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.

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

Enhanced non-linear optical properties of porphyrin-based polymers covalently functionalized with graphite phase carbon nitride

In our work, a flurry of original porphyrin-based polymers covalently functionalized g-C₃N₄ nanohybrids were constructed and nominated as PPorx-g-C₃N₄ (x = 1, 2 and 3) through click chemistry between porphyrin-based polymers with alkyne end-groups [(PPorx-C≡CH (x = 1, 2 and 3)] and azide-functionalized graphitic carbon nitride (g-C₃N₄-N₃). Due to the photoinduced electron transfer (PET) between porphyrin-based polymers [PPorx (x = 1, 2 and 3)] group and graphite phase carbon nitride (g-C₃N₄) group in PPorx-g-C₃N₄ nanohybrids, the PPorx-g-C₃N₄ nanohybrids exhibited better non-linear optical (NLO) performance than the corresponding PPorx-C≡CH and g-C₃N₄-N₃. It found that the imaginary third-order susceptibility (Im [χ⁽³⁾]) value of the nanohybrids with different molecular weight (MW) of the pPorx group in the nanohybrids ranged from 2.5×10³ to 7.0 × 10³ g mol^-1 was disparate. Quite interestingly, the Im [χ⁽³⁾] value of the nanohybrid with a pPorx group's MW of 4.2 × 10³ g mol^-1 (PPor2-g-C₃N₄) was 1.47 × 10^-10 esu, which exhibited the best NLO performance in methyl methacrylate (MMA) of all nanohybrids. The PPorx-g-C₃N₄ was dispersed in polymethyl methacrylate (PMMA) to prepare the composites PPorx-g-C₃N₄/PMMA since PMMA was widely used as an alternative to glass. PPor2-g-C₃N₄/PMMA showed the excellent NLO performance of all nanohybrids with the Im [χ⁽³⁾] value of 2.36 × 10^-10 esu, limiting threshold of 1.71 J/cm², minimum transmittance of 8% and dynamic range of 1.09 in PMMA, respectively. It suggested that PPorx-g-C₃N₄ nanohybrids were potential outstanding NLO materials.

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.

Pillar[5]arene-Derived endo-Functionalized Molecular Tube for Mimicking Protein-Ligand Interactions

Artificial tubular molecular pockets bearing polar functionalities on their inner surface are useful model systems for understanding the mechanisms of protein-ligand interactions in living systems. We herein report a pillar[5]arene-derived molecular tube, [P4-(OH)BPO], whose endo conformational isomer endo-[P4-(OH)BPO] possesses an inwardly pointing hydrogen-bond (H-bond) donor (OH) in its deep cavity and a strong H-bond acceptor (C═O) on its predominantly hydrophobic inner surface, rendering it a perfect protein binding pocket mimetic. A fragment-based drug design model was established using endo-[P4-(OH)BPO] and a library of various shape-complementary fragment ligands (1-38). On the basis of the binding affinity data for "fragment-pocket" complexes G⊂endo-[P4-(OH)BPO] (G = 1-38), two rationally designed "lead molecules" (39 and 40) were identified as being able to enhance binding affinity significantly by forming H-bonds with both the donor and acceptor of endo-[P4-(OH)BPO]. The described work opens new avenues for developing pillar[n]arene-derived protein binding pocket-mimetic systems for studies of protein-ligand interactions and mechanisms of enzymatic reactions.

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.

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.

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.

Aromaticity as a Guiding Concept for Spectroscopic Features and Nonlinear Optical Properties of Porphyrinoids

