10780
J. Phys. Chem. 1995, 99, 10780-10784
Prediction of the Molecular Shape of Lanthanide Trihalides Judit Molnilr and Magdolna Hargittai* Structural Chemistry Research Group of the Hungarian Academy of Sciences, Eotvos Universio, H-1431 Budapest, P$ 117, Hungary Received: March 8, 1995@
A simple model is offered to interpret and predict the shapes of lanthanide trihalide molecules. According to this model, the shape depends mostly on the asphericity of the 4f electron shell which is buried deep within the 5s5p shell but has relatively large density. The above effect, and to a lesser extent the polarizability of the metal ions, determines the molecular shape for the fluorides. For the larger halides the electronegativity and size of the halogen ligands also influence the outcome, and the shape is the result of competing effects.
Introduction The molecular shape of rare-earth metal trihalides is still a matter of controversy. There have been numerous experimental determinations of these structures with often contradictory results'-2' as summarized in Table 1. Quantum chemical calculations22-26have also been carried out for these systems, with simpler22*26or more sophisticated appro ache^.*^-*^ According to these experimental and computational studies, some of the LnX3 systems are planar and others are pyramidal. Various models have also been invoked, based on polarizability arguments,*' on effective nuclear charges?* and on valence bond consideration^.^^ All these models have predicted pyramidal geometry for all lanthanide trihalides. These substances are difficult objects for both experimental and computational studies, indeed. They have rather low volatility, and their gas-phase investigation requires high temperatures (well over 1000 K). In addition, these molecules are very floppy which hinders the unambiguous interpretation of electron diffraction and gas-phase infrared spectra. Electron diffraction detects a vibrationally averaged structure, corresponding to the experimental t e m ~ e r a t u r e .The ~ ~ symmetry of the structure is lower than that of the equilibrium geometry. Thus, electron diffraction is suitable for determining the shape of these molecules in conjunction with spectroscopic information only. The gas-phase vibrational spectra of these molecules suffer from peak broadening due to the many vibrationally as well as rotationally excited levels. Application of matrix isolation vibrational spectroscopy is more advantage~us,~' but matrix effects may influence the molecular shape emerging from these s t ~ d i e s . ~The ~ - infrared ~~ spectrum of LaF3 taken in Ar matrix, for example, was interpreted differently by different authors (C3r,,1.2 h3).
Electronic Configuration of the Lanthanides in Their Trihalides All lanthanides have a filled Xe core so their 5s and 5p subshells are rather strongly bound. The 4f subshell, which is being built up by electrons as we proceed in the lanthanide series from lanthanum toward lutetium, is much more loosely bound than the 5s and 5p subshells, in spite of its much smaller radius. Although this 4f subshell does not belong to the valence shell in the LnX3 molecules (its radius is 0.37-0.24 8, vs 1.98-1.55 A of the 6s shell in the series35),it may exert influence on the overall molecular structure due to its nonspherical electron @Abstractpublished in Advance ACS Abstracrs, June 15, 1995.
