Theoretical Study of Ln(III) Complexes with Polyaza-Aromatic Ligands: Geometries of [LnL(H2O)n]3+ Complexes and Successes and Failures of TD-DFT

LFDFT—A Practical Tool for Coordination Chemistry

The electronic structure of coordination compounds with lanthanide ions is studied by means of density functional theory (DFT) calculations. This work deals with the electronic structure and properties of open-shell systems based on the calculation of multiplet structure and ligand-field interaction, within the framework of the Ligand–Field Density-Functional Theory (LFDFT) method. Using effective Hamiltonian in conjunction with the DFT, we are able to reasonably calculate the low-lying excited states of the molecular [Eu(NO3)3(phenanthroline)2] complex, subjected to the Eu3+ configuration 4f6. The results are compared with available experimental data, revealing relative uncertainties of less than 5% for many energy levels. We also demonstrate the ability of the LFDFT method to simulate absorption spectrum, considering cerocene as an example. Ce M4,5 X-ray absorption spectra are simulated for the complexes [Ce(η8−C8H8)2] and [Ce(η8−C8H8)2][Li(tetrahydrofurane)4], which are approximated by the Ce oxidation states 4+ and 3+, respectively. The results showed a very good agreement with the experimental data for the Ce3+ compound, unlike for the Ce4+ one, where charge transfer electronic structure is still missing in the theoretical model. Therefore this presentation reports the benefits of having a theoretical method that is primarily dedicated to coordination chemistry, but it also outlines limitations and places the ongoing developmental efforts in the broader context of treating complex molecular systems.

Antenna triplet DFT calculations to drive the design of luminescent Ln3+ complexes

Density functional theory-based methods have been exploited to look into the structural, vibrational and electronic properties of antenna ligands, all of them being crucial factors for the reliable design of customized luminescent lanthanide (Ln3+) complexes. The X-ray structures, UV-Vis absorption spectra and triplet (T1) energies of three novel β-diketone ligands with a thienyl group and naphthyl (L1), phenanthryl (L2), and pyrenyl (L3) polycyclic aromatic hydrocarbons as substituents have been modelled. Vibronic progressions provide a strong contribution to the L1 and L2 absorption spectra, while the L3 absorption spectrum needs the assumption of different conformational isomers in solution. T1 energies have been estimated either through the vertical- or the adiabatic-transition approach. The comparison with the phosphorescence spectra of Gd3+ complexes allowed us to infer that the latter approach is the most suitable one, in particular when sizable ligands are involved. Results obtained for the isolated antennas can be directly compared with those of the corresponding Ln3+ complexes, due to the unanimously accepted assumption that the excitation is ligand-centred.

Unveiling the Relationship between Energy Transfer and the Triplet Energy Level by Tuning Diarylethene within Europium(III) Complexes

Luminescence performance and photoisomerization control of sensitized energy transfer in a series of Eu(acac)₃De complexes that contain photochromic diarylethene (De) as the ligand are studied by theoretical methods. Both the open-ring and closed-ring isomers exhibit a consistent coordination mode between the Eu^III ion and De. An unneglected weak interaction originating from electrostatic attraction is found in the region of the coordinate bond Eu-N. The open-ring isomer has higher triplet energy levels than ⁵D₁ and ⁵D₀ of the Eu^III ion, which facilitates forward energy transfer from De to the Eu^III ion. The closed-ring isomer, for the extended conjugated system formed in cyclization, has a much lower triplet energy level than ⁵D₀ of the Eu^III ion. The energy-gap deficit makes energy transfer unavailable. By utilization of this phenomenon, regulation of energy transfer and reversible on/off luminescence switching of the europium(III) complex can be achieved. The forward and backward energy-transfer rates in different channels are also calculated for the series of complexes. A statistics diagram is obtained to exhibit the change trend of energy-transfer rates in the forward and backward directions as a function of the triplet energy level, which indicates the contribution of different channels to energy transfer in each level region and figures out that the optimal triplet energy level should be in the range of 21740-19532 cm^-1.

