3587
J . Phys. Chem. 1984,88, 3587-3594
Anisotropic Ligand Polarizability Contributions to Intensity Parameters for the Trigonal Eu(ODA),’- and EU(DBM)~H,OSystems’ John J. Dallara, Michael F. Reid, and F. S. Richardson* Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901 (Received: November 7, 1983)
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A parametrization of the electric dipole line intensities observed within the 7Fo 5Dz,7F1 5DI,and 7F2 5Dotransition regions of Eu(II1) is carried out for two different systems, Na3[Eu(ODA)3].2NaC10,.6H20 and Eu(DBM)~H~O. This intensity analysis is based on the general parameter set, (Ah)(A = 2, 4, 6; t = A, X k l), introduced previously by us. Empirically derived values for the A; intensity parameters are reported for each system, and it is found that the t = X parameters are essential to fitting the experimental intensity results. These parameters are not contained in the Judd-Ofelt-Axe (A&t,X)) parametrization scheme, and their importance in the present analysis suggests lanthanide-ligand interactions which are either noncylindrically symmetric or nonindependent. Direct calculations of the Ah parameters, based on an electrostatic intensity model which includes contributions from both static-couplingand dynamic-coupling interaction mechanisms, are also reported. The dynamic-coupling contributions arising from ligand polarizability anisotropy are shown to account for the nonvanishing t = X parameters. The results of the model calculations are in good qualitative agreement with experiment, and these results provide useful clues regarding important spectra-structure correlations within the context of the electrostatic intensity model for lanthanide 4f 4f electric dipole transitions. Most of the qualitative discrepancies between the calculated and experimental results can be resolved by simple adjustments to the computational model. However, the major emphasis of this study is on the relative signs and magnitudes of the empirically derived intensity parameters, and the major finding is the importance of the t = X parameters. These points are independent of mechanistic considerations.
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I. Introduction
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In this paper we report a theoretical analysis of the 4f 4f electric dipole intensity data obtained on two different noncentrosymmetric europium(II1) complexes in the solid state. The analysis is restricted to intensity observed in the no-phonon (origin) 5DJ) lines resolved within several multiplet-to-multiplet (’F, transition regions (in absorption and emission), and is based on the A& parametrization scheme described in the preceding paper.2 Signs and magnitudes for the lower-order (A = 2) parameters are determined from the empirical intensity data, and these are compared to those calculated on the basis of the static-coupling and dynamic-coupling electrostatic intensity models (also described in the preceding paper).2 The systems examined in this study are each trigonally symmetric, but they differ with respect to their (1) exact site symmetries (D, vs. C3),( 2 ) coordination numbers (9 vs. 7), (3) ligand compositions, and (4) chelate ring distributions and sizes. The Eu(ODA)~,- complex, as it exists in Na3[Eu(ODA),]. 2NaC104-6H20, is 9-coordinate and tris-terdentate with D, point-group ~ y m m e t r y . ~The . ~ E u ( D B M ) ~ H ~complex O is trisbidentate with respect to the DBM ligands and is 7-coordinate overall, with C, point-group ~ y m m e t r y . ~It is clear from the polarized optical spectra obtained for each system that the “effective” crystal fields sensed by the Eu(II1) 4f electrons reflect the actual point-group symmetries of the respective system^.^-^ Most relevant to the present study is the highly anisotropic nature of each of the chelate systems contained in the Eu(ODA)?- and Eu(DBM),H,O complexes. Each chelate ring is very nearly planar, and each contains a variety of chemical bonds and substituent groups which are in close proximity to the Eu(II1). These structural features suggest that constructing an effective 4f-electron crystal-field potential based entirely on ligand point-charge and isotropic (atomic) polarizability distributions will not provide an accurate representation for either complex. The charge distributions localized in the chemical bonds and on the chelate substituent groups in the ligand environments of these two complexes
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(1) ODA = oxydiacetato (or diglycolato) ligand; DBM dibenzoylmethanato (or 1,3-diphenyl-1,3-propanedionato)ligand. (2) M.F. Reid and F. S. Richardson, J . Phys. Chem., preceding paper in this issue. (3) J. P. Morley, J. D. Saxe, and F. S. Richardson, Mol. Phys., 47,379 (1982). (4)A. F.Kirby and F. S. Richardson, J . Phys. Chem., 87,2557 (1983). (5) A. F.Kirby and F. S. Richardson, J . Phys. Chem., 87,2544 (1983).
