Lanthanide contraction-driven modulation of photoswitchable macrocyclic complexes reveals unprecedented glass-induced re-isomerization and luminescence thermometry

Abstract

Designing light-responsive supramolecular architectures with lanthanide ions offers a promising route towards multifunctional materials with tunable photophysical properties. Here, we report a systematic investigation across the lanthanide series of macrocyclic complexes incorporating azobenzene-functionalized diaza-crown ether ligands. We show that subtle changes in the ionic radius across the Ln³⁺ series dictate conformational preferences and modulate trans-to-cis photoisomerization efficiency under UV and visible light. Surprisingly, we uncover that the reverse cis-to-trans isomerization, which is here unresponsive to thermal or photonic stimuli, is uniquely triggered upon contact with glass surfaces, revealing a previously overlooked route for controlling molecular photoswitching. Additionally, selected complexes display efficient visible and near-infrared emission leveraged for robust luminescent thermometric behaviour in the solid state, with tunable sensitivity linked to the lanthanide ions. These findings advance the field of light-driven supramolecular materials and demonstrate how careful molecular-level design of lanthanide–azobenzene assemblies enables control over photoswitching, luminescence and thermal sensing properties, highlighting glass-mediated re-isomerization as a novel phenomenon with implications for future photoresponsive materials.

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1. Introduction

Light is a fundamental source of energy in photosynthesis, and harnessing light–matter interactions through artificial molecular systems opens pathways towards energy conversion and information processing at the molecular level. The design and synthesis of novel light-responsive supramolecular architectures are therefore of great importance for the development of smart, stimuli-responsive functional materials.^1,2 Advancing our understanding of these interactions through the engineering of new materials is a key scientific direction, with potential applications including electronic and optical devices,^3,4 data storage,^5–7 biological imaging, medical diagnostics, targeted drug delivery,^8,9 sensing,^10,11 encryption,¹² anti-counterfeiting technologies or multicolour QR codes.^1,13,14

There is growing interest in the development of macrocyclic systems functionalized with photoswitchable units, as light offers a non-invasive and highly tunable stimulus for dynamic control over molecular conformation and properties in supramolecular assemblies.^15,16 Among the most widely used photoresponsive motifs is azobenzene, which undergoes reversible photoisomerization between two different geometric isomers – a linear trans-form and a bent cis-form – enabling the modulation of supramolecular photophysical behaviour.^13,17,18 Many light-responsive macrocycles incorporating azobenzene have been reported, though predominantly in metal-free systems.^19–25 When metal ions are introduced, coordination can either quench the photoswitching activity²⁶ or, conversely, enhance the selectivity and accelerate and improve control over the photoswitching processes.²⁷ This demonstrates a crucial role of matching energy levels and photochromic units to achieve effective and tunable photoswitchable behaviour.

Recent studies have highlighted the impact of transition metal ions in expanding the functionalities of light-responsive systems, enabling properties that are otherwise unattainable in purely organic frameworks.^28,29 In particular, integrating luminescent lanthanide ions with light-responsive molecules has emerged as a promising strategy to enhance both emission and photoswitching behaviour.^26,30–32 Switchable lanthanide complexes align well with the concept of multi-stimuli-responsive architectures, exhibiting sensitivity to light but also to chemical, thermal, electrical or mechanical inputs. This multifunctionality makes such materials increasingly desirable for applications in chemical sensing, cellular imaging, security tagging, and, most recently, as advanced luminescent optical thermometers.^12,33–36 In d-block systems, temperature shifts the balance between ligand- and metal-centered excited states and their nonradiative decay, with ratiometric intensity or lifetime being the thermometric readout (e.g. Re₂-L anions bridged with diamine-organic linkers³⁷ or [Bz₂NH₂]₂[Mn(OC₆F₅)₄] ionic assembly³⁸). In f-block complexes, the response often follows redistribution among crystal-field mJ sublevels and thermally assisted antenna-4f energy transfer, enabling self-calibrated intensity ratios, lifetimes or band-shape changes. Examples include a self-calibrated Dy³⁺ thermometer that also shows single-ion magnet (SIM) behaviour³⁹ or dinuclear single-molecule magnet (SMM) Nd³⁺ platforms linking ligation to thermometric performance.⁴⁰ Independent magneto-optical readouts can further improve thermal sensitivity.⁴¹ Macrocyclic ligand designs further highlight multifunctionality: a Y³⁺–diluted Dy³⁺ complex acts as a bifunctional SIM and luminescent thermometer, with both functions active below its blocking temperature,⁴² and our Nd³⁺ macrocyclic SIM operates as a temperature-independent manometer and pressure-independent thermometer.⁴³ These precedents motivate the photoswitchable Nd³⁺/Yb³⁺ macrocyclic complexes studied here and frame our analysis of how lanthanide contraction shapes their near-infrared thermometric response.

A number of azobenzene-functionalized lanthanide complexes have been reported to date, and their photoisomerization behaviour and structure–function relationships remain under active investigation.^44–53 However, comprehensive studies encompassing a broad range of lanthanide ions with organic ligands are still rare, limiting a deeper understanding of lanthanide contraction effects and their influence on structure and functionality in photoresponsive systems. Although lanthanide–macrocyclic complexes have been widely studied in fields such as biomedical imaging,^54,55 antenna-based emission systems,^55,56 and molecular nanomagnets (SMMs/SIMs),^55,57 the integration of photoswitchable units into such systems remains extremely limited. Lariat-type macrocycles bearing azobenzene moieties have primarily been developed for s-block metal ion coordination or membrane-mimetic applications,²⁴ while analogous systems with lanthanides are exceedingly rare.

In this work, we present a systematic study on a diaza-crown ether macrocycle functionalized with azobenzene units, L-AzoH₂, forming a distinct class of lanthanide complexes designed to investigate the structural and photophysical effects of lanthanide contraction. Despite the common quenching of azobenzene switching by metal coordination, our system retains efficient light-induced isomerization while exhibiting high stability of the cis-form—reverting to the trans-isomer unusually fast upon contact with the glass surface. Finally, representative complexes from both the syn- and anti-conformational families were evaluated as luminescent thermometers, establishing a novel correlation among macrocyclic geometry, switching behaviour and near-infrared emissive sensing across the lanthanide series (Fig. 1).

Fig. 1 An overview of key concepts covered in this work, which demonstrate the photoactive Ln-macrocyclic complexes in the context of lanthanide contraction.

