Massive Stokes shift in 12-coordinate Ce(NO2)63−: crystal structure, vibrational and electronic spectra

The Ce3+ ion in Cs2NaCe(NO2)6 (I), which comprises the unusual Th site symmetry of the Ce(NO2)63− ion, demonstrates the largest Ce-O Stokes shift of 8715 cm−1 and the low emission quenching temperature of 53 K. The activation energy for quenching changes with temperature, attributed to relative shifts of the two potential energy curves involved. The splitting of the Ce3+ 5d1 state into two levels separated by 4925 cm−1 is accounted for by a first principles calculation using the crystal structure data of I. The NO2− energy levels and spectra were investigated also in Cs2NaLa(NO2)6 and modelled by hybrid DFT. The vibrational and electronic spectral properties have been thoroughly investigated and rationalized at temperatures down to 10 K. A comparison of Stokes shifts with other Ce-O systems emphasizes the dependence upon the coordination number of Ce3+.

In view of the high coordination number of the lanthanide ion in the hexanitritolanthanate anion, we envisaged that the properties of the cerium complex would be of interest. First, we anticipated a large Stokes shift (Fig. S1) between the emission and absorption spectral bands. The Stokes shift could thus provide long wavelength cerium(III) emission. Second, the repercussions of this shift upon the temperature quenching of the emission spectrum would need to be studied. In order to investigate these processes, we synthesized Cs 2 NaCe(NO 2 ) 6 and determined the crystal structure and vibrational properties, as well as measuring the electronic spectra at temperatures down to 10 K. It was indeed demonstrated that the Stokes shift is the largest ever reported for Ce 3+ emission in oxygen coordination.

Methods
Synthesis. The crystals of Cs 2 NaCe(NO 2 ) 6 were synthesized by dissolution of 337 mg (2 mmol) CsCl (Strem, 99.999%), 58 mg (1 mmol) NaCl (Dieckman, AR) and 373 mg (1 mmol) CeCl 3 .7H 2 O (Sigma-Aldrich, 99.9%) in 6 ml 37% aqueous HCl at 150 °C to obtain a white solid. A saturated solution of 1 ml NaNO 2 (9 M) was then added and yellow precipitate was obtained. A transparent solution was obtained after adding 5 ml H 2 O. The solution was housed in a desiccator in a refrigerator at 4 °C. After two days, transparent, yellowish crystals were obtained which were removed from the mother liquor and dried. Powders were also prepared by precipitation according to the method of Roser and Corruccini 6 . Cs 2 NaLa(NO 2 ) 6 and Cs 2 NaY 0.96 Ce 0.04 (NO 2 ) 6 were prepared analogously.
Instrumentation. X-ray diffraction patterns of crystals were recorded with a Bruker AXS D8 Advance X-Ray Diffractometer using non-monochromated Cu K α X-rays (λ = 1.5418 Å). FT-IR spectra were recorded at room temperature in the range from 400 to 4000 cm −1 using a PerkinElmer Paragon 1000 PC spectrometer with a resolution of 4 cm −1 . Raman spectra were taken by a Perkin-Elmer Spectrum 2000 spectrometer using a resolution of 4 cm −1 at room temperature. The emission and excitation spectra were recorded by a Horiba Fluorolog-3 spectrophotometer using a 450 W xenon lamp as the continuous light source and the signal was detected by a Hamamatsu R928 photomultiplier. The crystal was cooled down by an Optical Cryostat-CS202I-DMX-1SS from Advanced Research Systems Instruments Inc. Luminescence lifetimes were measured by a 340 nm laser diode with 1 ns pulse width. The laser system consisted of an Nd:YAG pump laser, a third-order harmonic generator (THG at 355 nm, 120 mJ), and an optical parametric oscillator (OPO, Spectra-Physics versaScan and UVScan) with a pulse duration of 8 ns and repetition frequency of 10 Hz. X-ray photoelectron spectra (XPS) were recorded by a SKL-12 spectrometer modified with a VG CLAM 4 multichannel hemispherical analyser. Emission spectra were recorded using a Horiba 0.5 m monochromator (iHR550) equipped with a 600 groove mm −1 grating blazed at 800 nm and with a CCD detector (Syncerity, 300-1100 nm). Selected crystals were used for intensity data collection on a Bruker AXS Kappa Apex II Duo diffractometer at 173 K using frames of oscillation range 0.3°, with 2° < θ < 28°. An empirical absorption correction was applied using the SADABS program 10 . The structures were solved by the direct method and refined by full-matrix least-squares on F 2 using the SHELXTL program package 11 , (Fig. 1).

