Theoretical Determination of Energy Transfer Processes and Influence

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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Theoretical Determination of Energy Transfer Processes and Influence of Symmetry in Lanthanide(III) Complexes: Methodological Considerations María J. Beltrán-Leiva,† Dayán Páez-Hernández,*,†,‡ and Ramiro Arratia-Pérez*,†,‡ †

Relativistic Molecular Physics (ReMoPh) Group, Ph.D. Program in Molecular Physical Chemistry, Universidad Andrés Bello, Av. República 275, Santiago 8370146, Chile ‡ Center of Applied Nanosciences (CANS), Facultad de Ciencias Exactas, Universidad Andrés Bello, Av. República 275, Santiago 8370146, Chile S Supporting Information *

ABSTRACT: This work presents a theoretical protocol to analyze the symmetry effect on the allowed character of the transitions and to estimate the probability of energy transfer in lanthanide(III) complexes. For this purpose, a complete study was performed based on the multireference CASSCF/PT2 technique along with TDDFT, to build the energy level diagrams and determine the spectral overlap integrals, respectively. This approach was applied on a series of LnIII complexes, viz. [LnCl3(DMF)2(Dpq)]/ [Ln(NO3)3(DMF)2(Dpq)], where Ln = SmIII, TbIII, ErIII/EuIII, NdIII and dpq = dipyridoquinoxaline, synthesized and characterized by Patra et al. (Dalton Trans. 2015, 44 (46), 19844−19855; CrystEngComm 2016, 18 (23), 4313− 4322; Inorg. Chim. Acta 2016, 451, 73−81). A fragmentation scheme was applied where both the ligand and the lanthanide fragments were treated separately but at the same level of theory. The symmetry analysis only partially reproduced the expected results, and a more detailed analysis of the crystal field became necessary. On the other hand, the most probable energy transfer pathways that take place in the complexes were elucidated from the energy gaps between the ligand-localized triplet state and the emitting levels of the lanthanide fragments. These gaps, which are related to the energy transfer rate, properly reproduced the trend reported experimentally for the best and worst yields. Finally, the spectral overlap integral was calculated from the emission spectra of the dpq ligand and the absorption spectra of the lanthanide fragment. The obtained values are in good agreement with the quantum yields calculated for the systems. The most remarkable aspect of this protocol was its ability to explain the emission and nonemission of the studied compounds.

1. INTRODUCTION The rare earths comprise Y, Sc, and elements from La to Lu. The last 15 elements make up the lanthanide series which, in spite of their scarcity and the fact that they are difficult to obtain, are highly valued for their unique and unrivalled spectroscopic properties. The electronic [Xe]4f n configurations (n = 0−14) for trivalent lanthanide ions (LnIII) generate a rich variety of electronic levels with well-defined energies due to the shielding of the 4f orbitals by the 5s25p6 subshells.1,2 In addition, these energies have a little variation, largely independent of the environments in which the lanthanides ions are inserted. Almost like a “fingerprint”, the 4f−4f emission bands are sharp and easily recognizable, which was an advantage in the discovery of these elements between 1803 and 1907. In fact, lanthanide luminescence is at the heart of applications as diverse as immunoassays, lasers, lighting systems, molecular thermometers, telecommunications, imaging agents, photodynamic therapy (PDT), among others.3−10 © XXXX American Chemical Society

The way to understand and rationalize the electronic structure and spectra of these elements started in the late 1930s, when Van Vleck published an article titled “The Puzzle of Rare-Earth Spectra in Solids”.11 Van Vleck addressed one main issue: assignment of the sharp spectral lines exhibited by the rare earths, which would be expected if the transitions occurred between levels inside the 4f shell. Nonetheless, it was well-known that 4f−4f transitions are parity forbidden. He postulated that these lines are observed because of a “distortion” of the electronic motion by noncentrosymmetric crystalline fields allowing orbital mixing. This was a first approach in order to explain the optical spectra of the lanthanide ions. Three years later, Racah published his seminal papers in which group theory was applied to problems of complex spectra and the required mathematical tools were Received: January 21, 2018

