Kotzian, M. and Roesch, N., (1992) Electronic Structure of Hydrated Cerium(III)

7/27/2019 Kotzian, M. and Roesch, N., (1992) Electronic Structure of Hydrated Cerium(III)

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7288 J . Phys. Chem. 1992,96, 7288-7293Electronic Structure of Hydrated Cerium(I ) . An INDOIS-CI Molecular Orbital StudyIncluding Spln-Orbit Interaction

Manfred Kotzian and Notker R&h*Lehrstuhl fiir Theoretische Chemie, Technische Universitirt Miinchen, W-8046 Garching, Germany(Received: December 19, 1991)

IND O/S-C I calculations including spin-orbit interaction have been performed on model complexes [Ce(H 20),,13+, =8,9, o rationalize the electronic structure and the spectrumof hydrated Ce(II1). We present the first molecular orbital investigationthat calculates the transition energies and oscillator strengths for the cerium &fold and 9-fold coordinated hydrates andgives a quantitat ive interpre tation of the solution spectru m. The transition moments and energies of the five observed 4f- d strong bands are verywell reproduced by using an enneahydrated model complex with a dis torted tricapped trigonalprismatic geometry. The influence of some struc tural variations of the enneahydrate on the spectrum are discussed and othermore symmetric structu res of the solvation shell are ruled out on account of the calculated transition energies. An additionalweak band in the solution spectrum is attributed to an octacoordinated complex as a dissociative product.woduction

Five ultraviolet absorption bands are known for [Ce (H z0) 9]3 +in single crystals of Ce3+-doped anthanum ethyl sulfate' (seeFigure 1). These are attributed to 4f - d transitions of theCt(111) ion and assigned to five transitions into the Kramersdoublets of th e excited 2D (5d') multiplet which is split by lig-and-field (LF) interactions and spin-orbit co ~ p li n g .' ~n aqueoussolutionthehydrated cerium ion exhibits an additional weak bandat about 34000 cm-' (Figure 1) which has been attributed to acontaminatingspecies since the 2D atomic multiplet yields a t mostfive Kramer doublets in the molecule. It has been suggested3 hatthis s@es is a lower coordinated omplex with one ligand partiallyor totally dissociated. T he energies of the observed band maxim aas well as he energy differences between the states are listed inTable I.This paper is concerned with the sp ectroscopic properties ofcerium hydrated complexes. Starting with a discussion of th e bondbetween the central ion and the water ligand@ ),we derive possiblestructures for the hydrated compounds. This is done mainly onthe basis of experimen tal structu ral data w hich are supplem entedby IND O geometry calculations. Th e model complexes withcoordination numbers of eight and nine with idealized structuresserve as first approximations. Th e spectra ar e calculated in aMO-based configuration interaction (CI) approach includingspin-orbit cou pling. These structures are then refined in orderto achieve better agreement with experimental data. In this way,we are able to propose tructur al distorsions of the hydration shellof such complexes.The electronic structure investigations were based on theIND O/S method that has recently been extended to allow thecalculation of spectm copic properties of lanthanideOn the basis of the INDO/S Hamiltonian, two different CIprocedures were made available to afford a nonperturbationaltreatmen t of the spin-orbit interaction. One is based on dou-ble-group adapted configurations (D GC I). It affords greatcompu tational economy but isrestricted o certain pointThis spin-orbit treatment is complemented by a CI formalismbased on Rum er spin functions which overcomes these symm etryrestrictions? Th e calculation of Mulliken populations of andtransition probabilities into such C I sta te wave functions was madepossible to facilitate the i nterpre tation of th e ra ther involved wavefunction^.^.^ Applications to lanthan ide monoxides have proventhe IN DO /S -C I method a useful tool for the investigation of theelectronic structure of lanthanide compounds.e6ComputationalDetails

Th e intermediate neglect of differential overlap (IND O) ap-proach to th e electronic structur e of molecules relies on separateAuthor towhom correspondence should be addressed.