Luminescent europium(iii) and terbium(iii) complexes of β-diketonate and substituted terpyridine ligands: synthesis, crystal structures and elucidation of energy transfer pathways

A series of coordinatively saturated Ln^III complexes: [Ln(R-TPY)(TTA)₃] (1–6) were designed and structurally characterized and plausible energy transfer (ET) pathways determined using a theoretical method.

Theoretical study of structure and stability of small gadolinium carboxylate complexes in liquid scintillator solvents

The structural properties of three small gadolinium carboxylate complexes in three liquid scintillator solvents (pseudocumene, linear alkylbenzene, and phenyl xylylethane) were theoretically investigated using density functional theory (B3LYP/LC-RECP) and polarizable continuum model (PCM). The average interaction energy between gadolinium atom and carboxylate ligand (E(int)) and the energy difference of the highest singly occupied molecular orbital and lowest unoccupied molecular orbital (Δ(SL)) were calculated to evaluate and compare the relative stability of these complexes in solvents. The calculation results show that the larger (with a longer alkyl chain) gadolinium carboxylate complex has greater stability than the smaller one, while these gadolinium carboxylates in linear alkylbenzene were found to have greater stability than those in the other two solvents.

Lanthanides caged by the organic chelates; structural properties

The structure, in particular symmetry, geometry and morphology of organic chelates coordinated with the lanthanide ions are analyzed in the present review. This is the first part of a complete presentation of a theoretical description of the properties of systems, which are widely used in technology, but most of all, in molecular biology and medicine. The discussion is focused on the symmetry and geometry of the cages, since these features play a dominant role in the spectroscopic activity of the lanthanides caged by organic chelates. At the same time, the spectroscopic properties require more formal presentation in the language of Racah algebra, and deserve a separate analysis. In addition to the parent systems of DOTA, DOTP, EDTMP and CDTMP presented here, their modifications by various antennas are analyzed. The conclusions that have a strong impact upon the theory of the energy transfer and the sensitized luminescence of these systems are based on the results of numerical density functional theory calculations.

Theoretical study of metal-ligand interaction in Sm(III), Eu(III), and Tb(III) complexes of coumarin-3-carboxylic acid in the gas phase and solution

The interaction of lanthanide(III) cations (Ln(III) = Sm(III), Eu(III), and Tb(III)) with the deprotonated form of the coumarin-3-carboxylic acid (cca-) has been investigated by density functional theory (DFT/B3LYP) and confirmed by reference MP2 and CCSD(T) computations. Solvent effects on the geometries and stabilities of the Ln(III) complexes were computed using a combination of water clusters and a continuum solvation model. The following two series of systems were considered: (i) Ln(cca)2+, Ln(cca)2+, Ln(cca)3 and (ii) Ln(cca)(H2O)2Cl2, Ln(cca)2(H2O)2Cl, Ln(cca)3. The strength and character of the Ln(III)-cca- bidentate bonding were characterized by calculated Ln-O bond lengths, binding energies, ligand deformation energies, energy partitioning analysis, sigma-donation contributions, and natural population analyses. The energy decomposition calculations predicted predominant electrostatic interaction terms to the Ln-cca bonding (ionic character) and showed variations of the orbital interaction term (covalent contributions) for the Ln-cca complexes studied. Electron distribution analysis suggested that the covalent contribution comes mainly from the interaction with the carboxylate moiety of cca-.

Assessment of several hybrid DFT functionals for the evaluation of bond length alternation of increasingly long oligomers

We have optimized the ground-state geometry of nine series of increasingly long oligomers, using six hybrid density functionals (O3LYP, B3LYP, B97-1, B98, PBE0, and BHHLYP) combined with three different atomic basis sets. In each case, the obtained bond length alternation (BLA) is compared to the corresponding MP2 values. Three phenomenological categories have been set up. In the first, the BLA exponentially decreases, in which case all the tested functionals give results in very good agreement with MP2. In the second category fall the symmetric oligomers that, due to the Peierls theorem, show large BLA. For these chains, BHHLYP tends to give too large and quickly converging BLA wrt chain length, while O3LYP often leads to the opposite misjudgments, and the remaining hybrids provide valuable results. In the third category, one finds asymmetric compounds presenting significantly unequal bond lengths, for which the divergence between DFT and wave function approaches can be dramatic. Indeed, all hybrids yield too small BLA values, especially for long chain lengths. We also study the effect of chain conformation on the BLA.