0022-3654/84/2088-3587$01 S O f 0
are likely to make significant contributions to the crystal-field potential at the Eu(II1) sites. Furthermore, many of the Eu-L pairwise interactions that enter into our dynamic-coupling 4f 4f intensity model2 are likely to be highly anisotropic about the respective Eu-L axes. (Note that in the present case, L can represent either atoms, groups of atoms, or chemical bonds in the ligand molecules.) We have previously shown that the noncylindrically symmetric components of each Ln-L pairwise interaction in a lanthanide complex may contribute to certain 4f 4f electric dipole intensity parameters which vanish under the assumption of Ln-L cylindrical , ~ , ~ “extra” paramsymmetry (i.e., C,, local ~ y m m e t r y ) . ~ These eters, required to accommodate the effects of noncylindrical symmetry in the Ln-L interactions, are the t = X members of the general parameter set (A&).2-6 The noncylindrically symmetric Ln-L interactions will, in general, also contribute to the other ( t = X f 1) members of this set, but these latter parameters need not vanish in the absence of noncylindrical Ln-L symmetry.2~6~s Therefore, the existence and properties of any A& parameters discovered in analyzing 4f 4f electric dipole intensity data can provide important information about the nature of the Ln-L pairwise interactions. As was noted above, many of the Eu-L interactions in the Eu(ODA),,- and E U ( D B M ) ~ H ~complexes O are expected to be noncylindrically symmetric (especially when L = a chemical bond within a ligand), and one may anticipate the need for including Aip parameters in a general parametrization of their intensity properties. The present study is the first to 4f electric dipole intensity include t = X parameters in a 4f analysis. Most previous intensity parametrization studies (excluding those based on the less detailed 0, parametrization scheme) have been carried out on systems which contain relatively simple ligands (e.g., monatomic anions), and for which Ln-L cylindrical symmetry is a good approximation.* In the dynamic-coupling (or ”ligand-polarization”) model for 4f 4f electric dipole intensity, the Ln-L-radiation field interaction potential is, in part, determined by the ligand’s dipolar polarizability t e n ~ o r . ~ *If~this , ~ ,tensor ~ is cylindrically symmetric about the Ln-L axis, or if the polarizability is isotropic (Le., a scalar property), then the dynamic-coupling mechanism can make
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( 6 ) M. F. Reid and F. S. Richardson, J . Chem. Phys., 79,5735 (1983). (7) M.F.Reid and F. S.Richardson, Chem. Phys. Lett., 95,501 (1983). (8) M.F. Reid, J. J. Dallara, and F. S. Richardson, J . Chem. Phys., 79, 5743 (1983). (9) B. Stewart, Mol. Phys., 50, 161 (1983).
