How Aromatic Are Molecular Nanorings? The Case of a Six-Porphyrin Nanoring*

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.

Open shell (4n + 2)π and closed shell 4nπ planar core-modified decaphyrins

Planar 44π and 46π core-modified decaphyrins with ten thiophene units have been synthesized from short thiophene oligomers. They have been structurally characterized by single crystal X-ray diffraction with further support from spectroscopic analysis and quantum chemical calculations. Our analysis revealed diradicaloid characteristics for 46π species in contrast to the closed shell property of the 44π congener. Further, 44π and 46π undergo reversible two-electron chemical oxidation, as observed by spectro-electrochemical measurements.

Spurious Oscillations Caused by Density Functional Approximations: Who is to Blame? Exchange or Correlation?

We analyze the varying susceptibilities of different density functional approximations (DFAs) to present spurious oscillations on the profiles of several vibrational properties. Among other problems, these spurious oscillations cause significant errors in harmonic and anharmonic IR and Raman frequencies and intensities. This work hinges on a judicious strategy to dissect the exchange and correlation components of DFAs and pinpoint the origins of these oscillations. We identify spurious oscillations in derivatives of all energy components with respect to nuclear displacements, including those energy terms that do not involve numerical integrations. These indirect spurious oscillations are attributed to suboptimal electron densities resulting from a self-consistent field procedure using a DFA that exhibits direct spurious oscillations. Direct oscillations stem from inaccurate numerical integration of the exchange and correlation energy density functionals. A thorough analysis of direct spurious oscillations reveals that only a handful of exchange and correlation components are insensitive to spurious oscillations, giving rise to three families of functionals, BH&H, LSDA, and BLYP. Among the functionals in these families, we encounter four widespread DFAs: BLYP, B3LYP, LC-BLYP, and CAM-B3LYP. Certain DFAs like PBE appear less sensitive to spurious oscillations due to compensatory cancellations between their energy components. Additionally, we found non-negligible but small oscillations in PBE and TPSS, which could be safely employed provided a sufficiently large integration grid is used in the calculations. These findings hint at the key components of current approximations to be improved and emphasize the necessity to develop accurate DFAs suitable for studying molecular spectroscopies.

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.

Understanding Aromaticity in [5]Helicene-Bridged Cyclophanes: A Comprehensive Study

This study explores the aromaticity of doubly [5]helicene-bridged (1,4)cyclophane and triply [5]helicene-bridged (1,3,5)cyclophane via calculations of the magnetic response and of electronic aromaticity indices. The primary objective is to assess the π-electron delocalization to determine whether they sustain global ring currents associated with π aromaticity. The molecules show local ring currents in the presence of an external magnetic field. The ring currents flow diatropically in the stacked six-membered rings and in the helicene arms. However, these π currents are not interconnected due to the discontinuity of the π delocalization at the C-C single bonds connecting the central six-membered rings to the helicene arms. Electronic indices suggest that the helicene-arm systems have significantly smaller electron delocalization than benzene. The reduction in the delocalization does not compromise their ability to exhibit ring currents in the presence of an external magnetic field. The analysis provides further evidence that the magnetic criteria yield a different degree of aromaticity for the helicene arms than obtained in the calculation of the electronic aromaticity indices. However, both approaches confirm that the studied molecules are not globally aromatic.

Electronic delocalization in charged macrocycles is associated with global aromaticity

When oxidized, cycloparaphenylenes and porphyrin nanorings can exhibit macrocyclic ring currents which have been used to assign these molecules as (anti)aromatic. These assignments have been controversial because the presence of ring currents does not always imply cyclic electronic delocalization, which is essential to the definition of aromaticity. Here, we show that the emergence of macrocyclic ring currents in these molecules is correlated with increased electronic delocalization, supporting assignments of these molecules as (anti)aromatic.