Calculations
Ligand electronic spectra. The structure of Q(NO 2 ) 6 3− (where Q is a 3 + Sparkle) was optimized in ORCA 12,13 using scalar relativistic and generalized gradient approximation (GGA) calculations. First, the BP86 functional was used with the basis set ZORA-def2-TZVP 14 which is a relativistically recontracted version of the all-electron def2-TZVP Ahlrichs basis 15,16 . The SARC/J auxiliary basis set, which is a decontracted def2/J auxiliary was employed. A time dependent density functional theory (td-dft) calculation was then carried out. Alternatively, the composite approach PBEh-3c was employed with the basis def2-mSVP and the auxiliary basis def2/J 17 . This functional is a reparameterized version of PBE0 (with 42% HF exchange) that uses a double-zeta basis set, def2-mSVP (unlike the minimal basis set in HF-3c) and adds 3 corrections that correct for dispersion (via D3), basis set superposition (via gCP) and other basis set incompleteness effects. The results of the td-dft calculation were in closer agreement with experiment and are as shown in Fig. 2(a). The structure was drawn in Chemcraft 18 according to the X-ray data and exported into ORCA 12,13 .
Ab-initio calculation of Ce 3+ crystal field parameters (CFP) and 5d 1 (1,2) splitting. We adopted a novel method for the 4 f 1 electron CFP, which was developed by Novak and his co-workers 19 to carry out first-principles calculations of the CFP of the 4 f configuration of a rare earth ion doped in a crystal host. Their calculated results match very well with the observed spectroscopic and magnetic data in lattices like aluminates, gallates, manganites and LaF 3 19-22 . In fact, the method was based on Richter et al. 's 23 earlier attempt to employ density functional theory (DFT) for band structure calculation of the lanthanide 4f-shell ions with transformation of the Kohn-Sham Hamiltonian to the Wannier basis [19][20][21] . For the present first-principles calculations of the CFP for the 5d 1 electron of Ce 3+ , Novak's novel method was also adopted with specific modifications and the whole procedures are concisely outlined as follows: 1. The WIEN2k program 24 was applied for standard self-consistent band calculation (for solution of the Kohn-Sham equations of the DFT) with explicit incorporation of the 5d state in the core, giving rise to the crystal potential for subsequent calculations. 2. The oxygen ligand 2 s and 2p states and lanthanide 5d states were treated as valence states for the calculation of the effective crystal field Hamiltonian from ingredients involving the shape of the 5d orbital, the effective potential and the hybridization with the oxygen ligand orbitals in which the energy difference between the 5d and ligand states is taken as a 'hybridization' parameter. 3. The Wien2wannier 25 and Wannier90 26 computer packages were employed to transform the lanthanide 5d band states to the Wannier basis. 4. The local d-orbital Hamiltonian was extracted from the Wannier basis for subsequent extraction of the CFP. 5. The local d-orbital Hamiltonian was expanded in a series of spherical tensor operators to get values of the CFP for the 5d electron.
One of the present authors (Y. Y. Yeung) has developed a set of user-friendly subroutines in his f-Spectra package to carry out the last two steps for both d-and f-orbital electrons of any rare earth ion and to automatically set the required input parameters for the first two steps. It is noted that band-structure calculations should be performed with the Wien2k software package, which is based on the full-potential linearized augmented plane wave method and is often considered as the most accurate package for calculating the electronic properties of atoms with highly correlated electrons like 4 f and 5d electrons of rare earths. Other packages are not accurate enough for the present approach because the small energies for crystal field splittings are easily affected by minor inaccuracies in the calculations of band structures.
The atomic positions were taken from the cif file for Cs 2 NaCe(NO 2 ) 6 (and the same for other lanthanide ions). The oxygen-ligand distance employed was 2.6525 Å.

