Relevance of the DFT method to study expanded porphyrins with different topologies

Can Aromaticity Be Evaluated Using Atomic Partitions Based on the Hilbert-Space?

Aromaticity is a fundamental concept in chemistry that explains the stability and reactivity of many compounds by identifying atoms within a molecule that form an aromatic ring. Reliable aromaticity indices focus on electron delocalization and depend on atomic partitions, which give rise to the concept of an atom-in-the-molecule (AIM). Real-space atomic partitions present two important drawbacks: a high computational cost and numerical errors, limiting some aromaticity measures to medium-sized molecules with rings up to 12 atoms. This restriction hinders the study of large conjugated systems like porphyrins and nanorings. On the other hand, traditional Hilbert-space schemes are free of the latter limitations but can be unreliable for the large basis sets required in modern computational chemistry. This paper explores AIMs based on three robust Hilbert-space partitions - meta-Löwdin, Natural Atomic Orbitals (NAO), and Intrinsic Atomic Orbitals (IAO) - which combine the advantages of real-space partitions without their disadvantages. These partitions can effectively replace real-space AIMs for evaluating the aromatic character. For the first time, we report multicenter index (MCI) and Iring values for large rings and introduce ESIpy, an open-source Python code for aromaticity analysis in large conjugated rings.

New Perspectives on Delocalization Pathways in Aromatic Molecular Chameleons

This study comprehensively analyzes the magnetically induced current density of polycyclic compounds labeled as "aromatic chameleons" since they can arrange their π-electrons to exhibit aromaticity in both the ground and the lowest triplet state. These compounds comprise benzenoid moieties fused to a central skeleton with 4n π-electrons and traditional magnetic descriptors are biased due to the superposition of local magnetic responses. In the S0 state, our analysis reveals that the molecular constituent fragments preserve their (anti)aromatic features in agreement with two types of resonant structures: one associated with aromatic benzenoids and the other with a central antiaromatic ring. Regarding the T1 state, a global and diatropic ring current is revealed. Our aromaticity study is complemented with advanced electronic and geometric descriptors to consider different aspects of aromaticity, particularly important in the evaluation of excited state aromaticity. Remarkably, these descriptors consistently align with the general features on the main delocalization pathways in polycyclic hydrocarbons consisting of fused 4n π-electron rings. Moreover, our study demonstrates an inverse correlation between the singlet-triplet energy difference and the antiaromatic character of the central ring in S0.

Dynamic effects on the nonlinear optical properties of donor acceptor stenhouse adducts: insights from combined MD + QM simulations

The second-order nonlinear optical (NLO) responses of a donor-acceptor stenhouse adduct (DASA) are investigated by using a computational approach combining molecular dynamics simulations and density functional theory (DFT) calculations. Specific force fields for the open and closed photoswitching forms are first parameterized and validated according to the Joyce protocol, in order to finely reproduce the geometrical features and potential energy surfaces of both isomers in chloroform solution. Then, DFT calculations are performed on structural snapshots extracted at regular time steps of the MD trajectories to address the influence of the thermalized conformational dynamics on the NLO responses related to hyper-Rayleigh scattering (HRS) experiments. We show that accounting for the structural dynamics largely enhances the HRS hyperpolarizability (βHRS) compared to DFT calculations considering solely equilibrium geometries, and greatly improves the agreement with experimental measurements. Furthermore, we show that the NLO responses of the NLO-active open form are correlated with the bond order alternation along the triene bridge connecting the donor and acceptor moieties, which is rationalized using simple essential state models.

Aromaticity Reversal Induced by Vibrations in Cyclo[16]carbon

Aromaticity is typically regarded as an intrinsic property of a molecule, correlated with electron delocalization, stability, and other properties. Small variations in the molecular geometry usually result in small changes in aromaticity, in line with Hammond's postulate. For example, introducing bond-length alternation in benzene and square cyclobutadiene by modulating the geometry along the Kekulé vibration gradually decreases the magnitude of their ring currents, making them less aromatic and less antiaromatic, respectively. A sign change in the ring current, corresponding to a reversal of aromaticity, typically requires a gross perturbation such as electronic excitation, addition or removal of two electrons, or a dramatic change in the molecular geometry. Here, we use multireference calculations to show how movement along the Kekulé vibration, which controls bond-length alternation, induces a sudden reversal in the ring current of cyclo[16]carbon, C16. This reversal occurs when the two orthogonal π systems of C16 sustain opposing currents. These results are rationalized by a Hückel model which includes bond-length alternation, and which is combined with a minimal model accounting for orbital contributions to the ring current. Finally, we successfully describe the electronic structure of C16 with a "divide-and-conquer" approach suitable for execution on a quantum computer.

Application of Inverse Design Approaches to the Discovery of Nonlinear Optical Switches

Molecular switches, in which a stimulus induces a large and reversible change in molecular properties, are of significant interest in the domain of photonics. Due to their commutable redox states with distinct nonlinear optical (NLO) properties, hexaphyrins have emerged as a novel platform for multistate switches in nanoelectronics. In this study, we employ an inverse design algorithm to find functionalized 26R→28R redox switches with maximal βHRS contrast. We focus on the role of core modifications, since a synergistic effect with meso-substitutions was recently found for the 30R-based switch. In contrast to these findings, the inverse design optima and subsequent database analysis of 26R-based switches confirm that core modifications are generally not favored when high NLO contrasts are targeted. Moreover, while push-pull combinations enhance the NLO contrast for both redox switches, they prefer a different arrangement in terms of electron-donating and electron-withdrawing functional groups. Finally, we aim at designing a three-state 26R→28R→ 30R switch with a similar NLO response for both ON states. Even though our best-performing three-state switch follows the design rules of the 30R-based component, our chemical compound space plots show that well-performing three-state switches can be found in regions shared by high-responsive 26R and 30R structures.