Absorption spectra of caffeic acid, caffeate and their 1:1 complex with Al(III): density functional theory and time-dependent density functional theory investigations

The UV-visible absorption spectra of caffeic acid, caffeate and of the predominant complex obtained in the presence of aluminum ion (1:1 stoichiometry) have been simulated by using the time-dependent density functional theory (TD-DFT) technique, taking into account solvent effects. Whereas the use of the B3LYP hybrid XC functional with the 6-31+G(d,p) basis set allows us to reproduce fairly well the essential features of the experimental spectra of caffeic acid and caffeate, it is necessary to introduce an effective core potential to properly describe the aluminum ion and its environment and to obtain a good agreement between theoretical and experimental spectra of the 1:1 complex. The ligand presents two potential complexing sites in competition. The results of our calculations show that the aluminum ion coordinates preferentially at the level of the catecholate group, and the [Al(H(2)O)(4)(CA)], [Al(H(2)O)(3)(OH)(CA)](-) and [Al(H(2)O)(4)(HCA)](+) complexed forms could coexist in aqueous solution at pH = 5.

On the performance of local, semilocal, and nonlocal exchange-correlation functionals on transition metal molecules

The lowest singlet-triplet transition (X (1)Sigma+-(3)Sigma+) of AgI has been used to study systematically the performance of local [local density approximation (LDA)], semilocal [generalized gradient approximation (GGA)], and nonlocal (semiempiric hybrid and meta)-type exchange-correlation functionals on a transition metal molecule where dynamic electronic correlation effects are essential. Previous benchmark ab initio calculations showed that the triplet ground state possesses a shallow well in the Franck-Condon region before becoming repulsive at longer internuclear distance [A. Ramirez-Solis, J. Chem. Phys. 118, 104 (2003)]. Several density functional theory (DFT) descriptions are compared with the benchmark complete active space self-consistent-field+averaged coupled pair functional results, using the same relativistic effective core potentials and optimized Gaussian basis sets. A rather unreliable performance of exchange-correlation functionals was found when ascending the various rungs in DFT Jacob's ladder for this complex molecule. While some of the simpler (LDA and GGA) functionals correctly predict the presence of a short-distance maximum for the (3)Sigma+ state, more sophisticated hybrid and meta-functionals lead to totally repulsive or oscillating curves for the ground triplet state. A thorough discussion addressing the local versus nonlocal character of the exchange and correlation effects on the triplet potential curve is presented. The author concludes that any new efforts directed at producing more accurate exchange-correlation functionals must take into account the more complex electronic structure arising in transition metal molecules, whether these efforts follow the dominant pragmatic semiempiric trend or the more philosophically correct nonempiric pathway to develop better exchange-correlation functionals; only then will the Kohn-Sham version of DFT make the necessary improvements to correctly describe the electronic structure of complex transition metal systems.

Luminescent Eu(III) and Gd(III) Trisbipyridine Cryptates: Experimental and Theoretical Study of the Substituent Effects

Synthesis, absorption spectra and luminescebce properties of a series of lanthanide trisbipyridine cryptates Ln within R-Bpy x R-Bpy x R-Bpy, where Ln = Eu, Gd and R = H, COOH, COOCH3, CONH(CH2)2NH2 are described. Comparison of the unsubstituted parent compound with the substituted compounds shows that bipyridine substitution doesn't alter significantly the photophysical properties of the lanthanide cryptate. The absorption maximum is slightly red-shifted when three bipyridines are substituted, whereas substituting one bipyridines has a negligible effect on the absorption spectra. The experimental triplet state energy is between 21600 and 22 100 cm(-1) for the series of compounds and the luminescence lifetimes at 77 K are between 0.5 and 0.8 ms in HO2 and equal to 1.7 ms in D2O. The experimental characterizations are completed by DFT and TD-DFT calculations to assess the ability of these approaches to predict absorption maxima, triplet state energies and structural parameters of lanthanide cryptates and to characterize the electronic structure of the excited states. The calculations on the unsubstituted parent and substituted compounds show that absorption maxima and lowest 3pipi* triplet state energies can be accurately determined from density functional theory (DFT) and time-dependent (TD) DFT calculations.

