The first example of ab initio calculations of f – f transitions for the case of [ Eu ( DOTP ) ] 5 complex — experiment versus theory †

Crystal structures and photophysical properties (IR and UV-vis-NIR) of two compounds, [C(NH2)3]5[Eu(DOTP)] 12.5H2O and K5[Eu(DOTP)] 11H2O (DOTP = 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrakis (methylenephosphonic acid)), were determined. The DOTP ligand is bonded to Eu via four O and four N atoms, filling thus eight coordination sites of Eu. The experimental structures of two [K4Eu(DOTP)] clusters were used as a starting point for theoretical ab initio calculations based on a multireference wavefunction approach. Positions of the energy levels of the 4f configuration of the Eu ion have been calculated and compared with those derived from the experimental spectra. This enabled us to tentatively assign energy levels of the Eu ion. The relationship between calculated energies of excited states and Eu–N and Eu–O bond lengths was discussed with respect to the nephelauxetic effect.


Introduction
Lanthanide complexes with polydendate amino acids, which are based on the cyclen backbone (1,4,7,10-tetraazacyclododecane), are of considerable interest at present, since Gd-DOTA (DOTA = 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacete ligand) and Tm-DOTP complexes were found to be useful in medical and biological diagnostics. 1 The Gd-DOTA complex serves as a MRI contrast agent while Tm-DOTP has been used as a NMR effective shift reagent and extracellular space marker. 2 Ligand modifications consisting of carboxylic or phosphonic arms substitution by an aromatic group may expand the applications of such complexes as potential multifunctional luminescence bioprobes 3 and single molecular magnets. 4In this context the Ln-DOTA and Ln-DOTP systems may be considered as model compounds.From this point of view, the physicochemical properties in relation to theoretical study are of utmost importance in designing compounds in new applications.It is worthwhile noting that the diversity of potential applications for this class of compounds is related to the presence of incompletely filled 4f orbitals, which are only slightly disturbed by the ligand field.This is a reason why ab initio calculations of lanthanide systems are not straightforward-they have to include electron correlation and relativistic effects simultaneously.4b Addressing the theoretical ab initio study to such group of compounds is of particular interest.For example, the ab initio calculations of the lowest energy levels of Dy-DOTA complex have already been performed in the context of its magnetic properties.4b,c Comparison of the results for such calculations with the experimental ones may verify the quality of the former.On the other hand, theoretical results may provide additional information about a particular system that cannot be extracted from the experiment.However, it should be pointed out that many theoretical studies devoted to structural properties of lanthanide molecular complexes have already been completed using density functional theory (DFT). 5In such an approach it is very common to represent the open 4f shell of the lanthanide ion by effective core pseudopotential due to computational savings and the inability of DFT methods to describe properly the highly localized and correlated f-electrons.Furthermore, the semi-empirical analysis of energy levels based on crystal-field theory needs a priori assumptions about the assignment of energy levels, which in low-symmetry systems is ambiguous and also suffers from the large number of adjustable parameters. 6his paper focuses on the experimental and ab initio theoretical study of the [Eu(DOTP)] 5À complex in single crystals of the following formulas: [C(NH 2 ) 3 ] 5 [Eu(DOTP)]Á12.5H 2 O and K 5 [Eu(DOTP)]Á11H 2 O.Only two crystal structures of monomeric Ln-DOTP complex (Ln = Gd, Tm) have been reported 7,8 and neither spectroscopic properties of monocrystals nor theoretical ab initio calculations have been described thus far.Theoretical calculations are performed for the two clusters {K 4 [Eu(DOTP)]} À representing two different Eu sites for the K 5 [Eu(DOTP)]Á11H 2 O crystal.Energies of the excited states for the 4f 6 configuration were obtained within the quantum chemistry ab initio methods based on the multireference wave-function approach, which allows accounting for static and dynamic electron correlation as well as relativistic effects.Selected Eu-O and Eu-N bond lengths are presented in Table 1.The average Ln-O and Ln-N distances in the case of Gd-DOTP and Tm-DOTP complexes are also presented in the table for comparison purposes. 7,8espective Eu-O and Eu-N distances for both isomers in I are similar.However, there are two exceptions-namely, Eu2-O201 and Eu2-N201 bond lengths in I are significantly shorter.For this reason the structure of the I Eu2 enantiomer is more distorted than the I Eu1 one.