A

DOI: 10.1021/acs.inorgchem.8b00159 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Scheme 1. Complexes under Studya

a The first three structures correspond to theoretical models that were optimized at the B3LYP/TZ2P level. The last two correspond to crystallographic structures which were not optimized. (a) [LnCl6]3−, (b) [Ln(CN)2Cl4]3−, (c) [LnCl4(Dpq)]− for Ln = Nd, Sm, Eu, Tb, Er, (d) [LnCl3(Dpq)(DMF)2] for Ln = Sm, Tb, Er, (e) [Ln(NO3)3(Dpq)(DMF)2] for Ln = Nd, Eu.

triplet state is a key piece of information in the understanding of the lanthanide emission. The intensity of lanthanide luminescence can be increased by many orders of magnitude through the coordination of chromophoric ligands with the lanthanide center. However, there is another relevant factor to consider: the symmetry. Upon coordination, mixing of ligand and lanthanide orbitals enhances the electric dipole metal-centered 4f−4f transitions, especially when the coordination lowers the symmetry around the lanthanide22−25 According to the Judd−Ofelt formalism, the concept of parity no longer applies when the ion is situated at a site without an inversion center, which enables opposite parity states (for example, d and f orbitals) to be mixed into the wave function by odd-parity crystal field terms. Nonetheless, this admixture is very small since it is inversely proportional to the separation of the 4f n and 4f n−15d configurations. Therefore, the symmetry defined by the ligands around the lanthanide ion in the complex (first coordination sphere) determines the allowed character of the transition and, thus, the relative intensity of the emission bands. In this respect, Bünzli et al. observed this effect in nine-coordinate europium complexes.26 They noticed that, in solid state, the first coordination sphere of the lanthanide exhibits a C3 symmetry; however, it was changed to a more common C1 upon dissolution of the compounds in dichloromethane. In addition, a change in the luminescence spectrum and a shortening of the Eu(5D0) radiative lifetime in going from the higher to lower symmetry was reported. Thus, they concluded that the lower the symmetry, the larger the number of forbidden 4f−4f transitions that become allowed. As can be noted, lanthanides have been widely analyzed experimentally. However, theoretical studies describing phenomena such as the antenna effect or the influence of symmetry on lanthanide luminescence are scarce. In this sense, it is essential to have a good description of the energy transfer mechanisms that take place between both lanthanide and antenna fragments in order to have a general idea of the sensitization feasibility. Furthermore, it is very important to study changes exhibited by the wave function when the symmetry is lowered to analyze, in a quantitative way, the allowed character of the transition. Therefore, to contribute and generate a deeper comprehension in this field, a theoretical protocol is proposed to properly determine the electronic states involved in the sensitization mechanism and to estimate the probability of energy transfer. The proposed methodology was evaluated on a series of lanthanide compounds synthesized and characterized by Patra et al.,27−29 viz. [Ln(NO3)3(Dpq)(DMF)2] (Ln = Eu, Nd) and [LnCl3(Dpq)(DMF)2] (Ln = Sm, Tb, Er), where Dpq = dipyridoquinoxaline and DMF =

developed to make detailed spectroscopic calculations involving states of the 4f shell.12−15 This work revolutionized the entire subject of rare earth spectroscopy and laid the foundations for the next major development: the Judd−Ofelt theory of the intensities of lanthanide ions transitions, published in 1962.16,17 In this theory, some modifications of the selection rules were introduced employing the intermediate-coupling scheme which allowed one to understand, among other things, transitions between states with different spin multiplicity. Although these studies made the development of many subsequent investigations possible, there is another equally important milestone for the synthesis of lanthanide-containing luminescent molecules and materials, called “luminescence sensitization” or “antenna effect”. In this mechanism, discovered by Weissman in 1942,18 a ligand absorbs light in the ultraviolet region and transfers energy from its excited level to the resonant level of the LnIII ion, which can emit light or decay nonradiatively. This indirect excitation strategy became the solution for the low absorption coefficients which make the direct excitation of these elements inefficient. Since Weissman’s discovery, luminescence sensitization of lanthanide ions has been widely explored. In this context, several classes of ligands have been tested in order to achieve an efficient energy transfer process.19 Some organic ligands that absorb in the UV region are known for their limitations in the sensitization of NIR luminescence. Nevertheless, strategies have been designed to address this problem, for example, the introduction of electron withdrawing/donating groups.20 Despite this drawback, organic ligands, such as phenanthroline derivatives, have been successfully employed to sensitize lanthanide ions due to (i) their rigid structure, minimizing the nonradiative deactivation generated by high-energy vibrations and (ii) their ability to saturate the coordination sphere of the ion, thus protecting it from the solvent effects. In addition, these molecules have proven to have a high binding affinity to CT-DNA, which makes them suitable for use in therapeutic applications such as PDT. In this treatment, they fulfill the role of double agent, that is to sensitize the lanthanide moiety and generate reactive oxygen species (ROS), which can induce cell death. The energy transfer processes have been wellelucidated from an experimental point of view. If the lightharvesting is performed by aromatic (π → π*) and/or (n → π*) transitions (organic antenna), one of the main energy migration paths implies ligand-centered absorptions, followed by intersystem crossing (ISC) reaching the long-lived ligandcentered triplet state from which energy transfer occurs (1S* → 3 T* → Ln*) obeying Fermi’s golden rule21 (see Theory section). As can be observed, the correct determination of the B