2. Results and discussion

2.1. Choice of the ligand, synthesis and characterization

The diaza-crown ether macrocyclic ligand was chosen because (1) macrocycles with N₂O₄ coordination cavities form stable lanthanide complexes and (2) allow symmetric functionalization with different groups, which should tune the photoresponsive properties. A pendant-arm azobenzene macrocyclic ligand named L-AzoH₂ was obtained through the Mannich reaction, based on a previously reported procedure⁵⁸ with a slight modification of the purification method (section 1.3 in the SI). The purity and homogeneity were confirmed using Fourier transform infrared spectroscopy (FT-IR), electrospray mass spectrometry (ESI-MS), nuclear magnetic resonance spectroscopy (NMR) and thermogravimetric analysis (TGA) (Fig. S1–S7).

2.2. Design, synthesis and characterization of complexes

To understand the influence of interactions between the metal centers and the ligand molecule for the development of stimuli responsive azobenzene systems, we focused on the synthesis and investigation of compounds with lanthanide ions, which are interesting due to their emissive properties. To better understand the role of deprotonation of the ligand for photoresponsivity, a neutral CuL-Azo system was also obtained. Simple complexes with a sodium ion, [NaL-AzoH₂]CF₃SO₃, and an uncoordinated ligand L-AzoH₂ molecule were also used as references. The [NaL-AzoH₂]CF₃SO₃ complex was synthesized in an acetonitrile solution by the complexation reaction of the NaCF₃SO₃ salt with the L-AzoH₂ ligand. Cu²⁺ and Ln³⁺ complexes were synthesized in a similar manner, in an acetonitrile (CuL-Azo) or acetonitrile/methanol (LnL-AzoCF₃SO₃) mixture (1 : 1, v : v) by the complexation reaction of the corresponding triflate salts with the L-AzoH₂ ligand in the presence of triethylamine (Et₃N), used as a deprotonating agent (Fig. 2). A detailed description of the synthesis, isolation, and spectroscopic and solid-state characterization of the complexes can be found in the SI (sections 1.4 and 1.5). The FT-IR spectra (Fig. S8–S12) of the lanthanide complexes from La³⁺ to Lu³⁺ are almost identical, which confirmed high isostructurality in the solid state. This is also consistent with the mass spectra of these assemblies, as the peaks observed in the positive mode of the ESI-MS spectra indicate the formation of mononuclear complexes containing one L-Azo ligand molecule with two deprotonated OH groups from the azobenzene pendant-arms of the macrocycle for all complexes (Fig. S13–S24).

Fig. 2 Scheme for the synthesis of macrocyclic complexes with included conformations of the L-AzoH₂ ligand scaffold.

2.2.1. Single crystal and powder X-ray crystallography. Single crystals suitable for X-ray diffraction studies were obtained by slow evaporation of a dimethyl sulfoxide solution for the L-AzoH₂ ligand, by the slow diffusion of diisopropyl ether into a solution of chloroform (CuL-Azo) or acetonitrile/dichloromethane for lanthanide complexes LnL-AzoCF₃SO₃ and by the slow diffusion of diisopropyl ether into a solution of acetonitrile for the [NaL-AzoH₂]CF₃SO₃ complex. For the sodium complex, two types of monocrystals were obtained under identical conditions, and they exhibited different space groups. Therefore, both structures were solved for comparison and designated as forms A and B, respectively.

Fig. 3 shows the comparison of the crystal structure of the free L-AzoH₂ ligand molecule (a), its complex with a sodium ion with a non-deprotonated ligand (b) and a complex with Cu²⁺ with a deprotonated ligand form (c); the molecular structure of the lanthanide complex in the syn-conformation (d) and the packing diagram (e) of the LaL-AzoCF₃SO₃ complex. The ligand molecule is C_i-symmetrical in the crystal structure, lying across the center of inversion in the space group P2₁/c (Fig. 3a). The conformation of the macrocycle changes significantly upon complexation (Fig. 3b–d), and the change directs all N and O atoms towards the center of the complex. For the sodium complexes [NaL-AzoH₂]CF₃SO₃ (A and B), which are observed in both forms of different space group symmetries, CF₃SO₃⁻ acts as a counterion and is not coordinated to the central metal ion. The coordination number of the sodium cation is in both cases 8 (N₂O₆), and the crystal lattices contain space which is filled by more (B) or less (A) ordered solvent molecules (Fig. 3b and Fig. S25). Fig. 3c shows the neutral CuL-Azo complex, which is also centrosymmetric (C_i) with the Cu²⁺ ion located on an inversion centre. The metal ion is six-coordinated and is best described as a Jahn–Teller-elongated octahedron (4 + 2): four donors define a nearly square equatorial plane, while two much longer axial Cu⋯O contacts complete the coordination sphere (see Table S4). Such pronounced axial elongation is typical of d⁹ Cu²⁺ and is well precedented with over 4000 six-coordinated Cu²⁺ entries in the CSD displaying comparably unequal axial Cu–O distances.

Fig. 3 Crystal structures of the (a) L-AzoH₂ ligand; (b) [NaL-AzoH₂]CF₃SO₃ (A) complex; (c) CuL-Azo complex; and (d) LaL-AzoCF₃SO₃ complex; (e) packing diagram of the LaL-AzoCF₃SO₃ complex.

The determined crystal structures for LaL-AzoCF₃SO₃, PrL-AzoCF₃SO₃, NdL-AzoCF₃SO₃, SmL-AzoCF₃SO₃, EuL-AzoCF₃SO₃, GdL-AzoCF₃SO₃, TbL-AzoCF₃SO₃ and ErL-AzoCF₃SO₃ macrocyclic complexes have established that all Ln-assemblies are highly isostructural (Fig. 3d,e and Fig. S26–S32). They crystallize in the same space group (P2₁/c) and with very similar disposition of molecules in the crystal structure. The isostructurality goes so far that even a similar disorder of one of the dinitrogen bridges is found in all the structures. The lanthanide ion is 9-coordinated (quite typically) by two nitrogen and six oxygen atoms from the ligand molecule, four oxygen atoms from the macrocyclic ring and two oxygen atoms from the phenol moiety of the azobenzene pendant-arms, which are positioned at the same side of the macrocyclic unit resulting in a syn conformation. The coordination sphere is filled additionally by one oxygen atom from the coordinated triflate anion positioned at the opposite side of the two azobenzene pendant-arms of the macrocycle. We have recently demonstrated the crucial effect of a disordered triflate in the Nd³⁺-macrocyclic assemblies for the implementation of multifunctional characteristics.⁴³ The crystal data, data collection, structure refinement and geometrical characteristics for the ligand and complexes are given in Tables S1–S4. The lanthanide contraction in the synthesized Ln-complexes influences the Ln–N and Ln–O bond distances, resulting in a general trend of gradual shortening of these bonds across the lanthanide series, with some exceptions to the expected trend (Table S4).