DFT potentials from a chemical perspective: Anatomy of electron (de)localization in molecules and crystals

We introduce a fermionic potential, v f $$ {v}_f $$ , as a comprehensive measure of electron (de)localization in atomic-molecular systems. Unlike other common descriptors as ELF, LOL, etc., it characterizes all physical effects responsible for (de)localization of electrons, namely: an exchange hole depth, its tendency to change, a sensitivity of an exchange correlation hidden in a pair density and kinetic potential to local variations in electron density. Wells in the v f $$ {v}_f $$ distribution correspond to the domains of maximum electron localization, while the potential's barriers prevent delocalization of electrons through them. It also estimates bond orders and successfully reveals the impact of chemical modifications or environmental effects on the delocalization of electrons in molecules and crystals. The v f $$ {v}_f $$ components provide a unique opportunity to compare the influence of the mentioned physical effects on electron (de)localization. This merges physical and chemical views of electron delocalization using functions appearing in density functional theory.

Designing hexaphyrins for high-potential NLO switches: the synergy of core-modifications and meso-substitutions

Due to the enormous size of the chemical compound space, usually only small regions are traversed with traditional direct molecular design approaches making the discovery for novel functionalized molecules for nonlinear optical applications challenging. By applying inverse molecular design algorithms, we aim to efficiently explore larger regions of the compound space in search of promising hexaphyrin-based molecular switches as measured by their first-hyperpolarizability (β_HRS) contrast. We focus on the 28R → 30R switch with a functionalization pattern allowing for centrosymmetric OFF states yielding zero β_HRS response. This switch is particularly challenging as full meso-substitution with a single type of functional group or core-modifications result in almost no contrast enhancement. We carried out four inverse design procedures during which two sets of core-modifications and three sets of meso-substitutions sites were systematically optimized. All 4 optimal switches are characterized by a mix of meso-substitutions and core-modifications, of which the best performing switch yields a 10-fold improvement over the parent macrocycle. Throughout the inverse design procedures, we collected and analyzed a database biased towards high NLO contrasts that contains 277 different patterns for hexaphyrin-based switches. We derived three design rules to obtain highly functional 28R → 30R NLO switches: (I) a combination of 2 strong EWG and 1 EDG group is the ideal recipe for increasing the NLO contrast, though their position also plays an important role. (II) The type of core-modification is less important when only the diagonal positions are core-modified. Switches with 4 core-modifications show a clear preference for oxygen. (III) Keeping centrosymmetry in the OFF state remains highly beneficial given the investigated functionalization pattern. Finally, we have demonstrated that combining meso-substitutions with core-modifications can synergistically improve the NLO contrast.

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.

Assessment of the performance of six indices in predicating the aromaticity of planar porphyrinoids

CONTEXT AND RESULTS

Aromaticity is a fundamental chemical concept that has been widely used in explaining the reactivity, stability, structure, and magnetic properties of many molecules such as conjugated macrocycles, metal heterocyclic compounds, and certain metal clusters. Porphyrinoids (including porphyrin) are of particular interest in terms of diverse aromaticity. Various indices therefore have been used to predict the aromaticity of porphyrin-like macrocycles. However, the reliability of these indices for porphyinoids is always questionable. In order to assess the performance of the indices, we have selected six representative indices to predict the aromaticity of 35 porphyrinoids. The calculated values were then compared with the corresponding results obtained from experiments. Our studies suggest that the theoretical prediction by nucleus independent chemical shifts (NICS), topology of the induced magnetic field (TIMF), anisotropy of the induced current density (AICD), and gauge including magnetically induced current method (GIMIC) are essentially consistent with experimental evidence in all 35 cases and thus are preferred indices.

COMPUTATIONAL AND THEORETICAL TECHNIQUES

Based on density functional theory, the performance of the NICS, TIMF, AICD, GIMIC, harmonic oscillator model of aromaticity (HOMA), and multicenter bond order (MCBO) indices were evaluated theoretically. Molecular geometries were optimized at the M06-2X/6-311G** level. NMR calculations using GIAO or CGST method were performed at the M06-2X/6-311G** level. The above calculations were carried out using Gaussian16 suite. The TIMF, GIMIC, HOMA, and MCBO indices were obtained using the Multiwfn program. The AICD outputs were visualized using the POV-Ray software.

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 AVmin remains the best tool to determine the main conjugation pathway of expanded porphyrins.

Theoretical analysis of expanded porphyrins: Aromaticity, stability, and optoelectronic properties

Expanded porphyrin systems are capable of binding a variety of substrates due to their increased cavity size and aromatic nature, holding important applications as magnetic resonance imaging contrast agents and as sensitizers for photodynamic therapy. It is there of fundamental interest to know the photoelectrical properties of expanded porphyrins using quantum chemistry calculations. In this work, we theoretically designed and screened a series of expanded porphyrins by incorporating terthiophene (TTH) and dithienothiophene (DTT) moieties. Our calculations showed that all the designed molecules exhibit excellent optoelectronic performance than the reference molecule. It is suggested that the porphyrin molecule with TTH moiety has better stability than the one with DTT moiety. Finally, we demonstrated that molecule 2 features with TTH moiety and the inverted selenophene ring outperform other molecules because it exhibits increased HOMO-LUMO gap, planar geometry, and strengthened aromaticity. We expect that this work can provide theoretical guidelines for the design of novel porphyrin materials.

The Ability of Chlorophyll to Trap Carcinogen Aflatoxin B1: A Theoretical Approach

The coordination of one and two aflatoxin B1 (AFB1, a potent carcinogen) molecules with chlorophyll a (chl a) was studied at a theoretical level. Calculations were performed using the M06-2X method in conjunction with the 6-311G(d,p) basis set, in both gas and water phases. The molecular electrostatic potential map shows the chemical activity of various sites of the AFB1 and chl a molecules. The energy difference between molecular orbitals of AFB1 and chl a allowed for the establishment of an intermolecular interaction. A charge transfer from AFB1 to the central cation of chl a was shown. The energies of the optimized structures for chl a show two configurations, unfolded and folded, with a difference of 15.41 kcal/mol. Chl a appeared axially coordinated to the plane (α-down or β-up) of the porphyrin moiety, either with the oxygen atom of the ketonic group, or with the oxygen atom of the lactone moiety of AFB1. The complexes of maximum stability were chl a 1-α-E-AFB1 and chl a 2-β-E-AFB1, at -36.4 and -39.2 kcal/mol, respectively. Additionally, with two AFB1 molecules were chl a 1-D-2AFB1 and chl a 2-E-2AFB1, at -60.0 and -64.8 kcal/mol, respectively. Finally, biosorbents containing chlorophyll could improve AFB1 adsorption.

