Theoretical study of the mechanisms of activation/deactivation of luminescence in a UiO-66 type sensor modified with Ln³⁺ (Eu and Tb) as dopant ions

Abstract

The luminescence properties of MOF-based materials have been improved by incorporating lanthanide ions (Ln³⁺) via post-synthetic modifications (PSM). In this report, a quantum chemical theoretical protocol was carried out to elucidate the detection principle of the turn-on luminescence mechanism in a modified MOF labeled as Ln³⁺@UiO-66-(COOH)₂ (Ln³⁺ = Eu³⁺ or Tb³⁺). The MOF is composed of Zr₆-octahedron {[Zr₆(μ₃-O)₄(μ₃-OH)₄]¹²⁺} nodes; ligands (also called linkers) of 1,2,4,5-benzenetetracarboxylic acid (H₄btec); and Eu³⁺ and Tb³⁺ ions, which coordinate through the free carboxylate groups. The multiconfigurational post-Hartree–Fock method via CASSCF/NEVPT2 calculations and the analysis of rate constants associated with radiative and nonradiative deactivations (k_F, k_P and k_ISC) were used to understand the photophysical processes governing the sensing mechanisms in the Ln³⁺@UiO-66-(COOH)₂ sensor. The most likely sensitization channel is the population of the first excited triplet (T₁) state of the H₄btec linker through intersystem crossing (S₁ → T₁), followed by energy transfer (ET) from H₄btec (T₁) to Eu³⁺ (⁵D₄), followed by vibrational relaxation (VR) processes from the ⁵D₄ state to the ⁵D₀ (Eu³⁺) state, producing radiative deactivation towards ⁷F_J states and enhanced luminescence. Moreover, the Tb³⁺ ion was considered an alternative to Eu³⁺. In this case, the results showed a similar sensitization channel in which energy transfer could occur, likely towards the ⁵D₂ state of Tb³⁺. This theoretical protocol offers a powerful tool to investigate the photophysical properties of MOF-based systems doped with lanthanide ions.

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Introduction

Chemical sensors represent a viable alternative to traditional analytical methods, such as gas chromatography/mass spectrometry (GC/MS) and high-performance liquid chromatography (HPLC), for detecting and monitoring species hazardous to the environment and human health.^1–4 These systems have been employed for the in situ selective detection of biological species,^5,6 volatile organic compounds,⁷ and metal ions.⁸ Their ability to provide accurate health data in real time, combined with their portability and capacity for rapid and reliable detection of various analytes of interest,^9,10 has garnered significant attention. These advantages have driven their widespread application in multiple fields, including medicine, environmental monitoring, and industrial safety.¹¹ An ideal chemical sensor should exhibit key attributes such as stability, reversibility, and high selectivity,^1–4 the latter being essential for differentiating individual compounds within mixtures of unknown composition.^2,3

Luminescent chemical systems have proven to be an effective alternative for the development of optical sensors. Luminescence-based techniques are particularly interesting since the variation in the intensity or energy of photons emitted after excitation can be related to the presence or absence of a particular analyte.^12–15 In this context, several studies have pointed to metal–organic frameworks (MOFs) as promising materials for chemical detection due to their exceptional optical and structural properties. These materials are porous and crystalline organic–inorganic hybrids. Their structure is composed of clusters or metal ions (nodes) coordinated with organic ligands (linkers), forming three-dimensional networks with unique chemical reactivity. Due to their organic and metallic composition, luminescence is produced through several types of mechanisms, including energy transfer (ET) and charge transfer (CT). CT can be categorized into linker-metal charge transfer (LMCT) or metal-linker charge transfer (MLCT).^16–18

Among MOFs, the zirconium-based MOF UiO-66 stands out. It was named in honor of the University of Oslo, where it was first synthesized by Lillerud et al. in 2008.^19,20 UiO-66 is composed of secondary building units (SBUs) based on Zr₆-clusters, specifically Zr₆(μ₃-O)(μ₃-OH)₄)(COO)₁₂⁻ octahedral SBUs, which are interconnected by twelve 1,4-benzenedicarboxylate (BDC) linkers. The remarkable chemical stability of UiO-66 under diverse conditions, including exposure to air, water, organic solvents, and elevated external pressures, can be attributed to the robust Zr–O bonds and high coordination number between the Zr₆-clusters and the BDC linkers.²¹ This stability is a result of the high charge density and bond polarization of Zr⁴⁺ ions, which demonstrate a strong electron affinity when interacting with the oxygen atoms of the carboxylate groups in the BDC linkers.²² This MOF demonstrates exceptional thermal and hydrolytic stability,²³ rendering it highly suitable for practical applications, such as chemical sensing, across diverse environments.²⁴ A distinctive characteristic of these materials is their capacity to enhance optical properties by strategically integrating functional groups²⁵ or metal ions²⁶ into their frameworks. This modification results in a material that is isostructural to UiO-66, maintaining its inherent chemical and physical properties, while significantly boosting its optical performance. UiO-66 exhibits several properties that make it promising for the detection of a wide range of analytes, including target molecules such as amyloid-β (Aβ) (1–42) monomers,²⁷ volatile organic compounds (VOCs),²⁸ and dimethyl methylphosphonate (DMMP),²⁹ and metal ions.³⁰ Among the studied sensor materials, MOFs are a very interesting type that possess an important advantage over other classes of chemical sensors. For instance, their exceptional properties have led researchers to explore post-synthetic modification techniques (PSM) to obtain new materials, modifying many of their original properties without altering their topology.^9,31–33 This approach has become an important area of research, as it offers the possibility of introducing functional groups into the pores of MOFs, including species such as anions and cations, achieving an improvement in the structural stability of MOFs and introducing the desired properties into the material.^34–37