DOI: 10.1021/acs.inorgchem.8b00159 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry dimethylformamide, employing multiconfigurational ab initio methods along with the scalar relativistic time-dependent density functional theory (SR-TDDFT) to elucidate the energy transfer pathways and to analyze the composition of the wave functions. In addition, to properly take into account the effects of symmetry, a series of complexes with different point groups (from Oh to C1) were modeled (see Scheme 1).

2. THEORY The standard theory of 4f−4f electric dipole transitions, the socalled Judd−Ofelt theory of intensities, is a landmark in the study of spectroscopic properties of lanthanides in crystals. The approach was introduced in 1962 to describe the one-photon processes, and is based on the single configuration approximation adopted within the free ionic system scheme. Due to the parity selection rules, electric dipole transitions between energy levels belonging to configurations of equivalent electrons are regarded as forced in origin. As a consequence of the lanthanide contraction, the optically active 4f electrons are screened by closed shells of 5s and 5p symmetry, which protect the ion from the perturbing influence of the environment in the molecule. Therefore, to break the selection rules and lower the spherical symmetry in the isolated ion, the effect of the crystal field potential produced by the surrounding ligands is taken into account.1,30 In the sensitization process of the LnIII ion, a fundamental aspect is the energy transfer where an initially excited molecule D* transfers its energy by a nonradiative mechanism to another molecule A (in this case, the lanthanide), following the sequence: D* + A → D + A*. The rate of this transfer process, based on the Fermi’s golden rule,21 can be expressed as follows WDA =

J=

2π |VDA|2 ℏ

∫ gD(E)gA (E) dE

∫ gD(E)gA (E) dE

Figure 1. Graphic representation of the energy transfer processes. (a) Förster energy transfer, (b) Dexter energy transfer (edited image).32

transfer rate decays exponentially as the distance between the two systems increases. For this reason, the Dexter mechanism is also called short-range energy transfer and not only involves spectral overlap but also requires overlapping of its wave functions. From a theoretical perspective, quantum chemical calculations provide important information about the electronic structure of lanthanide compounds. In the context of this work, an accurate prediction of the energy levels of both the antenna and lanthanide fragments, and a quantitative description of its wave function is fundamental. Therefore, the methodology needs to be selected carefully. In many studies, the position of the ligand-localized triplet state was predicted employing semiempirical or DFT-based methods.35−39 However, those methodologies can lead to an erroneous determination of this state. Semiempirical methods have been used in the determination of the spectroscopic properties of lanthanide systems. Under this methodology, the lanthanide ions are generally treated with the Sparkle model, which has been developed by parametrizing a semiempirical Hamiltonian, such as AM1 or PM3, and replacing the ion by a point charge.40,41 Excited state calculations are usually performed by using the INDO/S-CI approach, providing reliable results on the characterization of the ligand triplet states.42,43 But despite these promising results, such methods have a strong dependence on the parametrization, which can produce, in many cases, inaccurate values. On the other hand, TD-DFT has emerged as an accurate method applicable to large systems for the calculation of excited state properties, in spite of having some limitations that need to be considered. For example, TD-DFT provides unsatisfactory results when excitation energies for Rydberg states and charge transfer transitions are determined.36,44 For this reason, continuous efforts are made toward the development of new functionals and on the tuning process of existing ones, to improve the description of the excited states.45−48 In this context, the hybrid exchange-correlation functional CAM-B3LYP, which combines the hybrid qualities of B3LYP and the long-range correction presented by Yanai et al.,49 has provided significant improvements in the description of these transitions.50 Finally, in many of the studies mentioned above, energy level calculations of the lanthanide moiety were not performed, and the values were taken from experimental spectroscopic data,51 which does not allow one to study the composition of the wave function associated with the states among which the transition occurs. Therefore, higher level computational methods become necessary in order to under-