TABLE : Excited-StateEneqiea (Band Ma x im ) (em-') nd theCorrespoadine Energy Differences (cm-I) for the Experimental andthe Calculated Swct rnaqueous

crystal" solutionb IND O/S-CIC39 060 39 630 40 7041950 2890 41970 2340 42870 280044740 2790 45330 3360 45940 307041400 2660 47620 2290 48820 288050130 2730 50000 2380 51000 2180

"Crystal (Ce:La.ES) spectrum, refs 1 and 50. bAqueoussolutionspectrum, ref 61. This work.parametrizations for ground-state (IN DO / 1) and spectroscopic(IN DO /S) investigations. The ground-state version for lanthanidecompou ndsg s characterized by a basis set obtained from rela-tivistic Dirak-Fock'O atom ic calculatio ns, by the inclu sion of allone-center two-electron integrals, and by a parameter set basedon molecular geometry. In the spectroscopic variant on e-centertwo-electron integrals, y =P ( p ) re chosen according to thePariser approximation,ld'4 ~ ( p w ) (IP), - EA), (IP=ioni-zation potential, EA =electron affinity). Th e two-center two-electron integrals are calculated from Slater-Condon integralsPbp)using the Mataga-Nishimoto appr~ xim ation." -'~By thisprocedure new va lues are derived for the in tegrals ~ ( s s ) ,( dd ) ,and P (ff ) from the atomic spectra of the lanthanide elements!Integra ls not accessible via results from atomic spectroscopy, suchas P(sd ) , P(sf),nd P (d f) , are determined by fitting experi-mental data of atoms and molecules (LnO).4 Numerical Di-rac-Fock calculations on neutral lanthanide atoms and mono-cations in t he configurations 4fN-'6s26p, 4fN-'6s25d, and 4fN6s2were performed on those rare-earth elements where the corre-sponding experimental data a re not a~ ai la b le .~ ll other Sla-t e e o n d o n F and G integrals as well asR ntegrals are calculatedas described previously? The values of the various empirical andsemiempirical parameters defining the INDOIS method forlanthanides have been presented elsewhere! There, the generalizedrestricted open-shell Fock operator,15 which is used in the presentSC F calculations, is also described in detail.The spin-orbit interaction is treated in the spirit of the IND Oapproxim ation; i.e. it is limited to its major con tribution from theone-center terms.' In this way, it is possible to calculate theangu lar p art of the *ma_rix eleF ents involving the a ngu lar mo-mentum operators l,, l,,, and l, in the basis of real sphericalharmonics analytically. T he radial integrals tA(nr)are taken fromatomic spectroscopy in keeping with the IND O a p p r ~ a c h .~The Rumer C I method is based on spin-paired N-electron wavefunctions. Th e calculation of matrix elements between suchbonded functio ns is desc ribed elsewhere!Si6 Ins tead of the sym-metric orthonormalization of Rumer functions, we prefer the

0022-3654/92/2096-7288$03.00/0 1992 American Chemical Society


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Electronic Structure of Hydrated Cerium(II1) The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 72891000

wTABLE [I: ROHF C d - S t a t e Wave Fuactiorr for [ C e ( H P ) pwith a Ce-0 Bond Distance of 2.3 A (Orbitd Ewrnka ev)