0022-365419512099-10780$09.00/0
d i ~ t r i b u t i o n . ~Exceptions ~ are those Ln3+ ions that have symmetrical (empty, half-filled, or filled) f-electron occupation. Since these molecules are highly ionic,37the prediction of their shapes is best based on the electronic structure of the Ln3+ ions, at least for the trifluorides, rather than on the neutral atoms. The electronic configuration of lanthanide trihalides might be described similarly to the d-block transition metal dihalides for which both the Russel-Saunders coupling scheme and crystal field effects are important. There is, however, a major difference between these two classes of metal halides; while the 3d electrons in the first transition metal series are comparable in both their energy and radius to the valence shell, the 4f electrons are well buried in the inner electron core and are shielded from ligand effects by the 5s5p subshell. Thus, the lanthanide ions can be viewed at as having an asymmetrical 4f electron distribution within the spherically symmetrical 5s25p6 subshell, the latter having lower energy but much larger radius. This situation is similar to a Faraday cage in which the spherically symmetrical 5s25p6 subshell protects the inner subshells from external influence; thus, we do not have to expect that the ligand field would affect the 4f subshell, contrary to what the situation is with the 3d subshell of the first-row transition metal dihalides. Indeed, spectroscopic evidence supports this observation. While the splitting caused by a crystal field is of the order of 100 cm-' for lanthanide trihalides, the spin-orbit coupling is of the order of 2000 ~ m - ' .Thus, ~ ~ the Russel-Saunders coupling scheme suffices for the description of the electronic configuration of the lanthanide elements. Due to the asphericity of the 4f subshell, the shielding of the nuclear charge will be different in different directions about a lanthanide ion, and this will have its effect on the bond configuration of their trihalides. We have calculated the 4f subshell shapes using the expressions given in ref 36 and depicted them in Figure 1. The 4f subshell appears spherical for La3+, Gd3+, and Lu3+ only, Le., for ions with 0, 7, and 14 f electrons. There is either axial elongation (prolate ellipsoid) or axial compression (oblate ellipsoid) for the other 4f subshells. There is also a similarity between the distortions of the 4f subshell of the first part of the series with the 4f'+n subshell of the second part, with two exceptions, viz. Eu3+ vs Yb3+ and Sm3+vs Tm3+ (vide infra). For Eu3+not only the ground state but also the first excited multiplet state has been calculated, using the data of ref 39. The excitation energies of this element are so low that the first excited state is expected to prevail at the high temperatures of the experiments of these t r i h a l i d e ~ . ~ ~ We can reasonably expect that the shape of this inner 4f core will influence the shape of the lanthanide trihalide molecules. 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 27, 1995 10781
Molecular Shape of Lanthanide Trihalides
TABLE 1: Molecular Shape of Lanthanide Trihalides from Different Source9 experimental calculated molecule method ref sym method ref SYm molecule EH I,2 3 SCF 4 SCF 5 CISD CISD+Q SCF CAS CISD 6 EH 4 SCF 7 SCF, CI 8 SCF, CI, CAS 6 EH 4 SCF, CI 9 EH 6 4 SCF, CI EH 1,2 SCF, CI 3 5 10 EH EH EH 3 SCF, CI
experimental method ref sym
calculated method ref sym SCF, CI 24 22 EH SCF, CI 24 22 EH SCF, CI 24 22 EH SCF, CI 24 EH SCF, CI EH SCF, CI EH SCF, CI SCF, CI
22 24 22 24 22 26 24 24
SCF, CI
24
SCF, CI
24
EH SCF, CI EH EH EH SCF, CI SCF, CI SCF, CI SCF, CI SCF, CI EH SCF, CI EH SCF, CI EH SCF, CI EH
22 24 22 22 22 24 24 24 24 24 22 24 22 24 22 24 22 26 24
SCF, CI
IR(M) = matrix isolation infrared spectroscopy,RA(M) = matrix isolation Raman spectroscopy,IR(G) = gas-phase infrared spectroscopy,ED = electron diffraction, MBD = molecular beam deflection, EH = extended Huckel calculation, SCF = self-consistent-field calculation, CI = configurationalinteraction calculation, CISD = single double CI, CISD+Q = corrected CISD, CAS = complete active-space multiconfigurational SCF. For pyramidal molecules the halogen-metal-halogen bond angles are given in parentheses (in degrees). Obviously, no deviation from the ideal planar geometry can be expected for molecules in which the 4f subshell is symmetrically occupied. When, however, the deformation of the subshell is manifested in an electron density depletion along the molecular axis (axial compression), it seems preferable for the ligands to bend from the molecular plane toward the axis, resulting in a pyramidal distortion. On the other hand, with enhanced electron density along the axis, the planar configuration is maintained. Of course, there are other factors as well in determining the shape of these molecules, above all the size and electronegativity of the ligands. These are competing effects that may offset each other's influence on the molecular shape. The larger the halogen, the greater is the steric hindrance to deviation from planarity. As to the ligand electronegativity, with decreasing electronegativity from fluorine toward iodine, the oxidation state of the central lanthanide atom might be expected to decrease from f 3 toward +2. The Ln2+ ion is isoelectronic with the 34- oxidation state ion of the next lanthanide ion in the periodic
table. Considerations for all these effects facilitate the prediction of the molecular shapes of gaseous lanthanide trihalides.