Results and Discussion
Crystal structure. Complex Cs 2 NaCe(NO 2 ) 6 crystallizes in a cubic space group (#202) with Fm3 lattice symmetry. The crystal data are summarized in Tables 1 and S1-S4. In this face-centered cubic structure, the central Cs + ion is coordinated to twelve oxygen donor atoms from twelve symmetry-related nitrite ligands in the distance of 3.314(1) Å, as shown in Fig. 1. On the other hand, the Ce 3+ ions, at two pairs of diagonal corners with an unusual tetrahedral T h point group symmetry, are coordinated to twelve oxygen donor atoms from six symmetry-related nitrite groups. The Ce-O bond distance with twelve-coordinated oxygen is 2.653(1) Å, compared with the distance 2.82(2) Å reported for the corresponding La complex 27 . Six nitrogen atoms from the symmetrical nitrite groups are attached to each Na + cation, located at four corners, to construct the face-centered cubic structure.
Ligand electronic spectra. The previous assignments for the ultraviolet spectra of the NO 2 − ion have agreed that there are three electric dipole allowed transitions from the 1 A 1 ground state to 1 B 1 (~360 nm, ε~28), 1 A 2 (~290 nm, ε~9) and 1 B 2 (~210 nm, ε~5000) 9 , where the wavelength values indicate the maxima of the absorption bands. The lowest energy transition, 1 A 1 → 3 B 2 , is enhanced by about 100 times in Cs 2 NaLn(NO 2 ) 6 compared with NaNO 2 due to increased spin-orbit coupling by the heavy atom effect 8 . The NO 2 − transitions were investigated in Cs 2 NaLa(NO 2 ) 6 in addition to the Ce 3+ analogue. Simulations of the NO 2 − absorption spectra were carried out using the PBeh-3c functional 17 in the ORCA 12,13 program. The geometry optimization in ORCA did not give equal Ce-O bond distances. Hence each NO 2 − level was split into 6 levels in this case. In T h symmetry, with six NO 2 − groups, the B 1 and B 2 levels only each split into 2 levels, T g + T u , and the transition to the latter is electric dipole allowed from the A g ground state. Figure 2(a) shows the result of the PBeh-3c calculation with broadened absorption bands due to S 0 → S 1-3 transitions at 363, 336 and 232 nm. The locations of triplet states are also indicated in the diagram, with the lowest one, S 0 → T 1 , calculated to be at 525 nm.
The 10 K single crystal triplet state absorption spectrum of Cs 2 NaCe(NO 2 ) 6 is displayed in Fig. 2(b). The zero phonon line is the band at longest wavelength, observed at 499 nm (20053 cm −1 ), and a linear trend to higher energy is observed for this transition across the lanthanide series (Fig. S6). The peaks marked 1-8 in the figure exhibit a repeat with the interval corresponding to the totally symmetric NO 2 − scissor frequency of 627 cm −1 in the T 1 state and a marked broadening occurs at shorter wavelengths. Triplet state emission is observed at 20 K for Cs 2 NaLa(NO 2 ) 6 , commencing to low energy of 495 nm, as shown in Fig. 2(c), with the major vibrational progression frequency of ~820 cm −1 corresponding to the totally symmetric NO 2 − scissor mode in the S 0 state. Excitation into either one of the NO 2 − excited singlet states of Cs 2 NaLa(NO 2 ) 6 at 20 K gives a broad emission band with maximum at ~410 nm, accompanied by the triplet state emission (Fig. 2(c)). The band shifts to lower energy with increasing temperature and the triplet emission is quenched. The broad emission band was confirmed to be a transition between singlet states from the measured lifetime at wavelengths between 370-420 nm, <1 ns at 20 K (Fig. S7). The excitation spectrum of this singlet emission (Fig. 2(d)) shows singlet state absorption bands at 333, 318 and 271 nm.