0 1984 American Chemical Society
3588 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
no contributions to the t = h intensity parameters. If, on the other hand, the polarizability tensor is nonaxially symmetric about Ln-L, then the dynamic-coupling mechanism can contribute to the t = h (as well as the t = h f 1) intensity parameter^.^,^,^ The static-coupling mechanism contributes only to the t = h f 1 parameters. Therefore, within the framework of the static-coupling/ dynamic-coupling electrostatic intensity theory, the t = h intensity parameters may be rationalized entirely in terms of dynamiccoupling contributions arising from ligand polarizability anisotropy. The chemical bonds in the ODA and DBM ligands examined in this study all possess at least two-dimensional polarizability anisotropy, and in each case the principal axis of the bond polarizability ellipsoid is skewed away from the Eu-L axis (where L, here, is located at the midpoint of the chemical bond). The possible importance of taking ligand polarizability anisotropy into account for rationalizing 4f 4f transition intensities was first pointed out by Mason and co-workers.lOsll It was shown that the AMf = f l components of the 7Fo 5D2transition in the trigonal dihedral E u ( O D A ) ~ complex ~are forbidden to first order in the dynamic-coupling model unless ligand polarizability anisotropy is taken into account. Since both AMf = f2 and AMf = f l components are required to explain the observed distribution of intensity within the 7Fo 5D2absorption region, it was concluded that polarizability anisotropy plays a crucial role in the intensity mechanism for this system. Mason’s results and conclusions were later rationalized within a more general theoretical framework by Stewart9 and by Reid and R i c h a r d ~ o n . ~ , ~ The experimental data used in the present study were taken from three previous reports from this laborat~ry.’~In our previous work, on both E u ( O D A ) ~ ~and - Eu(DBM)~H~O we, were able to obtain sets of even-parity crystal-field coefficients that gave quite good agreement between calculated and experimentally determined crystal-field energy-level ordering and splittings. We also achieved good agreement between calculated and observed magnetic dipole strengths, for transitions which are predominantly magnetic dipole in character (e.g., 7Fo 5D, and 7F1 ’Do). On the other hand, our attempts to calculate electric dipole strengths directly from the static-coupling/dynamic-coupling electrostatic intensity model met with only mixed success. For several transitions and sets of transitions (in each system), the agreement between theory and experiment was excellent (indeed, remarkable), while for others the agreement was very poor. Since our energy-level and magnetic dipole strength calculations indicated that our 4f-electron wave functions were reasonably accurate (at least with respect to their JMf compositions), it seemed likely that the major deficiencies in the electric dipole intensity calculations could be traced to our treatment of the ligand properties. In the latter, we represented the ligand environment entirely by point charges and isotropic polarizabilities located on atoms or at the centroids of chelate substituent groups (e.g., the phenyl groups on the DBM ligands). Chemical bonds and ligand polarizability anisotropy were ignored. The present study was undertaken to obtain, for the first time, a set of empirical intensity parameters for two systems in which cylindrically symmetric Ln-L pairwise interactions cannot be (reasonably) assumed. Of particular interest were those parameters ( t = A) predicted to be nonvanishing only when noncylindrically symmetric Ln-L interactions are important. Two further objectives were to calculate and rationalize these parameters in terms of ligand polarizability anisotropy contributions to the dynamic-coupling intensity mechanism, and to correlate the details of ligand structure and overall coordination geometry with observed intensities and intensity distributions. Both of the systems examined in this study are noncentrosymmetric, so nearly all of the electric dipole intensity in their optical absorption and emission spectra is observed in purely electronic (origin) lines. One-phonon vibronic lines are observed, but these
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(10) R. Kuroda, S. F. Mason, and C. Rosini, Chem. Phys. Lett., 70, 11 (1980). (1 1) R. Kuroda, S . F. Mason, and C. Rosini, J. Chem. SOC.,Faraday Trans. 2, 77, 2125 (1981).
Dallara et al. TABLE I: Experimentally Determined Electric Dipole Strengths Used in the Intensity Analyses Eu(0DA) Eu(DBM) dipole dipole strength0/ strengtho/ transition lo-* D2 transition lo‘* D2 Ob
Ob 83.0 368 Ob
26 1 92.0 231‘ A(7F;)
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E(5D1)
3205
Dipole strengths given are DAe/g,, where g, is the degeneracy of the initial state (see text). bElectric dipole forbidden by symmetry. Total dipole strengths given for unresolved transitions.