Predicted Shapes The structure of the highly ionic LnF3 molecules can be best described by considering the behavior of the Ln3+ central ion. In the presence of the small fluorine ligands no other effect than asphericity of the 4f subshell can be expected to influence the molecular shape. No distortion from the planar geometry is anticipated for spherically symmetrical and axially elongated shapes of the 4f subshell. These will be LaF3, F " F 3 , SmF3, and G d S in the first half of the lanthanide series (see Figure 1). Deviation from planarity can be expected for the axially compressed 4f subshells of Ce3+, Pr3+, Nd3+, and Eu3+ in the first part of the series, with the largest deviation from planarity in RF3. For Eu3+ the shape of the first excited state is considered instead of the ground
10782 J. Phys. Chem., Vol. 99, No. 27, 1995
/-\ >x
,
/
\ 4
Molnk and Hargittai Thus, the bond angles of NdX3 and HoX3 molecules are expected to increase in the order F < C1 < Br < I. As to the shape of ErX3 molecules, either planar or slightly pyramidal shapes can be expected (see our reasoning for the Tm3+ ion above, which is isoelectronic with Er2+). For TmX3 molecules, the small electron density increase in the equatorial direction of the Tm3+ subshell may be compensated by increasing ligand size and by the fact that the 2+ oxidation state of this ion will be isoelectronic with spherical Yb3+, favoring a planar arrangement.
Experimental Support j
=r
Figure 1. Shapes of the 4f subshell in Ln3+ ions calculated using the expressions given in ref 36.
state due to the fact that it must be the dominant state under the experimental conditions (vide supra). As for the shape of the trihalides in the second half of the lanthanide series, it is helpful to consider their periodic similarity to the shapes of the 4f subshell of the first part of the series. With two exceptions similar geometries can be anticipated, that is, pyramidal arrangement for TbF3, DyF3, and HoF3 and planar for ErF3 and LuF3. The two exceptions are TmF3 and YbF3 as compared to their counterparts, namely, SmF3 and EuF3. The shape of the 4f subshell is axially elongated for Tm3+,similarly to Sm3+. However, a closer look at the shape of this subshell (Figure 1) reveals a slight local increase of electron density in the molecular plane, making a slight deviation from planarity, perhaps, more favorable. The other exception is YbF3, for which a planar arrangement can be expected in contrast to its counterpart EuF3 which is probably slightly pyramidal. The reason for this difference lies in their differing first excitation energies. Whereas the first excited multiplet state had to be taken into account for Eu3+,the ground state suffices for Yb3+. Its shape is a prolate ellipsoid, giving no reason for distortion from planar geometry. The above arguments referred to the lanthanide trifluorides. With increasing size and decreasing electronegativity of the ligand, other factors may also have to be taken into consideration, and to an increasing extent. For CeX3 (and TbX3), with decreasing the oxidation state from +3 toward +2, a larger deviation from planarity can be expected for the more oblate ellipsoid shape of the 4f shell, but the increasing size of the ligands may alleviate this influence. Therefore, it is difficult to predict the shape of these molecules, and we do not expect too much deviation from planarity. Planar geometry can be expected for all PmX3 molecules irrespective of the ligands, since the prolate shape of the lanthanide 4f subshells in both oxidation states favors this arrangement just as does the increase of the ligand size. Similarly, all SmX3 molecules can be expected to be planar; here the 2+ oxidation state of samarium will be isoelectronic with Eu3+ which is spherical in the ground state (see Figure 1). The situation is similarly straightforward with NdX3 (and HO&) molecules; here both the change of the 4f shell shape (from oblate to prolate ellipsoid, cf. Pm3+ and Er3+) and the increasing size of the ligands favor less deviation from planarity.