Cerium(III) electronic spectra. The 4f 1 Ce 3+ ion has a simple electronic energy structure, with the 2 F 5/2 ground state and the J-multiplet 2 F 7/2 at ~2000 cm −1 to higher energy. The 4f 1 → 5d 1 transition is located from the near red up to the ultraviolet spectral region [28][29][30] depending upon the crystal field and nephelauxetic effect experienced by the Ce 3+ ion. There are only two 5d Ce 3+ crystal field levels, 5d 1 (1,2) in T h symmetry Ce(NO 2 ) 6 3− and transitions to both are electric dipole allowed. The room temperature diffuse reflection spectrum of Cs 2 NaCe(NO 2 ) 6 (Fig. S8) exhibits a weak NO 2 − triplet state absorption starting at ~500 nm, with a stronger absorption band to shorter wavelength comprising the Ce 3+ 4f 1 → 5d 1 and NO 2 − singlet state transitions. A broad band with maximum intensity near 514-527 nm is observed in the low temperature emission spectrum of this compound which we assign to the Ce 3+ 5d 1 → 4f 1 2 F 5/2,7/2 transitions. The emission band shape changes for different crystals due to varying self-absorption by the NO 2 − triplet state, having a structured appearance to shorter wavelength of 500 nm. This is evident in Fig. 3(a) but not so in Fig. 3(b) for a different crystal. At 10 K, the emission is not excited by wavelengths longer than 380 nm (Fig. S9). At 20 K, the Ce 3+ 5d 1 lifetime was monitored at various wavelengths from 450 nm to 525 nm, being monoexponential and giving the average value of 25.8 ± 1.3 ns (Fig. S10), similar to that in YAG:Ce 3+31 .
The low temperature excitation spectra of the Ce 3+ emission at various wavelengths are displayed in Figs 3(c) and S11. Notice that the broad excitation band is associated with emission from Ce 3+ and not NO 2 − (Fig. S12) and that the excitation peak maximum varies slightly from sample to sample. The excitation band may be fit by two Gaussians with maxima at 352 and 300 nm, as in the inset, Fig. 3(c). These two wavelengths are associated with vibronic maxima of the transitions 4f 1 2 F 5/2 → 5d 1 (1,2) so that the 5d 1 splitting is 4925 cm −1 . The first principles calculation using the crystal structure of Cs 2 NaCe(NO 2 ) 6 gives the 5d 1 (1,2) splitting as 4625 cm −1 (Refer to the SI, Table S6), which is in reasonable agreement.
Temperature dependence. The dramatic quenching of emission with temperature (T q , the temperature where emission intensity is reduced to one-half of the initial value = 53 ± 2 K) is illustrated in Fig. 3(a) and the inset in 3(b). The Ce 3+ emission is almost quenched at 100 K (Fig. S13). A corresponding quenching is observed in the excitation spectra, Fig. 3(d).
Although the maximum phonon energy in the crystal is quite high (1334 cm −1 ), the quenching mechanism of 5d 1 → 4f 1 emission by multiphonon relaxation is discounted because the gap from 5d 1 to 4f 1 is bridged by ~16 phonons. By contrast, the 4f 2 → 4f 2 emission from the 3 P 0 level of Pr 3+ in Cs 2 NaPr(NO 2 ) 6 is quenched 3 because the energy gap 3 P 0 -1 D 2 is spanned by only 3 phonons. Three alternative quenching mechanisms are depicted in Fig. 4(a-c) by reference to configuration coordinate and valence band (VB)/conduction band (CB) diagrams. There have been various points of view put forward for other Ce 3+ systems, notably YAG:Ce 3+32 , with respect to these mechanisms. The energy transfer to another species is considered unlikely since no emission is observed to lower energy. The temperature-induced crossover to another potential energy surface ( Fig. 4(b)) and photoionization to the CB (Fig. 4(c)) are candidates. An Arrhenius plot of ln{[I(0)/I(T)]−1} (where I(T) denotes the counts at temperature T) against reciprocal temperature may be employed to estimate the activation energy of the quenching process. In the present case, the use of emission counts or excitation counts for several different samples gives linear plots of intensity versus temperature in the range from 20-100 K (e.g. inset Fig. 4(d)). The corresponding plots of ln{[I(0)/I(T)]−1} versus 1/T are not linear (Fig. 4(d)) and show that the activation energy E a for the quenching process changes from 29 ± 7 cm −1 in the range from 10-30 K to 429 ± 200 cm −1 in the range from 70-90 K. The overall quenching behaviour from 20-250 K is shown in Fig. S14 and follows an exponential decrease in intensity.
