Excited-State Dynamics of Crossing-Controlled Energy Transfer in Europium Complexes

Abstract

Photosensitized energy transfer (EnT) phenomena occur frequently in a variety of photophysical and photochemical processes and have traditionally been treated with the donor–acceptor distance-dependent Förster and Dexter models. However, incorrect arguments and formulae were employed by ignoring energy resonance conditions and the selection rules of the state-to-state transition in special cases, especially for the sensitive intramolecular EnT of lanthanide complexes. Herein, we proposed an innovative model of energy-degeneracy-crossing-controlled EnT, which can be experimentally confirmed by time-resolved two-dimensional photoluminescence measurements. The computationally determined energy resonance region provides the most effective channel to achieve metal-to-ligand EnT beyond the distance-dependent model and sensitively bifurcates into symmetry-allowed or -forbidden channels for some representative europium antenna complexes. The outcomes of the multidisciplinary treatment contribute to a complementary EnT model that can be tuned by introducing a phosphorescence modulator and altering the antenna-related parameters of the ligand-centered energy level of the ³ππ* state and its spin–orbit coupling for the ³ππ* → S₀^* transition through mechanism-guided crystal engineering and should motivate further development of mechanistic models and applications.

Lanthanide complexes rely on metal-centered f–f luminescence to exhibit unique optical properties, such as sharp emission lines, long decay times, a large Stokes shift, a low autofluorescence background, and a high penetration depth.¹⁻¹⁵ These excellent properties are utilized to achieve the application of these complexes in a wide range of techniques, such as asymmetric catalysts,^1,2 upconversion nanoparticles,³ functional materials,⁴⁻⁹ and optical imaging agents.¹⁰⁻¹⁵ Although most lanthanide ions are luminescent, the direct utilization of Ln-centered luminescence generally suffers from the low activation efficiency due to the forbidden electric-dipole f–f transition or the faint magnetic-dipole f–f excitation. However, perturbed by the ligand-field effect and spin–orbit interaction, the intraconfigurational electric-dipole transitions can be partly allowed.¹⁶⁻¹⁸ The breakthrough study of sensitized intramolecular energy transfer (EnT) was conducted by Weissman¹⁹ in 1942 and subsequently inspired researchers to seek suitable photoactive organic antennas that function as effective photosensitizers, achieving the light harvesting of lanthanide ions.^{9,10,14,20−22}

Gaining a mechanistic understanding of lanthanide luminescence is challenging and encompasses the wide scope of photosensitized EnT related to the sensitization efficiency and the compromise between luminescence and quenching.^{9,10,14,20−22} This intramolecular photosensitization is generally believed to be strongly distance-dependent from the ligand donor to the lanthanide acceptor (R_DA) and has traditionally been thought to proceed in the manners of Förster [with an (R_DA)⁻⁶ dependence], Dexter [with a distance dependence in exp(−βR_DA)], or dipole–multipole with distance dependences in 1/[(R_DA)^λ+2]² (λ = 2, 4, 6).^9,21,23,24 Electric dipole–quadrupole transitions are also parity-allowed, but they are weak and have been rarely identified unambiguously.²⁵ These weak interactions can be produced by using the mathematical treatment of the parity mixing with ligand-field perturbation. On the other hand, experiments with careful control were carried out to identify quadrupole transitions in the solar absorption spectra.²⁶ However, experimental evidence has revealed that the quantum yields of lanthanide luminescence exhibit a sensitive fluctuation with the energy level of the ligand triplet state²⁷ and are significantly altered with coordination geometry even without apparent variations in the coordination bond length.^21,28 Spectroscopic studies have previously shown that the quantum yield of metal-centered luminescence is largely attributable to the sensitization efficiency, which itself is a product of ligand-centered intersystem crossing (ISC) and ligand-to-metal EnT.^29,30 Although time-resolved luminescence imaging and semiempirical EnT rate estimations have been separately applied to a series of luminescent lanthanide probes,^31,32 a comprehensive understanding of the EnT mechanism of lanthanide complexes still lags behind. Ermolaev, Sveshnikova, and co-workers proposed the inductive-resonant theory to account for the nonradiative EnT from an electronically excited lanthanide ion to the surrounding molecular groups with the excitation of resonant vibrational states and made it possible to calculate the nonradiative transition rate constant.³³⁻³⁵ In 1997, Horrocks et al. observed that a tryptophan antenna group efficiently sensitizes protein-bound Yb³⁺ over a distance of 8–11 Å under the excitation of a 290 nm UV light, causing it to emit near-infrared light at 977 nm.³⁶ From a formal point of view, this is a typical Förster EnT mechanism. Nevertheless, zero overlap between the emission spectrum of the tryptophan donor and the Yb³⁺ spectrum ruled out a Förster EnT and led the authors to propose an oxidation–reduction electron transfer mechanism involving ligand-to-metal charge-transfer excitation.^36,37

Indeed, it was gradually recognized that the molecular mechanisms describing the lanthanide luminescence process remain poorly understood by using the current arguments and formulae.³⁸ Therefore, it is eagerly desired to develop an innovative model that provides the conceptual framework for identifying all possible determining factors, that is, the efficiency of ligand-centered ISC, the minimization of self-quenching luminescence, the ligand-to-metal EnT-mediated 4f electron redistribution, and the energy resonance conditions associated with selection rules aside from the donor–acceptor distance. As an important advancement toward this issue, in our group, a nonet–quintet state crossing was previously determined to govern the EnT through the rate-determining step of ligand-centered ISC concomitant with concerted 4f electron pairing on Eu³⁺ centers.³⁹ However, our model needs to pass the test of universality, impartiality, and rationality. Herein, we integrated high-level electronic structure calculations, photoluminescence-mechanism-based crystal engineering, and time-resolved spectroscopy to assign all transient and steady-state signals that are considered as the core issues for understanding complicated dynamics of lanthanide luminescence. These efforts aim to develop a universal theory for identifying the various spectral characteristics in the photoluminescence initiation, activation, deactivation, and treatment of photosensitized EnT. Thus, we can find feasible strategies to regulate ligand-centered ISC and the subsequent ligand-to-metal EnT rate. Moreover, the application scope of our model is required to be defined unambiguously, which facilitates the clarification of the relationship between our crossing-controlled model and the distance-dependent mechanism. Multidisciplinary perspectives in this work allow us to demonstrate some specific features of the dynamic control of photoluminescence and to provide a comprehensive understanding of crossing-controlled EnT for the photoactivated lanthanide complexes.