Several lanthanide trifluorides have been investigated by matrix isolation infrared and Raman spect~oscopy.~-~~” Various features of these matrix spectra provide experimental support for our predictions of the shape of lanthanide trifluorides. Infrared spectroscopy is well-suited for distinguishing planar and pyramidal geometries. For planar trihalides (D3h symmetry) the symmetric stretching frequency is inactive in the infrared, and only one band appears in the stretching region of the spectrum. For pyramidal C3bmolecules both stretching frequencies should appear. Looking at the spectra recorded by Wesley et al.,3 one sharp band can be seen only in the spectrum of LaF3 and SmF3. LaF3 with its 4fo electronic configuration has a symmetrical 4f subshell, implying planarity. As for SmF3, the prolate ellipsoid shape of its 4f subshell again favors planar geometry, in agreement with the observation. Two bands can be discerned in the IR spectrum of PrF3, indicating pyramidal geometry. According to our predictions, Pr3+ has an oblate ellipsoid-shaped 4f subshell, suggesting a pyramidal configuration. NdF3 is expected to have a pyramidal geometry, slightly less pyramidal though than PrF3, and this is not in contrast to the IR spectrum, although the relative intensities of the two bands are not quite what is expected. For CeF3 and EuF3 only a slight deviation from planarity is expected from our considerations which is supported by the shoulders on the observed IR bands. The bending frequency region is also consistent with our predictions. The two bending frequencies are both IR active for both D3h and CjV symmetry; thus both should appear. However, the out-of-plane character of the inversion frequency decreases with increasing pyramidality, causing this frequency to shift closer to the other bending frequency. According to the spectra of ref 3, these two bending frequencies are the closest in the spectrum of PrF3, in accordance with the expected largest deviation from planarity for this molecule. We also have to mention that the other two infrared spectroscopic studies of LaF3 concluded that the molecule is pyramidal.’%*There is only one ab initio frequency c a l ~ u l a t i o n ~ ~ for lanthanide trihalides that can be compared to the above results. The difference of the two stretching frequencies of LaF3 in this calculation (differences of values can more reliably be trusted than the actual values) is very small (for pyramidal and planar models 1-3 and 3-6 cm-I , respectively, depending on the basis), and this is why the assignment of refs 1 and 2 , reporting a considerably larger difference, 31 cm-’, is suspect. Unfortunately, some of the few ab initio calculations that have appeared for the lanthanide trihalides are at variance with our predictions. This is particularly so for LaF3, for which all calculation^^^-^^ predict pyramidal geometry, although most of the calculated bond angles are close to 120°, and they seem to be only slightly more stable than the planar arrangement. It is a question, of course, that possible inadequacies of these calculations, due to the large lanthanide atoms, the multiple open-shell nature of these molecules (neglect and treatment of
J. Phys. Chem., Vol. 99, No. 27, 1995 10783
Molecular Shape of Lanthanide Trihalides relativistic effects, treatment of electron correlation, or the lack of it, basis set superposition errors, etc.) can or cannot cause such differences. Also, at least in ref 24, only the LS states of the free atom and of the monovalent ion were considered, and those of the trivalent ion were ignored even though their Mulliken population analysis had shown very highly ionic characters for the lanthanides.
lanthanides, possessing smaller polarizabilities. Thus, it is possible that a very slightly pyramidal or "quasiplanar" arrangement and a very flat inversion potential curve describe the structure of LaF3 even if the 4f subshell of La3+ has a symmetrical electron distribution. For the other lanthanides, however, the decreased ionic polarizability probably has a negligible influence on the geometry, and our prediction, based on the asphericity of the 4f subshell, should apply for them.
