturbation theory. Their gauge invariance and invariance in passive translations of the coordinate system have been demonstrated (i) within the (long wavelengths) electric dipole approximation, in which only the electric field contributions to these densities are required, and (ii) within the electric quadrupole approximation, in which nonseparable terms provided by the magnetic field and by the electric field gradient, assumed uniform over the molecular domain, are needed. It is shown that the physical meaning of current density tensors depending on the frequency ω of the monochromatic wave shone on the molecule, and corresponding to derivatives of the current density J⁽¹⁾(r, ω) with respect to components of the perturbing fields, is that of property density. Therefore, frequency-dependent current density tensors can be interpreted as the integrand function in 3d-space integrals defining dynamic molecular response tensors, e.g., electric dipole, mixed electric dipole-magnetic dipole, and electric dipole-quadrupole polarizabilites. Plots of current density tensors are expected to provide important information on the molecular domains giving dominant contributions to these properties.

Local versus global aromaticity in azuliporphyrin and benziporphyrin derivatives

Carbaporphyrinoids afford fascinating examples of competition between local and global aromaticity in conjugated, polycyclic systems. Thus, whereas density functional theory calculations reveal only a modest effect of metal complexation on the current density profiles of true carbaporphyrins and azuliporphyrins, the impact is much greater for benziporphyrins, underscoring a strong competition between local and global aromaticity in the latter system. Furthermore, the calculations shed light on the remarkable efficacy of suitably placed electron-donating substituents on the benzene ring in boosting the global diatropic currents in a metallobenziporphyrin.

Gauge invariance and origin independence of electronic charge density and current density induced by optical fields

Expressions for the first-order polarization charge density ρ ⁽¹⁾ and current density J ⁽¹⁾ induced in a molecule by a monochromatic plane wave, obtained by time-dependent quantum mechanical perturbation theory, have been investigated to assess their gauge invariance and independence of the coordinate system in passive and active translations. The conditions arrived at show that, within the (long wavelengths) dipole approximation, only the electric contributions to these densities are needed to rationalize the phenomenology. To the next higher quadrupole approximation, assuming that the magnetic field and the electric field gradient are uniform over the molecular dimensions, corresponding contributions to ρ ⁽¹⁾ and J ⁽¹⁾ are considered. It has been found that total densities are independent of the origin, whereas the contributions from electric and magnetic fields are not separately invariant. A magnetic contribution to J ⁽¹⁾, which is by itself origin independent, can be defined by means of an approach based on continuous translation of the origin of the coordinate system.

Isocorroles as Homoaromatic NIR-Absorbing Chromophores: A First Quantum Chemical Study

Density functional theory calculations of magnetically induced current densities have revealed high diatropic ring currents in unsubstituted isocorrole consistent with homoaromatic character. An examination of the Kohn-Sham molecular orbitals showed clear evidence of homoconjugative interactions in four occupied π-type molecular orbitals as well as in the LUMO. Remarkably, substituents at the saturated meso position were found to exert a dramatic influence on the overall current density pattern. Thus, whereas bis(trimethylsilyl)-substitution strongly enhanced the peripheral diatropic current (consistent with enhanced homoaromaticity), difluoro-substitution engendered a strong, net paratropic current (consistent with antihomoaromaticity). In this respect, isocorroles stand in sharp contrast to benzenoid aromatics, for which substituents typically exert a small influence on the current density distribution.

New electron delocalization tools to describe the aromaticity in porphyrinoids

There are several possible pathways in the macrocycle of large porphyrinoids and, among aromaticity indices, only AV_minis capable of recognizing the most aromatic one.