Computational and Experimental Details

Ab Initio Calculations

In this work, the ab initio calculations of isolated antennas and their coordinated Eu(III) complexes were primarily performed at the CASSCF level of theory with the (12e/10o) and (12e/13o) active spaces, respectively. Based on the appropriate strategies of orbital localization and numerous computational tests, the selection criteria were adopted to make use of a balance model to describe the electron transitions in the specific chromophores of ligands and all configurations of 6f electrons in seven orbitals for the Eu³⁺ center (6e/7o). Energy-consistent scalar-relativistic Wood–Boring-adjusted 28-electron-core pseudopotentials were employed to account for the relativistic effects of Eu³⁺ and Br together with the corresponding basis sets.⁴⁰ The C, H, O, and N atoms were treated at the all-electron level with the 6-31G* basis set for the isolated antennas and the chromophores involved in primary light absorption and excitation transfer for the complexes 1–4, while the remaining moieties were calculated by using the small basis set (STO-3G) to reduce the computational burden. All minima of the free antennas and complexes 1–4 in their singlet excited states (S_CT and ¹ππ*/⁷F) were obtained by full system state-averaged CASSCF optimizations using a two-root equally weighted approach, whereas a single-root optimization was adopted for the ground (S₀ and S₀/⁷F) and triplet/nonet states (T_CT and ³ππ*/⁷F) and the metal-centered quintet state (S₀/⁵D). The minimum energy profiles of free antennas and the EnT of 1–4, as well as their radiative paths, were mapped by intrinsic reaction coordinate (IRC) computations to connect the above critical points. To consider the dynamic electron correlation effects, the single-point energies were recalculated at the CASPT2 level of theory based on the optimized structures of IRC/CASSCF computations. All CASSCF calculations, together with the IRC pathway for the isolated antennas were performed using the Gaussian 03 program package.⁴¹ The CASPT2 and SO calculations for the free ligands and all computations for complexes 1–4 except the SO calculations using Molpro 2012⁴² were carried out using the Molcas 8.0 program package.⁴³ More details are given in the Supporting Information.

Experimental Synthesis

The isolated antennas were synthesized via a routine preparation and separation procedure starting from commercially available reagents. A water solution of Eu(Ac)₃·6H₂O was used to form the coordinative bonds with 1-phenyl-3-pyridin-3-yl-propane-1,3-dione (PPPD), 1-(4-bromophenyl)-3-(pyridin-3-yl)propane-1,3-dione (para-Br-PPPD), and 1-(3-bromophenyl)-3-(pyridin-3-yl)propane-1,3-dione (meta-Br-PPPD) in a mixed solvent of an aqueous and nonaqueous (CH₃OH) matrix. The resulting solutions were stirred for several minutes, and then they underwent a series of solution transfer and filtration. Finally, the obtained solutions were left to evaporate at room temperature from several days to 1 month, eventually giving rise to the yellow crystals of complexes 1–4. Detailed procedures can be found in the Supporting Information.

X-ray Crystallography and Physical Measurements

The intensity data for the crystals of 1–4 were collected using a Rigaku Super Nova, Dual, AtlasS2 diffractometer with graphite-monochromated Cu Kα radiation (1.54184 Å) at 100 K. All structures were solved using the olex2.solve structure solution program and further refined using the olex2.refine refinement package using Gauss–Newton minimization. All nonhydrogen atoms were refined anisotropically. Hydrogen atoms were placed at the calculation positions. Details of the crystal parameters together with the structural refinement of 1–4 are listed in Table S3, and selected bond lengths are given in Table S4. Elemental analyses of carbon, hydrogen, and nitrogen were carried out with an Elementar Vario EL analyzer. The FTIR spectra were recorded in the range of 4000–400 cm^–1 using an AVATAR 360 Nicolet 380 FT/IR spectrometer using KBr pellets. Powder X-ray diffraction analyses were performed using a Rigaku Dmax-2000 X-ray diffractometer with Cu Kα (λ = 1.54059 Å) radiation. The luminescence spectra were recorded using an RF-5301PC spectrometer, and the emission quantum yields (the overall quantum yield, Φ_QY) were measured by using a HAMAMATSU Absolute PL Quantum Yield Spectrometer C11347 at room temperature.

Time-Resolved Luminescence Spectroscopy

The time-resolved luminescence spectra were collected using a commercial streak camera (Hamamatsu). In the system, a Ti:sapphire regenerative amplifier system produced a 90 fs laser pulse centered at 800 nm with a 3 mJ output energy at a 1 kHz repetition rate. The sample was agitated at 400 nm by doubling the 800 nm pulse using a beta barium borate crystal. The luminescence decay curve for each peak was plotted against the delay time and fitted in Figure 4a. The time-resolved and spectrally resolved luminescence images for each sample were recorded by averaging 100,000 laser shots and are shown in Figure 4b.

Figure 4.