Discussion There has been a lot of discussion of the variations in the shapes of alkaline-earth dihalide molecule^.^' The occurrence of the bent geometries has been successfully interpreted by polarizability argument^.^^.^^^^^ Considering the closeness of the alkaline-earth elements and the lanthanides in the periodic table, it is rather tempting to use the same arguments for the lanthanide trihalides. There are, however, additional factors that also have to be taken into account. First of all, ion sizes should be carefully considered before choosing the rare earth trivalent ions and the alkaline earth divalent ions for comparison. Thus, e.g., La3+ should be compared to Ca2+ rather than to neighboring Ba2+ (the ionic radii are 1.17 8, for La3+ and 1.14 A for Ca2+ versus 1.49 A for Ba2+;all radii are for 6-co0rdination~~).Therefore, although all barium dihalides are predicted to be bent both by the polarizability modelz7 and by ab initio c a l c ~ l a t i o n s , 4this ~~~~ cannot be taken as a serious clue for the pyramidality of all lanthanum trihalides. At most, if we compare them to the calcium dihalides, polarizability arguments can only predict LaF3 to have pyramidal geometry. Although, again, according to all calculations carried out for CaF2,42-45the bent configuration is only slightly more stable than the linear. (The difference is less than 1 kJ/mol, and the bending potential curve is very flat.) There is additional similarity between calcium difluoride and lanthanum trifluoride. The computed CISD+Q halogenmetal-halogen bond angles of refs 43 and 24 yield practically the same deviation from linearity and planarity, 11.3' and 11.8' for CaF2 and LaF3, respectively, while the same deviation for SrF2 and BaFz is appreciably larger (20.6' and 28.5', respectively). The difference in charges is another feature to consider in the comparison of the lanthanide ions with the alkaline earth ions. Taking this into account, it is not simply the polarizabilities of the metal ions but, rather, the induced dipole moments, depending both on the metal ion polarizability and on the electric field produced by the two versus three halogen ligands that have to be considered. We attempted a crude estimate of the dipole moments using the CISD+Q g e o m e t r i e ~ ~and ~ , ~the ~ ion polarizability data of P a ~ l i n g .We ~ ~ also applied a factor of 1.5 to take into account the stronger effective field by three halogens versus the two halogens. This latter assumption is strictly true only if the geometries are the same, but since they are very similar we may allow for this assumption. The calculated dipole moments compare the following way with the dipole moment of CaFz taken as 1.O: SrFz, 3.5; BaFz, 9.0; and LaF3, 3.7. In this respect LaF3 is more similar to SrFz than to CaFz, in spite of the fact that the ionic radius of Sr2+ (1.32 A) is larger than that of the La3+ ion (1.17 A). However, La3+ (with 54 electrons) has a more compact electronic distribution than Sr2+ (with only 36 electrons), and thus the same dipole moment of LaF3 can only be the result of a smaller distortion of the electronic distribution than that in the Sr2+ ion. From all the above it seems likely that metal ion polarization has a much smaller effect on the molecular structure of lanthanide trihalides than on that of the barium dihalides. Even then, it probably has an effect only on La3+but not on the other
Conclusions A simple model is offered to interpret and predict the shapes of lanthanide trihalide molecules. According to this model, the shape depends mostly on the asphericity of the 4f electron shell that is buried deep within the 5s5p shell but has relatively large density. For the fluorides the above effect determines the molecular shape. For the larger halides the electronegativity and size of the halogen ligands also influence the outcome, and the shape is the result of competing effects. Planar arrangement can be expected for the lanthanides with empty, half-filled, and completely filled 4f shell, i.e., for LaX3, GdX3, and LuX3. Similarly, planar geometries are predicted for the fluorides of those lanthanides whose 4f subshell has a prolate ellipsoid shape. These are h3+, Sm3+,E$+, and Yb3+. On the other hand, CeF3, PrF3, NdF3, EuF3, TbF3, DyF3, and HoF3 are expected to have a pyramidal configuration due to the oblate ellipsoid shape of their 4f subshell. Although Tm3+ has a prolate ellipsoid shape, it also has a local electron density concentration in the molecular plane, and thus a slight deviation from planarity may be favored. As to the other halides, the oxidation state of the lanthanide ion decreases toward 2+ as we go from fluoride toward iodide. Thus, the central ion will be isoelectronic with the following Ln3+ion in the periodic table, and their 4f subshell will be increasingly similar as well. This effect and the size of the ligands together will determine the shape of their molecules.