are easily distinguished from origin lines and their intensities are invariably less than 10% of the associated origin lines. In the present study, we consider only the electric dipole intensities observed in the origin lines. Throughout the remainder of this paper, we shall denote the E u ( O D A ) ~ ~complex by Eu(ODA), and the Eu(DBM),H,O complex by Eu(DBM). 11. Calculations A . Empirical Zntensity Parameters. Following our previous work,2,6the q-polarized component of the electric dipole strength B crystal-field transition may be expressed as for the A
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DAB,, = e21
A,w
A~C(hl,1-qltp)(-1)9C(‘kAalU:(\k,B)12 I
(1)
a0
where a and fl label the degenerate components of the A and B crystal-field levels, respectively, \kA, and ‘kBO are the nonradial parts of the 4f-electron crystal-field wave functions, and the A& are our intensity parameters. For isotropic spectra, we also define an isotropic electric dipole strength: DAB
= (1/3)CDAB,9
(2)
4
To determine “empirical” values for the A; parameters, we need experimentally measured values for the dipole strengths and calculated values for the Ut matrix elements. For the latter we need crystal-field wave functions. All of the empirical dipole strength data used in the present study were taken from our previous work (and references cited therein).3-5,12The most accurate and complete data were available for the following 7Ff 5Df transitions: ’FO 5D0,,,2;7F1 5Do,l; 7Fo,1,2 5Do;and 7Fo,l ’D,. Among these transitions, 7Fo ’D1 and 7F1 ’Do were observed to be almost entirely magnetic dipole in character, and their purely electric dipole intensity components could not be determined accurately. Therefore, these latter transitions were excluded from the data base used in determining the empirical A b parameters. This data base consisted of all the no-phonon line intensities associated with the 7F0 5Do,2, 7F1 5D,, 7F0,2 5Do,and 7F, 5D1transitions. The relevant electric dipole strengths are listed in Table I. These are given in terms of DAB/gA, where g A is the degeneracy of the initial state. There are several reasons for this approach, the most important being that for some transitions the initial state consists of unresolved A + E states and so determination of an experimental DAB is not possible. We use DAB/gA, rather than oscillator strength, because it is a more convenient quantity to work with in parameter-fitting calculations, oscillator strength being dependent on the energy of the transition. The Ut matrix elements of eq 1, expressed in terms of JMJ intermediate-coupled basis functions, may be written as
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(12) J. J. Dallara, M.S. Thesis, University of Virginia, Charlottesville, VA, 1983.
The Journal of Physical Chemistry, Vol, 88, No. 16, 1984 3589
Anisotropic Ligand Polarizability
In eq 8, BL is the isotropic, “mean” polarizability of ligand L, and = in eq 9 , .Z,(L) is defined according to CA,*(JMJ)c B s ( J ’ M ; ) ( ~ [ s ~ ] J M J I ~ ~ ( I c / ’ [ s ~ I I J ’ M ; ) J M J JIM’, a%) = (2/3)1~2PLcz,(sL’,dJL’) (10) (3) ., where pLdenotes the polarizability anisotropy of ligand L defined where the CA,(JMJ)and CBB(J’MIJ) coefficients are obtained as with respect to a local coordinate frame, and Ci(OL’,d’) rotates eigenvectors of the matrix that diagonalizes the even-parity this local coordinate system on L to one parallel with that defined crystal-field Hamiltonian in the intermediate-coupling basis. The for the overall complex. Expressing aLand pL in terms of local intermediate-cou ling functions and crystal-field eigenvectors used polarizability components, defined parallel (11) and perpendicular to evaluate the U, matrix elements in the present study were taken (I) to the ligand’s symmetry axis, we have directly from ref 4 for the Eu(0DA) system and from ref 5 for BL = (1/3)(~uil’+ 2 ~ ~ 1 ’ ) (11) the Eu(DBM) system. The Russell-Saunders (LS)basis set, the “free-ion” electronic parameters, and the crystal-field eigenvalues (12) P L = (a,,’ - a1’) and eigenvectors are described and listed in ref 4 and 5. The radial expectation values, ( r h ) ,required for evaluating eq All of the spectroscopicstates included in our empirical intensity 8 and 9 were taken from Freeman and Watson16 and were used parametrization (Le., the crystal-field levels split out of the 7Fo,,,2 directly without attempting to correct for shielding effects. Our and SDo,1,2multiplets, vide supra) can be described almost entirely choice of ligand sites (L) and their respective polarizability and in terms of intermediate-coupling functions within the J 5 2 geometrical properties will be discussed in section IID. m a n i f ~ l d . ~Only , ~ the A(’F2) level in Eu(DBM) has a J > 2 The total electrostatic contribution to the A b intensity paramcomponent exceeding 1% of the total eigenvector composition (in eter is given by this case, the IJMJ) = 13,f3) function contributes about 4.6%).5 We note, then, that each of the transitions listed in Table I can Ah = Ah[SC] A&[DC,n] + A&[DC,P] (13) be characterized by lAJl = 0, 1, or 2 values. Therefore, for the where t = X f 1 for the [SC] case, t = X 1 for the [DC,n] case, transitions considered here, only the X = 2 matrix elements will contribute significantly to eq 1, and only the A i intensity paand t = X, X f 1 for the [DC,p] case. For the Q A intensity rameters are accessible from our empirical analysis. In the D, parameters (applicable to the total isotropic intensities of mulpoint group of Eu(ODA), the symmetry-allowed A i parameters tiplet-to-multiplet transitions), we have are A:,(Im) and Ai3(Im), while in the C, point group of Eua), = ( 2 1 I)-’ C IAhl’ (14) (DBM), the symmetry-allowed A: parameters are A?,(Re), f,P Aio(Im), Aio(Im), and A:,(Re+Imf. From eq 13 and 14 we see that Q A will be comprised of purely The empirical Q2 parameter’, is obtained from the A i param[SC], [ D C p ] , and [DC,p] contributions, as well as cross-term eters according to2-6 contributions arising (in our model) from interferences between different mechanisms. Since the individual terms in eq 13 may be either positive or negative in sign, and the signs of the respective terms are not necessarily correlated (although they may be in B. Calculated Intensity Parameters. Electrostatic Model. In certain special cases), the cross-term contributions to the QA pacarrying out these calculations, we followed the general methods rameters may be of either sign. Because of this, it is not valid and procedures described in our earlier work.2-6 For the staticto represent the QA parameters as being simple sums of purely coupling contributions to the A: parameters, we have static-coupling and purely dynamic-coupling contributions (within A&[SC] = --Al,Z(t,X)[(2h + 1)(2t 1 ) - 9 (5) the context of the electrostatic intensity model). C. Ligand-Field Geometries. E u ( 0 D A ) . The Eu(ODA),~complex we consider in this paper is that which exists in the trigonal (R32 space group) Na3[Eu(ODA)3]-2NaC10,.6H20 where, in writing eq 6, we have adopted a ligand point-charge crystalline compound. All of the Eu(0DA) spectroscopic data representation for the odd-parity components of the (static) used in this study were obtained on single-crystal or microcryscrystal-field potential. Contributions to the latter by ligand talline samples of this The crystal structure charge-polarization effects (due to presence of charged groups of this system has been described else where,,^^ so here we shall or ions lying in the vicinity of each ligand) are ignored in the only describe the Eu(ODA),~-chromophoric unit of interest. present study. The values of E(t,A) used in this study are those The E u 0 9 coordination polyhedron in Eu(ODA),,- has a disreported by Krupke.I4 Our choice of ligand sites (L) and their torted tricapped trigonal prism structure with exact D3 point-group respective charges (eqL) will be discussed later in the paper (see symmetry. The vertices of the top and bottom triangles of this section IID) for each system, Eu(0DA) and Eu(DBM). structure are occupied by carboxylate oxygen atoms, while the In calculating the dynamic-coupling contributions to the A b vertices of the equatorial triangle (representing the capping intensity parameters, we made the assumption that each ligand positions) are occupied by ether oxygen atoms. Distortion away perturber site (atom, group of atoms, or chemical bond) has a from a regular tricapped trigonal prism structure (which would polarizability which is at least cylindrically symmetric in some have D3hpoint-group symmetry) is described by counterdirectional local coordinate system. Therefore, following our previous work: twists of the top and bottom triangles (about the trigonal axis) we can express A;[DC] as a sum of two contributions: away from a superimposable configuration. Each terdentate Eu(0DA) chelate ring is very nearly planar, and these bicyclic A&[DC] = A&[DC,n] + A&[DC,P] (7) rings stretch diagonally across the (nearly) rectangular faces of where the trigonal prism. A projection of the Eu(0DA) chelate structure onto a plane perpendicular to the C, symmetry axis is shown in Figure 1. The angle T shown in this figure describes the deviation of the Eu09 coordination cluster away from a regular tricapped trigonal prism (*Aal~?l*Bd
cc
R
+
+
+
+
(13) R. D. Peacock, Struct. Bonding (Berlin),22, 83 (1975). (14) W. F. Krupke, Phys. Reu., 145, 325 (1966).