(1) (2)

where |VDA|2 represents the excitonic coupling matrix between D and A, which interact by means of a physical interaction that leads to energy transfer, and gD(E) along with gA(E) are functions that describe emission and absorption spectra of D and A, respectively. The last factor in the equation is the socalled spectral overlap integral (J), which implicitly establishes a resonant transfer process and allows the determination of the degree of energetic coupling between the donor and the acceptor, that is, the extent to which the acceptor absorbs within the energy range in which the donor emits.31 The greater this coupling, the greater the overlap, which will favor the transfer rate. In general, this process can occur through two mechanisms: one involving dipole−dipole exchange called Förster’s energy transfer32,33 and another involving exchange interactions known as Dexter electronic transfer (see Figure 1).34 The mechanism proposed by Förster involves a donor in an excited electronic state that can transfer energy to an acceptor through dipole− dipole interactions. In this case, the transfer rate has a dependence on the distance between both systems of R6. Therefore, this mechanism can be classified as a long-range interaction that requires spectral overlap but no physical contact between the involved molecules. On the other hand, the transfer described by Dexter is a process in which two molecules bilaterally exchange their electrons. In this case, the C

DOI: 10.1021/acs.inorgchem.8b00159 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

predict molecular transitions in which a charge transfer takes place.49 This functional has proven to be successfully applied in lanthanide compounds to determine this kind of transitions improving, in this way, the limitations of the TD-DFT.50 The emission spectra of dpq was determined as follows: from the geometry of the ground S0 state, the first singlet S1 state was optimized (following the methodology previously described) in order to use it as input for the spectrum calculation. To obtain the spectral overlap integral (J) both, absorption and emission spectra, were normalized and numerical integration was performed employing the trapezoid rule. All of these spectra were built using a Lorentzian line shape. Finally, the correlated calculations using multireference ab initio methods were carried out to (i) obtain accurate wave functions to quantitatively analyze their composition on all studied complexes and (ii) properly characterize ground and excited states in those systems in which the fragmentation scheme was applied (structures (c), (d), and (e)). This enabled the determination of the energy levels on both antenna and lanthanide fragments to predict the energy transfer pathways. These calculations were performed employing the MOLCAS 8.0 program package.69 The scalar relativistic effects were included by the second-order Douglas−Kroll−Hess (DKH) approximation.70 All-electron ANO-RCC Gaussian-type basis sets contracted to TZP quality were used.71,72 SOC was treated by state interactions between the CASSCF wave functions, employing the restricted active space interaction (RASSI) program.73 The spin−orbit operator matrix was calculated from an atomic mean-field (AMFI) approximation.74 The dynamic correlation was incorporated at the second order of perturbation using the multistate CASPT2 method.58,59 For the lanthanide fragments, a minimal active space (only 4f orbitals) was chosen to perform the CASSCF calculations, on the basis of previous works and literature75−77 Therefore, for Nd, Sm, Eu, Tb, and Er compounds, a CAS(n,7) for n = 3, 5, 6, 8, and 11 was employed, respectively. In the case of compounds (c), (d), and (e), the antenna was also treated at the same level of theory, employing an active space selected to properly describe its electronic transitions. It consists of 10 electrons in 10 orbitals: 2 of nonbonding nature and 8 with p character (CAS(10,10)). The calculations were performed on the antenna obtained as a fragment from the optimized geometry of the entire complexes.