Experimental and theoretical studies have investigated the electronic structures of UiO-66-type MOFs.^38–41 Research employing density of states (DOS) analysis⁴⁰ and electron paramagnetic resonance spectroscopy (EPR)³⁸ have indicated that electron transitions between ligands and metals have a low probability. These materials, which include both substituted and unsubstituted BDC linkers, suggest that the optical (absorption and emission) properties arise from the building components due to the linkers (conjugated organic ligands). DOS calculations for UiO-66(Zr) have shown that the lowest unoccupied metal orbital of Zr 4d is positioned approximately 2.0 eV above the lowest unoccupied linker orbital, highlighting the inefficient linker-to-metal charge transfer (LMCT) process.⁴¹ This is characteristic of secondary building units (SBUs) based on closed-shell metal-ion complexes.¹³

A new generation of L-MOFs are those functionalized with lanthanide (Ln) ions (Ln@MOF) through PSM to activate the emission properties of the material and generate new emission signals centered on the lanthanide ions.^32,33,42,43 The improvements in the luminescent properties of these Ln ion-modified materials are the main attraction, which is due to the sharp line emissions, high color purity, high luminescence quantum yield and large Stokes shifts, attributed to the 4f–4f transitions and relativistic effects of Ln ions.^44–46

The functionalization of UiO-66 with Ln(III) ions, referred to as Ln(III)@UiO-66, has emerged as a promising platform to develop luminescent chemical sensors for detecting metal ions.⁴⁷ This is attributed to the exceptional structural properties and chemical stability of UiO-66, combined with the remarkable luminescent properties of Ln(III) ions. For UiO-66, it has been reported that the light absorption depends on the linker, and for Ln(III)@UiO-66, the sensitization and emission pathways involve a linker that absorbs light in the UV region and transfers energy from its excited electronic state to the resonance level of the Ln(III) ions.^22,48–50 Upon interaction with an analyte, several phenomena can occur that affect the luminescence behavior: the analyte may quench the emission by introducing non-radiative decay pathways, modify the energy levels of the linker and thereby disrupt the energy transfer mechanism, or, in some cases, enhance the emission by stabilizing the excited states or facilitating more efficient energy transfer.^4,51–53 Another mechanism of sensing recently investigated for Ln(III)@UiO-66 sensors is the exchange of the emitted center (Ln³⁺) in the coordination environment of the antenna ligand by the analyte.⁵⁰ This process quenches luminescence (turn-off sensing) by locking the sensitization path between ISC and ligand-to-metal energy transfer due to substitution of the Ln³⁺ ions. These luminescence modulations form the basis for detecting and quantifying the presence of specific analytes using Ln(III)@UiO-66 as an optical sensor.

For the specific case of compounds that present lanthanide Ln(III) ions in their structure, the most relevant properties that support many of the applications of these compounds originate from symmetry-forbidden 4f–4f transitions. However, these transitions exhibit very weak absorption, which results in very weak luminescence. Their luminescence arises from a sensitization process carried out by ET through a suitable organic linker to the Ln ions, which is called the “antenna effect”.^55–57 The process requires ISC (S₁ → T₁) in the linker, with a ΔE(S₁ → T₁) of ∼5000 cm⁻¹ (Reinhoudt's rule) to ensure efficient ISC.⁵⁸ This ISC will show a large rate if the transition involves a change in the type of molecular orbitals (El-Sayed rules).^59,60 Thus, to efficiently sensitize Ln ions, the T₁ energy should be higher than the resonance energy of Ln, with ΔE (T₁ → Ln) ∼ 2500–4000 cm⁻¹ (Latva's rule).⁶¹ In this regard, it is important to consider the structure of antenna linkers that act as good sensitizers, which is a critical point in the development of good Ln(III) compounds and a valid elucidation of the energy transfer pathways, which is essential for accurate determination of the electronic states of the lanthanide fragment.^55,57,62,63

Accurate and fine computational approaches have been rigorously applied by our group for the study of MOFs with Ln in their nodes. In this regard, Zarate et al.¹⁴ carried out theoretical procedures, via quantum chemical computations, to elucidate the detection principle of the turn-off luminescence mechanism of an Eu-based metal–organic framework sensor (Eu-MOF). The analyte in this study was the nitroaromatic compound aniline. Specifically, the energy transfer channels that operate in this MOF, as well as the mechanism of luminescence quenching by interaction with the analyte, were investigated using well-known and accurate multiconfigurational ab initio methods along with TD-DFT. A detailed study of the sensitization pathway from the linker (antenna) to the lanthanide was accomplished. It starts with the intersystem crossing (ISC) from the first excited singlet (S₁) to the first excited triplet (T₁) electronic states of the linker, with subsequent energy transfer to the ⁵D₀ state of Eu³⁺ followed by the emission to the ground multiplet ⁷F_J. In the same framework, Zarate et al.⁶⁴ employed computational quantum chemistry methods to demonstrate the importance of the host–guest interaction simulations and the rate constants of the radiative and nonradiative processes, to understand the sensing mechanism in the Ln-MOF sensors; in this case, a sensor with Tb³⁺.