(15) A. J. Freeman and R. E. Watson, Phys. Reo., 127, 2058 (1962). (16) A. K. Banerjee, R. K. Mukherjee, and M. Chowdhury, J. Chem. SOC., Faraday Trans. 2, 75, 337 (1979). (17) A. C. Sen, M. Chowdhury, and R. W. Schwartz, J . Chem. SOC., Faraday Trans. 2, 71, 1293 (1981). (18) A. K. Banerjee, R. W. Schwartz, and M. Chowdhury, J . Chern. Soc., Faraday Trans. 2,17, 1635 (1981).
3590
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 Ligand Atomic Labels
Dallara et al.
Atomic Labelling Scheme
c2b
0, Im Bi4) > 0, Re E p < 0, and Im E$6)> 0. If the signs of the latter are changed, then the signs of the A b must be changed. TABLE VII: Comparison of Calculated Intensity Parameters with Those Determined by Parameter Fits
parameter Ai0 A:!
A;/10-" cm Eu(0DA) Eu(DBM) model parameter model parameter calcn fit calcn fit -46 -40 15.3i 15% 8.49i 70i 69.5 50 -39.2i -15.6i -16.4 + 38.91 -10 + 40i
A comparison of calculated, fitted, and empirical dipole strengths of crystal-field transitions within several multiplet-tomultiplet transitions is given in Table VIII. Total multipletto-multiplet dipole strengths are given in Table IX. We see that the fitted parameters give a reasonable, though not entirely satisfactory, explanation of the experimental dipole strength distributions, at least within the multiplet-to-multiplet transitions. Comparison of intensity parameters calculated from our model with those obtained from the fit (Table VII) shows that for each system the problem with the model calculations is that the ratio of Aio to the other parameters is too small. In the case of Eu(ODA), small adjustments of the qL, aL,and pLligand parameters would resolve the discrepancies. However, the underestimation
of Aio for Eu(DBM) is much more serious, and it is unlikely that these types of parameter adjustments could resolve the problem. In what follows we shall discuss the possibility that inaccurate crystal-field wave functions are responsible for our problems with this system, but it is also possible that intensity mechanisms not included in our electrostatic model are important in this case. Unlike ODA, the donor moieties (ketonate groups) in DBM have substantial r-electron densities which may be delocalized around the chelate rings. Lanthanide-ligand orbital overlap, charge penetration, and charge exchange effects are likely to be more important in this case. These effects are, of course, ignored in our electrostatic intensity model. Recall, however, that our empirical intensity parametrization scheme (eq 1) is sufficiently general to absorb all of these effects. Returning to the distribution of dipole strengths, we consider first the Eu(0DA) results. From Table VI11 we see that, while our parameter fit reproduces the experimentally determined relative magnitudes of the dipole strengths within the Fo D2 and F, Do transitions, the model calculations do not. However,
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TABLE VIII: Comparison of Relative Dipole Strengths within Multiplet-Multiplet Transitions dipole strength@(relative)
transition
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Ad7Fo) AI(~Fo) Ed7F2) Ea(7F2)
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+
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N7FO) A(7F0) ~ ( 7 ~ A(7F,) A(7F;) E(7Fl) Ed7F2) A(7F2) Ea(7F2)
Ea(Q2Y Eb(SD2)C A~('Do)* A,(5Do)c
1
1
0.94
4.25
expt
1
1
1 4.43 1
0.85
3.76
2.84
B. Eu(DBM)
Ed5D2)' A(5D2)d ~E,(SD,)~ 1 EPD,)' A(5D;)d E,A(SD,)
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model parameter calcn fit A. Eu(0DA)
A(SDO)b
A(SDO)d A('DO)'
1
7.34 1.89 1
109 59.7
1
6.70 11.01 1 2.38 4.28
1
3.38 22.22 1
2.21 6.52
1 3.49
1 7.52
3.80
0.890
14.53
5.91
1
a Dipole strengths given are DAB/gA, where gA is the degeneracy of the initial state (see text). bThese transitions are calculated to have predominantly AM, = f 2 chara~ter.~.'These transitions are calculated to have predominantly AM, = f l chara~ter.~.'dThese transitions are calculated to have predominantly AM, = 0 ~haracter.~
we have already noted that minor adjustments to the model would correct this discrepancy. The inclusion of the intensity parameter A:o is crucial to the success of our parameter fit in the Fo D, and F2 Do regions, because this parameter makes the only contribution to AMJ = *1 transitions7 (see eq 1). Since the most intense transitions are observed to be those with predominantly AMj = f l character, the importance of this parameter is clear. Only mechanisms which do not assume strictly pairwise, cylindrically symmetric, lanthanide-ligand interaction can contribute to Aio,and in our electrostatic model the only contribution comes from the [DC,P] mechanism. Comparisons of the relative dipole strengths of the crystal-field 5Di, and 7F2 5D0. components within the 7F0 5D,,'F, transitions of Eu(DBM) (Table VIII) reveal major discrepancies between our model calculations and experiment. In all cases the A A component is calculated to have the largest dipole strength, but the experimental value is intermediate between the other two E components. The relative dipole strengths of the two A
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3594 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
Dallara et al.