Results and discussion
Average Eu-O and Eu-N distances are longer compared to those determined for [Gd(DOTP)] 5À and [Tm(DOTP)] 5À complexes. 7,8his is brought about by the lanthanide contraction.
The coordination polyhedra in I and II may be described as twisted square antiprism (TSAP), in which the corners are occupied by four O atoms (O IV -plane) and four N atoms (N IV -plane).In I the O IV and N IV planes are almost parallel to each other, with the dihedral angle between them equal to 0.61 and 0.91 in enantiomers I Eu1 and I Eu2 , respectively.In II both O IV and N IV planes are perfectly parallel owing to the fact that the Eu 3+ ion is located in fourfold axes.The twist angles of rectangles formed by four O IV atoms as well as by four N IV atoms in I and II are schematically presented in Fig. 2a.The small twist angle values between the O IV and N IV planes and the absence of a water molecule in the first coordination sphere of Eu 3+ , indicate that the crystals contain a minuscule type of the m 0 isomer as a racemic mixture of two L(llll) and D(dddd) enantiomers.The average distances between O IV and N IV planes are similar in both crystals and range from 2.73 Å to 2.79 Å.The Eu 3+ cation is located inside the square antiprism at a distance of 1.03-1.07Å to O IV and 1.70-1.72Å to N IV planes (Fig. 2b).
All phosphonic groups are deprotonated; thus the P-O bond lengths are similar and range from 1.508(4) Å to 1.550(5) Å.The average P-O bond length is equal to B1.527(8) Å, and is very close to those found in other lanthanide aminophosphonates such as Ln-EDTMP and Ln-CDTMP. 9,10here are no water molecules coordinated to Eu 3+ in the [EuDOTP] 5À complexes in I and II, while in its carboxylic analogue, [Eu(DOTA)(H 2 O)] À , one water molecule is directly bonded to the Eu 3+ ion. 11The absence of the water molecule in the closest neighbourhood of [Eu(DOTP)] 5À is likely caused by the spherical hindrance connected with an accumulation of highly negative phosphonic oxygen atoms, which strongly repels water molecules and prevents their coordination to Eu 3+ .The water molecules were found in the second coordination sphere of [Eu(DOTP)] 5À complex.The nearest H 2 O molecule is about 4 Å from the Eu 3+ cation as shown in Table 2.
Taking into account the structural variations of the [Eu(DOTP)] 5À complex in I and II, the question that arises is how they are reflected in the IR and UV-vis spectra of both crystals.