Diketo-Pyrrolo Pyrrole-Based Acceptor-Acceptor Copolymers with Deep HOMO and LUMO Levels Absorbing in the Near Infrared

A series of acceptor-acceptor (A-A’) alternated copolymers based on dithienodiketopyrrolo pyrrole were synthesized by copolymerizing it with itself and other different electron-poor monomers. The experimental and computed optoelectronic properties of four DPP-based copolymers, P(DPP-DPP) (with linear and branched chains), copolymer with diazapentalene P(DPP-DAP) and also with dioxothienopyrrolebenzodifurandione P(DPP-BTPBF), as well as thermal characterizations were described. UV-visible spectrophotometry and cyclic voltammetry were used to estimate the optical and electrochemical bandgaps, and were found as very small: 1.3, 1.0, and 0.9 eV for P(DPP-DPP), P(DPP-DAP), and P(DPP-BTPBF), respectively. The BTPBF unit allowed a strong reduction of the bandgap, leading to a broad absorption in the visible and near infra-red regions from 650 to 1450 nm. These results were compared to analogous donor-acceptor (D-A) copolymers previously reported, in which DPP is replaced by DTS, P(DTS-DPP), P(DTS-DAP), and P(DTS-BTPBF). The same trend was observed. By comparing A-A’ to D-A’ copolymers analogues, it was shown that the bandgap remained the same while both HOMO and LUMO levels were lowered by roughly 0.2 eV.

From six to eight Π-electron bare rings of group-XIV elements and beyond: can planarity be deciphered from the "quasi-molecules" they embed?

Ab initio molecular orbital theory is used to study the structures of six and eight π-electron bare rings of group-XIV elements, and even larger [n]annulenes up to C₁₈H₁₈, including some of their mono-, di-, tri-, and tetra-anions. While some of the above rings are planar, others are nonplanar. A much spotlighted case is cyclo-octatetraene (C₈H₈), which is predicted to be nonplanar together with its heavier group-XIV analogues Si₈H₈ and Ge₈H₈, with the solely planar members of its family having the stoichiometric formulas C₄Si₄H₈ and C₄Ge₄H₈. A similar situation arises with the six π-electron bare rings, where benzene and substituted ones up to C₃Si₃H₆ or so are planar, while others are not. However, the explanations encountered in the literature find support in ab initio calculations for such species, often rationalized from distinct calculated features. Using second-order Møller-Plesset perturbation theory and, when affordable (particularly tetratomics, which may allow even higher levels), the coupled-cluster method including single, double, and perturbative triple excitations, a common rationale is suggested based on a novel concept of quasi-molecules or the (3+4)-atom partition scheme. Any criticism of tautology is therefore avoided. The same analysis has also been successfully applied to even larger [n]annulenes, to their mixed family members involving silicon and germanium atoms, and to the C₁₈ carbon ring. Furthermore, it has been extended to annulene anions to check the criteria of the popular Hückel rule for planarity and aromaticity. Exploratory work on cycloarenes is also reported. Besides a partial study of the involved potential energy surfaces, equilibrium geometries and harmonic vibrational frequencies have been calculated anew, for both the parent and the actual prototypes of the quasi-molecules.

Fine-Tuning of Nonlinear Optical Contrasts of Hexaphyrin-Based Molecular Switches Using Inverse Design

In the search for new nonlinear optical (NLO) switching devices, expanded porphyrins have emerged as ideal candidates thanks to their tunable chemical and photophysical properties. Introducing meso-substituents to these macrocycles is a successful strategy to enhance the NLO contrasts. Despite its potential, the influence of meso-substitution on their structural and geometrical properties has been scarcely investigated. In this work, we pursue to grasp the underlying pivotal concepts for the fine-tuning of the NLO contrasts of hexaphyrin-based molecular switches, with a particular focus on the first hyperpolarizability related to the hyper-Rayleigh scattering (β_HRS). Building further on these concepts, we also aim to develop a rational design protocol. Starting from the (un)substituted hexaphyrins with various π-conjugation topologies and redox states, structure-property relationships are established linking aromaticity, photophysical properties and β_HRS responses. Ultimately, inverse molecular design using the best-first search algorithm is applied on the most favorable switches with the aim to further explore the combinatorial chemical compound space of meso-substituted hexaphyrins in search of high-contrast NLO switches. Two definitions of the figure-of-merit of the switch performance were used as target objectives in the optimization problem. Several meso-substitution patterns and their underlying characteristics are identified, uncovering molecular symmetry and the electronic nature of the substituents as the key players for fine-tuning the β_HRS values and NLO contrasts of hexaphyrin-based switches.

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

Large conjugated rings with persistent currents are novel promising structures in molecular-scale electronics. A six-porphyrin nanoring structure that allegedly sustained an aromatic ring current involving 78π electrons was recently synthesized. We provide here compelling evidence that this molecule is not aromatic, contrary to what was inferred from the analysis of 1 H-NMR data and computational calculations that suffer from large delocalization errors. The main reason behind the absence of an aromatic ring current in these nanorings is the low delocalization in the transition from the porphyrins to the bridging butadiyne linkers, which disrupts the overall conjugated circuit. These results highlight the importance of choosing a suitable computational method to study large conjugated molecules and the appropriate aromaticity descriptors to identify the part of the molecule responsible for the loss of aromaticity.