The computational protocol developed by our group^14,52,65 has proven to be a valuable tool for studying luminescent MOFs modified with lanthanide ions (Ln@MOFs). This methodology allows for a rigorous analysis of the activation and deactivation mechanisms responsible for lanthanide-centered luminescence within these materials. This protocol was successfully applied in a previous study by our group, in which we studied an analogous system, Eu@UiO-66(DPA), designed as a selective turn-off luminescent sensor for Hg²⁺ ions.⁵⁴ In that study, the MOF incorporated 2,6-pyridinedicarboxylic acid (DPA) as an antenna ligand, which allowed us to elucidate how the substitution of Eu³⁺ with Hg²⁺ affected the electronic structure of the system and caused the suppression of emission. Based on this methodology, the present work applies the same theoretical framework to investigate a different MOF platform.

In this paper, the system of interest is a modified MOF labeled as Eu³⁺@UiO-66-(COOH)₂, which is composed of nodes of Zr₆-octahedron {[Zr₆(μ₃-O)₄(μ₃-OH)₄]¹²⁺}, linkers of 1,2,4,5-benzenetetracarboxylic acid (H₄btec), and Eu(III), which is coordinated through the free carboxylate groups, forming a rigid coordination network, as reported by Ji-Na Hao et al.⁵² (Fig. 1). The structural difference presented by this MOF implies that the detection mechanisms are intrinsically different from the systems recently studied by our research group, which is relevant from the point of view of its practical application. Although the system investigated in this work includes Eu³⁺ ions as the emitting center, the theoretical prediction of the photophysical behavior when Eu³⁺ is replaced with Tb³⁺ is also explored for the first time, with the aim of evaluating its potential performance in optical sensors. This study focuses on a systematic comparison of the luminescence sensitization mechanisms of both ions (Eu³⁺ and Tb³⁺) incorporated into the UiO-66-(COOH)₂ structure, an aspect that was not addressed in previous research recently carried out by our research group, which focused exclusively on Eu³⁺. This comparative approach allowed the optical response of the material to be optimized, revealing that the incorporation of Tb³⁺ significantly improves the luminescent efficiency of the system, highlighting its potential in the design of advanced optical sensors and light-emitting devices.

Fig. 1 Simplified scheme showing the increase in light emission by sensitization from the linker to the inserted Eu³⁺ ion.

Computational details

A representative cluster model, corresponding to a finite fragment of the extended UiO-66, was constructed by truncating the crystalline structure derived from the experimental crystal data available in the Cambridge Crystallographic Data Centre (CCDC 1018045).⁶⁶ This procedure was performed due to the large size of the MOF, considering the particularities of the system that represents the structure of interest.^52,67,68 This methodology is based primarily on the fact that these materials exhibit a unique electronic structure with highly localized electronic states.^67–69 In the theoretical study reported here, UiO-66-(COOH)₂ was truncated to a fragment constituted by the Zr₆-octahedron {[Zr₆(μ₃-O)₄(μ₃-OH)₄]¹²⁺} node, four linkers of 1,2,4,5-benzenetetracarboxylic acid (H₄btec) and eight truncated linkers, as can be seen in Fig. 2a. Afterwards the Lanthanide (Ln³⁺) was coordinated as a doping species, which we refer to as Ln³⁺@UiO-66-(COOH)₂ (Fig. 2b). In this work, we have also considered the potential sensitization of luminescence for the Tb³⁺ ion because it shares a similar electronic structure to Eu³⁺ in terms of electrons and holes. In previous work, the sensitization of these ions by similar antennas has been successfully studied using the fragmentation scheme described above.^{55,57,63,70,71}

Fig. 2 Optimized geometry of the truncated systems at the BP86/def2-TZVP theoretical level: (a) UiO-66-(COOH)₂ and (b) Ln³⁺@UiO-66-(COOH)₂ (Ln³⁺ = Eu³⁺ or Tb³⁺).

Geometry optimizations of the ground state (S₀) of both systems, UiO-66-(COOH)₂ and Ln³⁺@UiO-66-(COOH)₂, including for the latter the coordination sphere of lanthanide, were carried out using density functional theory (DFT), with the ORCA 5.0.3 software package.⁷² Generalized Gradient Approximation (GGA) Becke-Perdew (BP86)⁷³ exchange–correlation functional was employed together the basis set, triple-ζ valence with one sets of polarization functions, def2-TZVP⁷⁴ for all atoms except for Eu and Tb which were computed with the DKH optimized SARC with TZVP quality.^75–78 The structure of the T₁ state of the UiO-66-(COOH)₂ system was optimized at the same level of theory.