IR spectroscopy
The IR spectra of both compounds were measured and the theoretical IR spectra of {K 4 [Eu(DOTP)]} À clusters representing II Eu1 and II Eu2 sites were obtained within the DFT approach for the B3LYP exchange-correlation functional.Because the theoretical DFT calculations were performed for isolated the {K 4 [Eu(DOTP)]} À anion (C 1 symmetry) in the simulated spectra, there are no bands attributed to internal vibrations of water molecules and guanidinium cations.The complex anion {K 4 [Eu(DOTP)]} À contains 61 atoms giving rise to 177 fundamental vibrations that may be decomposed into 45A + 44B + 44E, where A, B and E denote irreducible representations of the C 4 point group.Owing to the selection rules, all A -B fundamental excitations are forbidden in the IR spectra.The spectra of crystals under study are presented in Fig. 3.As seen here the spectral features of both crystals are similar.Theoretical study results enabled us to assign the bands observed in the experimental spectrum (see Table S1, ESI †).
The main differences between the experimental spectra of both compounds are observed for bands located between 1490 cm À1 and 4000 cm À1 .In this spectral range, the broad bands centered at B1630 cm À1 and B3425 cm À1 are attributed to the d OH 2 and n OH vibrations, respectively, from the lattice water molecules.The d OH 2 band in the I spectrum is partly covered by the intense d NH 2 band from the guanidine cations.Certain differences appear in the spectral pattern of bands centered at B1070 cm À1 .These bands are ascribed to n POsym and n POasym .In general, splitting and shape changes of the n PO bands reflect various geometrical changes of phosphonic groups as shown previously. 9The bands attributed to the Eu-O and Eu-N vibrations are located below 450 cm À1 .
Observed similarities of the spectral features of I and II strongly suggest that the geometry of [Eu(DOTP)] 5À complexes is substantially the same.Therefore, it seems to be justified to consider the local symmetry of both complex anions as C 4 in spite of the fact that there is some certain deformation of [Eu(DOTP)] 5À complex in I.
Experimental absorption spectra consist of narrow bands attributed to transitions from the ground 7 F 0 state to the excited levels of the 4f 6 configuration.The experimental emission spectra comprise bands corresponding to transitions from the excited 5 D 0 state to lower-lying 7 F J levels (where J = 0, 1, 2, 3, 4, 5, 6).Mechanisms of the electric-dipole f-f transitions, where J = 0-J 0 = 2, 4, 6, observed in Eu 3+ materials can be described via standard Judd-Ofelt theory, 14,15 whereas the electric-dipole J = 0-J 0 = 0, 3, 5 demands extended theory. 16,17 7  0 -5 D 1 and 5 D 0 -7 F 1 transitions are of magnetic dipole character.The DS = 0 selection rule for both electric-and magneticdipole transitions is relaxed via the spin-orbit interaction within the lanthanide ion. Nw, consider the selection rules from the point of view of the local symmetry of the europium crystallographic site.
In the case of the Eu 3+ cation, both ground ( 7 F 0 ) and emission excited ( 5 D 0 ) states are fully symmetric.According to group theory, the A 2 A,E electronic-dipole and magnetic-dipole transitions between the crystal field (CF) states are allowed in the C 4 symmetry; at the same time, the A 2 B transitions are forbidden.The numbers of spectral lines expected for Eu 3+ ion in the site of C 4 symmetry are collected in Table 3 along with the total numbers of experimentally observed lines in the absorption and emission spectra of I and II.
In most cases, the experimental number of observed spectral lines is smaller compared to the theoretical prediction.We were unable to separate CF levels of individual Eu sites.To unequivocally assign the bands observed in the spectra of I and II, the analysis was extended into theoretical calculations.

Theoretical energy levels
The ab initio calculations of energies of the II Eu1 and II Eu2 complexes were performed in the following steps: complete active space self-consistent field method (CASSCF) 18 complete active space perturbation theory of second-order (CASPT2) 19,20 restricted active space state interaction (RASSI) 21 CASSCF and CASPT2 methods account for non-dynamic (static) and dynamic correlation effects, respectively, whereas the RASSI one includes the spin-orbit (SO) interaction.This sequence of calculations, denoted here by CASSCF/CASPT2/RASSI-SO, was performed for the active space that corresponds to the 4f 6 configuration of the Eu 3+ ion.In this way the energies of 7 F and 5 D, 5 F, 5 G, 5 H, 5 I, 5 K and 5 L states were calculated within the ab initio approach (for details see Section 3.4).Selected experimental and theoretical energy levels are collected in Table 4.A complete list of calculated energy levels is presented in Table S2 in ESI.† Absolute differences of the ab initio energies of respective levels (vis-a-vis 7 F 0 ground level) between II Eu1 and II Eu2 do not exceed 82 cm À1 , and these differences are much lower in most pairs of states.Almost all theoretically determined energy levels with respect to 7 F 0 ground level in II Eu1 are larger than in II Eu2 .Such a relationship does not seem to be accidental if the Eu-N and Eu-O bond lengths are considered.As shown in Section 2.1, the Eu1-N1 bond length in isomer II Eu1 is about 0.039 Å longer than the Eu2-N2 in II Eu2 .In the case of Eu-O bond lengths, the opposite situation is observed-the Eu1-O13 bond length is 0.026 Å shorter in II Eu1 than the corresponding Eu2-O22 in II Eu2 .The obtained lowering of the energy levels of 4f 6 of II Eu2 with respect to the 7 F 0 level is theoretical evidence that weak donor atoms (such as N) brings about a bathochromic shift of f-f transitions.At the same time, in the case of hard, highly negatively charged O donor atoms, the reverse effect is expected such that the result reinforces the considered energy shift.