The powder X-ray diffraction (PXRD) patterns for LaL-AzoCF₃SO₃, PrL-AzoCF₃SO₃, NdL-AzoCF₃SO₃, SmL-AzoCF₃SO₃, EuL-AzoCF₃SO₃, GdL-AzoCF₃SO₃, TbL-AzoCF₃SO₃ and ErL-AzoCF₃SO₃ complexes also confirmed their isostructurality. The experimental powder X-ray diffraction (PXRD) patterns of the lanthanide complexes were in accordance with simulated PXRD patterns based on single crystal diffraction data, indicating phase purity (Fig. S33). The differences in the sharpness and narrowness of the corresponding PXRD signals are due to the poor crystallinity of the powdered samples. In the case of the DyL-AzoCF₃SO₃, HoL-AzoCF₃SO₃, YbL-AzoCF₃SO₃ and LuL-AzoCF₃SO₃ complexes, the obtained samples are not in the crystalline state but in the amorphous phase, so their PXRD patterns were not possible to determine, but the experimental characterization confirmed their purity and uniformity (see section 1.5).

2.2.2. ¹H NMR spectroscopy. The LaL-AzoCF₃SO₃ and LuL-AzoCF₃SO₃ macrocyclic complexes were characterized using NMR spectroscopy (¹H, ¹³C, and 2D NMR: COSY and HSQC) in CDCl₃ (Fig. S34–S41). The ¹H NMR spectra show significant differences from those of the free L-AzoH₂ ligand in both aromatic and aliphatic regions, indicating coordination of the lanthanide ions through donor atoms of the macrocycle and azobenzene arms (Fig. 4). Both La³⁺ and Lu³⁺ complexes exist as single species in solution. The ¹H NMR spectrum of the La³⁺ complex is symmetric, indicating that the protons on both sides of the crown ether are chemically equivalent. This observation is consistent with X-ray crystallographic data, which show that the La³⁺ ion is centrally positioned within the macrocycle. In this complex, the azobenzene arms adopt a syn-conformation (both on the same side of the ring). In contrast, the Na⁺ complex adopts an anti-conformation (arms on opposite sides), while also featuring a centrally located metal ion. The broad signals in the aliphatic region of the ¹H NMR spectra for both the La³⁺ and Na⁺ complexes are likely due to fast dynamic exchange processes. The Lu³⁺ complex shows an asymmetric ¹H NMR pattern, indicating a distinct structure. The smaller Lu³⁺ ion, due to lanthanide contraction, is likely coordinated asymmetrically and displaced from the macrocycle center (see section 2.4). The reorganization of the coordination environment around larger and smaller lanthanide ions and distinct conformational preferences in solution are recognized in the literature.^59–64

Fig. 4 Stacked ¹H NMR spectra for L-Azo (black), [NaL-AzoH₂]CF₃SO₃ (violet), LaL-AzoCF₃SO₃ (blue) and LuL-AzoCF₃SO₃ (green), along with a representation of the coordination around cations.

Besides different conformations of the macrocycle cavity around the Ln centre in La³⁺ and Lu³⁺ assemblies, we suppose that the arrangement of coordinated azobenzene pendant-arms is also different. Firstly, the benzylic hydrogen resonances (methylene groups linking the crown moiety and azobenzene pendant-arms) differ between La³⁺ and Lu³⁺ complexes. These protons are a broad singlet in La³⁺, while in Lu³⁺ they show a typical AX (δ₁ = 4.60 ppm; δ₂ = 3.35 ppm; J = 12.6 Hz; spectrometer frequency = 600 MHz; Δν/J ∼ 60) spin system and resonate as doublets of doublets with significantly different chemical shifts. It indicates that benzylic protons are diastereotopic thanks to the different chemical environment. This result, together with the difference of the crown-ether signals, indicates that the latter complex is more rigid on the NMR timescale. Moreover, comparing the aromatic region, we can see that chemical shifts in the Lu³⁺ are more closely related to the ligand, where from the crystal structure data determination we observe that azobenzene pendant-arms are preorganized at the two opposite sides of the macrocyclic ligand skeleton (Fig. 3a). Integration of all these results allows us to predict that the azobenzene pendant arms adopt an anti-conformation in the Lu³⁺ complex. This is accompanied by a closely coordinated triflate anion near the Lu³⁺ center, which helps explain the observed conformational differences in solution. A comparison of energetic profiles via density functional theory (DFT) studies also supports the proposed anti-conformation in the LuL-AzoCF₃SO₃ complex (see section 2.4).

2.3. Photoisomerization studies

2.3.1. Trans-to-cis isomerization. Due to the distinct shape and properties of the azobenzene molecule in its trans- and cis-forms, the characteristic absorption bands (π–π* and n–π*) for these two states of the molecules make them detectable.¹ The photoisomerization properties of the synthesized compounds were studied in chloroform solution and monitored using UV-vis absorption spectroscopy. Typically, trans-to-cis photoisomerization of the azobenzene moiety is induced by UV or visible light irradiation.^24,65 We demonstrate that incorporating a lanthanide metal center into the azobenzene macrocyclic ligand scaffold, L-AzoH₂, uncovers a light-responsive system with tunable photoswitchable properties. Investigation of the photoresponsive behaviour of the L-AzoH₂ macrocycle in chloroform showed that the free ligand does not exhibit any photoswitching properties under UV (320 nm) or visible (520 nm) light, with no observable changes in the absorption spectrum (Fig. S42). Photoresponsive behaviour of the NdL-AzoCF₃SO₃ macrocyclic complex in a chloroform solution has shown that this system is a dual-responsive supramolecular assembly, as the photoswitching and photochromic properties were observed under UV light (320 nm) and visible light (520 nm). Upon irradiation of the NdL-AzoCF₃SO₃ complex with 320 nm UV light, the absorbance of the π–π* band at 403 nm gradually decreases, with a noticeable appearance of the n–π* band as the intensity increases above 500 nm (Fig. 5a).