stand and describe in detail the influence of the symmetry and all of the processes involved in the emission of LnIII complexes. Due to the heavy nature of lanthanide elements, it is necessary to consider some factors to properly describe its electronic states. Relativistic effects (scalar and spin−orbit coupling), electronic correlation, and ligand field are the main effects that must be included in the theoretical treatment of this ions. For lanthanides, the inner character of the 4f shell makes the orbital moment largely unquenched, which favors the spin− orbit coupling (SOC) interaction relative to ligand field effect. Therefore, instead of the spin−orbit interaction acting as a perturbation on the ligand field, the reverse is usually a more accurate description.52−54 In addition, the large number of near degeneracy states generated from a 4f n configuration introduces a strong multireference character in the wave function of the system due to electron correlation; this effect can also be observed for the antenna, which, due to its delocalized nature, acquires a multiconfigurational character.55 In this context, multiconfigurational wave functions are required in order to include all of these effects to properly analyze the systems under study. For this reason, several methods have been developed such as the complete active space self-consistent field (CASSCF),56,57 second-order perturbation theory applied to multiconfigurational wave functions (CASPT2),58,59 multireference configuration interaction (MRCI),60 etc. Thus, in this work, the application of a systematic ab initio approach based on a multireference CASSCF/PT2 technique along with the use of TD-DFT is proposed to perform a complete theoretical analysis, with the objective of quantifying and interpreting transcendental aspects of part of the theory that underlies the understanding of the photophysics in this kind of compounds.

3. COMPUTATIONAL DETAILS The first step in this theoretical protocol consists of the optimization of some of the structures employed in the study. The geometries of the nonsymmetrical lanthanide compounds (structures (d) and (e) in Scheme 1) were obtained from crystallographic data reported by Patra et al.27−29 The symmetrical compounds were modeled in order to obtain the different symmetries shown in the Scheme 1 (structures (a), (b), and (c)). All the systems were optimized using the Amsterdam Density Functional (ADF) package.61 The scalar relativistic effects were incorporated by means of a two-component Hamiltonian with the zeroth-order regular approximation (ZORA).62,63 The hybrid exchange and correlation functional, B3LYP,64 was employed with the standard Slater-type orbital (STO) basis set and the triple-ξ quality double plus polarization function for all of the atoms (TZ2P).65−67 In all cases, the frequency calculations were performed to verify the quality of the minimum found in the optimization step. Once the optimization process has been performed, the fragmentation scheme proposed in our recent work68 was applied on the structures (c), (d), and (e) in order to treat the ligand and the lanthanide fragment separately. This was possible because in, all of these complexes, the absorption was ligand-localized and the emission lanthanide-centered, which constituted the basis of the developed method. Under these conditions, the study was carried out as follows: First, all the fragments were defined. Thus, for model (structure (c)) and crystallographic structures, the fragments used were [LnCl4]− Ln = Nd, Sm, Eu, Tb, Er, and [dpq], and [LnCl3(DMF)2]/[Ln(NO3)3(DMF)2] Ln = Sm, Tb, Er/Eu, Nd, and [dpq], respectively. Then, the probability of energy transfer was estimated calculating the spectral overlap integral. For this, the emission (and absorption) spectra of the ligand and absorption spectra of the lanthanide fragments were obtained using relativistic time-dependent density functional theory (SR-TDDFT) with the Coulomb-attenuated hybrid exchangecorrelation functional (CAM-B3LYP) which was designed to properly

4. RESULTS AND DISCUSSION The theoretical protocol proposed in this work is based on two main aspects: (i) a quantitative determination of the allowed character of the 4f−4f transitions, which was analyzed in all systems taking into account the symmetry effect on the first coordination sphere of the ion and (ii) the study of the emission mechanisms and the estimation of the energy transfer probability in those compounds that include the dpq ligand. For this, the fragmentation method was employed, and the spectral overlap integral was calculated. In this sense, the results are presented as follows: First, the properties of the antenna ligand are analyzed; second, the lanthanide fragment is discussed to determine the symmetry effect (in all studied complexes) and their energy levels (complexes (c), (d), and (e)) in order to finally discuss their transfer mechanisms. 4.1. Spectroscopic Properties of the Antenna. The calculated ground state geometries for the complexes are in good agreement with the available experimental data78−82 (see Section 1, Supporting Information). As we reported in our recent work,68 the theoretical treatment of the antenna is a key step in the correct determination of its spectroscopic properties, mainly the calculation of its first triplet state, which is the state responsible for the energy transfer to the lanthanide ion. For this reason, the structure of the dpq ligand was not optimized; instead, it was obtained as a fragment from the entire optimized complexes. Otherwise, its properties cannot be accurately reproduced. D