Assignment of experimental energy levels
Comparison of theoretical and experimental energy levels of II allowed us to tentatively assign the irreducible representations of C 4 point group to experimental energy levels of II (Table 4).
The ordering number preceding the symbol of the irreducible representation is added in order to uniquely identify the states    of the same symmetry.It is seen in Table 4 that the ordering of theoretical energy levels is almost the same in the case of II Eu1 and II Eu2 , with the exception of two pairs-1B and 3A, energy levels of 7 F 2 multiplet and 5B and 7A ones of 7 F 4 -where the ordering of levels is interchanged.
As seen from the theoretical results, differences between corresponding CF levels of individual 2S+1 L J multiplets in both isomers are usually only of a few cm À1 .For this reason it was not possible to separate CF levels of the individual Eu sites in the experimental spectra of I and II.
In the emission spectrum of II there are two relatively strong spectral lines originating from 5 D 0 level centered at 16 335 cm À1 and 16 140 cm À1 (energy separation 195 cm À1 ).A closer look at the line at 16 140 cm À1 (inset in Fig. 5) shows that in fact it consists of two lines separated by 50 cm À1 .A similar spectral pattern is observed in the case of 5 D 0 -7 F 2 of I.At the same time, only two distinct lines separated by only 25 cm À1 and 28 cm À1 for II Eu1 and II Eu2 , respectively, that originate from 5 D 0 -7 F 2 (2E) and 5 D 0 -7 F 2 (3A) transitions can be derived from the ab initio calculations.Therefore the symmetry of the CF components of the 7 F 2 multiplet at 1129 cm À1 and 1179 cm À1 derived from the luminescence spectrum of II were ascribed as 2E and 3A, respectively.Despite of its relatively high intensity, the position of the line centered at 16 335 cm À1 matches relatively well the energy of the cooperative vibronic transition that couples the electronic 7 F 0 state with one of the n P-O stretching vibrations of the energy ranging between 900 cm À1 and 1000 cm À1 .In this way the number of CF levels is in accordance with that predicted by the theory.Similar vibronic lines were observed in emission spectra of other Eu 3+ complexes containing phosphonic groups, 9,22 but authors of those papers interpreted the lines as of pure electronic origin.