Magnetically Induced Ring-Current Strengths of Planar and Nonplanar Molecules: New Insights from the Pseudo-π Model

The pseudo-π model yields current densities and induced magnetic fields that mimic the π-component, allowing investigations of large molecular structures, whether they are planar or not, at a low computational cost but with high accuracy. Herein the π-contribution to the magnetically induced current densities and induced magnetic fields of large planar molecules and nonplanar molecules (such as [10]cyclophenacene and chiral toroidal nanotubes C₂₀₁₆ and C₂₁₉₆) were computed using the pseudo-π model with the gauge-including magnetically induced currents method. Additionally, we provide a way to determine the π-component of the ring-current strengths, which can be used for assessing the aromatic character of large carbon molecules.

How Many Electrons Does a Molecular Electride Hold?

Electrides are very peculiar ionic compounds where electrons occupy the anionic positions. In a crystal lattice, these isolated electrons often form channels or surfaces, furnishing electrides with many traits with promising technological applications. Despite their huge potential, thus far, only a few stable electrides have been produced because of the intricate synthesis they entail. Due to the difficulty in assessing the presence of isolated electrons, the characterization of electrides also poses some serious challenges. In fact, their properties are expected to depend on the arrangement of these electrons in the molecule. Among the criteria that we can use to characterize electrides, the presence of a non-nuclear attractor (NNA) of the electron density is both the rarest and the most salient feature. Therefore, a correct description of the NNA is crucial to determine the properties of electrides. In this paper, we analyze the NNA and the surrounding region of nine molecular electrides to determine the number of isolated electrons held in the electride. We have seen that the correct description of a molecular electride hinges on the electronic structure method employed for the analyses. In particular, one should employ a basis set with sufficient flexibility to describe the region close to the NNA and a density functional approximation that does not suffer from large delocalization errors. Finally, we have classified these nine molecular electrides according to the most likely number of electrons that we can find in the NNA. We believe this classification highlights the strength of the electride character and will prove useful in designing new electrides.

Assessment of New Expanded Porpholactones as UV/Vis/NIR Chromophores for Dye-Sensitized Solar Cell Applications

Expanded porphyrins arise as an alternative for potential application as chromophores in dye-sensitized solar cells. (DSSCs). The modification of the core of these compounds provides remarkable changes in the photoelectronic behavior. In the present article, the improvement of its properties for a potential application as UV/vis/NIR chromophores in DSSCs has been studied, when an oxazolone moiety has replaced an imine ring in analogy to the porpholactones first synthesized by Crossley et al. ( J. Chem. Soc., Chem. Commun. 1984, 920-922). These expanded porpholactones present a noticeable red shift as well as an increase in the intensity of the Q-bands regarding the parent compounds. The photophysical properties of Sapphyrin have been explored through DFT calculations and vibrationally resolved absorption spectra simulations. Energetic parameters showed favorable electron injection from the chromophore to the TiO₂ semiconductor. In addition, aromaticity was analyzed and rationalized using magnetic and delocalization criteria. Results showed qualitatively similar trends between aromaticity descriptors and Q bands giving a great opportunity to the use this property in the rational design of chromophores. Finally, the nonequilibrium Green's function formalism shows the ability of expanded porpholactones in electron transport.

Mechanochemically Triggered Topology Changes in Expanded Porphyrins

A hitherto unexplored class of molecules for molecular force probe applications are expanded porphyrins. This work proves that mechanical force is an effective stimulus to trigger the interconversion between Hückel and Möbius topologies in [28]hexaphyrin, making these expanded porphyrins suitable to act as conformational mechanophores operating at mild (sub-1 nN) force conditions. A straightforward approach based on distance matrices is proposed for the selection of pulling scenarios that promote either the planar Hückel topology or the three lowest lying Möbius topologies. This approach is supported by quantum mechanochemical calculations. Force distribution analyses reveal that [28]hexaphyrin selectively allocates the external mechanical energy to molecular regions that trigger Hückel-Möbius interconversions, explaining why certain pulling scenarios favor the Hückel two-sided topology and others favor Möbius single-sided topologies. The meso-substitution pattern on [28]hexaphyrin determines whether the energy difference between the different topologies can be overcome by mechanical activation.

Triplet State Baird Aromaticity in Macrocycles: Scope, Limitations, and Complications

The aromaticity of cyclic 4nπ-electron molecules in their first ππ* triplet state (T1), labeled Baird aromaticity, has gained growing attention in the past decade. Here we explore computationally the limitations of T1 state Baird aromaticity in macrocyclic compounds, [n]CM's, which are cyclic oligomers of four different monocycles (M = p-phenylene (PP), 2,5-linked furan (FU), 1,4-linked cyclohexa-1,3-diene (CHD), and 1,4-linked cyclopentadiene (CPD)). We strive for conclusions that are general for various DFT functionals, although for macrocycles with up to 20 π-electrons in their main conjugation paths we find that for their T1 states single-point energies at both canonical UCCSD(T) and approximative DLPNO-UCCSD(T) levels are lowest when based on UB3LYP over UM06-2X and UCAM-B3LYP geometries. This finding is in contrast to what has earlier been observed for the electronic ground state of expanded porphyrins. Yet, irrespective of functional, macrocycles with 2,5-linked furans ([n]CFU's) retain Baird aromaticity until larger n than those composed of the other three monocycles. Also, when based on geometric, electronic and energetic aspects of aromaticity, a 3[n]CFU with a specific n is more strongly Baird-aromatic than the analogous 3[n]CPP while the magnetic indices tell the opposite. To construct large T1 state Baird-aromatic [n]CM's, the design should be such that the T1 state Baird aromaticity of the macrocyclic perimeter dominates over a situation with local closed-shell Hückel aromaticity of one or a few monocycles and semilocalized triplet diradical character. Monomers with lower Hückel aromaticity in S0 than benzene (e.g., furan) that do not impose steric congestion are preferred. Structural confinement imposed by, e.g., methylene bridges is also an approach to larger Baird-aromatic macrocycles. Finally, by using the Zilberg-Haas description of T1 state aromaticity, we reveal the analogy to the Hückel aromaticity of the corresponding closed-shell dications yet observe stronger Hückel aromaticity in the macrocyclic dications than Baird aromaticity in the T1 states of the neutral macrocycles.

Can the relative positions (cis–trans) of ligands really modulate the coordination of NO in ruthenium nitrosyl complexes?