DOI: 10.1021/acs.inorgchem.8b00159 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 1. Experimental Data for the Systems under Studya,b

a

system

QLn L

τrad (ms)

λex (nm)

[Nd(NO3)3(DMF)2(Dpq)] [SmCl3(DMF)2(Dpq)] [Eu(NO3)3(DMF)2(Dpq)] [TbCl3(DMF)2(Dpq)] [ErCl3(DMF)2(Dpq)]

0.048 0.081 0.082 0.023

0.140 0.185 0.348 0.100

326 340 272 272 340

absorption (nm)b 272, 272, 272, 272, 272,

340 340 340 340 340

emission (nm)b 360, 450 ∼600 (4G5/2 → 6H7/2), ∼648 (4G5/2 → 6H9/2) ∼590 (5D0 → 7F1), ∼616 (5D0 → 7F2) ∼489 (5D4 → 7F6), ∼543 (5D4 → 7F5) 545 (4S3/2 → 4I15/2)

These values were obtained from refs 27−29. bOnly the most intense absorption and emission bands are shown.

4.2. Spectroscopic Properties of the Lanthanide Fragments. 4.2.1. TDDFT Calculations. On the basis of Fermi’s golden rule, to obtain the spectral overlap integral, both emission and absorption spectra of the antenna and lanthanide fragments are required, respectively. For this, the systems (c), (d), and (e) were analyzed taking the lanthanide moieties as fragments from the optimized structure, like in the dpq treatment. It is known that the luminescence from lanthanide ions is weak due to the forbidden character of the 4f−4f transitions; however, charge transfer transitions are allowed and have high energies.52,88 Under these considerations, absorption spectra of the lanthanide fragments were calculated and their bands were characterized (see Sections 4 and 5, Supporting Information). For model and synthesized crystalline compounds, absorption bands involving p molecular orbitals from the nitrate ligands to f orbitals of the lanthanide ion, were found. In the case of model systems, the absorption bands were located around 510−600 nm for [NdCl4]−, 250−350 nm for [Eu/TbCl4]−, and 250−425 nm for [ErCl4]−. For those synthesized systems, the absorption bands were located around 200−300 nm for [Nd(NO3)3(DMF)2], 300−500 nm for [Eu(NO3)3(DMF)2], 300−375 nm for [TbCl3(DMF)2], and 250−350 nm for [ErCl3(DMF)2]. All the results are in agreement with the available experimental data in literature. For example, according to reports of the lanthanide series published by Carnall et al.,89 the location of the absorption bands for the studied lanthanide ions is in accordance with the location of the energy levels of each ion. Furthermore, based on experimental data of molecules in which a similar coordination environment exists for the lanthanide centers, similar transitions have been obtained in correct agreement with the results of this work.90−92 Finally, in spite of the lack of experimental information about these specific fragments, the accurate results obtained employing the same methodology on other lanthanide systems support the robustness of the calculations.75,76,93,94 At this point, it is necessary to emphasize that the main objective in this part of the theoretical protocol is to calculate the spectral overlap integral. This in order to have an estimation of the energy transfer probability and to analyze if J, in itself, reproduces the reality observed from experimental data. Therefore, a fundamental aspect in the validation of the proposed methodology is to reproduce the trends obtained from the experimental quantum yield with those obtained from the calculation of J. As in the treatment of the ligand, the LB94 functional was also employed to predict the electronic transitions in all the lanthanide fragments. However, the spectra could not be reproduced under this methodology due to problems found in the Davidson’s procedure for the calculation of the excitation energies. This can be attributed to the distinct nature of the asymptotic corrections that these functionals contain. It is known that the long-range corrected (LC) hybrid functionals