Experimental versus theoretical energies
There are two energy scales that govern the energy level schemes of ground 4f n configurations of Ln 3+ ions, namely the energy separations between barycentres of 2S+1 L J multiplets (10 3 -10 4 cm À1 ) and the crystal field splittings (10 1 -10 2 cm À1 ) of these multiplets.
The centres of gravity of experimental (for I and II) and theoretical energy levels 2S+1 L J are listed and compared in Table 5.The table shows that calculated energies of states are overestimated in the case of majority 7 F J levels with the one exception of the 7 F 2 energy level, for which the experimental energy is larger than the theoretical counterpart.The absolute differences between experimental and theoretical energies of 7 F J states (hereinafter referred to as D) do not exceed 280 cm À1 .Direct comparison of theoretical energies for the excited states with respect to the 7 F 0 ground level with experimental counterparts shows that they may differ even by thousands of cm À1 , reaching 3500 cm À1 for the 5 L 6 level.Such discrepancies are expected in the case of many-electron systems in which electron correlation and relativistic effects are important.Theoretical studies for the CaF 2 :Pr 3+ case have shown that discrepancies in energy calculations of free lanthanide ions are transferred to more complex systems containing lanthanide ions. 23To illustrate this problem we have performed similar CASSCF/CASPT2/RASSI-SO calculations for the Eu 3+ free ion that were compared with energy levels of the experimental Eu 3+ aqua ion 24 as presented in Table 6.Energy levels of Eu 3+ free ion calculated within the Dirac-Fock multiconfiguration interaction approach (MCDF-CI) 25 are presented in Table 6.More recently the ab initio calculations within fully relativistic Kramers pairs configuration interaction method for free Eu 3+ ions as well as for aqua ions were reported. 26e experimental energy levels of the Eu 3+ free ion are not known to the authors.At the same time the aqua ion seems to be the system reasonably ''similar'' to the free ion; for example, it is interesting to note that the experimentally observed Eu 3+ aqua ion energy levels 24 are very close to those interpolated to approach the Eu 3+ free ion ones. 27Comparison of the performance of the present theoretical approach with the benchmark MCDF-CI calculations presented in Table 6 shows that the discrepancies with respect to the experiment of the order of thousands of cm À1 is what one can expect from ab initio calculations performed for the Eu 3+ ion.Furthermore, similarities of the energy differences between the CASSCF/CASPT2/RASSI-SO calculations and experimental counterparts presented in Tables 5 and  6 support the conclusion that the main deficiencies in the proper theoretical description of f-electron systems are due to insufficient accounting for correlation effects within the lanthanide ion.For example, detailed analysis of radial correlation effects in free lanthanide ions based on ab initio calculations was performed by Barandiaran and Seijo. 28Their study indicated that the most probable improvement of the description of energies for excited states of heavy lanthanide ions-for example, of Eu 3+ -was obtained by inclusion of 5f orbitals into the active space.However, such enlargement of the active space in the case of considered (large) Eu-DOTP complexes is not tractable with the authors' available computational resources.
The other energy scale is associated with splitting of the 2S+1 L J energy levels in the crystal field potential.Absolute values of differences between the theoretical and experimental crystal field splittings-that is, splittings of 2S+1 L J levels-do not exceed the value of 220 cm À1 ; this maximum discrepancy is observed within 5 L 6 multiplets and can be derived from Table 4.However, it should not be interpreted as the crystal field splittings being much better described within CASSCF/CASPT2/RASSI-SO approach than positions of levels with respect to the energy of the ground state 7 F 0 .Rather, it is attributed to the fact that differences between theoretical and experimental energies follow the scale of considered energies.Namely, upon considering relative energy differences, then it would turn out that the relative differences are larger in the case of crystal field splittings.
2.7 5 D 0 -7 F 0 transition energy Among the f-f transitions observed in the electronic spectra of Eu 3+ , the 7 F 0 2 5 D 0 transition is the most suitable for a study of Eu-ligand interaction.The ground 7 F 0 and the excited 5 D 0 states are non-degenerated and do not split in the crystal field of any symmetry.Therefore, the number of components observed in the spectrum of this transition indicates the minimal number of chemically distinct environments of the Eu 3+ ion.
The energy of the 7 F 0 -5 D 0 transition is also used to study the nephelauxetic effect of europium compounds.This effect is probably connected with the covalent contribution to the bonding between the Eu 3+ ion and the ligands, metal-ligand distances, coordination numbers and the total charge and acid base properties of ligands bonded with Eu 3+ . 29However, there is no simple correlation between the energy of the 7 F 0 -5 D 0 transition and these physical quantities. 30Bathochromic shifts of the 7 F 0 -5 D 0 band are very often explained as resulting from the change in the interelectronic repulsion Slater F k parameters of Eu 3+ ion in the ligand field with respect to those for the free ion

!
. 31 In general in the case of the rare earth complexes for which the semi-empirical values of the F k parameters of the free ions are not known, the nephelauxetic ratio is approximated as b ¼ n7 F 0 ! 5 D 0 complex n7 F 0 ! 5 D 0 aqua ion , where n7 F 0 ! 5 D 0 complex and n7 F 0 ! 5 D 0 aqua ion are the wavenumbers of the 7 F 0 -5 D 0 bands for the complex and the aqua ion, respectively.Present work allows for the direct calculation of the nephelauxetic ratios.All the nephelauxetic ratios b calculated using the formula with F k radial integrals (obtained within the ab initio approach) are equal to about 0.99.Radial 4f functions used for calculating Slater radial integrals were extracted from the molecular orbitals of II Eu and Eu 3+ free ions obtained within the CASSCF method.Details of calculations for radial integrals based on molecular orbitals will be presented elsewhere. 32The result that the values of b are close to unity supports the ionic character of Eu-L interaction.Furthermore, the nephelauxetic ratios b are smaller than unity, which is expected from the point of view of the nature of the nephelauxetic effect.
It is worth stressing that the energy of the 7 F 0 -5 D 0 transition of [Eu(DOTP)] 5À (17 269 cm À1 ) and Eu 3+ aqua ion (17 277 cm À1 ) 24 differs by 6 cm À1 only.Usually, for eightcoordinated Eu 3+ complexes, the shift of the 7 F 0 -5 D 0 band to the lower energies in relation to the aqua ion is much larger.The opposite relation is obtained in the CASSCF/CASPT2/ RASSI-SO approach, where the energy of the 5 D 0 level with respect to 7 F 0 ground state of free Eu 3+ , 17 733 cm À1 , is smaller than the 7 F 0 -5 D 0 transition energies obtained for II Eu1 and II Eu2 , 18 169 cm À1 and 18 156 cm À1 , respectively.At first glance it may be considered as being in contradiction to the result of the ab initio calculations that b o 1.However, the fact that the theoretical free ion 7 F 0 -5 D 0 transition energy is smaller than that of the Eu-DOTP complex probably can be ascribed to the effect of the crystal-field upon the lowest 7 F J levels. 33Unfortunately, the preliminary analysis within the crystal field approach has not succeeded in clarifying this problem.Using available spectroscopic techniques, it was not possible to distinguish the spectral lines coming from two Eu sites existing in both crystals.Therefore, results of ab initio calculations allowed us to assign the spectral lines tentatively to particular crystal field components of the energy levels for the 4f 6 configuration of the Eu 3+ ion.