Fig. 5 UV-vis absorption spectra of the NdL-AzoCF₃SO₃ complex as a function of irradiation time, measured after (a) 320 nm and (b) 520 nm light irradiation. The inset photographs show the colour change of the macrocyclic complex upon (a) UV and (b) visible light exposure of the NdL-AzoCF₃SO₃ complex in chloroform solution.

These dependencies are typical of the trans-to-cis isomerization of azobenzene molecules.^1,66 Therefore, this observation is an obvious confirmation of the UV light-induced isomerization to the cis-conformation of the azobenzene moiety in the Nd³⁺ macrocyclic complex. The photostationary state for the Nd³⁺ complex was reached after 3 h of irradiation, as indicated by intensity saturation of the band from the n–π* transition (Fig. 5a). We also revealed that the Nd³⁺ macrocyclic complex is sensitive to visible light irradiation, as exposure of the chloroform solution of the neodymium complex to 520 nm light irradiation induces the same photochromic and photoisomerization behaviour. This is indicated by identical changes in the absorption spectrum profile (Fig. 5b). The same rate of change from trans to cis-form under irradiation of the Nd³⁺ complex with visible light (4.00 mW cm⁻²) compared to UV light (1.68 mW cm⁻²) was observed after exposure to more intense light irradiation, as under the same conditions, the photoresponsive behaviour was practically invisible (for details, see section 1.1, in the SI). This suggests greater sensitivity to far UV light exposure, as trans-to-cis photoisomerization is faster even at a lower intensity of incident UV light (Fig. 5).

This led us to investigate whether L-AzoH₂ photoisomerization properties depend on the nature of the metal ion and protonation state of the ligand. Accordingly, we studied the influence of s-block metal ion–Na⁺ coordination and d-block metal ion–Cu²⁺ coordination in comparison with f-electron cation–Nd³⁺. No evidence of the photoisomerization behaviour was observed for the [NaL-AzoH₂]CF₃SO₃ complex under exposure either to 320 nm or 520 nm light irradiation (Fig. S43a). In situ deprotonation of the ligand in the sodium complex also did not change these results (Fig. 43b). However, we observed that the copper complex (CuL-Azo), with the ligand in its deprotonated form (for details, see sections 2.2.1, 1.4 and 1.5) exhibits reversible, photoswitchable behavior (Fig. S43c), though no visible colour change of the investigated solution was noted. Finally, in situ preparation of [Nd(CF₃SO₃)₃-L-AzoH₂] without deprotonation of the phenolic lariat arms also leads to a photoresponsive system, which is switched off after the demetallation of the system with excess trifluoroacetic acid (Fig. S43d). This demonstrates that photoisomerization of the azobenzene moiety is dependent on both the protonation state of the ligand (see also section 2.3.3) and the electronic nature of the metal ion.

2.3.2. Isomerization at different wavelengths and stability studies of the cis-form. While the Nd³⁺ macrocycle responds efficiently to 320 nm and 520 nm light, its photoisomerization under other wavelengths in the 340–720 nm range is negligible (Fig. S44a). A minor response appears in the 480–580 nm region, though significantly slower than the isomerization observed at 320 nm and 520 nm, where efficient isomerization to the cis-form occurs within 15 minutes (Fig. S44a). These findings confirm that 320 nm and 520 nm are the most effective excitation wavelengths, prompting us to select 320 nm for detailed characterization due to its comparable efficacy and experimental consistency.

Based on these results, we focused our investigation on the stability of the photoinduced cis-isomer and its reversibility to the thermodynamically favoured trans-isomer. We examined the influence of various external stimuli known to trigger cis-to-trans back-isomerization – i.e. light, heat and dark storage – on the stability of the cis-isomer and recovery of the trans form of the Nd³⁺ macrocyclic complex in solution. The cis-isomer remained highly stable at an elevated temperature (40 °C), showing no significant change in absorption intensity after 2 hours in a chloroform solution (Fig. 6a and Fig. S44b). Further temperature increase led to decomposition (Fig. S44b). Visible light irradiation across 380–720 nm failed to induce re-isomerization (Fig. S45a). Dark storage in a sealed quartz cuvette (wrapped in aluminium foil) also showed minimal recovery of the trans form after 24 hours, indicating high kinetic stability of the cis isomer (Fig. S45b). After 14 days of storage in the dark, the absorption band corresponding to the n–π* transition at ∼505 nm decreased by about 50%, while the π–π* transition band at 403 nm recovered to 82% of its original trans-isomer intensity, indicating a very slow back-isomerization (Fig. 6b and Fig. S45b). These findings demonstrate the remarkable stability of the cis-form in the lanthanide macrocyclic complex, even under conditions typically efficient for the induction of back-isomerization of azobenzene based compounds. Surprisingly, we observed that repeatedly aspirating the cis-rich solution of the Nd³⁺ complex with a glass Pasteur pipette led to a visible colour change from orange to yellow, suggesting a return to the trans-form. Indeed, after 5 minutes of repeated pipetting, approximately 90% recovery of the trans-isomer was confirmed, regardless of whether the isomerization had originally been induced with 320 nm or 520 nm light (Fig. 6c and Fig. S46a, b).

Fig. 6 Stability of the cis-isomer Nd³⁺ complex after 320 nm irradiation under varying conditions. (a) Effect of elevated temperature; (b) stability during dark storage; (c) manual agitation using a soda-lime-silicate glass pipette; (d) UV-vis absorption spectra illustrating the response to various stimuli: 1 – before irradiation, 2 – after 20 minutes of 320 nm UV irradiation, 3 – after 320 nm UV irradiation followed by 15 s shaking in a cuvette, 4 – manual agitation with a plastic pipette (5 min), 5 – manual agitation with a soda-lime-silicate glass pipette (5 min), 6 – shaking with a crushed soda-lime-silicate glass (15 s), 7 – manual stirring in a borosilicate or soda-lime-silicate vial (15 s), 8 – manual stirring in a silanized borosilicate vial (5 min). Colour changes (inserted photographs) – legend for figures a, b, c: A – before irradiation, B – after irradiation at 320 nm, C – temperature exposure (a), storage in the dark (b), contact with a glass pipette (c); for figure d: A – before irradiation, B – after irradiation at 320 nm, after 320 nm irradiation and stirring in borosilicate vial-X, or in soda-lime-silicate glass-Y. (e) Graphical representation of protonation and its effect on the photoresponsive behaviour of the macrocyclic lanthanide assemblies; for better demonstration of the process, the phenolic arm is presented as non-coordinating, but solution and solid state studies demonstrate coordination in the deprotonated form.