TABLE IX: Comoarison of Total DiDole Strengths for Multiolet-MultiDlet Transitions
dipole strength“/
D2
Eu(0DA)
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7Fo 7F2 7F,
model calcn 5Do
parameter fit
Ob
5D0 5D1
“The dipole strengths are sums of
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DAB/gA,
7F,
--
’F4
Ob
3.83 1.90 1.05
3.53 2.31 4.51
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5Do Emission
Z[Eu(DBM)]: ZIEu(ODA)lU
Q,[Eu(DBM)]: Q,IEu(ODA)lb
X
8.01 0.54
3.19 0.40
2 4
5Do
5D0
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components in the F, D2 and F2 Do are also not well reproduced. Intensity distributions among the A E components of the 7F0 5D2and 7F2 5Dotransitions are very sensitive to the relative MJ = f 1 vs. M J = f 2 compositions of the E crystal-field states. To first order in our crystal-field calculations, these compositions are determined by the Bi4)crystal-field parameters. If we use the Bi4)values listed in Table IV, these compositions are given as follows (expressed as percent of total eigenvector). Eu(0DA): E,(7F2), 79% 12,fl), 21% 12,f2); Eb(7F2),20% 12,f1), 78% 12,f2); E,(5D2), 22% 12,f1), 78% 12,f2); Eb(5D2), 78% 12,fl), 22% 12,f2). Eu(DBM): Ea(7Fz),60% 12,f1), 37% 12,f2); Eb(7F2), 38% 12,f1), 57% 12.f2); E,(5D2), 52% (2,f1), 48% 12,352); E@2), 48% 12,*1), 52% 12,f2). Clearly, whereas the E levels of the 7F2 and 5D2 multiplets of Eu(0DA) may be characterized as having predominantly M J = f l or MJ = f 2 character, such characterization of the E levels in the 7F2and ’D2 multiplets of Eu(DBM) are not so clear-cut. The MJ compositions given above for the 7F2and 5D2crystal-field levels of Eu(0DA) agree with those deduced from magnetooptical measurements on E u ( O D A ) ~ ~ - .However, ~~,~~ we have no confirmatory evidence for the accuracy of the MJ compositions given above for the 7F2and 5D2crystal-field levels of Eu(DBM). Thus, we have much more confidence in the empirical intensity parameters for Eu(ODA), than those for Eu(DBM), which may be distorted by inaccurate crystal-field eigenfunctions. and 7F4 $DoIntensities. The D. Comparison of 7F2 7F2 5Dotransition in Eu(DBM) is observed to be about 8 times more intense than this same transition in Eu(0DA). On the other hand, the 7F4 5Dotransition is observed to be almost twice as intense in Eu(0DA) as in Eu(DBM). These results could not be explained by the calculations presented in our earlier papers.4~~ However, the Q2 and Q4 parameters calculated in the present study for Eu(0DA) and Eu(DBM) account for these results reasonably well, as is shown by the data given in Table X.