Excited-state dynamics of 1–4. (a) Time-resolved luminescence spectra of 1–4 irradiated by visible light at 400 nm. The colored lines indicate the fittings to the dynamic data by using four exponential functions, which can be theoretically assigned to emissions from ligand-centered fluorescence (black), nonet-state phosphorescence (green), and the quintet-state (blue) and metal-centered (red) luminescence. (b) Time-resolved 2D photoluminescence spectra captured by a streak camera at the time delays of 50 ns, 1 μs, and 1 ms for samples 1–4.

Transient Mid-IR Spectroscopy

The conformational changes and the energy relaxation dynamics in excited-states were investigated using a home-built ultrafast transient mid-IR system. In brief, the experimental setup consists of a Ti:sapphire regenerative amplifier (SpectraPhysics, Spitfire) seeded using a Ti:sapphire oscillator (Spectra Physics, Tsunami) to produce a 1 kHz train of 100 fs pulses centered at 800 nm with an average pulse power of 5 mJ. The corresponding output is split into two components, and 30% of the output power can be used to generate 400 nm pump pulses (ca. 100 μJ per pulse at the sample) via the second harmonic generation. The remaining 70% is employed to pump an automated optical parametric amplifier TOPAS (Spectra-Physic, Spitfire) to produce mid-IR probe pulses centered at 5 μm with a 350 cm^–1 spectral width and 35 μJ output energy. The probe pulse and pump pulse were overlapped at the sample position with the spot sizes of 80 and 120 μm, respectively. The time delay between these two pulses was precisely regulated by a mechanical translation stage (IMS600LM, Newport). The produced signals were collected using a 64-channel detector (FPAS 0144 Infrared Systems Development) combined with a 300 mm focal-length spectrometer (Princeton Instruments 2300i).

Results and Discussion

Photoluminescence-Mechanism-Based Crystal Engineering

Computational tests together with an extensive literature survey show that the β-diketone ligand class contains a negatively charged binding site to facilitate the formation of stable, neutral, 3:1 ligand–lanthanide luminescent complexes with the trivalent lanthanide cation (i.e., Eu³⁺). The CASPT2//CASSCF calculations demonstrate that the introduction of suitable electron acceptor groups in the β-diketone ligand instantaneously imposes a bright charge-transfer excitation state that results in electron promotion from the diketone center to substituted groups. By using the feasible approach of molecular engineering, the excitation energies of the ligand-centered bright state can be regulated to the appropriate resonance level, thereby sensitizing the lanthanide luminescence effectively.⁴⁴⁻⁴⁸ Based on numerous test calculations, a pyridine ring was eventually selected as the electron-acceptor group for the photoinduced charge transfer (PICT) along the desired direction, which can be enhanced by the incorporation of an electron-donating group of the phenyl ring on the other side of the diketone center, resulting in the PPPD (Figure 1) antenna ligand. Benefiting from the ingeniously designed molecular skeleton bearing the enhanced PICT, the antenna ligand of PPPD exhibits strong absorption with a large oscillator strength (f = 0.47) over the visible-light range (λ_max: ca. 400 nm, Table S1). More importantly, the ³ππ* triplet energy level of the PPPD ligand is computationally predicted to be 52.2 kcal mol^–1 (18,270 cm^–1, Table S2) and is very close to the optimal 19,000 cm^–1 above the ground-state ⁷F₀ of Eu³⁺.^23,44 On the other hand, nine possible active sites can be present in the pyridine and phenyl rings of PPPD to tune the corresponding spin–orbit couplings (SOCs) for the ³ππ* → S₀ transition of antenna ligands. Computational tests have demonstrated that the utilization of the heavy atom Br in the meta-position of the phenyl moiety (i.e., 3-Br-PPPD) notably improves SOC but imposes a negligible influence on the triplet energy level of antenna ligands (Table S2). This implies that the meta-phenyl group may function as an ideal ligand-centered ISC moderator to cooperatively regulate the efficiencies of ligand-to-metal EnT associated with the photoluminescence of Eu³⁺–diketonate complexes.

Figure 1.

Coordination modes of β-diketone-chelated complexes 1–4. Left panel, structures of complexes 1 and 2 formed with PPPD and para-Br-PPPD, respectively. Right panel, complexes 3 and 4 constructed by using meta-Br-PPPD. For complexes 1–4, all the Eu³⁺ ions are octa-coordinated. For 1 and 2, six oxygen atoms of diketone and two nitrogen atoms of pyridine are employed to form the O₆N₂ chemical environment. In the 3 and 4 dinuclear complexes, one or two nitrogen atoms of pyridine are substituted by the solvent molecules, resulting in the O₇N₁ and O₈ chemical environments, respectively.

Following these valuable theoretical insights, we successfully synthesized the PPPD ligand and its para- and meta-bromine-substituted derivatives (para-Br-PPPD and meta-Br-PPPD). Careful crystal engineering was further performed by using the prepared ligands in a methanol solution with Eu(Ac)₃·6H₂O in a mixed solvent of CH₃OH and H₂O, eventually giving rise to bright yellow crystals of the Eu–PPPD (1), Eu–para-Br-PPPD (2), and Eu–meta-Br-PPPD (3) complexes (Figures 1 and S2). Single-crystal X-ray structure analyses reveal that both 1 and 2 crystallize in the orthorhombic space group Pbcn and display an interesting two-dimensional (2D) layer structure sustained by the meta-pyridine nitrogen atoms of the PPPD ligands (Figures S3 and S4). The β-diketone parts of all three coordination PPPD ligands adopt bidentate chelating modes, whereas the meta-pyridine-N atoms of two PPPD ligands connect adjacent Eu³⁺ ions to form a 2D layer parallel to the ab plane, with the intralayer Eu···Eu distances from 8.2 to 9.4 Å. Unlike the spatial arrangement of 1 and 2, the crystal structure of 3 undergoes a remarkable variation due to the squeezed coordination space in the presence of meta-bromine, in which one coordination site around the Eu³⁺ ion occupied by the meta-pyridine group is replaced with small molecules of water or methanol, forming a dinuclear structure of [Eu₂(meta-Br-PPPD)₆(H₂O) (CH₃OH)]·H₂O (3) (Figure S5). To avoid a possible quenching effect from the O–H vibrations in H₂O/CH₃OH,^{4,6−11,13−15,20−22} pyridine-N-oxide (PNO) ligands are employed to replace H₂O and MeOH, generating another dimeric complex of Eu₂(meta-Br-PPPD)₆(PNO)₂ (4) connected by double PNO bridges.