In the second stage of this work, a study of the optical properties related to light absorption of the UiO-66-(COOH)₂ and Ln³⁺@UiO-66-(COOH)₂ systems was carried out, using the time-dependent DFT (TD-DFT) approach as implemented in the ORCA 5.0.3 software package.⁷² The polarized triple-ζ basis set (TZV) def2-TZVP⁷⁴ was used with the hybrid-GGA Perdew–Burke–Ernzerhof (PBE0).⁷⁹ The RIJCOSX approximation was used to accelerate the SCF calculation by the combination of the RIJ method for the Coulomb term with the “chain of spheres” COSX approximation and their respective auxiliary basis set for computation of two-electron integrals.⁸⁰

Starting from the optimized structure in the excited state T₁ of the UiO-66-(COOH)₂ system, the emission energies were assessed to analyze the optical properties through the time-dependent DFT (TD-DFT) approach, using the hybrid exchange and correlation functional, Perdew–Burke–Ernzerhof (PBE0)⁷⁹ via the ORCA 5.0.3 software package.⁷² Furthermore, the polarized triple-ζ basis set (TZV) quality def2-TZVP⁷⁴ was used for the C, H, N, and O atoms.

To elucidate the sensitization and emission pathways, the theoretical procedure reported by Beltrán-Leiva et al.^55,57,63 was applied. The wave function that describes the ground- and excited-states of the Eu-fragment and the linker fragment was obtained through CASSCF methods.⁸¹ A dynamic correlation was also included by means of the n-electron valence state perturbation theory (NEVPT2) approach.⁸² In this approximation, for trivalent Eu³⁺, all possible distributions of six unpaired electrons among the seven 4f active orbitals CAS (6,7) were considered, which included 7 septuplets, 40 quintuplets, 30 triples, and 20 singles.⁶³ Similarly, for Tb³⁺, the active space considered was CAS (8,7), including the same number of states in each multiplicity. The same level of theory was used to obtain the energy values of the S₀, S₁, and T₁ electronic states for the [H₄btec]⁻ linker. For this fragment, an active space of ten electrons in ten orbitals CAS (10, 10) was used, all of them with π character.

We analyzed the excited-state dynamics of the antenna linker [H₄btec]⁻ to establish the activation/deactivation channels of the photophysical processes that introduce Eu³⁺ as a doping species. The calculations of the excited state dynamics of the antenna linker were performed based on the strategy (fragmentation scheme) proposed by M. J. Beltrán-Leiva et al.⁵⁷ for organometallic complexes based on lanthanides. This procedure involved the geometry optimizations and frequency calculations of the ground state and the first excited states (singlet and triplet) of the linkers of the Ln³⁺@UiO-66-(COOH)₂ system. Using the ORCA ESD module of the ORCA 5.0.3 software package,⁷² we calculated the intersystem crossing (ISC), phosphorescence, and fluorescence rates, which we will refer to as k_ISC, k_P, and k_F, respectively.^57,62 The energy transfer rates were determined using time-dependent density functional theory (TD-DFT) calculations in conjunction with the LUMPAC software package⁸³ (https://lumpac.pro.br/).

Due to the availability of experimental results for the Eu³⁺ system, the discussion will focus on this ion in the following section, leaving the discussion of Tb³⁺ for the luminescence sensitization section.

Results and discussion

Optical properties and structure

The structural models proposed for both systems, in general, successfully reproduce the geometrical parameters. The computed and experimental bond lengths for [Zr–O(linker)], [Zr–O(μ₃-OH)] and [Zr–O(μ₃-O)] displayed a good correlation. The theoretical magnitudes are 2.22 Å, 2.24 Å and 2.09 Å, respectively, and the reported experimental data are 2.23 Å, 2.25 Å and 2.06 Å, respectively, for this MOF.⁸⁴

The vertical excitation energies also agree with the experimental values reported for both systems, as can be seen in Table 1. In the computed absorption spectrum of UiO-66-(COOH)₂ (see Fig. S1a in the SI), absorption bands centered at 294 and 295 nm appear, which are attributed to several configurations with vertical transitions from the frontier molecular orbitals. These correspond to π–π* transitions of the linker (H₄btec), which is in good agreement with the reported experimental excitation wavelength at around 350 nm.⁵² The molecular orbitals involved in these electronic transitions can be seen in Fig. S2. The difference in energy is within the error range of the TD-DFT method (roughly 50 nm).^64,85 In case of the Eu³⁺@UiO-66-(COOH)₂, the simulated absorption spectrum displays absorption bands centered at 296 and 299 nm, which correspond to π–π* transitions (see Fig. S1b and Fig. S3), and is in great accordance with the reported experimental absorption wavelength at 322 nm.⁵² Small variations in the position of the bands towards higher wavelength values are observed because the coordination of the Eu³⁺ ion produces polarization effects on the linker, resulting in an increase in the electron cloud and a stabilization in energy.⁵⁵

Table 1 Electronic transitions for the absorption and emission processes of the linkers at the PBE0/def2-TZVP theoretical level for UiO-66-(COOH)₂ and Eu³⁺@UiO-66-(COOH)₂^a