Current-Density Calculations on Zn-Porphyrin40 Nanorings

Two porphyrinoid nanorings have been studied computationally. They were built by linking 40 Zn-porphyrin units with butadiyne bridges. The molecular structures belonging to the D40h point group were fully optimized with the Turbomole program at the density functional theory (DFT) level using the B3LYP functional and the def2-SVP basis sets. The aromatic character was studied at the DFT level by calculating the magnetically induced current-density (MICD) susceptibility using the GIMIC program. The neutral molecules are globally non-aromatic with aromatic Zn-porphyrin units. Charged nanorings could not be studied because almost degenerate frontier orbitals led to vanishing optical gaps for the cations. Since DFT calculations of the MICD are computationally expensive, we also calculated the MICD using three pseudo-π models. Appropriate pseudo-π models were constructed by removing the outer hydrogen atoms and replacing all carbon and nitrogen atoms with hydrogen atoms. The central Zn atom was either replaced with a beryllium atom or with two inner hydrogen atoms. Calculations with the computationally inexpensive pseudo-π models yielded qualitatively the same magnetic response as obtained in the all-electron calculations.

Tetra-tert-butyl-s-indacene is a Bond-Localized C2h Structure and a Challenge for Computational Chemistry

Whether tetra-tert-butyl-s-indacene is a symmetric D2h structure or a bond-alternating C2h structure remains a standing puzzle. Close agreement between experimental and computed proton chemical shifts based on minima structures optimized at the M06-2X, ωB97X-D, and M11 levels confirm a bond-localized C2h symmetry, which is consistent with the expected strong antiaromaticity of TtB-s-indacene.

Alternating behavior in furan-acetylene macrocycles reveals the size-dependency of Hückel's rule in neutral molecules

Aromaticity can be assigned by Hückel's rule, which predicts that planar rings with delocalized (4n + 2) π-electrons are aromatic, whereas those with 4n π-electrons are antiaromatic. However, for neutral rings, the maximal value of "n" to which Hückel's rule applies remains unknown. Large macrocycles exhibiting global ring current can serve as models for addressing this question, but the global ring current are often overshadowed in these molecules by the local ring current of the constituent units. Here, we present a series of furan-acetylene macrocycles, ranging from the pentamer to octamer, whose neutral states display alternating contributions from global aromatic and antiaromatic ring currents. We find that the odd-membered macrocycles display global aromatic characteristics, whereas the even-membered macrocycles display contributions from globally antiaromatic ring current. These factors are expressed electronically (oxidation potentials), optically (emission spectra), and magnetically (chemical shifts), and DFT calculations predict global ring current alternations up to 54 π-electrons.

An ultrasensitive solid-state ECL biosensor based on synergistic effect between Zn-NGQDs and porphyrin-based MOF as "on-off-on" platform

To develop an ultra-sensitive solid-state electrochemiluminescence (ECL) biosensor for detection of miRNA 24, three different forms of porphyrin metal-organic framework (MOF) nanomaterials with good biocompatibility were synthesized through small molecule ligand modulation. We investigated various properties of synthesized MOFs in the presence of different small molecule ligands. The as-obtained 2D MOF nanodisk exhibited high ECL intensity and outstanding stability in the presence of a co-reactant at low concentrations. We also synthesized zinc-based quantum dots (Zn-NGQDs) with excellent photovoltaic properties by doping zinc dithiothreitol (DTT-Zn) into quantum dots. Accordingly, an enzyme-free solid-state ECL biosensor for miRNA 24 based on the "on-off-on" signal conversion strategy was created. Dependent on the synergy between the luminophor 2D MOF and Zn-NGQDs, the biosensor achieves a wide linear range from 1.00 × 10^-16 to 1.00 × 10^-10 mol·L^-1 and an exceedingly low detection limit of 0.03 fM. Furthermore, the ECL biosensor exhibits outstanding selectivity, repeatability, and stability. The method has great potential for investigating sensitive detection models for various biomolecules and the design of highly efficient MOF luminescent materials.

Are Accelerated and Enhanced Wave Function Methods Accurate to Compute Static Linear and Nonlinear Optical Properties?