2.3.3. Investigation of the underlying cause of the cis-to-trans re-isomerization mechanism. This unexpected observation prompted a series of control experiments to identify the underlying cause of the glass-induced re-isomerization. To test whether mechanical force was responsible, we subjected the solution to ultrasonic treatment. However, this led to the decomposition of both trans- and cis-isomers of the complex (Fig. S47a). Stirring the solution with a magnetic stir bar or shaking the quartz cuvette had no effect on the absorption spectra or colour of the solution (Fig. 6d). The cis-isomer also remained stable in the presence of molecular oxygen (Fig. S47b) and manual pipetting with a plastic pipette (Fig. 6d). Furthermore, we demonstrated that transferring the orange cis-rich solution of the Nd³⁺ complex from a quartz cuvette into a borosilicate or soda-lime-silica vial and gently mixing for 15 seconds led to an immediate colour change to yellow, with full recovery of the trans-isomer absorption spectrum—consistent with results obtained via manual agitation using a glass pipette (Fig. 6d). Similarly, adding crushed soda-lime-silicate glass (sourced from a pipette) to the cis-rich solution and shaking for 15 seconds also triggered immediate colour change and restoration of the original absorption profile, indicating that the glass surface itself is responsible for the back-isomerization (Fig. 6d). To further investigate this, we added crushed soda-lime glass to the cuvette and left the sample undisturbed in the dark. A gradual return to the initial spectrum was observed after ∼3 hours (Fig. S48a). These experiments collectively support the conclusion that the re-isomerization is not mechanically induced but rather driven by surface interactions with glass.

Intriguingly, although glass has been shown to accelerate certain chemical reactions,^67,68 this effect has not been reported for photochemical processes—particularly not for azobenzene-based photoswitches. To probe the origin of the glass-mediated re-isomerization, we examined the effect of individual components of the glass. A large excess of NaCl (500× molar) did not induce re-isomerization over 24 h, excluding Na⁺ leached from the glass as an operative factor and suggesting that the lack of photoresponsivity of [NaL-AzoH₂]CF₃SO₃ arises from metal identity. Silanized borosilicate slowed the recovery of the trans isomer from ca. 15 s to ca. 5 min (Fig. 6d). Since silanization caps surface OH groups and suppresses formation of basic siloxide sites (SiO⁻/M⁺), this attenuation points to basic surface sites – not neutral Si–OH – as the active species. Consistently, adding even an excess of triphenyl silanol, Ph₃SiOH, to a cis-enriched solution produced no measurable effect (Fig. S48b). Finally, excess of borax triggered an immediate spectral recovery in a few seconds but led to a slow decomposition of the complex over 24 h (Fig. S48c), consistent with the basic character accelerating re-isomerization.

To assess whether protonation of phenoxide donors affects the photostationary state, we titrated a cis-rich NdL-AzoCF₃SO₃ complex with acetic acid and trifluoroacetic acid (TFA). Acetic acid produced a modest increase in the cis fraction, and re-isomerization to trans remained inducible by glass contact (Fig. S48d). TFA increased the cis fraction at substoichiometric loadings, but once the acid exceeded ca. 0.5 equiv., it induced demetallation and the spectrum converged to that of the protonated ligand and the trans isomer with a loss of reversibility (Fig. S48e). In a trans-rich solution of NdL-AzoCF₃SO₃, TFA likewise generated cis, which triethylamine (TEA) cleanly reverted; several cycles were feasible provided the acid remained below the demetallation threshold (Fig. S48f). Similar titration/irradiation cycles can be performed using glass instead of TEA (Fig. S48g). To probe direct protonation, we assembled a [Nd(CF₃SO₃)₃-L-AzoH₂] complex in situ and the solution immediately adopted the cis state, remained switchable by glass back to trans, and was again re-enriched to cis upon 320 nm irradiation. Storage in the dark for 2 days increased the cis fraction, again recoverable to trans by glass or TEA (Fig. S48h and i). The spectra of cis generated by protonation and by 320 nm irradiation were indistinguishable within experimental uncertainty (Fig. S48j). To complement the UV-vis studies, we recorded ¹H NMR spectra on diamagnetic La³⁺ analogues (deprotonated LaL-AzoCF₃SO₃ and the in situ assembled [La(CF₃SO₃)₃-L-AzoH₂]). These observations are qualitative only, due to concentration-related aggregation and higher concentrations required for NMR (≥10⁻³ M vs. ∼10⁻⁵ M for UV-vis). Irradiation and acid/base/glass treatments produced diagnostic, reversible changes in the azobenzene-adjacent aromatic region consistent with trans/cis interconversions and protonation/deprotonation (Fig. S48k).

All data converge on the protonation–deprotonation mechanism that influences the photostationary state. Mild protonation (acetic acid; substoichiometric TFA) biases the system toward cis, consistent with the literature showing that protonation can facilitate azobenzene isomerization, in part by enabling the azo–hydrazone tautomerism and altering excited-state pathways.⁶⁹ In our system, we hypothesize that protonation of the phenolic lariat arms promotes intramolecular proton transfer to the azo group, generating a hydrazone-type tautomer in which the N–N single bond lowers the rotational barrier (Fig. 6e). This proposal is consistent with our observations that mild acid modestly enriches the cis form, strong acid initially increases cis but ≥0.5 equiv. induces demetallation, and that base/glass (SiO⁻) restores the trans, deprotonated state. The cis state can likewise be generated photochemically (UV/Vis), whereas deprotonation restores the trans state. In this context, glass surfaces act as a benign heterogeneous base: interfacial SiO⁻ sites rapidly and reproducibly reintroduce the trans isomer without increasing the bulk pH or degrading the complex (Fig. 6d and Fig. S48d–k). Controls support this assignment: NaCl is inactive; silanized glass (fewer/basic sites) slows re-isomerization; a molecular silanol (Ph₃SiOH) has no effect; and borate/TEA also regenerates trans but can compromise stability with repeated cycles or higher loadings. Thus, glass functions as a solid–liquid “pH probe” and a gentle base, enabling cis/trans recovery that is otherwise difficult to achieve with chemical reagents.