System	λmax (nm)	ƒ	Active MO	Assignment
a H is HOMO, L is LUMO. Abbreviations: HOMO (highest energy occupied orbital); LUMO (unoccupied orbital of lower energy); MO (molecular orbital). Experimental values for absorption bands of UiO-66-(COOH)2 and Eu^3+@UiO-66-(COOH)2 are 350 and 322 nm (ref. 52) and emission for UiO-66-(COOH)2 is observed at 393 nm.^53
UiO-66-(COOH)2 absorption	295	0.03	H−1 → L+3	π(L^H4btec) → π*(L^H4btec)
	294	0.03	H−1 → L	π(L^H4btec) → π*(L^H44btec)
	294	0.02	H−1 → L+1	π(L^H4btec) → π*(L^H4btec)
Eu^3+@UiO-66-(COOH)2 Absorption	299	0.01	H−4 → L+1	π(L^H4btec) → π*(L^H4btec)
	296	0.03	H−5 → L+1	π(L^H4btec) → π*(L^H4btec)
UiO-66-(COOH)2 Emission	338	0.05	L → H	π(L^H4btec) → π*(L^H4btec)

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It is interesting to note that, according to the results obtained by TDDFT calculations, the presence of the lanthanide ion does not notably influence the absorption spectrum. The absorption bands are localized on the linker, since the molecular orbitals involved in the S₀ → S₁ electronic transition remain mostly located on the π system of the organic linker, without a relevant participation of the Eu³⁺ ion. This indicates that the adsorption process is mainly governed by the electronic structure of the antenna ligand, independently of the lanthanide center. It is known that the metal–ligand interaction in these complexes is ionic in nature, and the internal character of the 4f shell prevents any metal–ligand charge transfer. The ligand–metal transfer is likewise impeded because the vacant orbitals of the metal are usually sufficiently high in energy and cannot be accessed by electrons of the ligand.

Consequently, no direct electronic transfer between the lanthanide ion and the ligand occurs, which validates the approach of considering the ligand model in isolation in the CASSCF/NEVPT2 multiconfigurational calculations, since the sensitization of Ln³⁺ occurs by nonradiative energy transfer from the ligand triplet state (T₁) to the emissive levels of the lanthanide ion, and not by direct coupling via charge transfer.

Regarding the emission, UiO-66-(COOH)₂ shows a broad emission band, arising from the π–π* transitions of the linkers (H₄btec).⁵² TD-DFT results show a π–π* transition centered on the linker, which is composed of the frontier molecular orbitals shown in Fig. S4. The emission band obtained theoretically is centered at 338 nm, which is in good agreement with the experimental emission wavelength reported for the isolated ligand at around 393 nm.⁵³ The difference in energy is within the error range of the TD-DFT method (approximately 50 nm).^64,85

Sensitization and emission pathways

The sensitization and emission pathways in MOF modified with lanthanides (Ln@MOF) involve a step in which energy is transferred from the T₁ electronic state of the linker to a resonant level of the Ln³⁺ ions, [Linker (T₁) → Ln³⁺]. This ET process is possible because spin–orbit coupling (SOC) induces a mixture of states of different multiplicities of the metal.^14,55 In this regard, Crosby et al.⁸⁶ point out that the energy of the T₁ electronic state of the linker respects the 4f excited states energy of the lanthanide ion, as well as the vibrational coupling between these states, allowing efficient sensitization to the lanthanide. In addition, Latva et al.⁶¹ emphasize that the accurate estimation of the T₁ electronic state energy of the antenna plays a key role in determining the most likely sensitization mechanism, with this energy being in the range of 2500–4000 cm⁻¹.

To gain a deeper understanding of the most probable sensitization and emission mechanisms, further ab initio calculations were performed to correctly determine the electronic states of the linkers and lanthanide ions involved in the sensitization mechanism.

Based on the foregoing and considering that the absorption in the Eu³⁺@UiO-66-(COOH)₂ system is linker-centered H₄btec, we applied the fragmentation scheme reported by Beltrán-Leiva et al.^57,63 in 2017 for lanthanide(III) complexes. Based on this methodology, we separate the systems into two fragments, one of which consists of the lanthanide moiety, while the other constitutes the linker according to the system (see Fig. S5 in the SI). For the theoretical treatment of the europium fragments, due to the ionic nature of the metal–ligand interaction and the internal nature of the 4f shell, a crystal field model, considering the first coordination sphere and simplifying the rest of the ligand, is enough to correctly describe the electronic states of the lanthanide ion.^57,63 In this sense, the CASSCF approximation in combination with the NEVPT2 method is a powerful methodology to treat the electronic static and dynamic correlation effects, respectively.

Based on the above and in accordance with the results obtained through TD-DFT, the [H₄btec]⁻ fragment is responsible for the photon absorption; therefore, it was studied to evaluate the sensitization channels in the Eu³⁺@UiO-66-(COOH)₂ system. The [H₄btec]⁻ fragment was treated at the same theoretical level as for the europium fragment (CAS (6,7) SCF/NEVPT2), considering an active space of ten orbitals CAS (10,10) all π character. In Table 2, the S₁ electronic state, with a 63% contribution of the configuration (π → π*) at 39 853 cm⁻¹, and the T₁ electronic state, with a 72% contribution of the same configuration at 32 148 cm⁻¹, correspond to the excited states of the antenna linker [H₄btec]⁻. These results are analyzed in detail by means of CASSCF/NEVPT2 calculations, which provide information on the active orbitals involved and their fractional occupancy. This occupancy, which can be complete or intermediate, is in an optimal range, suggesting that the selected orbitals are adequate to correctly describe the electronic behavior of the molecule.^55,57,81 Thus, the correct distribution of electrons in the active orbitals allows an accurate description of the excited states observed, as listed in the SI Table S1, confirming the validity of the results obtained for the S₁ and T₁ electronic states in the framework of the theoretical calculations.