Key components of organic-based electro-optic devices are challenging to design or optimize because they exhibit nonlinear optical responses, which are difficult to model or rationalize. Computational chemistry furnishes the tools to investigate extensive collections of molecules in the quest for target compounds. Among the electronic structure methods that provide static nonlinear optical properties (SNLOPs), density functional approximations (DFAs) are often preferred because of their low cost/accuracy ratio. However, the accuracy of the SNLOPs critically depends on the amount of exact exchange and electron correlation included in the DFA, precluding the reliable calculation of many molecular systems. In this scenario, wave function methods such as MP2, CCSD, and CCSD(T) constitute a reliable alternative to compute SNLOPs. Unfortunately, the computational cost of these methods significantly restricts the size of molecules to study, a limitation that hampers the identification of molecules with significant nonlinear optical responses. This paper analyzes various flavors and alternatives to MP2, CCSD, and CCSD(T) methods that either drastically reduce the computational cost or improve their performance but were scarcely and unsystematically employed to compute SNLOPs. In particular, we have tested RI-MP2, RIJK-MP2, RIJCOSX-MP2 (with GridX2 and GridX4 setups), LMP2, SCS-MP2, SOS-MP2, DLPNO-MP2, LNO-CCSD, LNO-CCSD(T), DLPNO-CCSD, DLPNO-CCSD(T0), and DLPNO-CCSD(T1). Our results indicate that all these methods can be safely employed to calculate the dipole moment and the polarizability with average relative errors below 5% with respect to CCSD(T). On the other hand, the calculation of higher-order properties represents a challenge for LNO and DLPNO methods, which present severe numerical instabilities in computing the single-point field-dependent energies. RI-MP2, RIJK-MP2, or RIJCOSX-MP2 are cost-effective methods to compute first and second hyperpolarizabilities with a marginal average error with respect to canonical MP2 (up to 5% for β and up to 11% for γ). More accurate hyperpolarizabilities can be obtained with DLPNO-CCSD(T1); however, this method cannot be employed to obtain reliable second hyperpolarizabilities. These results open the way to obtain accurate nonlinear optical properties at a computational cost that can compete with current DFAs.

Organic-Inorganic Porphyrinoid Frameworks for Biomolecule Sensing

Porphyrinoids and their analogous compounds play an important role in biosensing applications on account of their unique and versatile catalytic, coordination, photophysical, and electrochemical properties. Their remarkable arrays of properties can be finely tuned by synthetically modifying the porphyrinoid ring and varying the various structural parameters such as peripheral functionalization, metal coordination, and covalent or physical conjugation with other organic or inorganic scaffolds such as nanoparticles, metal-organic frameworks, and polymers. Porphyrinoids and their organic-inorganic conjugates are not only used as responsive materials but also utilized for the immobilization and embedding of biomolecules for applications in wearable devices, fast sensing devices, and other functional materials. The present review delineates the impact of different porphyrinoid conjugates on their physicochemical properties and their specificity as biosensors in a range of applications. The newest porphyrinoid types and their synthesis, modification, and functionalization are presented along with their advantages and performance improvements.

Disentangling global and local ring currents

Magnetic field-induced ring currents in aromatic and antiaromatic molecules cause characteristic shielding and deshielding effects in the molecules' NMR spectra. However, it is difficult to analyze (anti)aromaticity directly from experimental NMR data if a molecule has multiple ring current pathways. Here we present a method for using the Biot-Savart law to deconvolute the contributions of different ring currents to the experimental NMR spectra of polycyclic compounds. This method accurately quantifies local and global ring current susceptibilities in porphyrin nanorings, as well as in a bicyclic dithienothiophene-bridged [34]octaphyrin. There is excellent agreement between ring current susceptibilities derived from both experimental and computationally-predicted chemical shifts, and with ring currents calculated by the GIMIC method. Our method can be applied to any polycyclic system, with any number of ring currents, provided that appropriate NMR data are available.

Switch from local to global aromatic character in Möbius carbon nanobelts upon dioxidation. Evaluation of magnetic behavior in neutral and charged species

Here we show that recent Möbius carbon nanobelts (MCNBs) can be switched from a local to a global aromatic behavior upon dioxidation. Hence, large aromatic structures can be achieved by the choice of the charge states, giving rise to shielding cone characteristics extended within the overall structure at the nanoscale regime, pushing the limit of aromatic circuits to 198 π-electrons.