These results demonstrate that NdL-AzoCF₃SO₃ functions as a dual photoswitch, undergoing efficient trans-to-cis isomerization under both UV and visible light – an uncommon feature in azobenzene-based systems.^66,70–74 Strikingly, the reverse cis-to-trans isomerization cannot be triggered by conventional stimuli such as heat (40 °C), visible light (380–720 nm) or O₂⁷⁵ highlighting the high kinetic stability of the cis-form. Remarkably, we discovered that contact with glass surfaces induces rapid recovery of the trans-isomer, revealing an unprecedented case of glass surface catalyzed re-isomerization. This behaviour was consistent across all synthesized lanthanide series (see section 2.4), distinguishing our system from typical metal–azobenzene complexes and underscoring the critical role of ligand design and coordination environment in tuning the photoresponsive behaviour. Studies on related photoswitches are underway in our laboratory to ascertain if such an approach is compound specific or can be of general use and was up to now overlooked in the literature.

2.4. The effect of lanthanide contraction on structural formation and photoisomerization properties: DFT studies

The photoisomerization behaviour of the free L-AzoH₂ ligand and the [NaL-AzoH₂]CF₃SO₃ and CuL-Azo complexes, compared with that of the NdL-AzoCF₃SO₃ system, highlights the critical role of the lanthanide ion in enabling light-responsive functionality. Coordination of Ln³⁺ ions to the macrocyclic scaffold significantly alters the electronic environment, directly impacting absorption profiles and photoisomerization efficiency.^76–79 Furthermore, structural variation across azobenzene-based metal complexes is known to affect their photochemical behaviour^28,80,81 so we examined photoisomerization across the lanthanide series accordingly.

The LaL-AzoCF₃SO₃, PrL-AzoCF₃SO₃, SmL-AzoCF₃SO₃, EuL-AzoCF₃SO₃, and GdL-AzoCF₃SO₃ complexes exhibit photoisomerization behaviour similar to that of the NdL-AzoCF₃SO₃ macrocyclic complex. All undergo efficient trans-to-cis switching under both 320 nm and 520 nm irradiation, accompanied by pronounced changes in absorption spectra and visible photochromic effects. cis-to-trans back-isomerization occurs rapidly via contact with glass surfaces, consistent across these early lanthanide complexes. Interestingly, they show greater sensitivity to UV light, with low-intensity 320 nm radiation yielding changes comparable to those induced by higher-intensity 520 nm light (Fig. S49–S53). A shift in behaviour appears with the TbL-AzoCF₃SO₃ complex, which shows reduced switching under UV but improves responsiveness to 520 nm visible light (Fig. S54). For later lanthanides (Dy³⁺ to Lu³⁺), 320 nm irradiation induces only minimal spectral changes, indicating suppressed photoisomerization under UV light (Fig. S55a–S59a). The efficiency of photoswitchable behaviour in LnL-AzoCF₃SO₃ complexes is closely governed by the ionic radius of the lanthanide ion, reflecting the influence of lanthanide contraction. Based on this trend, the complexes can be broadly grouped into two categories. The first group (La³⁺ to Tb³⁺) exhibits photoisomerization under both UV (320 nm) and visible (520 nm) light, with generally higher efficiencies under higher energy light, even at lower intensities (Fig. 7a – blue). Within this group, Tb³⁺ shows a noticeable decline in responsiveness. The second group (Dy³⁺ to Lu³⁺) displays little to no response to UV irradiation, though some photoisomerization persists under visible light (Fig. 7a – green). Among the smallest ions (Ho³⁺, Er³⁺, Yb³⁺, Lu³⁺), the observed spectral changes and photochromism are minimal, underscoring a contraction-driven reduction in switching efficiency. Interestingly, it can be related to even smaller Cu²⁺ ions, further showing a combined influence of both the size and electronic nature of the chosen cation on the photoresponsiveness. It remains plausible that metal-dependent electronic structures (e.g., heavy-atom/spin–orbit effects, ligand-field coupling, and differences in nonradiative pathways) modulate the azobenzene excited-state landscape. Direct evidence would require time-resolved spectroscopy and electronic-structure calculations, which will be demonstrated in forthcoming studies.

Fig. 7 (a) Schematic representation of how the lanthanide contraction phenomenon influenced the photoresponsive behaviour of specific groups of lanthanide-based macrocycles, (b) computed rotational energy profiles for azobenzene isomerization in syn-LaL-AzoCF₃SO₃ (red circles) and anti-LuL-AzoCF₃SO₃ (black squares) complexes, showing relative energy (kcal mol⁻¹) as a function of dihedral rotation angle (°) around the N=N bond. Both profiles display distinct minima at cis (0°, 360°) and trans (180°) geometries, with the trans-form being the global minimum in each case.

These distinct behaviours prompted further investigation into the kinetics of photoisomerization across the series. The macrocyclic complexes NdL-AzoCF₃SO₃ and YbL-AzoCF₃SO₃ were chosen as representatives of the early and late lanthanides, respectively. Notably, the Yb³⁺ complex reached its photostationary state faster – after 105 minutes of irradiation – compared to 180 minutes for the Nd³⁺ analogue (Fig. S60 and Fig. 5a). The determined rate constants of the photoisomerization reaction for NdL-AzoCF₃SO₃ (UV light – 320 nm) and YbL-AzoCF₃SO₃ (visible light – 520 nm) were calculated as k_Nd = 7.67 × 10⁻⁵ s⁻¹ and k_Yb = 4.10 × 10⁻⁵ s⁻¹ respectively, using a first-order kinetic equation (Fig. S61). These values are lower than those typically reported for photoactive lanthanide complexes.^{44–46,48,50,51} A comparison of the two reveals that the syn-configured Nd³⁺ complex switches more rapidly than the anti-configured Yb³⁺ analogue.

To explore the structural origin of this behaviour and the influence of lanthanide contraction, we optimized the geometry of the LaL-AzoCF₃SO₃ complex based on its solid-state structure and modeled the lutetium analogue by substituting La³⁺ with Lu³⁺—which was not available in crystalline form. In both models, the coordinating triflate anion was included, yielding nine-coordinate structures (Fig. S62). To validate the predicted structures, ¹HNMR chemical shifts were calculated for both conformers. The simulated spectra (Fig. S63) matched well with the experimental data. In the Lu³⁺ complex, methylene protons adjacent to the crown ether nitrogen atoms appeared at 3.2 and 4.6 ppm – consistent with the anti-conformation (compare with Fig. 4). The deshielding of the aromatic protons further supported this assignment, with a para-positioned proton shifting downfield to 7.83 ppm.