Table 2 Singlet and triplet energy states and the most important configurations obtained from a CAS (10,10) SCF/NEVPT2 calculation for the linker [H₄btec]⁻ fragment

States		Energy, cm^−1
		CASSCF	NEVPT2	Weight (%)	Configuration
All the values reported in the table were computed by means of CASSCF and NEVPT2 using the ORCA 5.0.3 software package.^72
Singlet	S1	36 989	39 853	28	π^2 π^2 π^2 π^1 π^2 π^1 π^0 π^0 π^0 π^0
				21	π^2 π^2 π^2 π^2 π^1 π^0 π^1 π^0 π^0 π^0
				14	π^2 π^2 π^2 π^2 π^1 π^1 π^0 π^0 π^0 π^0
	S2	53 455	42 698	41	π^2 π^2 π^2 π^2 π^1 π^1 π^0 π^0 π^0 π^0
				17	π^2 π^2 π^2 π^1 π^2 π^1 π^0 π^0 π^0 π^0
Triplet	T1	28 078	32 148	43	π^2 π^2 π^2 π^2 π^1 π^1 π^0 π^0 π^0 π^0
				17	π^2 π^2 π^2 π^1 π^2 π^1 π^0 π^0 π^0 π^0
				12	π^2 π^2 π^2 π^1 π^2 π^0 π^1 π^0 π^0 π^0
	T2	36 246	36 338	25	π^2 π^2 π^2 π^2 π^1 π^1 π^0 π^0 π^0 π^0
				25	π^2 π^2 π^2 π^1 π^2 π^1 π^0 π^0 π^0 π^0
				12	π^2 π^2 π^2 π^1 π^2 π^0 π^1 π^0 π^0 π^0

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According to Reinhoudt's rule,⁵⁸ the intersystem crossing (ISC, S₁ → T₁) is most efficient when the energy difference between the first singlet and triplet excited states is around 5000 cm⁻¹. However, this rule is empirical and should be understood as an optimal range rather than an absolute limit. Therefore, the efficient occurrence of the ISC process is not ruled out when the energy difference is outside this range, since it depends on the specific characteristics of the system under study. In case of the Eu³⁺@UiO-66-(COOH)₂ system, the calculated energy difference between the S₁ and T₁ states is 7704 cm⁻¹, a value larger than the one proposed by that rule. Despite this, experimental evidence reports the characteristic emission bands of the Eu³⁺ ion, indicating that the population of the T₁ state and the subsequent energy transfer to the Eu³⁺ ion occur efficiently.⁵² To validate this hypothesis beyond an empirical estimate, we further consider the strong spin–orbit coupling (SOC) effect characteristic of Ln³⁺ ions in this type of material, which induces a significant mixing of electronic states with different multiplicities. This phenomenon alters the electronic levels distribution and favors the coupling between singlet and triplet states, facilitating an efficient intersystem crossing (ISC), even when the S₁-T₁ energy difference is outside the empirically proposed optimal range. Furthermore, the excited state dynamics of the [H₄btec]⁻ antenna ligand were studied to perform a more rigorous quantitative analysis. This approach allowed us to determine the rate constants associated with the photophysical deactivation processes (fluorescence (k_F) and intersystem conversion (k_ISC)), thus providing a solid quantitative basis for assessing the efficiency of the proposed sensitization mechanism. The obtained results show that the ISC channel is favored over fluorescence. In particular, the rate constant for the ISC process (S₁ → T₁) was 4.43 × 10⁸ s⁻¹, being three orders of magnitude higher than the k_F fluorescence constant (S₁ → S₀), which was found to be 3.18 × 10⁵ s⁻¹ (see Fig. 3). These results confirm that, although the S₁–T₁ energy difference is above the empirical optimal range, the ISC mechanism remains highly efficient, constituting the predominant pathway for the population of the T₁ state and subsequent sensitization of the Eu³⁺ ion.

Fig. 3 Diagram of energy levels illustrating the most probable pathways for sensitization and emission for the Ln³⁺@UiO-66-(COOH)₂ (Ln³⁺ = Eu³⁺ or Tb³⁺) system. Intersystem crossing, phosphorescence, fluorescence, energy transfer, and back energy transfer rates are represented by k_ISC, k_P, k_F, k_ET and k_BET, respectively.

The proposed structural model for the europium fragment and the selection of the active space in the CAS (6,7) SCF/NEVPT2 calculations have proven to be effective in accurately reproducing the energy values of the Eu³⁺ ion electronic states, which are in agreement with the experimental values reported for this lanthanide.⁸⁷ The obtained results, reflected in the SI Table S2, show the selected active orbitals and their respective fractional occupancy numbers, which are in the optimal range.^55,57,81 This fit in orbital occupancy indicates that the orbitals were adequately chosen to describe the excited states of the system, ensuring that the theoretical calculations faithfully reflect the electronic behavior of the europium fragment and provide an accurate representation of its electronic properties.