As nitric oxide is involved in several biological routes, DFT calculations were performed to compare the cis and trans influence of different ligands with regard to the capability of model ruthenium complexes to control the NO availability.

Reduction of peroxynitrite by some manganoporphyrins of AEOL series: DFT approach with dispersion correction and NBO analysis

The AEOL series of manganoporphyrins (MnP; AEOL compounds were named by US Aeolus pharmaceuticals) designed as superoxide dismutase mimic are well-known for their powerful catalytic activity to neutralize reactive oxygen and nitrogen species. Reductive oxygen atom cleavage from peroxynitrite (ONOO^-) to form NO₂ in aqueous solution by some AEOL compounds (AEOL-10113, AEOL-10150, AEOL-11114 and AEOL-11203) was studied by DFT/M06-2X computations with D3 dispersion correction and gCP (geometrical counterpoise correction) for basis set superposition error. DFT computation showed that AEOL-10150 can form the most stable association complex {MnP^…OONO} among four AEOL models. AEOL-10150 complex with ONOO^- has the lowest deformation energy. In AEOL compounds and their association complexes with ONOO^-, Mn atom prefered the high spin state (S = 2) to the intermediate spin state (S = 1). Natural bond orbital analysis showed that electron transfer from the most negative oxygen atom in ONOO^- to Mn atom in MnP has the biggest interaction energy among all kinds of donor-acceptor interactions between ONOO^- and MnP.

Stability, Aromaticity, and Photophysical Behaviors of Macrocyclic Molecules: A Theoretical Analysis

The macrocyclic molecules with terthiophene (TTH) isomers unit exhibit intriguing properties in terms of aromaticity, stability, and absorption. In this work, we theoretically designed a series of macrocyclic molecules featured with TTH and dithienothiophene (DTT) π-conjugated building units, which are used to permute pyrrole unit in porphyrin skeleton. Density functional theory and time-dependent DFT methods are used to evaluate the performance of the designed molecules. Our simulations show that molecules 1–3 exhibit excellent optoelectronic performance. Specifically, the molecule with the DTT unit is more stable than the one with TTH unit in terms of aromaticity and aromatic stabilization energy. This is because DTT unit enhances the coplanarity of the molecular material, facilitating electronic communication. Calculation of vertical electronic excitations suggests the absorption feature of these molecules is mainly contributed by the electronic excitations of higher occupied molecular orbital (HOMO) → lowest unoccupied molecular orbital (LUMO)+1 and HOMO-1 → LUMO. Judging from the key parameters determining the overall performance, 3 stands out because of its good planarity, large HOMO–LUMO gap, and strong aromaticity among all molecules. Interestingly, molecule 1 has the current density flow distributes around the outer section of TTH unit; in contrast, molecule 3 with DTT unit has the current density flow located at the inner section of DTT, which is beneficial for stability and aromaticity. Second-order perturbation energies are calculated to rationalize this observation. We expect that these research results can provide valuable insights into the rational design of novel molecular materials for a variety of applications.

Local and macrocyclic (anti)aromaticity of porphyrinoids revealed by the topology of the induced magnetic field

The aromaticity in porphyrinoids results from the π conjugation through two different annular perimeters: the macrocyclic ring and the local heterocyclic rings appended to it. Analyses, based on aromatic stabilization energies (ASE), indicate that the local circuits (6π) are responsible for the significant aromatic stabilization of these systems. This local aromaticity can be coupled with the one from 4n + 2π macrocyclic circuit. It can either compensate for the destabilization due to a 4n π macrocyclic circuit, or be the only source of aromatic stabilization in porphyrinoids with macrocycles without π-conjugated bonds. This "multifaceted" aromatic character of porphyrinoids makes it challenging to analyze their aromaticity using magnetic descriptors because of the intricate interaction of local versus macro-cyclic circulation. In this contribution, we show that the analysis of the bifurcation of the induced magnetic field, Bind, allows clear identification and quantification of both local, and macrocyclic aromaticity, in a representative group of porphyrinioids. In porphyrin, bifurcation values accurately predict the local and macrocyclic contribution rate to overall aromatic stabilization determined by ASE.

Performance of Localized Coupled Cluster Methods in a Moderately Strong Correlation Regime: Hückel-Möbius Interconversions in Expanded Porphyrins

Localized orbital coupled cluster theory has recently emerged as a nonempirical alternative to DFT for large systems. Intuitively, one might expect such methods to perform less well for highly delocalized systems. In the present work, we apply both canonical CCSD(T) approximations and a variety of localized approximations to a set of flexible expanded porphyrins—macrocycles that can switch between Hückel, figure-eight, and Möbius topologies under external stimuli. Both minima and isomerization transition states are considered. We find that Möbius(-like) structures have much stronger static correlation character than the remaining structures, and that this causes significant errors in DLPNO-CCSD(T) and even DLPNO-CCSD(T₁) approaches, unless TightPNO cutoffs are employed. If sub-kcal mol^–1 accuracy with respect to canonical relative energies is required even for Möbius-type systems (or other systems plagued by strong static correlation), then Nagy and Kallay’s LNO-CCSD(T) method with “tight” settings is the suitable localized approach. We propose the present POLYPYR21 data set as a benchmark for localized orbital methods or, more broadly, for the ability of lower-level methods to handle energetics with strongly varying degrees of static correlation.

Reversal of Clar's Aromatic-Sextet Rule in Ultrashort Single-End-Capped [5,5] Carbon Nanotubes

The three-fold HOMO-LUMO gap oscillation, typical of finite length armchair carbon nanotubes (CNT), has a major effect on the magnetic response of ultrashort, single-end-capped [5,5] carbon nanotubes to a perturbing magnetic field parallel to the main symmetry axis. For the CNT's containing 40, 70, and 100 carbon atoms, for which 100 % of the C=C double bonds can be grouped into aromatic-sextets, i. e., fully or complete Clar networks, large paratropic (antiaromatic) global circulations around the cylindrical axis are predicted at the DFT level of calculation. Local and semi-global diatropic (aromatic) currents of strengths not larger than that of the benzene molecule are determined for a perpendicular perturbing magnetic field. CNTs of intermediate lengths do not display this enhanced antiaromatic response. The paratropic current flow clearly shows that these complete Clar networks can be viewed as stacked cycloparaphenylene belts, each providing a double 4 n annulene circuit as a consequence of the quinoidal resonance structure that results from their closure. Paradoxically, the fully aromatic Clar structure itself is responsible for the enhanced global antiaromaticity.