This structural differentiation aligns with the DFT-calculated isomerization energy profiles. Since trans/cis photoisomerization of the azobenzene moiety was experimentally observed to be wavelength dependent, the rotational barrier associated with the trans/cis isomerization was calculated. The same procedure was carried out for comparison with the La³⁺ complex in the syn-conformation, which isomerizes under both 320 nm and 520 nm irradiation and the results are shown in Fig. 7b. As observed and expected, the trans-isomer is more stable in both cases. Notably, the anti-configured Lu³⁺ complex is thermodynamically less stable than the syn-structure by 8.4 kcal mol⁻¹, suggesting that its formation is kinetically driven by the smaller ionic radius of Lu³⁺. However, for the La³⁺ complex, the rotational barrier enabling cis-to-trans conversion is 16.49 kcal mol⁻¹, whereas for the Lu³⁺ complex, a higher barrier of 23.48 kcal mol⁻¹ was calculated. The computed energy profiles reveal that the anti-LuL-AzoCF₃SO₃ complex exhibits significantly higher isomerization barriers (∼35 kcal mol⁻¹) than the syn-LaL-AzoCF₃SO₃ analogue, consistent with the experimentally observed differences in photoisomerization efficiency. These findings collectively indicate that lanthanide contraction imposes rigidity and steric constraints around the azobenzene moiety, reducing conformational flexibility and suppressing photoisomerization.

2.5. Photoluminescence studies and luminescent temperature sensors

Based on the absorption characteristics, the luminescence properties of the sequence of lanthanide-based macrocyclic complexes were investigated in a solid-state form, using a 370 nm excitation source. It is noted that the investigated solid materials have a rigid structure; hence, they do not undergo isomerization and are stable under elevated temperature conditions, at least up to 220–270 °C (see the TGA – Fig. S64–S75), making them suitable candidates for optical sensing applications.

All of the lanthanide-based macrocyclic complexes show the characteristic broad emission band of the L-AzoH₂ macrocyclic ligand (see the spectra for the L-AzoH₂ ligand and complexes in Fig. S76 and S77), with a maximum at around 650 nm, as a result of the π* → π transitions within the macrocyclic ligand (Fig. 8a). Photoluminescence intensity of the macrocyclic complexes decreases when Ln³⁺ ions are incorporated into the complex, which is evidence of ligand-to-metal energy transfer (LMET) from the L-Azo ligand to Ln³⁺ ions, as depicted in the energy level diagram in Fig. 8b. First, the deprotonated L-Azo ligand is excited by UV light from the singlet S₀ to S₁ state, then the intersystem crossing (ISC) process occurs, and the energy is transferred to the triplet state of the ligand. Finally, ligand emission from the excited T₁ state can be observed, together with a simultaneous LMET process, which results in the characteristic emission from Ln³⁺ ions.

Fig. 8 (a) Emission spectra of the L-AzoH₂ macrocyclic ligand (black), and Ln-based macrocyclic complexes in the solid-state form under 370 nm excitation. (b) Energy level diagram for the exemplary NdL-AzoCF₃SO₃ and YbL-AzoCF₃SO₃ macrocyclic complexes (continuous lines – emission; dotted arrows – multiphonon relaxation; dashed arrows – intersystem crossing and energy transfer).

Importantly, three of the Ln-based macrocyclic complexes show the characteristic Ln³⁺ ion emission bands, i.e. SmL-AzoCF₃SO₃ (λ ≈ 680 nm), NdL-AzoCF₃SO₃ (λ ≈ 890 nm) and YbL-AzoCF₃SO₃ (λ ≈ 1000 nm), as a result of the most efficient LMET process. These low-energy NIR-red emissions of the mentioned Ln³⁺ ions are observable because these Ln³⁺ ions have their emitting states located below (in energy) the lowest excited triplet state of the ligand. It is noteworthy that due to the same excitation mechanism for all complexes and inefficient direct excitation of the Ln³⁺ in complexes (forbidden 4f–4f transitions), the excitation spectra for all compounds are almost identical and exhibit the same excitation band, as shown in the exemplary spectrum shown in Fig. S76, which was used to estimate energies of S₁ and T₁ for the purpose of drawing the mentioned energy level diagram, indicating the possible radiative and nonradiative processes occurring in the studied system.

Following an initial evaluation, two materials with the most intense lanthanide emissions, i.e. NdL-AzoCF₃SO₃ and YbL-AzoCF₃SO₃ macrocyclic complexes, were selected, and their emission properties were investigated under varied temperature conditions, from cryogenic to high temperature, i.e. from −180 to 160 °C (Fig. 9). The first NdL-AzoCF₃SO₃ macrocyclic complex shows a broad emission band in the visible (red) range, centred at ≈650 nm, associated with π* → π transition from the macrocyclic part of the complex, as well as sharp emission bands from Nd³⁺ at around 890 nm (⁴F_3/2 → ⁴I_9/2) and 1050 nm (⁴F_3/2 → ⁴I_11/2), accompanied by characteristic narrow peaks due to crystal-field split mJ sublevels (Fig. 9a). It is noteworthy that, in this case, the influence of the Nd³⁺ absorption is also clearly visible in the form of intensity drops (due to Nd³⁺ reabsorption) at around 580, 670, 750 and 800 nm (⁴I_9/2 → ²G_9/2, ⁴F_9/2, ²G_7/2 and ⁴F_5/2 Nd³⁺ transitions, respectively), altering the expected round shape of the broad emission band (π* → π) from the organic component.

Fig. 9 (a and b) Emission spectra of the NdL-AzoCF₃SO₃ (a) and YbL-AzoCF₃SO₃ (b) complexes as a function of temperature; (c and d) the calculated LIRs for the NdL-AzoCF₃SO₃ (c) and YbL-AzoCF₃SO₃ (d) complexes; emission band centroids of Ln³⁺ for the NdL-AzoCF₃SO₃ at ≈890 nm (e) and YbL-AzoCF₃SO₃ at ≈1000 nm (f).