According to the CAS(6,7)SCF/NEVPT2 calculations, the S₁ electronic state [H₄btec]⁻ is situated in energy well above the electronic states of the lanthanide, for this reason the probability of an ET process from this state can be considerably reduced, but this is not the case for the electronic state T₁ [H₄btec]⁻, which is situated 3589 cm⁻¹ above the electronic state ⁵D₄ (28 558 cm⁻¹) of the Eu³⁺ ion. Therefore, the most likely mechanism is an ET channel from the T₁ [H₄btec]⁻ to the ⁵D₄ electronic state of Eu³⁺, with this energy gap being in good agreement with the optimal range, to sensitize Eu³⁺ ion luminescence based on Latva's rule⁶¹ ΔE (Linker T₁ → Ln³⁺) ∼ 2500–4000 cm⁻¹. Moreover, as shown in Fig. 3, the k_P rate is 1.11 × 10³ s⁻¹, which means that the lifetime of the T₁ [H₄btec]⁻ electronic state favors ET channels from the [H₄btec]⁻ (T₁) → Eu³⁺ (⁵D₄) electronic state, from where ⁵D₄ vibrational relaxation processes occur until populating the electronic state ⁵D₀ electronic state (18 637 cm⁻¹) from which radiative deactivation to ⁷F_J states occurs, resulting in the luminescence turn-on of Eu³⁺@UiO-66-(COOH)₂ system (see Fig. 3).

Based on the previously discussed ISC process, favored by the presence of a heavy metal and the S₁–T₁ energy difference, it is correct to assume that the energy transfer mechanism can also occur for the Tb³⁺ ion. In fact, even when the energy difference between the ⁵D₄ (∼23 600 cm⁻¹) emissive state of Tb³⁺ and the triplet state of the antenna is out of the range set by Latva's rule, the energy transfer mechanism would favor higher energy electronic states. The energy difference between the T₁ electronic state of the antenna ligand and the ⁵D₂ (∼29 300 cm⁻¹) excited state of the ion is ∼2800 cm⁻¹. From these results, it is possible to conclude that a mechanism like that described for Eu³⁺ will be possible for the Tb³⁺ ion, with sensitization occurring most likely through the ⁵D₂ electronic state (see Fig. 3).

While empirical rules, such as Latva's rule, provide general guidelines on the efficiency of sensitization based on the energy differences between the triplet state of the ligand and the excited states of the lanthanide ion, they should not be interpreted as absolute limits. In this study, such rules serve as a starting point to suggest the feasibility of the ET process. However, to quantitatively validate this hypothesis, ET and back energy transfer (BET) rates were calculated using LUMPAC software⁸³ for the Eu³⁺ doped system. Thus, this analysis was not performed for the material containing the Tb³⁺ ion as a dopant species, due to the absence of reported experimental data for this system. The obtained values allow a more precise determination of the efficiency of the sensitization process, overcoming the limitations of a purely qualitative or empirical evaluation.

As shown in Fig. 3, ET rates (k_ET) are distributed in a range from 10⁻⁷ to 10⁷ s⁻¹. This behavior reflects the negative values of k_ET, corresponding to the electronic state S₁, indicating unfavorable or even nonexistent energy transfer from that state to the Eu³⁺ ion. In contrast, the k_ET values associated with the T₁ state suggest that this state does allow a viable and efficient energy transfer channel. Consequently, the T₁ state of the ligand is identified as the primary sensitization pathway.

In contrast, the S₁ state is found to be inadequate for ET processes, which is attributed to its energy mismatch and the low probability of resonant coupling with the electronic levels of the Eu³⁺ ion. The k_ET (S₁–⁵D₄) = 1.83 × 10⁻¹ s⁻¹, k_ET (S₁–⁵D₁) = 1.92 × 10⁻⁵ s⁻¹ and k_ET (S₁–⁵D₀) = 2.58 × 10⁻⁷ s⁻¹ are lower than the corresponding values for probable ET from the T₁ electronic state, with k_ET (T₁–⁵D₄) = 1.58 × 10² s⁻¹, k_ET (T₁–⁵D₁) = 1.45 × 10⁷ s⁻¹ and k_ET (T₁–⁵D₀) = 1.01 × 10⁷ s⁻¹. This result supports the hypothesis raised from the empirical rules and sustains the conclusion that the sensitization process is feasible, being quantitatively more efficient from the triplet state of the ligand. In particular, the magnitude of the k_ET rates from the T₁ state (on the order of 10²–10⁷ s⁻¹) evidences that this channel represents the dominant pathway for the luminescence activation process in the Eu³⁺@UiO-66-(COOH)₂ system.

Based on the BET values rates: k_BET (⁵D₄–T₁) = 4.01 × 10¹² s⁻¹, k_BET (⁵D₁–T₁) = 5.48 × 10⁻¹ s⁻¹ and k_BET (⁵D₀–T₁) = 9.39 × 10⁻⁵ s⁻¹, the high value of k_BET from the ⁵D₄ state to the T₁ state could imply a competitive effect favoring non-radiative processes, negatively affecting the emission quantum yield. However, this phenomenon does not invalidate the efficiency of the sensitization mechanism, since the k_BET values for the lower emissive states of Eu³⁺, ⁵D₁ and ⁵D₀, turn out to be significantly lower. This suggests that, once the lower emissive levels are reached, radiative emission can proceed efficiently, without considerable energy loss to the triplet state of the ligand. Thus, these results support the experimental observations of luminescence in the system, demonstrating that, despite the possible unfavorable effect of k_BET from the ⁵D₄ level, the emission process is still viable and effective. Likewise, the BET rates k_BET (⁵D₄–S₁) = 3.12 × 10⁻²⁷ s⁻¹, k_BET (⁵D₁–S₁) = 4.87 × 10⁻⁴⁹ s⁻¹ and k_BET (⁵D₀–S₁) = 1.60 × 10⁻⁵⁴ s⁻¹ confirm the negligible role of the BET process for the electronic state S₁ in this system.