Photoluminescence Performance of 1–4

The luminescence properties of 1–4 in their solid state were investigated experimentally at room temperature and theoretically assigned based on CASPT2//CASSCF computations. The decay curves of 550–750 nm emissions were recorded unambiguously upon visible-light irradiation at 410–440 nm (Figure S2). For all crystals, the decay curves were well fitted to a single-exponential function (Figure S7), which indicates that there exists a uniform coordination environment around the Eu³⁺ ion for each crystal. The computational results well reproduce the features of the experimental spectra, revealing that the antenna ligand-centered absorptions cause the PICT along a desired direction from diketone to pyridine moieties, which can be enhanced by the introduction of electron-donating Br atoms in the phenyl group. This accounts for a significant improvement in the intensity of optical absorption for bromine-substituted complexes 2–4 compared with that of 1 in the absence of Br, which is also confirmed by the calculated oscillator strengths (f) for the intra-ligand CT ππ* transitions of S₀ → S_CT(¹ππ*) (Table S7).

The visible-light absorption bands of 1–4 extend to the region of more than 500 nm and are seamlessly connected with the emission bands of metal-centered luminescence. Compared with the corresponding absorption spectra, the luminescence spectra of 1–4 exhibit more informative signals and originate from the lowest level of the excited quintet state (⁵D₀) to the J levels of the septet ground state of ⁷F_J (J = 0–6).^23,49,50 Unlike the tunable absorption spectra, the metal-centered emission spectra of 1–4 remain almost unchanged. Accurate calculations at the CASPT2//CASSCF level reveal that the f electron unpairing of ⁵D₀ → ⁷F₂ takes place in a symmetry-allowed manner (m_l = −2 → m_l = +2). The corresponding SOC upon ligand-field perturbation is predicted computationally to be 433–1679 cm^–1 and is much larger than those for the assignable transitions of ⁵D₀ → ⁷F_J (J = 1, 3, 4) in the emission spectra of 1–4 (Figure 2 and Table S8). The present computational evidence reveals that the dominant ⁵D₀ → ⁷F₂ transition peaking at 612–617 nm originates intrinsically from the strong coupling between the sublevel of quintet–septet states to contribute to the strengthened intensity of the favorable transition via symmetry-allowed f electron unpairing.

Figure 2.

Photoluminescence properties of 1–4. Visible-light absorption (black) and emission (red) spectra for 1–4. The maximum absorption and the most relevant Eu(III) emission lines are theoretically assigned and labeled by calculating the vertical excitation energies (cal., nm) and oscillator strengths (f) of the intra-β-diketone ligand S₀ → S_CT(¹ππ*) transition, as well as the spin–orbit matrix elements (cm^–1) among the sublevels of the metal-centered ⁵D₀ → ⁷F_J (J = 1, 2, 3, 4) transitions. The overall photoluminescence quantum yield (Φ_QY) and lifetimes (τ, ms) are provided in blue for the europium(III) complexes of 1–4.

In addition to the absorption and emission spectra, the experimentally recorded overall quantum yields (Φ_QY), lifetimes (τ), calculated rate constants of radiative/nonradiative relaxations (k_rad/k_nr, s^–1), and metal radiative decay efficiency (η_Eu) serve as the key physical parameters to describe the photoluminescence properties of 1–4. Parent complex 1 exhibits strong visible-light-sensitized luminescence with a high quantum yield (69%) and a moderate lifetime (0.17 ms). The quantum yield of 2 decreases sensitively to 55% but shows an increase in lifetime to 0.20 ms, although its crystal structure and coordination environment remain almost unchanged in comparison with the case of 1. A relatively low quantum yield (46%) was found in the photoluminescence of 3 when the infinitely extended structure for 1 and 2 underwent dramatic structural deformation, generating a dimeric arrangement with a shortened Eu³⁺–Eu³⁺ distance from ca. 9.3 Å (1 and 2) to 7.5 Å (3). As a consequence of the structural modification from the O₆N₂ chemical environment for 1 and 2 to O₇N₁ for 3, the radiative/nonradiative rate constant (k_rad/k_nr) of 3 simultaneously shows a noticeable decrease compared with those of 1 and 2 (see Table 1). This quantum yield reduction was measured previously in the dimeric structure of the carbazole-based β-diketonate Eu³⁺ complex with respect to its mononuclear counterpart, which was roughly explained by the concentration quenching in the case of the closer Eu³⁺–Eu³⁺ distance by neglecting the forbidden nature of ⁵D₀ → ⁷F₀ transition.⁵¹ In our case, the decreasing quantum yield of 3 mainly suffers from the nonradiative quenching by O–H vibrations in the presence of coordinated water/methanol around lanthanide ions, while possible vibronically assisted nonradiative deactivation cannot be excluded. This drawback is overcome by eliminating coordinated H₂O/CH₃OH via the introduction of the PNO solvent to improve the quantum yield (56%) of dimeric complex 4. Consequently, the nonradiative rate for 4 (O₈ surroundings) is effectively suppressed, thereby giving rise to a 12% higher efficiency of metal radiative decay (η_Eu, 0.28) compared with 3 (0.25) by changing the coordinated solvent molecule to PNO. The lifetime of 4 increases doubly to 0.35 ms compared with that of 1 (0.17 ms), which is mainly attributed to the rigidity enhancement from 1 to 4, thus largely shutting down the quenching channels via vibrations. Overall, the modification of the Eu chemical environment from the mixed O/N-donor to the fully O-donor atoms exhibits an increasing lifetime from 0.17 to 0.35 ms (see Table 1), which demonstrates an effective suppression of nonradiative decay, particularly from the Eu–O/N vibration deactivation. The present crystal samples exhibit diverse photoluminescence properties and different microcoordination environments around the Eu³⁺ metal, which provides a versatile platform for investigating the dynamic mechanisms of the visible-light-sensitized luminescence of europium complexes.