Stokes shift. The peak maxima are at 355 nm (excitation spectrum) and 514 nm (emission spectrum) in Fig. 5(a) for Cs 2 NaCe(NO 2 ) 6 so that the Stokes shift of 8715 cm −1 is the maximum reported for cerium coordinated to oxygen in the literature. The progression-forming mode is most likely the totally-symmetric Ce-O stretch, which has a magnitude near 240 cm −1 (Fig. S5(a)). Technically, this Stokes shift does not correspond to the 'same transition' in absorption (4 f 1 2 F 5/2 → 5d 1 (1,2)) and emission (5d 1 (1) → 4f 1 2 F 5/2 , 7/2 ) 33 . The shift represents the interactions taking place within the CeO 12 cluster, although the embedding effect of this cluster is also important. Contrary to the traditional depiction in many textbooks, the excitation of the Ce 3+ 4f electron to the first 5d state often involves a bond length contraction, not expansion 34,35 . In fact, in solution, this contraction can lead to the expulsion of a ligand 36 . The great change in equilibrium bond distance between the ground and excited states gives the possibility that the potential energy curves overlap ( Fig. 4(b)) 37 . Hence inefficient fluorescence occurs. The location of the 4f 1 → 5d 1 (1) zero phonon line can be roughly estimated from the midway point of the band maxima or band onsets in Fig. 5(a) and is in the region of 400-420 nm. The thermal crossover thus occurs just above this energy (i.e. above 23800-25000 cm −1 ) because vibrational relaxation to the electronic ground state is much faster than the crossover rate. Hence the crossover, Fig. 4(b), could occur to 4f 1 Ce 3+ or to possibly to the NO 2 − singlet state potential energy curve. In fact, just as for Cs 2 NaLa(NO 2 ) 6 , room temperature singlet state emission is also observed for Cs 2 NaCe(NO 2 ) 6 ( Fig. 5(b)). The change in activation energy with temperature arises from the bond length change and relative zero phonon line shift with temperature, which serve to displace the two potential energy curves.
Literature tabulations of Stokes shifts [38][39][40][41] include materials with Ce 3+ ions occupying several sites in the crystal lattice, such as the hosts Lu 4 AI 2 O 9 , LaLuO 3 , Ba 3 Gd(BO 3 ) 3 and Mg 2 Y 8 (SiO 4 ) 6 O 2 . We have excluded these more complex materials, which may not be sufficiently-well characterized, from Table S7 which compares the Stokes shift for cerium in oxygen coordination with other parameters. The plot of Stokes shift versus coordination number, Fig. 5(c), demonstrates larger Stokes shifts for Ce 3+ ions with higher coordination number showing that Ce 3+ ions with larger ionic radii (i.e. from Ce 3+ (VI) 101 pm to Ce 3+ (XII) 134 pm) can contract more when transiting  Table S7). Small Stokes shifts have been associated with rigid lattices 42 . The weaker metal-ligand bonding is in line with a lower value of T q .

Conclusions
In summary, the hexanitrito complex Cs 2 NaCe(NO 2 ) 6 , with 12-coordinated Ce 3+ situated at a site of T h symmetry, exhibits a very large energy shift between the peak maxima in absorption and emission. The 4f 1 ground state and 5d 1 potential surfaces are displaced so much along the configuration coordinate that overlap takes place above the 5d 1 minimum, leading to thermal quenching of emission at a low temperature. The features due to NO 2 − and Ce 3+ ions in the electronic spectra have been rationalized by theory. Figure 5. (a) Large Stokes shift of Ce 3+ in Cs 2 NaCe(NO 2 ) 6 ; (b) Room temperature 350 nm-excited singlet emission in Cs 2 NaLa(NO 2 ) 6 (red) and Cs 2 NaCe(NO 2 ) 6 (black). The scale expansion is shown for the latter. (c) Stokes shifts for different coordination numbers of Ce-O systems. The number of compounds of each type is indicated together with the standard deviation. Data from Table S7 and this work.