To design luminescent sensors based on MOFs, it is crucial to emphasize the central role played by the Ln³⁺ ion in the mechanism of luminescence activation and deactivation. The efficiency of the sensitization process depends directly on the proper energy transfer from the triplet state (T₁) of the antenna ligand to the emissive electronic levels of the Ln³⁺ ion, such as the ⁵D₀ (Eu³⁺) or ⁵D₄ (Tb³⁺) states. This adequate transfer refers to an optimal energy match between the T₁ state of the ligand and the excited levels of the Ln³⁺ ion, where the energy difference must be within a range that favors coupling without inducing unwanted processes such as backward energy transfer (BET) or non-radiative relaxation. Various empirical rules, such as Latva's rule,⁶¹ suggest that effective coupling occurs when this difference is 2500–4000 cm⁻¹. Furthermore, the modulation of the emission efficiency is conditioned by the ability of the Ln³⁺ to compete effectively against non-radiative deactivation routes, such as vibrational relaxation (VR) and backward energy transfer (BET). Therefore, the Ln³⁺ ions not only act as an emissive center but also regulate the viability of the entire photoactive process, positioning itself as the key element in the design of highly efficient luminescent materials.

Conclusions

In this investigation, TD-DFT and multireference calculations were used to evaluate the potential energy transfer mechanism and to assess the rate constants associated with the radiative and nonradiative deactivations involved in the sensitization process. The results help to explain the photophysical processes that govern the sensing mechanisms in the Eu³⁺@UiO-66-(COOH)₂ sensor and demonstrate the potential extension to Tb³⁺. In this work, truncated versions of the extended structures of UiO-66-(COOH)₂ and Ln³⁺@UiO-66-(COOH)₂ (Ln³⁺ = Eu³⁺ or Tb³⁺) systems were constructed as finite structural models that successfully reproduced the geometric parameters and photophysical properties of the systems. The most probable sensitization channels for the Ln³⁺@UiO-66-(COOH)₂ system were described based on CASSCF/NEVPT2 calculations and by examining the antenna excited state dynamics, taking into account intersystem crossing (k_ISC), fluorescence (k_F), and phosphorescence (k_P) rate constants. The results indicate that the most likely sensitization pathway involves the population of the T₁ electronic state of the [H₄btec]⁻ linker through the ISC process (S₁ → T₁) and subsequent ET of the [H₄btec]⁻ (T₁) → Eu³⁺ (⁵D₄) linker, from where VR processes occur until the ⁵D₀ electronic state is populated, from which radiative deactivation to ⁷F_J states occurs, resulting in luminescence in this system. Similarly, it was established that the possible sensitization pathway of Tb³⁺ could occur through an energy transfer to the ⁵D₂ state of the ion.

The results obtained using LUMPAC confirm that ET is the dominant sensitization mechanism in the Eu³⁺@UiO-66-(COOH)₂ system, despite possible competition from the BET process from higher excited levels (⁵D₄). The low probability of BET from the ⁵D₁ and ⁵D₀ emissive states ensures efficient emission, which validates the proposed mechanism and supports the efficiency of the sensor.

Finally, the theoretical protocol employed provides a powerful tool to investigate various lanthanide ion-modified MOF systems, elucidating the sensitization and emission pathways that govern the sensing mechanisms and guiding the design of such chemical sensors. With this work, we can also conclude that a reliable theoretical protocol has been established for simulating the optical properties of lanthanide-doped MOFs based on the construction of a truncated but representative model of the extended system, followed by the application of a fragmentation scheme to determine the sensitization mechanism by the antenna effect. The application of this protocol to a significant number of systems of this nature has proven to be useful not only as a complement to experimental research but also as a predictive tool to guide such work.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the SI.

Calculated UV-vis spectra and assignment of the transition for both UiO-66-(COOH)₂ and Eu@UiO-66-(COOH)₂ models and the active orbitals considered for the antenna and lanthanide ion in the CASSCF/NEVPT2 calculations are presented. See DOI: https://doi.org/10.1039/d5dt01615k.

Acknowledgements

The authors thank the PhD Program in Molecular Physical Chemistry from University Andrés Bello, the financial support from ANID/Chile under Doctoral Fellowship 21240110 and Projects FONDECYT 1231194, FONDECYT 1241917 FONDECYT 1220442, FONDECYT Postdoctoral 3210271, FONDECYT Postdoctoral 3230141, Anillos de Ciencia y Tecnología ACT210057. ANID/FONDAP/1523A0006. This material is based upon work supported by the Air Force Office of Scientific Research under award number FA8655-25-1-8759.

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