Performance of Electronic Structure Methods for the Description of Hückel-Möbius Interconversions in Extended π-Systems

Expanded porphyrins provide a versatile route to molecular switching devices due to their ability to shift between several π-conjugation topologies encoding distinct properties. DFT remains the workhorse for modeling such extended macrocycles, when taking into account their size and huge conformational flexibility. Nevertheless, the stability of Hückel and Möbius conformers depends on a complex interplay of different factors, such as hydrogen bonding, π···π stacking, steric effects, ring strain, and electron delocalization. As a consequence, the selection of an exchange-correlation functional for describing the energy profile of topological switches is very difficult. For these reasons, we have examined the performance of a variety of wave function methods and density functionals for describing the thermochemistry and kinetics of topology interconversions across a wide range of macrocycles. Especially for hexa- and heptaphyrins, the Möbius structures have a stronger degree of static correlation than the Hückel and twisted-Hückel structures, and as a result the relative energies of singly twisted structures are a challenging test for electronic structure methods. Comparison of limited orbital space full CI calculations with CCSD(T) calculations within the same active spaces shows that post-CCSD(T) correlation contributions to relative energies are very minor. At the same time, relative energies are weakly sensitive to further basis set expansion, as proven by the minor energy differences between the extrapolated MP2/CBS energies estimated from cc-pV{T,Q}Z, diffuse-augmented heavy-aug-cc-pV{T,Q}Z and explicitly correlated MP2-F12/cc-pVDZ-F12 calculations. Hence, our CCSD(T) reference values are reasonably well-converged in both 1-particle and n-particle spaces. While conventional MP2 and MP3 yield very poor results, SCS-MP2 and particularly SOS-MP2 and SCS-MP3 agree to better than 1 kcal mol-1 with the CCSD(T) relative energies. Regarding DFT methods, the range-separated double hybrids, such as ωB97M(2) and B2GP-PLYP, outperform other functionals with RMSDs of 0.6 and 0.8 kcal mol-1, respectively. While the original DSD-PBEP86 double hybrid performs fairly poorly for these extended π-systems, the errors drop down to 1.9 kcal mol-1 for the revised revDOD-PBEP86-NL, which eliminates the same-spin correlation energy. Minnesota meta-GGA functionals with high fractions of exact exchange (M06-2X and M08-HX) also perform reasonably well, outperforming more robust and significantly less empirically parametrized functionals like SCAN0-D3.

Switching between Hückel and Möbius aromaticity: a density functional theory and information-theoretic approach study

Benziporphyrins are versatile macrocycles exhibiting aromaticity switching behaviors. The existence of both Hückel and Möbius (anti)aromaticity has been reported in these systems, whose validity is respectively governed by the [4n + 2] and [4n] π-electron rule on the macrocyclic pathway. Despite the experimental evidence on the floppiness of benziporphyrins, the switching mechanism between Hückel and Möbius structures is still not clear, as well as the factors influencing the stability of the different π-conjugation topologies. For these reasons, we performed a systematic study on A,D-di-p-benzihexaphyrins(1.1.1.1.1.1) with two redox states corresponding to [28] and [30] π-electron conjugation pathways. Whereas benzi[28]hexaphyrin obeys Möbius aromaticity, benzi[30]hexaphyrin follows Hückel aromaticity. The dynamic interconversion between Möbius and Hückel aromaticity is investigated through the rotation of a phenylene ring, which acts as the topology selector. Further analyses of the energy profiles using energy decomposition and information-theoretic approaches provide new insights into conformational stability, aromaticity and antiaromaticity for these species. Strong and opposite cross correlations between aromaticity indexes and information-theoretic quantities were found for the two macrocyclic systems with opposite global aromaticity and antiaromaticity behaviors. These results indicate that Hückel and Möbius aromaticity and antiaromaticity, though qualitatively different, are closely related and can be interchanged, and information-theoretic quantities provide a novel understanding about their relevance. Our present results should provide in-depth insights to appreciate the nature and origin about Möbius (anti)aromaticity and its close relationship with Hückel (anti)aromaticity.

How do the Hückel and Baird Rules Fade away in Annulenes?

Two of the most popular rules to characterize the aromaticity of molecules are those due to Hückel and Baird, which govern the aromaticity of singlet and triplet states. In this work, we study how these rules fade away as the ring structure increases and an optimal overlap between p orbitals is no longer possible due to geometrical restrictions. To this end, we study the lowest-lying singlet and triplet states of neutral annulenes with an even number of carbon atoms between four and eighteen. First of all, we analyze these rules from the Hückel molecular orbital method and, afterwards, we perform a geometry optimization of the annulenes with several density functional approximations in order to analyze the effect that the distortions from planarity produce on the aromaticity of annulenes. Finally, we analyze the performance of three density functional approximations that employ different percentages of Hartree-Fock exchange (B3LYP, CAM-B3LYP and M06-2X) and Hartree-Fock. Our results reveal that functionals with a low percentage of Hartree-Fock exchange at long ranges suffer from severe delocalization errors that result in wrong geometrical structures and the overestimation of the aromatic character of annulenes.

Performance of DFT functionals for calculating the second-order nonlinear optical properties of dipolar merocyanines

Evolution of the static HRS hyperpolarizability of a tricyanopropylidene-based merocyanine dye with the length of the polyenic bridge, as calculated using various ab initio and DFT approximations.

Comprehensive theoretical and experimental study of near infrared absorbing copolymers based on dithienosilole

A new conjugated copolymer with alternating dithienosilole and thienoisoindigo units displays improved near-infrared absorption compared to previously reported dithienosilole-based copolymers.