The optical properties of the free dpq ligand have been widely reported.83−85 In this context, it is well-known that dpq absorbs within an energy range of 250−350 nm. The UV− visible absorption spectra of (d) and (e) lanthanide compounds in DMF show two ligand-centered transitions at 272 and 340 nm characterized as π → π* and n → π* transitions, respectively. As can be observed, in different lanthanide systems containing the same antenna, the positions of the absorption bands are only slightly affected by the nature of the central ion (see Table 1). This means that the absorption depends on the dpq ligand and suggests a possible lanthanide sensitization process. On the other side, the fluorescence spectra of dpq show two main emission peaks at 360 and 450 nm approximately upon excitation at 326 nm. TD-DFT calculations were employed to determine the spectroscopic properties of the antenna. For the absorption spectra, two bands were obtained at 282 and 310 nm ascribed as π → π* transitions, which is in correct agreement with the experimental reports. In the case of the fluorescence spectra, the two emission peaks were properly reproduced and were located at 361 and 417 nm, respectively (see Section 3, Supporting Information). According to the calculated oscillator strength, the excitation was estimated at 360 nm. All of this data was also collected using the LB94 functional,86 obtaining absorption peaks at 282 and 317 nm characterized as π → π* transitions and emission bands at 367 and 435 nm. As can be observed, both functionals calculated accurately both spectra of the ligand. This is not a surprise, since these methods have corrections that make them suitable for the calculation of transitions in organic molecules, as was observed by Blase et al.87 in 2014 in which excited states and intramolecular transitions were determined in organic molecules employing different functionals, and those with long-range corrections, such as CAM-B3LYP, showed the best performance in the determination of the π → π* transitions. The localization of the lowest triplet state (T1) in the antenna fragment is an important factor influencing the luminescence properties in lanthanide complexes, because generally from this state the energy transfer is produced. Thus, if the energy gap between T1 and the resonance levels in lanthanide ions is too large, other deactivation paths could take place in the ligand, and if this gap is too small, the energy can back-transfer from the lanthanide to the antenna. In this context, Zhao et al.83 determined experimentally the localization of T1 for the dpq at 23800 cm−1 (420 nm). From a theoretical point of view, TD-DFT calculations were used to describe the S0 → S1 transitions. Nonetheless, to localize the lowest triplet state, multiconfigurational methods were employed. Thus, CAS(10,10)SCF/PT2 calculations were performed on the geometry of dpq obtained as a fragment from the entire complex and T1 was found at 24463 cm−1 (409 nm), in perfect agreement with the experimental value. This is evidence of the good performance of the selected active space. E

DOI: 10.1021/acs.inorgchem.8b00159 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 2. Composition of Ground and Excited States Involved in the Most Important Transition in Experimental Compounds ((d) and (e)) Ln

[LnCl3(DMF)2]

Sm [4G5/2 → 6HJ] Eu [5D0 → 7FJ] Tb [5D4 → 7FJ]

|4G′5/2⟩ = 100%|4G5/2⟩ |6H′J⟩ = 93.5%|6HJ⟩ + 9.3%|4G5/2⟩

[Ln(NO3)3(DMF)2]

|5D′0⟩ = 100%|5D0⟩ |7F′J⟩ = 93.4%|7FJ⟩ + 6.6%|5D0⟩ |5D′4⟩ = 94.8%|5D4⟩ + 5.2%|7FJ⟩ |7F′J⟩ = 91.1%|7FJ⟩ + 8.9%|5D4⟩

Table 3. Composition of Ground and Excited States Involved in the Most Important Transition in Model Compounds ((a), (b), and (c)) Ln

[LnCl6]3−

[Ln(CN)2Cl4]3−

[LnCl4(Dpq)]−

Sm [4G5/2 → 6HJ] Eu [5D0 → 7FJ] Tb [5D4 → 7FJ]

| G′5/2⟩ = 100%| G5/2⟩ |6H′J⟩ = 100%|6HJ⟩ |5D′0⟩ = 100%|5D0⟩ |7F′J⟩ = 99.95%|7FJ⟩ + 0.05%|5D0⟩ |5D′4⟩ = 98.8%|5D4⟩ + 1.2%|7FJ⟩ |7F′J⟩ = 98%|7FJ⟩ + 2%|5D4⟩

| G′5/2⟩ = 100%| G5/2⟩ |6H′J⟩ = 96.1%|6HJ⟩ + 2.1%|4G5/2⟩ |5D′0⟩ = 99.98%|5D0⟩ + 0.02%|7FJ⟩ |7F′J⟩ = 100%|7FJ⟩ |5D′4⟩ = 97.2%|5D4⟩ + 3.6%|7FJ⟩ |7F′J⟩ = 96%|7FJ⟩ + 5.5%|5D4⟩

| G′5/2⟩ = 100%|4G5/2 |6H′J⟩ = 91.7%|6HJ⟩ + 8.3%|4G5/2⟩ |5D′0⟩ = 99%|5D0⟩ + 1%|7FJ⟩ |7F′J⟩ = 92.7%|7FJ⟩ + 7.3%|5D0⟩ |5D′4⟩ = 100%|5D4⟩ |7F′J⟩ = 91.1%|7FJ⟩ + 8.9%|5D4⟩