The gradual decrease of luminescence intensity of the deprotonated L-Azo ligand and Nd³⁺ as a function of temperature is a result of thermal quenching of emission in a non-radiative way (inset in Fig. 9a).^82,83 A similar tendency was observed for the YbL-AzoCF₃SO₃ macrocyclic complex in Fig. 9b. However, the change of intensity for both bands (L-Azo and Ln³⁺) was not the same; hence, we could calculate the luminescence intensity ratio (LIR) parameter for both macrocyclic complexes, which can work as a thermometric parameter utilized in optical thermometry. The LIR between two emission bands of the L-Azo ligand and Ln³⁺ ions (i.e.L-Azo/Nd³⁺ and L-Azo/Yb³⁺) changes monotonously from around −70 to 110 °C for the Nd³⁺ complex and from 20 to 160 °C for the Yb³⁺ complex, allowing their use as luminescent thermometers in the indicated operating temperature ranges (Fig. 9c and d). Based on the calculated thermometric parameters, we also calculated the relative thermal sensitivity (S_r) of the developed sensors using eqn (1):

The S_r parameter for the NdL-AzoCF₃SO₃ complex reaches the maximum value of ≈0.89%/°C at around 55 °C (see the inset in Fig. 9c). However, for the YbL-AzoCF₃SO₃ complex, the S_r parameter has the maximum value of ≈1.289% per °C at the highest operating temperature, i.e. at 160 °C (see the inset in Fig. 9d).

Another observed temperature-dependent spectroscopic effect is the spectral shift with temperature. In both materials the spectral position of the L-Azo moiety emission band changes non-monotonously with temperature (data not shown), in contrast to the emission band centroids for the Nd³⁺ and Yb³⁺, which linearly change with temperature. Both emission bands, centered at λ ≈ 890 nm for Nd³⁺ and at λ ≈ 1000 nm for Yb³⁺, show a linear blue-shift, with a rate Δλ = −0.0151 and −0.0381 nm °C⁻¹, respectively, caused by the thermal expansion of the unit cell. Specifically, the observed spectral shift is due to the static contribution caused by the changes in the site geometry, which is occupied by the lanthanide ion in the crystal, as a result of lattice thermal expansion.^82,84 The observed spectral shifts, together with the discussed LIRs allow multi-parameter temperature sensing in a relatively broad T-range. It is worth noting that due to severe quenching of Ln³⁺ luminescence by the solvent molecules, the characteristic emission bands originating from Ln³⁺ ions could be observed only in the solid-state form of the metal–organic complexes studied (see Fig. S78 for comparison). Nonetheless, broad ligand centered emission overlaps the region typically used to excite the cis n → π* band and could possibly be the reason visible irradiation does not drive efficient cis/trans re-isomerization. While metal coordination, aggregation effects and matrix rigidity may also play a role in this, a definitive mechanism will require time-resolved and solvent-dependent studies that are beyond the scope of this study.

3. Conclusions

We report the development of a new class of photoswitchable lanthanide-based macrocyclic complexes, where trans-to-cis isomerization is induced by light and reversed through an unprecedented glass surface-mediated mechanism. Structural and spectroscopic studies across the LnL-AzoCF₃SO₃ series revealed two distinct structural regimes. Complexes from La³⁺ to Tb³⁺ and Er³⁺ adopt a consistent nine-coordinate geometry comprising donor atoms from the diazacrown ether, azobenzene moiety and a monodentate triflate anion. Despite this apparent structural consistency, ¹H NMR and DFT studies identified a conformational shift from a syn- to anti-arrangement as the lanthanide series progresses – correlated with increased ligand rigidity and higher isomerization barriers.

All synthesized Ln-complexes display light-responsive behaviour, with most undergoing reversible trans-to-cis photoisomerization in solution under UV and/or visible light irradiation. Switching efficiency depends on the nature of the lanthanide ion and its electronic structure, with suppression observed in certain cases, particularly for smaller lanthanides, aligning with computational findings and highlighting the impact of lanthanide contraction on the photoswitching dynamics. Notably, the reverse cis/trans isomerization proved unresponsive to conventional triggers such as heat, visible light, or oxygen, but it occurred rapidly upon contact with the glass surface. This unusual recovery combined with the high stability of the cis-isomer introduces an unprecedented case of glass-driven re-isomerization of diazobenzene photoswitches and can be explained on the basis of protonation/deprotonation behaviour.

In addition to the photoresponsive solution behaviour, the solid-state luminescence properties of the complexes were also investigated, with Nd³⁺ and Yb³⁺ complexes exhibiting promising thermosensitive emissions. These systems function as dual VIS/NIR luminescent thermometers, based on LIR and band shifts, representing the first example of such dual photoswitchable and luminescent macrocyclic systems. The combined study of isomerization and emission behaviour under light irradiation underscores the potential of these macrocycles as multi-stimuli-responsive lanthanide platforms. This work provides new insights into the interplay between macrocyclic conformation, metal ion size and external stimuli, offering a valuable design strategy for future development of functional lanthanide-based supramolecular materials.

Author contributions

Dominika Prętka: conceptualization, data curation, investigation, visualization, writing – original draft, and writing – review & editing; Dawid Marcinkowski: formal analysis and resources; Nahir Vadra: investigation and resources; Przemysław Woźny: data curation, investigation, and writing – original draft; Marcin Runowski: conceptualization, visualization, writing – review & editing, and resources; Maciej Kubicki: data curation, formal analysis, visualization, and writing – original draft; Violetta Patroniak: supervision, resources, visualization, and writing – review & editing; Giuseppe Consiglio: formal analysis, methodology, and writing – review & editing; Giuseppe Forte: formal analysis, methodology, and writing – review & editing; Adam Gorczyński: conceptualization, methodology, investigation, visualization, writing – original draft, writing – review & editing, project administration, supervision, resources, and funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the SI and are also available in the public open repository Zenodo at https://doi.org/10.5281/zenodo.15790031.

Supplementary information is available. See DOI: https://doi.org/10.1039/d5qi01461a.

CCDC 2406250–2406258, 2435298, 2435299 and 2480151 contain the supplementary crystallographic data for this paper.^85a–l

Acknowledgements

We acknowledge B.Sc. Antoni Stefaniak for help in the synthesis of the CuL-Azo complex. This work was supported by the National Science Centre, Poland (grant no. 2020/39/D/ST4/01182 (PI: A. G.), 2022/45/N/ST4/00344 (PI: D. M.), 2023/50/E/ST5/00021 (PI: M. R.), 2024/52/C/ST5/00047 (PI: N. V.)).

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Footnote

† Dedicated to Professor Bronisław Marciniak on the occasion of his 75th birthday.

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