With their versatile molecular topology and aromaticity, porphyrinoid systems combine remarkable chemistry with interesting photophysical properties and nonlinear optical properties. Hence, the field of application of porphyrinoids is very broad ranging from near-infrared dyes to opto-electronic materials. From previous experimental studies, aromaticity emerges as an important concept in determining the photophysical properties and two-photon absorption cross sections of porphyrinoids. Despite a considerable number of studies on porphyrinoids, few investigate the relationship between aromaticity, UV/vis absorption spectra and nonlinear properties. To assess such structure-property relationships, we performed a computational study focusing on a series of Hückel porphyrinoids to: (i) assess their (anti)aromatic character; (ii) determine the fingerprints of aromaticity on the UV/vis spectra; (iii) evaluate the role of aromaticity on the NLO properties. Using an extensive set of aromaticity descriptors based on energetic, magnetic, structural, reactivity and electronic criteria, the aromaticity of [4n+2] π-electron porphyrinoids was evidenced as was the antiaromaticity for [4n] π-electron systems. In agreement with previous studies, the absorption spectra of aromatic systems display more intense B and Q bands in comparison to their antiaromatic homologues. The nature of these absorption bands was analyzed in detail in terms of polarization, intensity, splitting and composition. Finally, quantities such as the average polarizability and its anisotropy were found to be larger in aromatic systems, whereas first and second hyperpolarizability are influenced by the interplay between aromaticity, planarity and molecular symmetry. To conclude, aromaticity dictates the photophysical properties in porphyrinoids, whereas it is not the only factor determining the magnitude of NLO properties.

Theoretical exploration on switchable NLO response induced by redox properties of polyoxometalates [XNbW11O40]n-/(n+1)- (X = Al, Si, P, S, Ga, Ge, As, Se)

Calculations based on density functional theory (DFT) have been performed to investigate the relationship between redox properties and second-order nonlinear optical (NLO) responses of Keggin-type anions [XNbW₁₁O₄₀]^n- (X = Al, Si, P, S, Ga, Ge, As, Se) and their corresponding heteropoly blues. The frontier molecular orbitals, NLO responses and electronic transition properties of fully oxidized anions and heteropoly blues were discussed. It is noticeable that the second-order NLO behaviors can be switched by reduced electrons for these Keggin-type anions. The calculated β₀ value of heteropoly blues [XNbW₁₁O₄₀]^(n+1)- (X = P, As, S) are 21-23 times as large as those of fully oxidized anions [XNbW₁₁O₄₀]^n- (X = P, As, S) according to CAM-B3LYP/6-31G* (LANL2DZ basis sets for metal atom) calculations in CH₃CN. The aim of this work is to combine the attractive redox properties and NLO response of polyoxometalates to obtain the switchable NLO materials.

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.

Expanded, Contracted, and Isomeric Porphyrins: Theoretical Aspects

The use of cyclic polyene perimeter-model approaches, such as Gouterman's four-orbital model and Michl's perimeter model, to analyze trends in the electronic structures and optical properties of expanded, contracted, and isomeric porphyrins is described with an emphasis on the use of magnetic circular dichroism (MCD) spectroscopy to validate the results of TD-DFT calculations. Trends in the electronic structures and optical properties of isomeric porphyrins are examined by comparing the properties of porphycenes, corrphycenes, hemiporphycenes, isoporphycenes, N-confused and neoconfused porphyrins, and norroles, whereas those of ring-contracted porphyrins are examined by comparing the properties of subporphyrins, triphyrins, and vacataporphyrins. The ring-expanded compounds that are examined include cyclo[n]pyrroles, [22]pentaphyrins(1.1.1.1.1), sapphyrins, smaragdyrins, isosmaragdyrins, orangarins, ozaphyrins, [26]hexaphyrins(1.1.1.1.1.1), rubyrins, rosarins, amethyrins, isoamethyrins, bronzaphyrins, and doubly N-confused hexaphyrins.

Flexible Porphyrinoids

This review underscores the conformational flexibility of porphyrinoids, a unique class of functional molecules, starting from the smallest triphyrins(1.1.1) via [18]porphyrins(1.1.1.1) and concluding with a variety of expanded porphyrinoids and heteroporphyrinoids, including the enormous [96]tetracosaphyrin(1.0.1.0.1.0.1.0.1.0.1.0.1.0.1.0.1.0.1.0.1.0.1.0). The specific flexibility of porphyrinoids has been documented as instrumental in the designing or redesigning of macrocyclic frames, particularly in the search for adjustable platforms for coordination or organometallic chemistry, anion binding, or mechanistic switches in molecular devices. A structural prearrangement to coordinate one or more metal ions has been outlined. The coverage of the topic focuses on representative examples of geometry or conformational rearrangements for each selected class of the numerous porphyrinoids accordingly categorized by the number of built-in carbo- or heterocycles.

Understanding conductivity in molecular switches: a real space approach in octaphyrins

In recent years, expanded porphyrins have emerged as a promising class of π-conjugated switches whose conductance is studied from the electron density.