Table 1. Kinetic Parameters for the Crossing-Controlled EnT of Complexes 1–4.

	calculated by our crossing-controlled model			derived from experimental measurement
complexes	⟨7F0|HSO|5DJ⟩a	⟨S0|HSO|3ππ*⟩a	kISC (106s–1)b	τEnT (ns)c	τ (ms)	ΦQY	krad (s–1)d	knr (s–1)d	ηEud
1	137–1515 (5D1)	0.2–0.8	2.6–41.0	12	0.17	0.69	983	4899	0.17
2	34–657 (5D0)	0.3–1.7	5.9–190.4	28	0.20	0.55	1013	3987	0.20
3	373–1444 (5D1)	0.3–1.9	5.7–229.4	6	0.28	0.46	883	2688	0.25
4	35–969 (5D0)	0.3–2.2	6.3–338.0	8	0.35	0.56	812	2045	0.28

^aSpin–orbit matrix elements (SOMEs) of ⟨S₀|H^SO|³ππ*⟩ and ⟨⁷F₀|H^SO|⁵D_J⟩ at NQC(T₁/⁷F–S₀^*/⁵D) are provided in cm^–1, accounting for the ligand-centered ISC to the ground S₀ state and the metal-centered f electron pairing to the excited ⁵D_J state, respectively.

^bLigand-centered ISC (k_ISC) of ³ππ* → S₀^* is theoretically obtained based on the SOMEs of ⟨S₀|H^SO|³ππ*⟩ and the corresponding energy gaps.

^cThe durations (τ_Ent, ns) of EnT, which can be estimated by the delay time differences between the phosphorescent emission of the nonet state and the photoluminescence of the ⁵D₀ state at the NQC on the basis of time-resolved spectral data.

^dThe rate constants of radiative/nonradiative relaxations (k_rad/k_nr, s^–1) and the metal radiative decay efficiencies (η_Eu) were calculated by using the experimentally recorded overall quantum yields (Φ_QY) and lifetimes (τ) based on the previously reported method.⁵²

Dynamic Mechanisms of Crossing-Controlled EnT

To elucidate the dynamic events of photoluminescence, the minimum-energy profiles for the visible-light-initiated complexes 1–4 were first computed and summarized, as shown in Figure 3. These dynamic processes were further monitored by using transient luminescence spectra and are displayed in Figure 4. Visible-light irradiation instantaneously takes complexes to the bright spectroscopic septet state ⁷(S_CT(¹ππ*)/⁷F₀), which originates from the spin-allowed ligand-centered CT excitation but exhibits a more localized character than that of the isolated antenna ligand (Tables S1 and S7). Eu–O coordination imposes a structural constraint on the rotational deformation of pyridine or benzene rings along the C–C bond of the diketone plane that is mainly responsible for the nonradiative decay of visible-light-irradiated free antenna ligands (Figure S1). As a consequence, the ligand-centered radiative channels for the Eu–O coordinated complexes open and thus give rise to ligand-centered luminescence (cal. 480 nm for 1) at the minimum of the bright septet state of ⁷(¹ππ*/⁷F₀)–Min. Consistently, the first intermediate state with a noticeable band at 463 nm was observed at a time delay of 155 ns in four componential time-resolved luminescence spectra of 1 (Figure 4a). Careful energy analyses and SOC calculations reveal that the presence of relativistic effects and coordinative constraints resulting from the heavy Eu³⁺ atom causes a significant increase in the spin–orbit interaction of the complexes among singlet–triplet states, that is, coupling between ⁷(¹ππ*/⁷F₀) → and ⁹(³ππ*/⁷F₁) up to 317 cm^–1 (involves an Eu-based ⁷F₀ → ⁷F₁ transition), compared with those of the free ligands (0.9–9.0 cm^–1, Figure S1). Benefiting from the structural rigidity and enhanced coupling, the ligand-centered singlet ⁷(¹ππ*/⁷F₀) state energetically matches the low-lying sublevel of the ligand-centered triplet state, which is the nonet ⁹(³ππ*/⁷F_0–6) state of Eu³⁺–antenna complexes. As shown in Figure 3a, the ⁷(¹ππ*/⁷F₀) state of the complex is exactly degenerate with its ⁹(³ππ*/⁷F₁) state in the minimum ⁷(¹ππ*/⁷F₀)–Min when the visible-light-initiated complex just moves out of the Franck–Condon region with a 1–2 kcal mol^–1 energy decrease. Kinetic calculations show that the ISC of ⁷(¹ππ*/⁷F₀) → ⁹(³ππ*/⁷F₁) takes place within a picosecond timescale (k_ISC: up to 6.2 × 10¹² s^–1). The occurrence of ultrafast ISC allows ligand-centered luminescence to incorporate a considerable triplet component since the emission from ⁷(¹ππ*/⁷F₀)–Min becomes a slow process with a nanosecond timescale (Figure 4a). As expected, the SOC component analyses demonstrate that the ligand-centered ¹ππ* state in ⁷(¹ππ*/⁷F₀)–Min partially exhibits a singlet state character but mixes with the contribution of a 66% triplet counterpart (Figure 3a). The present computational evidence explains why the ligand-centered fluorescence in the singlet state of ⁷(¹ππ*/⁷F₀)–Min largely acts as a phosphorescence-like emission with an extremely long lifetime (up to 155 ns). Moreover, the ligand-centered luminescence of 2–4 (with a lifetime of 60–66 ns) appears much earlier than that of 1 (155 ns, Figure 4a) since the introduction of the heavy atom Br in the para- or meta-position of the phenyl moiety leads to the improvement of the ligand-centered ISC (¹ππ* → ³ππ*) rate.