Tracking the role of trans-ligands in ruthenium–NO bond lability: computational insight

Ruthenium–NO tetraamine structures control the nitric oxide bioavailability. The ligand trans to NO modulates the Ru–NO bond stability.

Computational study of aromaticity, 1H NMR spectra and intermolecular interactions of twisted thia-norhexaphyrin and its multiply annulated polypyrrolic derivatives

The recently synthesized twisted thia-norhexaphyrin and its multiply annulated polypyrrolic derivatives have been studied computationally. Gauge-including magnetically induced current calculations predict a global nonaromatic character of the initial thia-norhexaphyrin due to the highly-twisted conformation of the macrocycle. Upon the oxidation of the thia-norhexaphyrin four multiply annulated polypyrrolic aromatic macrocycles are formed for which the global aromatic character is confirmed in agreement with experimentally measured ¹H NMR spectra. The calculation of the proton chemical shifts for the studied compounds by direct comparison with the tetramethylsilane standard leads to a significant mean absolute error. At the same time a linear regression procedure for the two selected groups of protons (CH and NH protons) provides much better values of calculated chemical shifts and tight correlation with experiment. The separate consideration of NH protons is motivated by the numerous intermolecular hydrogen bonds in which the protons are involved, which induce considerable upfield shifts, leading to a significant underestimation of the corresponding chemical shifts. Such a selected correlation can be used for accurate estimation of proton chemical shifts of the related porphyrinoids. Bader's theory of Atoms in Molecules has been applied for the studied twisted thia-norhexaphyrin and its multiply annulated polypyrrolic derivatives to characterize intramolecular H-bonds and other non-covalent interactions.

Origins of the Electronic Modulations of Bacterio- and Isobacteriodilactone Regioisomers

Advances in the utilization of porphyrinoids for photomedicine, catalysis, and artificial photosynthesis require a fundamental understanding of the relationships between their molecular connectivity and resulting electronic structures. Herein, we analyze how the replacement of two pyrrolic C_β═C_β bonds of a porphyrin by two lactone (O═C-O) moieties modulates the ground-state thermodynamic stability and electronic structure of the resulting five possible pyrrole-modified porphyrin isomers. We made these determinations based on density functional theory (DFT) and time-dependent DFT computations of the optical spectra of all regioisomers. We also analyzed the computed magnetically induced currents of their aromatic π-systems. All regioisomers adopt the tautomeric state that maximizes aromaticity, whether or not transannular steric strains are incurred. In all isomers, the O═C_β-O_β bonds were found to support a macrocycle diatropic ring current. We attributed this to the delocalization of nonbonding electrons from the ring oxa- and oxo-atoms into the macrocycle. As a consequence of this delocalization, the dilactone regioisomers are as-or even more-aromatic than their hydroporphyrin congeners. The electronic structures follow different trends for the bacteriochlorin- and isobacteriochlorin-type isomers. The presence of either oxo- or oxa-oxygens conjugated with the macrocyclic π-system was found to be the minimal structural requirement for the regioisomers to exhibit distinct electronic properties. Our computational methods and mechanistic insights provide a basis for the systematic exploration of the physicochemical properties of porphyrinoids as a function of the number, relative orientation, and degree of macrocycle-π-conjugation of β-substituents, in general, and for dilactone-based porphyrinic chromophores, in particular.

Can Density Functional Theory Be Trusted for High-Order Electric Properties? The Case of Hydrogen-Bonded Complexes

This work reports on an extensive assessment of the performance of a wide palette of density functional approximations in predicting the (high-order) electric properties of hydrogen-bonded complexes. To this end, we compute the electronic and vibrational contributions to the electric polarizability and the first and second hyperpolarizabilities, using the CCSD(T)/aug-cc-pVTZ level of theory as reference. For all the studied properties, the average absolute errors below 20% can only be obtained using the CAM-B3LYP functional, while LC-BLYP and MN15 are shown to be only slightly less accurate (average absolute errors not exceeding 30%). Among Minnesota density functionals, i.e., M06, M06-2X, and MN15, we only recommend the latter one, which quite accurately predicts the electronic and vibrational (hyper)polarizabilities. We also analyze the optimal tuning of the range-separation parameter μ for the LC-BLYP functional, finding that this approach does not bring any systematic improvement in the predictions of electronic and vibrational (hyper)polarizabilities and the accuracy of computed properties is largely system-dependent. Finally, we report huge errors in predicting the vibrational second hyperpolarizability by ωB97X, M06, and M06-2X functionals. Based on the explicit evaluation of anharmonic terms contributing to the second hyperpolarizability, this failure is traced down to a poor determination of third- and fourth-order energy derivatives with respect to normal modes. These results reveal serious flaws of some density functional approximations and suggest caution in selecting the appropriate functional to calculate not only electronic and vibrational (hyper)polarizabilities but also other molecular properties that contain vibrational anharmonic contributions.

A Benchmark of Density Functional Approximations For Thermochemistry and Kinetics of Hydride Reductions of Cyclohexanones

The performance of density functionals and wavefunction methods for describing the thermodynamics and kinetics of hydride reductions of 2-substituted cyclohexanones has been evaluated for the first time. A variety of exchange correlation functionals ranging from generalized gradient approximations to double hybrids have been tested and their performance to describe the facial selectivity of hydride reductions of cyclohexanones has been carefully assessed relative to the CCSD(T) method. Among the tested methods, an approach in which single-point energy calculations using the double hybrid B2PLYP-D3 functional on ωB97X-D optimized geometries provides the most accurate transition state energies for these kinetically-controlled reactions. Moreover, the role of torsional strain, temperature, solvation, noncovalent interactions on the stereoselectivity of these reductions was elucidated. Our results indicate a prominent role of the substituent on the cis/trans ratios driven by the delicate interplay between torsional strain and dispersion interactions.