Acknowledgment. Helpful discussions with Professor Istvin Hargittai and Dr. LBsz16 Nemes are greatly appreciated. This research was supported by the Hungarian Scientific Research Fund (OTKA T 014073). References and Notes (1) Hauge, R. H.; Hastie, J. W.; Margrave, J. L. J. Less-Common Met. 1971, 23, 359. (2) Hastie, J. W.; Hauge, R. H.; Margrave, J. L. J. Less-Common Met. 1975, 39, 309. (3) Wesley, R. D.; De Kock, C. W. J. Chem. Phys. 1971, 55, 3866. (4) Akishin, P. A.; Naumov, V. A.; Tatevski, V. M. Nauchn. Dokl. Vysshei Shkoly, Khim. Khim. Tekhnol. 1959, 229; Chem. Abstr. 1959,53, 19493e. ( 5 ) Kaiser, E. W.; Falconer, W. E.; Klemperer, W. J. Chem. Phys. 1972, 56, 5392. (6) Kovfics, A.; Konings, R. J. M.; Booij, A. S. To be published. (7) Spiridonov, V. P.; Gershikov, A. G.; Lyutsarev, V. S . J. Mol. Stmct. 1990, 221, 79. (8) Danilova, T. G.; Girichev, G. V.; Giricheva, N. I.; Krasnov, K. S.; Zasorin, E. Z. Izv. Vyssh. Ucheb. Zaved. Khim. Khim. Tekhnol. 1979, 22, 101; Chem. Abstr. 1979, 90, 1445842. (9) Giricheva, N. I.; Zasorin, E. 2.; Girichev, G . V.; Krasnov, K. S . ; Spiridonov, V.P. Izv. Vyssh. Ucheb. Zaved. Khim. Khim. Tekhnol. 1977, 20, 284; Chem. Abstr. 1977, 87, 11948n. (10) Kovfics, A.; Konings, R. J. M.; Booij, A. S . Vib. Specfrosc., in press. (11) Lesiecki, M.; Nibler, J. W.; De Kock, C. W. J. Chem. Phys. 1972, 57, 1352. (12) Zasorin, E. Z.; Ivanov, A. A.; Ermolaeva, L. N.; Spiridonov, V. P. Zh. Fiz. Khim. 1989, 58, 669; Chem. Abstr. 1989, 1 1 1 , 160690~. (13) Girichev, G. V.; Danilova, T. G.; Giricheva, N. I.; Krasnov, K. S.; Petrov, V. M.; Utkin, A. N.; Zasorin, E. Z. Izv. Vyssh. Ucheb. Zaved. Khim. Khim. Tekhnol. 1978, 21, 626; Chem. Abstr. 1978, 89, 83266~.
10784 J. Phys. Chem., Vol. 99, No. 27, 1995 (14) Popenko, N. I.; Zasorin, E. 2.; Spiridonov, V. P.; Ivanov, A. A. Inorg. Chim. Acta 1978, 31, L371. (15) Akishin, P. A.; Naumov, V. A. Nauch. Dokl. Vysshei Shkoly, Khim. Khim. Tekhnol. 1959, 5 ; Chem. Absrr. 1959, 53, 13702~. (16) Wells. Jr.. J. C.; Gruber, J. B.; Lewis, M. Chem. Phys. 1977, 24, 391. (17) Danilova. T. G.;Girichev, G.V.; Giricheva, N. I.; Krasnov, K. S.; Zasorin, E.Z. Izv. Vyssh. Ucheb. Zaved. Khim. Khim. Tekhnol. 1977, 20, 1069; Chem. Abstr. 1977, 87, 192318a. (18) Loktyushina, N. S.; Zaitsev, S. A.; Osin, S. B.; Sevelkov, V. F. Vestn. Mosk. Univ. Ser. 2 Khim. 1987, 28, 434; Chem. Absrr. 1987, 108, 132242. (19) Giricheva, N. I.; Zasorin, E. Z.; Girichev, G. V.; Krasnov, K. S.; Spiridonov, V. P. Izv. Vyssh. Ucheb. Zaved. Khim. Khim. Tekhnol. 1974, 17. 616; Chem. Abstr. 1974, 81, 4 2 5 9 ~ . (20) Girichev. G. V.; Danilova, T.G . ;Giricheva, N. I.; Krasnov, K. S.; Zasorin, E.Z. Izv. Vyssh. Ucheb. Zaved. Khim. Khim. Tekhnol. 1977, 20, 1233; Chem. Abstr. 1977, 88, 14580t. (21) Giricheva, N. I.; Zasorin, E. Z.; Girichev, G. V.; Krasnov, K. S.; Spiridonov, V. P. Zh. Strukt. Khim. 1976, 17, 797; Chem. Abstr. 