Figure 3.

Crossing-controlled EnT and radiative paths of 1–4. (a) Minimum-energy profiles for the crossing-controlled EnT of complex 1 obtained at the CASPT2//IRC//CASSCF level of theory. (b) Electron shift mode of EnT for 1. (c) Energetic diagrams of the NQC region for 1–4, with the relative energy of each state (in kcal mol^–1) given in parentheses. The SOCs between two specific states ψ₁ and ψ₂ (⟨ψ₁|H̃^SO|ψ₂⟩) are given in cm^–1 with an interval showing the minimum (nonvanishing) and maximum spin–orbit matrix elements.

Unlike the triplet-state decay of the isolated ligands (Figure S1), the relatively flat downhill paths instantaneously take the complexes to their nonet-state minima, ⁹(³ππ*/⁷F₀)–Min. As shown in Figure 3a,c, the ⁹(³ππ*/⁷F₀)–Min of 1–4 was computationally determined to be energetically degenerate with low levels of the corresponding quintet states, ⁵(S₀^*/⁵D_0,1). This computational evidence suggests that there exists a nonet–quintet crossing NQC(T₁/⁷F–S₀/⁵D) at ⁹(³ππ*/⁷F₀)–Min, in which the ligand-centered triplet state can relax to its hot ground state (S₀^*), while the released excitation energies promote the ground-state Eu³⁺ to the excited ⁵D_0,1 state through 4f electron pairing. The SOC calculations demonstrate that the NQC for complex 1 is composed of 43% nonet and 57% quintet components. Consistently, a two-component regulatory system was experimentally recorded and characterized by the biexponential decay signals of time-resolved luminescence. As illustrated in Figure 4a, typical experimental and fitting results of the biexponential decay data were measured to be located between the ligand-centered (black line) and metal (red line)-centered luminescence at the wavelengths of 536–550 nm (green line) and 581–590 nm (blue line) within the 67–202 and 75–214 ns time regimes, respectively. Computational results show that the two-component signals at the calculated wavelengths of 537–593 nm originate from the phosphorescent emission of the nonet state and the photoluminescence of the ⁵D₀ state under the same minimum structure of the NQC, as shown in Figure 3a,c. To evaluate their efficiencies, the rates for the ligand-centered ISC of ³ππ* → S₀ were computed to be 2.6 × 10⁶ to 3.4 × 10⁸ s^–1 for complexes 1–4 owing to the relatively small SOC values (Table 1, 0.2–2.2 cm^–1) and large energy splitting (Figure 3c, 45.8–53.2 kcal mol^–1). The relatively slow rates of the nonradiative processes for the ligand-centered ISC indicate that the lifetimes of the NQC are long enough to trap the Eu–antenna complexes in the minima of the nonet state within timescales of tens to hundreds of nanoseconds.

As shown in Figure 3c and Table 1, there are two types of energy resonances for the ligand-to-metal EnT of lanthanide complexes in the sensitive resonance region arising from the small ⁵D₀–⁵D₁ splitting of the metal (3.0–4.0 kcal mol^–1). The EnT of 1 and 3 proceeds along the energetically matched ⁵D₁ channel, whose f electron pairing takes place in a symmetry-allowed manner (m_L = +2 → m_L = −2). In contrast, the occurrence of a forbidden ⁷F₀ → ⁵D₀ transition (m_L = +2 → m_L = −3) is mainly responsible for the significant decline in the ligand-to-metal EnT rates of 2 and 4via NQC(T₁/⁷F–S₀^*/⁵D₀), in which the calculated SOC of ⁷F₀ → ⁵D₀ is 1-fold smaller than that of ⁷F₀ → ⁵D₁ (Table 1). In the present work, the energetic resonance model is theoretically identified by the energy profiles of the NQC associated with the kinetic assessments of the ligand-centered ISC of ³ππ* → S₀*. Moreover, this theoretical model associated with the operational process of EnT can be further confirmed by the dynamically measured time of ligand-to-metal EnT, which is estimated by the delay time differences between the ligand-centered phosphorescence emission of the nonet state and the photoluminescence of the ⁵D₀ state at the minimum structure of ⁹(³ππ*/⁷F₀)–Min (i.e., NQC).

Compared with 1, the nonet state level of 2 slightly decreases and is degenerate with ⁵D₀ of Eu³⁺ instead of the favorable ⁵D₁ channel. In addition to the decreased energy level in the nonet state, the switching of the EnT channel is also attributed to the persistence of the crystal structure and coordination environment around the Eu³⁺ center, which leads to negligible variation in the energy levels of the ⁵D₀ and ⁵D₁ states (Figure 3a). As a consequence, the time of EnT for 2 increases to 28 ns (⁵D₀) from 12 ns (⁵D₁) of 1 (Table 1). A 1-fold decrease in the EnT rate is quantitatively correlated with the calculated SOC difference between the ⁷F₀ → ⁵D₁ (1) and ⁷F₀ → ⁵D₀ (2) transitions (1: 1515 → 2: 657 cm^–1). Although the ligand-centered ³ππ* → S₀^* ISC notably accelerates in the presence of para-Br (1: 2.6 × 10⁶ to 4.1 × 10⁷ s^–1 → 2: 5.9 × 10⁶ to 1.9 × 10⁸ s^–1), the ligand-centered excitation energies of 2 are unlikely to transfer smoothly to the Eu³⁺ metal via an unfavorable ⁵D₀ channel but release largely through an alternative channel of competitive phosphorescent emission. Consistently, dynamic measurements reveal that the time of phosphorescent emission decreases to 79 ns (2) from 202 ns (1). An approximate 3-fold increase in phosphorescent emission associated with a more than 1-fold decrease in the ligand-to-metal EnT rate mainly accounts for the decreased quantum yield of metal-centered red luminescence from 69% (1) to 55% (2) in the presence of the para-substituted Br phosphorescence modulator.