Second-order nonlinear optical properties of Stenhouse photoswitches: insights from density functional theory

We report the first investigation of the second-order nonlinear optical (NLO) properties of donor-acceptor Stenhouse adducts (DASAs), an emerging class of colored photochromes that undergo photoswitching with visible light to a colorless form. By using time-dependent density functional theory, we provide insights into the relationships linking the nature of the chemical substituents to the amplitude and contrasts of the NLO response. Solvent and frequency dispersion effects are also analyzed. The calculations predict that DASAs behave as high contrast NLO switches, a finding that extends their potential applications to photo-responsive NLO materials and devices.

Theoretical Study on Open-Shell Singlet Character and Second Hyperpolarizabilities in Cofacial π-Stacked Dimers Composed of Weak Open-Shell Antiaromatic Porphyrins

From the analysis based on the broken-symmetry density functional theory (DFT) calculations, we in this study propose a strategy to enhance the open-shell characters and third-order nonlinear optical (NLO) properties of π-stacked dimers composed of antiaromatic molecules with weak open-shell characters. For this purpose, we here constructed cofacial π-stacked dimer models composed of aromatic and antiaromatic Ni^II porphyrins in order to examine the π-π stacking distance (R) dependence of the diradical characters (y) and static second hyperpolarizabilities (γ). The antiaromatic porphyrin dimers are found to have intermediate y around R∼3.3 Å, the result of which originates in the unique intermolecular interactions between the antiaromatic monomers. Static γ along the stacking direction of such antiaromatic porphyrin dimers with intermediate diradical characters are shown to be enhanced significantly as compared to those of the isolated monomers and the aromatic porphyrin dimers.

Reversible π-system switching of thiophene-fused thiahexaphyrins by solvent and oxidation/reduction

The concept of chemical topology has generated considerable interest among chemists and one of the state-of-the-art topics is Möbius topology in cyclic π-conjugated molecules. In this regard, expanded porphyrins have been extensively studied because of their facile topological interconversions and attractive optoelectronic properties. A typical example involves [28]hexaphyrins: they show topological conversion between planar Hückel and twisted Möbius topologies owing to their flexible structure. With this in mind, we designed a [28]hexaphyrin where one dimethine pyrrole unit was replaced with dithieno[3,4-b:3',4'-d]thiophene (β-DTT), aiming at a reversible switching between macrocyclic and cross-conjugated π-systems by a change in molecular topologies. Considering that the β-DTT unit can offer both macrocyclic and cross-conjugated π-circuits, we envisioned that a combination of the topological interconversion of [28]hexaphyrin with the two π-circuits of the β-DTT unit would enable a reversible switching between macrocyclic and cross-conjugated π-circuits on Möbius and Hückel topologies, respectively, by a simple conformational change. Unexpectedly, the hexaphyrin revealed a unique, unprecedented π-system switching between a Möbius cross-conjugated π-system and a Hückel antiaromatic π-system, which was fully supported by both experimental and theoretical investigations. Meanwhile, the [28]hexaphyrin was also found to be redox interconvertible with the corresponding [26]hexaphyrin with a Hückel cross-conjugated π-system. These results demonstrate that the β-DTT unit is a new effective motif to realize π-system switching by changing molecular and π-system topologies. Importantly, external stimuli, i.e., solvent, as well as oxidation/reduction can be used to trigger the topological changes in expanded porphyrins with the help of the β-DTT unit.

Bicycloaromaticity and Baird-type bicycloaromaticity of dithienothiophene-bridged [34]octaphyrins

Aromatic properties of two recently synthesized dithienothiophene-bridged (DTT) [34]octaphyrins have been investigated by calculating magnetically induced current densities and vertical excitation energies. These intriguing molecules have been proposed to be the first synthesized neutral bicycloaromatic compounds. The triplet state of their dications was even suggested to be Baird-type bicycloaromatic rendering them very interesting as a new prototype of molecules possessing simultaneously the two rare types of aromaticity. Here, we investigate computationally the aromatic properties of the neutral as well as the singly and doubly charged DTT-bridged [34]octaphyrins. Our study provides unambiguous information about changes in the aromatic properties of the DTT-bridged [34]octaphyrins upon oxidation. The calculations identify two independent diatropic ring currents in the neutral DTT-bridged [34]octaphyrins, showing that they are indeed bicycloaromatic. The current-density flow of the two independent ring currents of the bicycloaromatic compounds are visualized and individual aromatic pathways are quantified by performing numerical integration. The calculations show that two independent diatropic ring currents can indeed be sustained by molecules consisting of two aromatic rings that share a common set of π electrons. The current density calculations on the singly charged DTT-bridged [34]octaphyrins show that they are weakly antiaromatic, which does not agree with the suggested aromatic character deduced from spectroscopical studies. The triplet state of the two DTT-bridged [34]octaphyrin cations with very similar molecular structures have unexpectedly different aromatic character. One of them is Baird-type bicycloaromatic, whereas the triplet state of the other dication has one aromatic and one nonaromatic ring, which could not be resolved from available spectroscopical data. Calculations of excitation energies reveal that a simple model cannot be employed for interpreting the electronic excitation spectra of the present molecules, because more than 20 excited states contribute to the spectra above 2.5 eV (500 nm) showing the importance of computations. The present work illustrates how detailed information about molecular aromaticity can nowadays be obtained by scrutinizing calculated current densities.

Charge-Transfer Character Drives Möbius Antiaromaticity in the Excited Triplet State of Twisted [28]Hexaphyrin

Möbius aromatic molecules have attracted great attention as new functional materials because of their π-orbital cyclic conjugations lying along the twisted Möbius topology. To elucidate the electronic character of the lowest excited triplet (T₁) state of a Möbius aromatic [28]hexaphyrin, we employed a time-resolved electron paramagnetic resonance (TREPR) method with applied magnetophotoselection measurements at 77 K. Analyses of the EPR parameters have revealed that the T₁ state possesses intramolecular charge-transfer (CT) character together with local excitation character residing at one side in the Möbius strip ring. We have also demonstrated that the CT character between orthogonal unpaired orbitals triggers quick triplet deactivation by spin-orbit coupling. This deactivation can be an important barometer to represent the "antiaromaticity" because of a connection between the orthogonal CT character and instability by a weakened spin-spin exchange coupling in the T₁ state.