Conclusions
Differences between theoretical and experimental values of the energies of Eu-DOTP complexes can reach about 3500 cm À1 , as observed in the case of 5 L 6 energy levels.At the same time the structure of Eu-DOTP energy levels is retained strictly up to 5 D 3 energy levels.Such calculations are of general interest because it is possible to conclude that the correlation between structure and spectroscopic features is by its very nature discrete for the case of lanthanide systems.
The correlation between Eu-ligand bond lengths and energies of excited energy levels is obtained.It was shown that weak donor atoms (such as N) bring about the bathochromic shift of f-f transitions and reverse hard, highly negatively charged O donor atoms reinforcing the energy shift.
Discrepancies between theoretical and experimental values of energies of states for the 4f 6 configuration of Eu 3+ ion can be mainly attributed to treatment of correlation effects in the Eu-DOTP complex in the present ab initio approach.Considering the details of CASSCF/CASPT2/RASSI-SO calculations and results of other ab initio calculations, 24 it may be concluded that theoretical energies are expected to be improved via inclusion of the ''double f-shell'' into the CASSCF/CASPT2/RASSI-SO approach, which means that the radial correlation between 4f and 5f shells is treated in a non-perturbative way.In the present work this correlation effect was taken into account perturbatively within the CASPT2 method.
To summarize, the experimental and theoretical properties of Eu-DOTP complex were studied and discussed in detail.Although there are some discrepancies between experimental and theoretical results, the presented results enabled us to calculate the energies of 4f 6 configuration of Eu 3+ in molecular [EuDOTP] 5À complex, for the first time.It is worth noting that the energies of the lower lying 7 F J states are relatively well described.
The energies of the 7 F J states are particularly important from the application point of view of Eu 3+ compounds as luminescent materials, since the emission spectra of Eu 3+ usually consist of 5 D 0 -7 F J lines.Another important aspect of the [EuDOTP] 5À spectra is connected with the f-f transition intensities, therefore our future study will be focused on this problem. 34

X-ray crystal analysis
An appropriate crystal was cut from a larger one and mounted on a Kuma KM4 diffractometer equipped with a CCD counter.The collected data were corrected for polarization, Lorentz and absorption, the latter calculated from the crystal habits captured from photo scans.The positions of Eu were found from Patterson maps and the remainder of non-H atoms from difference Fourier maps.Positions of the C-and N-bonded hydrogen atoms were calculated geometrically.It was found that three water molecules and two guanidinium cations in I, and 1.5 H 2 O molecules in II were disordered.The final refinements were anisotropic for all ordered non-H atoms, whereas the disordered C, N and O atoms were treated isotropically.The refinement was full matrix with all non-H atoms anisotropic.All computations were performed using SHELXS97 and SHELXL97 programs. 35,36Molecular graphics were prepared with XP-Interactive Molecular Graphics. 37C(NH 2

Spectroscopic analysis
IR spectra were recorded with a Bruker IF S66 spectrometer.The spectra of crystalline complexes in KBr pellets and nujol suspension were recorded in the range of 50-4000 cm À1 .Electronic absorption spectra were recorded with a Cary 500 UV/Vis/NIR spectrophotometer.The corrected emission spectra were recorded with an Edinburgh Instruments FLS 920 spectrofluorometer.