As revealed in Figure 3c, the NQCs of 3 and 4 are 8.0–10.0 kcal mol^–1 energetically lower than those for 1 and 2 in the presence of a meta-Br-substituted antenna group, which is mainly attributed to the formation of photostable complexes for 3 and 4 exhibiting a dinuclear structure compared with the 2D layer structure of 1 and 2. Accordingly, the NQC of 3 is regulated to be located at the optimal level of 19,166 cm^–1 (54.8 kcal mol^–1), allowing the occurrence of ligand-to-metal EnT along a favorable ⁵D₁ channel. Benefiting from the precisely controlled ligand-centered triplet energy and an advantageous channel of intramolecular EnT, the time of EnT for 3 reduces to a minimum value of 6 ns among the four investigated complexes herein (Table 1). The loss of quantum yield arising from the quenching effect in the presence of Eu–H₂O (MeOH) coordination for 3 can be largely compensated by the highly efficient EnT along a favorable ⁵D₁ channel, which produces an acceptable quantum yield of metal-centered red emission (46%). Since the energetic levels of ⁵D_0,1 sensitively fluctuate with the coordination microenvironment around the Eu³⁺ center, the attempt to eliminate the drawback of vibrational quenching unexpectedly leads to the EnT channel switching from the favorable ⁵D₁ channel of 3 to the unfavorable ⁵D₀ channel of 4 in the presence of the PNO ligand, resulting in a slightly increased time constant of EnT (8 ns). The introduction of meta-Br and PNO ligands significantly narrows the energy splitting (4: 45.8 kcal mol^–1vs1–3: 51.3–53.2 kcal mol^–1) with the enhanced SOC between the ligand-centered ³ππ* and the corresponding hot ground (S₀^*) states. As a result of regulation in the NQC region, the rate of the ligand-centered ISC for 4 reaches the maximum values (6.3 × 10⁶ to 3.4 × 10⁸ s^–1) compared with those of 1–3. On the other hand, however, the time constants of competitive fluorescence (60–65 ns) and phosphorescent (67–79 ns) emissions for 2–4 are considerably accelerated by 2–3-fold compared with that of 1 (Flu.: 155 ns, Phos.: 202 ns). This acceleration is mainly due to the enhanced spin–orbit interaction and the decreased energy splitting imposed by the relativistic effect of the Br heavy atom. The increased radiative rate of the ligand-centered luminescence undesirably contributes an external funnel of excitation energy, thereby reducing the metal-centered emission. This explains why the quantum yield of the metal-centered red emission of 4 (56%) is still lower than that of 1 (69%), although the rate of ligand-to-metal EnT controlled by the ligand-centered ISC has been accelerated considerably. It should be noted that the forward EnT from the ligand to metal is quantitatively characterized by the barrierless paths (see Figure 3), in which the ligand-centered SOC (³ππ* → S₀) acts as the most important controlling factor. By contrast, the occurrence of back-EnT from the metal to ligand encounters small barriers (1: 2.6 kcal mol^–1, 2: 0.2 kcal mol^–1, 3: 3.8 kcal mol^–1, 4: 0.3 kcal mol^–1), which ensures the efficiencies for the ligand-to-metal EnT and subsequent emission from Eu³⁺ in the repeated forward–backward EnT cycles. Our model differs from the case proposed by Hatanaka and co-workers⁵³⁻⁵⁵ in which the reasonable barriers (instead of SOCs) separately control the dynamics of ligand-to-metal EnT and the ligand-centered ISC in the relaxation paths of terbium(III) complexes.

Rigidity-related excitation-state behaviors of complexes 1–4 are further inspected by the transient mid-IR spectra, which have been measured dynamically within the time delay of 0–100 ps (Figure S8). Two characteristic vibrational bands of 1550–1650 and 1650–1750 cm^–1 were monitored experimentally and confirmed theoretically to originate from the twisting vibrational components of the benzene or pyridine rings and the C=O group in the diketone center, respectively. The visible-light-initiated extra-vibrational signals progressively weaken (benzene or pyridine rings) or disappear totally (C=O) from complexes 1 to 4 within the same timescale (Figure S8) and fit dynamically to the biexponential decay that can be assigned theoretically to the excitation-state relaxations of ligand-centered singlet (fast) and triplet (slow) states, respectively (Figure S8e). The transient mid-IR data clearly demonstrate that with the rigidity enhancement from 1, 2, to 4, the excitation-state energy relaxations become more effective (Figure S8e: up to a more than 1-fold decrease in the decay time). Moreover, the rigidity enhancement of 4 causes a significant decrease in the vibrational contribution for the excited-state nonradiative deactivation, showing a noticeable quantum yield of emission along an unfavorable EnT path (⁵D₀).