A Theoretical Characterization of Covalency in Rare Earth Complexes through Their Absorption Electronic Properties: f−f Transitions

Experimental uncertainties concerning the coordination mode of trivalent plutonium in concentrated LiCl have led us to theoretically evaluate the f-f transitions of a series of rare earth aquo and chloro complexes. The calculation of Pr(III), U(III), Np(III), and Pu(III) systems' spectra was undertaken using the LFDFT (ligand field density functional theory) route that combines the backgrounds of ligand field (LF) theory with Kohn-Sham orbitals. LF parameters are fitted to previous DFT calculations, thus preventing the use of empirical data. The f-f transitions values are globally well predicted, but the lack of accurate experimental references can sometimes hinder reliable comparisons. Despite this, the nephelauxetic effect from aquo to chloro complexes is clearly observed through both spectral red shifts and the decrease in F2, the Slater-Condon parameter. Accordingly, this work provides the first theoretical characterization of covalency in trivalent f elements through their electronic spectra.

Density-functional theory structures of 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid complexes for ions across the lanthanide series

The use of organically chelated lanthanides in diagnosis and treatment is a rapidly growing field in medicine. In order to gain a deeper understanding into the properties of these chelates, particularly spectroscopic, density-functional calculations have been performed on a series of lanthanide ions chelated with 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid. Based on the results of these calculations, it has been concluded that the local symmetry experienced by the chelated lanthanide ion may be treated as being axial, which will make the interpretation of their spectroscopic properties greatly simplified. It has also been suggested that the so-called "capping" water molecule at the ninth coordination position of the lanthanide is hydrogen bonded to the acetate oxygens of the sidearms, rather than coordinated as the ninth ligand of the lanthanide.

Density Functional Theory Investigation of Eu(III) Complexes with β-Diketonates and Phosphine Oxides: Model Complexes of Fluorescence Compounds for Ultraviolet LED Devices

The density functional theory was employed to investigate Eu(III) complexes with three beta-diketonates and two phosphine oxides (complex M1: Eu(bdk)3(TPPO)2, complex M2: Eu(bdk)3(TMPO)2, and complex M3: Eu(bdk)3(TPPO)(TMPO)) deemed to be the model complexes of the fluorescence compounds for the ultraviolet LED devices we have recently developed. For each complex, two minimum energy points corresponding to two different optimized geometries (structures A and B) have been found, and the difference of the energy between two minimum energy points is found to be quite small (less than 1 kcal/mol). Vertical excitation energies and oscillator strengths for each complex at two optimized geometries have been obtained by the time-dependent density functional theory, and the character of the excited states has been investigated. For complex M3, the absorption edge is red-shifted, and the oscillator strengths are relatively large. The efficiency of intersystem crossing and energy transfer from the triplet excited state to the Eu(III) ion is considered by calculating DeltaE(ISC) (the energy difference between the first singlet excited state and the first triplet excited state) and DeltaE(ET) (the difference between the excitation energy of the complex for the first triplet excited state and the emission energy of the Eu(III) ion for 5D to 7F).

Characterization and Comparison of Cm(III) and Eu(III) Complexed with 2,6-Di(5,6-dipropyl-1,2,4-triazin-3-yl)pyridine Using EXAFS, TRFLS, and Quantum-Chemical Methods

The complexation of Cm(III) and Eu(III) with 2,6-di(5,6-dipropyl-1,2,4-triazin-3-yl)pyridine (n-C3H7-BTP) in nonaqueous organic solution is studied with extended X-ray absorption spectroscopy. Bond lengths are the same in both complexes. Quantum-chemical calculations performed at different levels support this finding. On the other hand, the Cm.(n-C3H7-BTP)3 complex is formed at much lower ligand-to-metal concentration ratio than the Eu.(n-C3H7-BTP)3 complex, as shown by time-resolved laser-induced fluorescence spectroscopy. This is in good agreement with n-C3H7-BTP's high selectivity for trivalent actinides over lanthanides in liquid-liquid extraction.