4

4

4

4

4

ations from group theory (Section 2, Supporting Information).96 For [Tb(CN)2Cl4]3−, the SF multiplet 7F6 was split into 7A2u⊕7B1u⊕7B2u⊕27Eu in a D4h environment and the states produced by SOC were 2A1u⊕2B1u⊕2B2u⊕2Eu⊕A2u⊕Eu. The location of both ground and excited multiplets is in good accordance with the reported experimental data (see Section 4.2.3) for all of these lanthanide compounds and did not vary much from the symmetry point of view. This can be seen in terbium systems, where the 7F0 and 5D4 states are located at ca. 6069 and 22367 cm−1, respectively, regardless of whether the first coordination sphere of the LnIII ion had high or low symmetry. These results corroborate the assumption that the ligand environment does not generate meaningful differences between the energy levels of lanthanide compounds.22,23,52 Nonetheless, it is necessary to consider other factors in which the symmetry effect becomes relevant, such as the wave function composition of those states involved in the main transitions that take place in these systems. The 4f−4f transitions are electric dipole (ED) forbidden because the initial and final states have the same parity. For this, forced ED transitions were introduced to explain the emission bands observed in LnIII ions. In this context, Judd and Ofelt set up some simplifications in the selection rules for forced ED transitions taking into account two main factors: symmetry and the spin−orbit coupling.16,17,24 In lanthanide-containing systems, this interaction is especially important because it leads to mixing of states which partially lift the selection rules for these transitions. Consequently, the classic spin rule (ΔS = 0) can be fulfilled if the emitting state has small contributions from the receiving state and vice versa, depending upon how far apart their energies are. Now, the question is why is it important to analyze the wave function composition of those states involved in a determined transition? Due to the multireference character of the wave function in the compounds studied herein, small contributions from other states can be observed in its composition·97 Then, if a transition takes place between two states named xAj and yBj, where x and y are the spin of each state, it would be expected that A contains a small amount of B and vice versa. Therefore, the transition becomes r[xAj] + t[yBj] → r[yBj] + t[xAj], where, although r ≫ t (r and t are the wave function coefficients), there is now a

have advantages relative to the asymptotically corrected (AC) models such as LB94. In this sense, the long-range HF exchange kernel included in the LC scheme is essential for the accurate description of the long-range transitions between two well-separated molecules (or regions in a molecule), which cannot be described by the AC scheme due to the lack of the discontinuity of the exchange-correlation (XC) kernel.95 Therefore, the CAM-B3LYP functional was chosen for the determination of the optical properties of both ligand and lanthanide moieties in order to subsequently obtain J. As expected, the main differences between model and experimental compounds were observed for those containing Nd and Eu. This was due to the different nature of the lanthanide coordination sphere, which changes from three chloride atoms (in model systems) to three nitrate groups (in experimental systems). This difference is more noticeable in the case of neodymium-containing compounds, which can be attributed to the electronic structure of the NdIII ion, which generates a rich variety of energy levels that can participate in these transitions at different energy ranges. 4.2.2. Wave Function Calculations. Higher level calculations are necessary for the theoretical treatment of the lanthanide ions owing to their particular electronic structure. In this context, multiconfigurational methods were used to determine the location of the energy levels in the systems under study and to analyze the composition of their wave functions. First, according to the Russell−Saunders scheme, the predicted ground spin-free (SF) ion terms are 4I9/2, 6H5/2, 7F0, 7 F6, and 4I15/2 for NdIII, SmIII, EuIII, TbIII, and ErIII, respectively. All of these were perfectly reproduced employing the minimal active space (seven 4f orbitals). The SF states issued from the ground SF terms are shown in Section 2, Supporting Information, and were ordered at the SF-CASSCF calculation level, according to their splitting in an Oh, C4v, and other less symmetric (C2 and C1) crystal environments. An example of this is that, in the case of terbium-containing compounds, the following can be observed: for [TbCl6]3−, the SF multiplet 7F6 was split into 7A2u