Theoretical calculations
Vibrational frequencies of {K 4 [Eu(DOTP)]} À clusters representing II Eu1 and II Eu2 sites were obtained via the DFT approach for the B3LYP exchange-correlation functional.The Eu ion was represented by the quasi-relativistic effective core potential (ECP) created by Dolg et al., 38 along with the valence basis set [5s4p3d]-GTO.Remaining atoms, C, N, O, P, K, H, were represented by the 6-31G* basis set.Both structures of the {K 4 [Eu(DOTP)]} À cluster were optimized (in vacuum) and harmonic vibrational frequencies were calculated for their optimized structures.Cartesian coordinates of the optimized geometries of {K 4 [Eu(DOTP)]} À cluster are listed in Table S3 of the ESI.† Energy levels were obtained via ab initio calculations based on the multireference wave function approach.These single-point calculations were performed for the two clusters {K 4 [Eu(DOTP)]} À representing two different Eu sites of K 5 [Eu(DOTP)]Á11H 2 O crystal.Ab initio model potentials (AIMP) were used to represent the [Kr]-core of Eu ion closed shells along with the valence basis set of Gaussian-type orbitals (14s10p10d8f3g) contracted to obtain the [6s5p6d4f3g] basis set. 39For the remaining atoms of the considered system, C, N, O, P, K, the AIMP effective core potentials along with valence Gaussian-type basis sets follow: 40 O [Mg]-core, (9s7p)/[2s3p] basis set In the case of H atoms, the 6-31G* basis set was used. 41All effective core potentials account for mass-velocity and Darwin relativistic corrections by means of Cowan-Griffin approach. 42he calculations were performed within C 2 symmetry with the MOLCAS package. 43he open-shell character of the Eu 3+ ion ([Xe]4f 6 configuration) causes strong non-dynamic correlations effects.In this work the non-dynamic effects of electron correlation were taken into account within complete active space self-consistent field method (CASSCF), 18 where the active space was set by distributing six electrons onto one molecular orbital (MO) of a symmetry, two MOs of b symmetry and four MOs of e symmetry; all seven MOs defining the active space were predominantly of the Eu 3+ ion 4f character.The molecular orbitals were optimized within separate state average (SA) CASSCF calculations minimizing the average energy of the following sets of spin-free states: one 7 A and two 7 B states; four 7 E; 19 5 A and 20 5 B states; and 38 5 E states.In this way the following states of 4f 6 for the Eu 3+ ion were taken into account: 7 F, 5 D, 5 L, 5 G, 5 H, 5 F, 5 I and 5 K.The effects of dynamical electron correlation were taken into account via second-order correction to the energy obtained within complete active space perturbation theory CASPT2. 19,20n this work the multistate (MS) CASPT2 19,20 approach was used for the same sets of states as in the case of SA-CASSCF calculations.IPEA shift was set to zero. 44In order to avoid the effect of so-called weak intruder states, the imaginary shift of 0.1 a.u.value was applied.Since the main interest of the present work is focused on low-lying states of the 4f 6 configuration of the Eu 3+ ion, accounting for dynamical effects is limited to the central ion by means of the AFREeze option in the MOLCAS ''caspt2'' program, where inactive molecular orbitals with density on the Eu ion smaller than 0.1 were kept frozen during the MS-CASPT2 calculations.As a result, only three occupied orbitals localized on oxygens non-bonded to the Eu ion were correlated explicitly by means of the CASPT2 This journal is © the Owner Societies 2016 method.Cholesky decomposition 45 was performed for the matrix of the electron repulsion integrals with the threshold 10 À8 Hartree, and consequently used thoroughout each step of calculations.In fact, just-mentioned approximations made these calculations tractable considering the particular choice of active space and accessible computational resources.Spinorbit interaction was taken into account via the RASSI-SO approach, 21 where the matrix of the Hamiltonian including spin-orbit operator (coming from Douglas-Kroll Hamiltonian) over all considered above, MS-CASPT2 spin-free mixed states were constructed and diagonalized.