Similar to the quenching effect in the Eu³⁺–H₂O/CH₃OH coordination, the unrestricted OH vibration largely inhibits the excitation-state energy relaxation of 3, showing a relatively long decay time (τ₁ = 3.69 ps, τ₂ = 22.32 ps). Moreover, the combined transient mid-IR and luminescence spectra reveal that the most rigid dinuclear complex 4 not only facilitates excitation-state energy relaxation (τ₁ = 0.79 ps and τ₂ = 12.58 ps) but also significantly accelerates the rate of ligand-to-metal EnT (Figure S8e). As shown by the streak camera measurements (Figure 4b), the biexponential decay of luminescence at 500–600 nm for 4 totally disappears in the time delay of 50 ns, but these dynamic signals can still be observed at 1 μs in 1–3, demonstrating an extremely high efficiency of ligand-to-metal EnT for the most rigid 4 (Figure 4b). However, the undesirable ligand-centered luminescence (400–500 nm) of 4 is enhanced simultaneously, and its intensity is 2–3-fold stronger than that its counterparts 1–3 at a time delay of 1 μs (Figure 4b). The increased excitation energies funneling from the competitive channel and the coexistent duration of ligand-dependent deactivation greatly reduce the quantum yield of metal-centered red luminescence for 4.

Taken together, the present computational results and dynamic data suggest that intramolecular EnT-driven lanthanide luminescence is a very complicated photophysical process with multifactor coupling interactive effects. The sensitivity of EnT inherently originates from the existence of symmetry-allowed and symmetry-forbidden channels in the narrowed energy resonance region for some special lanthanide ions, such as Eu³⁺, bearing a small energy splitting among the metal-centered sublevels (for instance, the energy gap of ⁵D₁–⁵D₀ is 3–5 kcal mol^–1 for Eu³⁺). It has been shown theoretically and verified experimentally that the variation in the luminescence quantum yield controlled by the NQC is a result of the bifurcation into the fast (⁵D₁) and slow (⁵D₀) EnT channels, as well as the tunable ligand-centered SOC. Structural comparisons reveal that there are no principal differences in the donor–acceptor distance along the EnT and radiative paths of 1–4, which can be confirmed by the Eu–O distances of the crystal structures (Table S4) and the optimized stationary points (Figures S19–S22). A combination of experimental and computational results indicates that the intramolecular EnT of lanthanide complexes proceeds in an energy-dependent fashion beyond the distance-dependent Förster or Dexter EnT model.

The possible distance dependence via a Dexter mechanism for these europium(III) coordination complexes was also examined by employing the strategies developed by our group for treating the photosensitization phenomena of materials and catalytic systems.^56,57 However, extremely small coupling constants were obtained for the coupling terms of Dexter electron exchange, which originates from the weak overlap between the emission spectrum of the ligand and the Eu³⁺ spectrum. In addition, these photoluminescent systems bear the same magnitude of the donor–acceptor distance between the coordinated ligands and Eu³⁺ center. All computational results demonstrate that the distance-dependent models are unlikely to explain the sensitive variation in quantum yield for metal-centered red emission. Based on the multidisciplinary evidence, we can unambiguously conclude that the crossing-controlled EnT model is predominant over the donor–acceptor distance-dependent Förster or Dexter EnT model in the energy degeneracy region. Practical strategies not only require a careful ligand design to strike a delicate balance between the energy level and the spin–orbit interaction for the ligand-centered ³ππ* toward the ⁵D₁/⁵D₀ states of metal and the ligand-centered hot ground state (S₀^*) but also need to establish compromises among the luminescence of the metal, the competitive ligand-centered emission, and the uncontrolled vibrational quenching with vibronic coupling arising from the coordination microenvironment with solvent molecules. This novel crossing-controlled model would be applicable to analogous lanthanide complexes and some representative organic systems, especially when Förster or Dexter EnT models become invalid. This means that once the photoactivated systems evolve into the energy-degenerated crossing, the energy resonance EnT model will be predominant over the donor–acceptor distance-dependent mechanisms and act like an energetically related resonant manner beyond the classical Förster or Dexter EnT models. In our proposed model, the introduction of ligand-centered phosphorescence modulators, which simultaneously improve the ligand-centered ISC and the subsequent ligand-to-metal EnT rate, play a key role in regulating the photoluminescence performance of lanthanide complexes. We envisioned that numerous studies will be inspired by this design principle to achieve highly efficient light-emitting materials.

Conclusions

In summary, an innovative model of energy-degeneracy-crossing-controlled EnT has been theoretically determined and experimentally confirmed by using the multiconfigurational second-order perturbation theory, photoluminescence-mechanism-based crystal engineering, and time-resolved spectroscopy. The newly emerged model evaluates the dynamic behaviors of ligand-to-metal EnT related to multifactor coupling interactive photoluminescence for lanthanide complexes as comprehensively as possible. By using this model, many confusing issues will be clarified along the ligand-to-metal EnT and radiative paths of lanthanide complexes and the related systems, that is, the sensitive fluctuation of the quantum yield for metal-centered luminescence with the energy level of the ligand-centered triplet state, the good compromise between the excitation energies funneling from the competitive channel, and the coexistent duration of ligand-dependent deactivation and metal-centered emission, as well as the selection-rule-controlled EnT channel. All this evidence reveals that once the photoactivated systems evolve into the energy degeneracy crossing, the energy resonance EnT model becomes predominant over the donor–acceptor distance-dependent Förster or Dexter mechanisms.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.1c00584.

• Computational mechanism-based design for the candidate antennas, synthesis and characterization of the ligand and Eu-complexes, and computational details (PDF)

Author Contributions

X.C. and W.F. designed the experiments and guided the project. L.W., J.W., and X.C. performed theoretical calculations of the radiative and EnT paths and made the assignments of optical properties for the absorption–emission spectra and the time-resolved spectroscopies. H.S. and Y.F. synthesized the antenna ligands and Eu-complexes and performed the X-ray crystallography and physical measurements. Y.L., W.Z., J.W., S.W., and Z.C. performed the optical measurements and analyzed the dynamic data. All of the authors were involved in the analyses and interpretation of data. X.C. wrote the paper, with help from the coauthors.

The authors declare no competing financial interest.