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IV. Conclusions The major objective of this study was to parametrize the 4f 4f electric dipole intensity data available for the E u ( O D A ) ~ and ~E u ( D B M ) ~ H ~systems, O using a parametrization scheme that can accommodate any one-photon, one-electron lanthanide-ligandradiation field interaction mechanism. Of special interest was determining the importance of certain parameters in this scheme which can be nonvanishing only for cases in which the lanthanide-ligand interactions are noncylindrically symmetric and/or nonindependent. The major finding of the study is that such a parameter is essential to fitting the 7Fo 5D2,7F1 5D,, and 7F2 5Do intensity data reported for both E u ( O D A ) ~ ~and -
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~~~
parameter fit
expt
0.43 52.8 31.6 15.4
0.26 62.5 39.0 18.3
1.07 28.3 312 76.1
E u ( D B M ) ~ H ~and O that the empirically determined magnitude of this parameter (Aio) is, in both cases, at least as great as the magnitudes of the A:+l,p parameters. Only the latter have counterparts in the A,%(t,X) parametrization scheme normally used in 4f 4f intensity a n a l y s e ~ . ~ fThis ’ ~ ~ study reports the first intensity analyses, based on the general A ; parametrization scheme, which include t = X parameters. The relatively large magnitude of the Aio parameter determined for both Eu(0DA);- and E u ( D B M ) ~ H ~suggests O that any model 4f electric dipole constructed to rationalize or calculate the 4f intensities for these systems must include either noncylindrically symmetric lanthanide-ligand interactions or interactions which are not strictly pairwise. In other words, the “superposition of cylindrically symmetric and independent Ln-L pairwise interactions” approximation cannot be used. The [DC,p] part of the electrostatic intensity model employed in this study allows for the inclusion of noncylindrically symmetric lanthanide-ligand interactions and, therefore, it may contribute to the t = X intensity parameters. Large contributions from this mechanism are to be expected in the E u ( O D A ) ~ ~ and - E u ( D B M ) ~ H ~systems O since both contain highly anisotropic ligand entities which are in close proximity to the metal ion. It is possible that other mechanisms (not considered in this study) may make equally important contributions to the t = X parameters, but so far only the [DC,p] mechanism is developed enough to be useful. The model calculations reported here met with mixed success. In each case, these calculations gave A:, intensity parameters of the correct sign and, in the case of the Eu(ODA),~-system, small adjustments to the model would remove the remaining discrepancies. However, in the case of E u ( D B M ) ~ H ~the O underestimation of A:o is rather serious. It is possible that inaccurate crystal-field wave functions are responsible for the discrepancy. If this is not the case, it would be difficult to find realistic adjustments to our model which would remove the discrepancy. In spite of this, the qualitative success of our calculations is an encouraging step in the effort to make spectra-structure correlations in systems with complex ligands. The utility of extracting empirical parameters as an intermediate step in intensity analyses is obvious. Direct calculations, using model parameters, did not give good quantitative results, particularly for the Eu(DBM),H20 system, but a comparison of model and empirical parameters (Table VII) shows that, apart from the underestimation of Aio, our model calculations are quite reasonable. Furthermore, the parameters determined here should be transferable to other lanthanide ODA and DBM systems. We reiterate that the crystal-field level intensity parameters, Ah, contain much more information than the J multiplet to J multiplet Qx parameters. For the transitions considered here, a multiplet-to-multiplet analysis would only give one parameter: Q 2 . Obviously, little could be learned about the importance of ligand anisotropy by scrutinizing that single parameter. Further studies of other lanthanide ions in these systems will be the subject of future communications. The use of other lanthanides will allow the determination of complete sets of intensity parameters (with X = 4 and 6, as well as 2). This will provide a more thorough test of our theoretical model, and other models that may be developed.
-
Intensity ratio from experimental data.4*5 Parameter ratio from model calculations (see Tables V and VI).
-
model calcn
where g A is the degeneracy of the initial state (see text). bThis transition is symmetry forbidden.
TABLE X: Comparison of 7F2 5Doand ‘IFq vs. Eu(ODA)** Intensities for EU(DBM)~H?O
transition
expt
Ob
17.4 7.21 4.68
7F0 5D2
Eu(DBM)
-
~~
( 2 5 ) D. R. Foster and F. S.Richardson, Znorg. Chem., 22, 3996 (1983).
-
Acknowledgment. This work was supported by the National Science Foundation (NSF Grant CHE-8215815). Registry No. Na3[Eu(ODA),].2NaC104, 43030-82-6; Eu(DBM),H20, 12121-06-1.