Quest for the Most Aromatic Pathway in Charged Expanded Porphyrins

Despite the central role of aromaticity in the chemistry of expanded porphyrins, the evaluation of aromaticity remains difficult for these extended macrocycles. The presence of multiple conjugation pathways and different planar and nonplanar π-conjugation topologies makes the quantification of global and local aromaticity even more challenging. In neutral expanded porphyrins, the predominance of the aromatic conjugation pathway passing through the imine-type nitrogens and circumventing the amino NH groups is established. However, for charged macrocycles, the question about the main conjugation circuit remains open. Accordingly, different conjugation pathways in a set of neutral, anionic, and cationic expanded porphyrins were investigated by means of several aromaticity indices rooted in the structural, magnetic, and electronic criteria. Overall, our results reveal the predominance of the conjugation pathway that passes through all nitrogen atoms to describe the aromaticity of deprotonated expanded porphyrins, while the outer pathway through the perimeter carbon atoms becomes the most aromatic in protonated macrocycles. In nonplanar and charged macrocycles, a discrepancy between electronic and magnetic descriptors is observed. Nevertheless, our work demonstrates AV_min remains the best tool to determine the main conjugation pathway of expanded porphyrins.

On the JAP Method for the Indirect Determination of Delocalized Currents from Experimental Chemical Shifts

The JAP model (after Jirásek, Anderson, and Peeks) to retrieve global current strengths from experimental ¹ H chemical shifts has been tested with DFT computations. Both global and local tropicities are correctly predicted in most cases and the quantitative agreement is overall fair. An extension of the model is found to give improvement in an exemplary critical case, where the global delocalized current is negligible and the current density map is dominated by local currents.

Magnetic response properties of carbon nano-onions

The magnetic response of a number of double- and triple-layer carbon nano-onions (CNOs) is analyzed by calculating the magnetically induced current density and the induced magnetic field using the pseudo-π model. Qualitatively the same magnetic response was obtained in calculations at the all-electron level. The calculations show that the CNOs exhibit strong net diatropic (paratropic) ring currents when the external magnetic field points perpendicularly to one of the six-membered (five-membered) rings. They are deshielded inside and shielded outside the CNO; the latter dominates for larger CNOs. The magnetic response originates from a combination of spherical paratropic current densities on the inside of each carbon layer and diatropic current densities on the outside of them. The quantitative differences in the aromaticity of the CNOs as compared to single fullerenes are discussed in terms of ring-current strengths. The magnetic response of some of the CNOs is approximately the sum of the magnetic response of the individual layers, whereas deviations are significant for CNOs containing C₈₀. For the largest CNOs, the deviation from the sum of the fullerene contributions is larger, especially when the external magnetic field is perpendicular to a six-membered ring.

A QCT View of the Interplay between Hydrogen Bonds and Aromaticity in Small CHON Derivatives

The somewhat elusive concept of aromaticity plays an undeniable role in the chemical narrative, often being considered the principal cause of the unusual properties and stability exhibited by certain π skeletons. More recently, the concept of aromaticity has also been utilised to explain the modulation of the strength of non-covalent interactions (NCIs), such as hydrogen bonding (HB), paving the way towards the in silico prediction and design of tailor-made interacting systems. In this work, we try to shed light on this area by exploiting real space techniques, such as the Quantum Theory of Atoms in Molecules (QTAIM), the Interacting Quantum Atoms (IQA) approaches along with the electron delocalisation indicators Aromatic Fluctuation (FLU) and Multicenter (MCI) indices. The QTAIM and IQA methods have been proven capable of providing an unbiased and rigorous picture of NCIs in a wide variety of scenarios, whereas the FLU and MCI descriptors have been successfully exploited in the study of diverse aromatic and antiaromatic systems. We used a collection of simple archetypal examples of aromatic, non-aromatic and antiaromatic moieties within organic molecules to examine the changes in π delocalisation and aromaticity induced by the Aromaticity and Antiaromaticity Modulated Hydrogen Bonds (AMHB). We observed fundamental differences in the behaviour of systems containing the HB acceptor within and outside the ring, e.g., a destabilisation of the rings in the former as opposed to a stabilisation of the latter upon the formation of the corresponding molecular clusters. The results of this work provide a physically sound basis to rationalise the strengthening and weakening of AMHBs with respect to suitable non-cyclic non-aromatic references. We also found significant differences in the chemical bonding scenarios of aromatic and antiaromatic systems in the formation of AMHB. Altogether, our investigation provide novel, valuable insights about the complex mutual influence between hydrogen bonds and π systems.