1976, 86, 131435~. (22) Myers, C. E.; Normann 11, L. J.; Loew, L. M. Inorg. Chem. 1978, 17, 1581. (23) Lohr, L. L.; Jia, Y. Q.Inorg. Chim. Acta 1986, 119, 95. (24) Dolg, M.; Stoll, H.; Preuss, H. J. Mol. Struct. (THEOCHEM) 1991, 235, 67. (25) Di Bella. S.; Lanza, G.; Fragalh, I. L. Chem. Phys. Lett. 1993,214, 598. (26) Pyykko. P.; Lohr Jr., L. L. Inorg. Chem. 1981, 20, 1950. (27) Drake, M. C.; Rosenblatt, G. J. Electrochem. SOC.1979, 126, 1387. (28) Jia, Y. G.: Zhang, S. G.Inorg. Chim. Acta 1988, 143, 137. (29) Charkin, 0. P.; Dyatkina, M. E. Zh. Strukt. Khim. 1964, 5,921. (30) Hargittai, M.; Hargittai. I. Int. J. Quantum Chem. 1992, 44, 1057. (31) Hastie, J. W.; Hauge, R. H.; Margrave, J. L. Matrix Isolation Spectroscopy. In Spectroscopy in Inorganic Chemistry; Rao, C. N. R., Ferraro, J. R.. Eds.; Academic Press: New York, 1970; Vol. 1, p 57.
Molnir and Hargittai (32) Hargittai, M. In Stereochemical Applications of Gas-Phase Electron Difraction; Hargittai, I., Hargittai, M., Eds.; VCH Publishers: New York, 1988; Part B, Chapter 9. (33) Hargittai, M. Coord. Chem. Rev. 1988, 91, 35. (34) Beattie, I. R.; Jones, P. J.; Young, N. A. Mol. Phys. 1991, 72, 1309. (35) The 4 f shell decreases gradually from 0.366 A for Ce3+ to 0.244 8, in Lu3+,while the radius of the 6s shell vanes from 1.978 A for Ce3+ to 1.553 in Lu3+: Waber, J. T.; Cromer, D. T. J. Chem. Phys. 1965, 42, 41 16. (36) Severs, J. Z. Phys. B: Condens. Matter 1982, 45, 289. (37) Greenwood, N. N., Eamshow, A. Chemist? of the Elements; Pergamon Press: Oxford, 1984; Chapter 17, p 963. (38) Reference 37; Chapter 30, p 1441. (39) Walter, U. Z. Phys. B: Condens. Matter 1986, 62, 299. J 1) (40) The excitation energy of the first intermultiplet ( J transition for Eu3+ is extremely small (46.5 meV) compared to the other lanthanide ions (e.g., Ce3+,274 meV; Pr3+,261 meV; and Nd3+. 234 meV) and falls within the thermal energy limit (103.8 meV) at 1200 K. The excitation energies are taken from: Tompkinson, J.; Carlile, C. J.; Lovesey, S. W.; Osbom, R.; Taylor, A. D. Pulsed Neutron Studies of Materials. In Spectroscopy of Advanced Materials; Advances in Spectroscopy Vol 19; Clark, R. J. H., Hester, R. E., Eds.; Wiley: Chichester, 1991; p 163. (41) Gillespie, R. J.; Hargittai, I. The VSEPR Model of Molecular Geometry; Allyn and Bacon: Boston, 1991; Chapter 5 , p 99. (42) Seijo, L.; Barandiarin, Z.; Huzinaga, S. J. Chem. Phys. 1991, 94, 3762. (43) Kaupp, M.; Schleyer, P. v. R.: Stoll, H.; Preuss, H. J. Am. Chem. Soc. 1991, 113, 6012. (44) Dyke, J. M.; Wright, T. G. Chem. Phys. Lett. 1990, 169, 138. (45) Wright, T. G.; Lee, E. P. F.; Dyke, J. M. Mol. Phys. 1991, 73, 941. (46) Shannon, R. D. Acta Crystallogr. 1976, A32, 751. (47) Pauling, L. Proc. R. Soc. London 1927, 114, 191. These polarizability values were confirmed later for alkaline earth ions by SCF calculation of Mahan, G. D. Phys. Rev. A 1980, 22, 1780.
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