2. 1
Crystal structures The [Eu(DOTP)] 5À complex crystallizes in the form of compounds of the following formulas: [C(NH 2 ) 3 ] 5 [Eu(DOTP)]Á12.5H 2 O (hereinafter I) and K 5 [Eu(DOTP)]Á11H 2 O (hereinafter II).The crystals of I are monoclinic and belong to the P2/n space group while those of II crystallize in the tetragonal system (P4cc space group).The crystals of I comprise [Eu(DOTP)] 5À complexes, guanidinium cations and water molecules, while II consist of [Eu(DOTP)] 5À complexes, potassium cations and lattice water molecules.In both compounds the [Eu(DOTP)] 5À complex anions are deprotonated and their negative charge is compensated by [C(NH 2 ) 3 ] + (in I) or K + (in II) cations.The [DOTP] 8À ligand is bonded to the Eu 3+ cation by four oxygen and four nitrogen atoms, filling thus eight coordination places of the Eu 3+ cation.Both structures contain two symmetry-independent [Eu(DOTP)] 5À anions that differ in the conformation of the DOTP ligand, giving rise to two enantiomers L(llll) (hereinafter I Eu1 , II Eu1 ) and D(dddd) (hereinafter I Eu2 , II Eu2 ).The molecular structures of [Eu(DOTP)] 5À anions are presented in (Fig. 1).

Fig. 2
Fig. 2 (a) Twist angle and (b) schematic coordination polyhedron and distances of Eu 3+ from O IV and N IV planes.
symmetry of I is not exact, thereby allowing larger number of spectral lines than expected for C 4 symmetry.b Line at 16 400 cm À1 in Fig.5finally interpreted as of cooperative vibronic origin was taken into account here.
Structural, spectroscopic and theoretical studies of two monocrystals, namely [C(NH 2 ) 3 ] 5 [Eu(DOTP)]Á12.5H 2 O and K 5 [Eu(DOTP)]Á 11H 2 O, were performed.Both compounds contain [Eu(DOTP)] 5À complex in the form of minor m 0 (L(llll) and D(dddd)) isomers.The [DOTP] 8À ligand is bonded to the Eu 3+ cation via four oxygen and four nitrogen atoms, thereby filling eight coordination places of Eu 3+ cations.Symmetry of the [Eu(DOTP)] 5À complexes in the II crystal are of C 4 , whereas their structures are slightly disrupted in the case of I crystal resulting in C 1 symmetry.It is found that the closest outer sphere water molecule is 4.374(20) Å and 4.105(107) Å away from the Eu 3+ in I and II, respectively.This weak interaction of outersphere water molecules with [Ln(DOTP)] 5À anions, is probably one of the reasons for high relaxivity of the [Gd(DOTP)] 5À system in MRI.

3. 1
Preparation of crystalsTwo samples each of which contained a suspension of Eu 2 O 3 (0.250 g, Stanford Materials) and H 8 DOTP (0.75 g, Macrocyclics) in 25 ml of H 2 O were heated at ca. 80 1C.Next, a small portion of [C(NH 2 ) 3 ] 2 CO 3 was added to the first one and KOH to the other until the precipitate was dissolved.The final pH of solutions was 7.5.Solutions were filtrated and left for crystallization.This journal is © the Owner Societies 2016 Phys.Chem.Chem.Phys., 2016, 18, 27808--27817 | 27815 Colourless crystals of [C(NH 2 ) 3 ] 5 [Eu(DOTP)]Á13H 2 O and K 5 [Eu(DOTP)]Á11H 2 O were formed during very slow evaporation of water after s few months.

Table 1
7elected Ln-O and Ln-N bond lengths for crystals under study and for Gd-DOTP7and Tm-DOTP 8 complexes

Table 3
Number of spectral lines predicted from group theory and those observed in I and II

Table 4
7heoretical energies (in cm À1 ) of septet7F and quintet 5 D, 5 L states of II Eu1 and II Eu2 with respect to7F 0 ground level along with experimental energy levels obtained from UV-vis spectra of I and II at room temperature

Table 5
Experimental and theoretical centres of gravity, 2S+1 L J energy levels of 4f 6 configuration for Eu-DOTP complex in I, II and theoretical values obtained for energies listed in Table4.Differences between the experimental and theoretical values D are provided in the last two columns Theoretical values are averaged over the SA-CASSCF/MS-CASPT2/ RASSI-SO energies obtained for both sites II Eu1 and II Eu2 . a

Table 6
24perimental (Eu 3+ aqua ions24) and theoretical energies of 4f 6 configuration of Eu 3+ free ion.Energies are provided with respect to the ground energy level 7 F 0 .In this work the energies were calculated within CASSCF/CASPT2/RASSI approach active space corresponding to 4f 6 configuration This journal is © the Owner Societies 2016