Molecular Electrides: An In Silico Perspective

Electrides are defined as the ionic compounds where the electron(s) serves as an anion. These electron(s) is (are) not bound to any atoms, bonds, or molecules rather than they are localized into the space, crystal voids, or interlayer between two molecular slabs. There are three major categories of electrides, known as organic electriades, inorganic electrides, and molecular electrides. The computational techniques have proven as a great tool to provide emphasis on the electride materials. In this review, we have focused on the computational methodologies and criteria that help to characterize molecular electrides. A detailed account of the computational methods and basis sets applicable for molecular electrides have been discussed along with their limitation(s) in this field. The main criterion for the identification of the electrides has also been discussed thoroughly with proper examples. The molecular electrides presented here have been justified with all the required criteria that support and proved their electride characteristics. We have also presented a few systems which have similar properties but are not considered as molecular electrides. Moreover, the applicability of the electrides in catalytic processes has also been presented.

Correspondence on "How Aromatic Are Molecular Nanorings? The Case of a Six-Porphyrin Nanoring"

A recent Research Article in this journal by Matito and co-workers claimed that none of the oxidation states of a butadiyne-linked six-porphyrin nanoring exhibit global aromaticity or antiaromaticity. Here we show that this conclusion is incorrect. Experimental data from NMR spectroscopy for a whole family of nanorings provide strong evidence for global ring currents. The NMR data reveal these ring currents directly, without needing analysis by density functional theory (DFT). Furthermore, DFT calculations reproduce the experimental results when a suitable functional is used.

Aromaticity and Extrusion of Benzenoids Linked to [o-COSAN]- : Clar Has the Answer

Benzene and pyrene can be synthetically linked to [o-COSAN]^- keeping their aromaticity. In contrast, naphthalene and anthracene are extruded in the same reaction. We have proven that extrusion is only favorable if the number of Clar's π-sextets remains constant. Thus, Clar has the answer to whether an attached polycyclic aromatic hydrocarbon to [o-COSAN]^- is extruded or not.

Porphyrinoids, a unique platform for exploring excited-state aromaticity

Recently, Baird (anti)aromaticity has been referred to as a description of excited-state (anti)aromaticity. With the term of Baird's rule, recent studies have intensively verified that the Hückel aromatic [4n + 2]π (or antiaromatic [4n]π) molecules in the ground state are reversed to give Baird aromatic [4n]π (or Baird antiaromatic [4n + 2]π) molecules in the excited states. Since the Hückel (anti)aromaticity has great influence on the molecular properties and reaction mechanisms, the Baird (anti)aromaticity has been expected to act as a dominant factor in governing excited-state properties and processes, which has attracted intensive scientific investigations for the verification of the concept of reversed aromaticity in the excited states. In this scientific endeavor, porphyrinoids have recently played leading roles in the demonstration of the aromaticity reversal in the excited states and its conceptual development. The distinct structural and electronic nature of porphyhrinoids depending on their (anti)aromaticity allow the direct observation of excited-state aromaticity reversal, Baird's rule. The explicit experimental demonstration with porphyrinoids has contributed greatly to its conceptual development and application in novel functional organic materials. Based on the significant role of porphyrinoids in the field of excited-state aromaticity, this review provides an overview of the experimental verification of the reversal concept of excited-state aromaticity by porphyrinoids and the recent progress on its conceptual application in novel functional molecules.

Impact of van der Waals interactions on the structural and nonlinear optical properties of azobenzene switches

The geometrical structures, relative Z-E energies, and second-order nonlinear responses of a collection of azobenzene molecules symmetrically substituted in the meta-position with functional groups of different bulkiness are investigated using various ab initio and density functional approximations. We show that RI-MP2 and RI-CC2 approximations provide very similar geometries and relative energies and evidence that London dispersion interactions existing between bulky meta-substituents stabilize the Z conformer. The ωB97X-D exchange-correlation functional provides an accurate description of these effects and gives a good account of the nonlinear optical response of the molecules. We show that density functional approximations should include no less than 50% of Hartree-Fock exchange to provide accurate hyperpolarizabilities. A property-structure analysis of the azobenzene derivatives reveals that the main contribution to the first hyperpolarizability comes from the azo bond, but phenyl meso-substituents can enhance it.

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.