x rUI 1.:- - - -,.0 30 35 40 45 50Energy [ l o 3 cm-11

Figure 1. Comparison of the experimental absorption spectrum of Ce -(111) aquo complexes in crystalline environment (-*)I and in solution(--)3 with the calculated INDO/S-CI spectrum of [C C (H ~ O )~ ]~ +-).Schmid t procedure since it yields the branchin g diagram func-tions" and renders a back-transformation ~n ne ce ss ar y. ~urtherdetails of the fo rmalism have been discussed previously, e.g. theevaluation of spin-dependent matr ix elements16and their imple-mentatio n as well as efficient algorithm s for the calcu lation oftransition moments and Mulliken populations that account forthe complex-valued CI wave functions.'Results and DiscussionC P - H 2 0 Boding. The nature of the interaction between themetal ion Ce3+ nd surrounding water molecules is explained mosteasily by using the example of the hypothetic monohydrate[Ce(H20)l3+. The ROHF ground-state wave function in C,symmetry is listed in Table 11. Similar to other lanthanidecompounds, e.g. the monoxides: the elect ron occupying thecompact 4f orbitals is found not to contribute to the bonding. Thecorresponding molecular orbitals consist of almos t pure atom icorbitals. This is also reflected by the sum of the Mulliken pop-ulations over all M Os with pre domin ant 4f co ntribution whichamo unts to 1.01 electrons. The refor e the bonding is determinedby electron donation from the ligand to the metal.Among all orbitals of H 2 0 he u type lone pair 2al has thelargest overlap with the m etal orbita ls 6s, 6p,, and 5d9. The secondlone pair 1b2 and the H -O bonding orbital 1bl overlap with theSd, o rbitals (Sd,,, 5dyz). The interacti on of the H -O bondingorbital is somewhat sm aller because the orbital lobes point awayfrom the cerium ion. The corresponding bonding molecular or-bitals 2al, 1b2, and lb l contain mainly contributions from theligand (compare Table 11). Th e net effect of the interactionbetween Ce3+ nd H 2 0 s a charge donation mostly into the ceriumorbitals 5d9 (u), 5dx,, and 5d, (r) hich is about 75% of th e totalelectron donation.So far the molecule [Ce(H20)l3+was assumed to be planar(in the x z plane). But methods exploring the struc ture of theh ydrated ion in ~ o l u t i o n ~ ~ ~ ' ~s well as in crystals' show that theH-O-H plane is tilted against the Ln3+-0 axis. In our modelcomplex such a structural change is accompanied by a slightincrease in energy. For example, a distorsion to an angle of 20increases the total energy by about 0.01 5 eV (1.4 kJ/m ol). Thi sresult is very similar to findings in ab initio calculations on aquocomplexes of transition metal cations.36 Judging from the IND Ocalculations the experimen tally observed distorsions ar e not ofelectronic origin but probably du e to the interaction with sur-rounding molecules. This explana tion is corroborated by recen tinvestigations on NiC12 where the tilt angle was found to beconcentratio n dependent.20 I t inc reases from 0 (f20) o 42'(So)or concen tratio ns of 0.086-1.46 m .Shucture of Modd Complexes. The coordination of lanthanidetrivalent cations n aqueous solution isone of the most controversialproblems of lan thanide chemistry, and despite many valiant effortsthe value for n in [Ln(H 2O) J+ will probably continue to be amatter for debate for some th11e.3~9~~t therefore seemsworthwhileto review the existing structural information on the solvation shellof trivalent lanthanide ions. Before discussing the structu re of

~ ~energy M@ occb composition of wave function'-61.09-38.25-36.22-34.16-36.1 1-36.05-36.01-35.96-28.93-28.24-28.05-27.20-23.60 7al

2 91% H 2 0 (l al ), 4% Ce (6p,)2 95% H,O ( lb i )222/7 100% Ce (4f&2/ 7 100% Ce (4fd)2/ 7 100% Ce (4fJ99% Ce (4fJ100% Ce (5d 396% Ce (Sd,,), 3% H 2 0 1 b,)94% Ce (Sd,,), 6% H 2 0 (Ib2)87% Ce (5d.), 1 1% Ce (6p,),

81% Ce (6s), 10%Ce (6p,),

88% H i 0 (2a;), 7% Ce (5d9)94% H2 0 ( lb2 ), 6% Ce (Sd,,)

5% H 2 0 2a1)5% Ce (5dJ-19.95 5b2 99% Ce (6py)-19 .92 5b1 98% Ce (6p,)66% Ce (6p,), 20% H 2 0 (3al),

-11.73 9al 77% H 2 0 3al), 16% Ce (6p,)-18.25 8al 3% Ce ( 6s)-11.45 6bl 98%H20 2bl)

*Mo lecula r orbitals. The labeling of the irreducible representations(C, symmetry) starts with the valence orbitals. bo wu pa tio n number.In the ROHF procedure the 4f shell is formally occupied with oneelectron. 'The composition of the wave function is listed in terms ofthe atomic orbitals of cerium and the molecular orbitals of H 2 0(Cb).Only contributions larger than 3% are shown.the hy dration complexes of Ce3 + ha t were included in the elec-tronic stru cture investigations, we willgive an overview of availableexperime ntal data. Struc tural inform ation in solution has beencollectedby a variety of methods, such asX-ray diffraction,21zm 2n eu tro n d i f f r a c t i ~ n , ' ~ . ~ ~nd extended X-ray absorption finestructure (EX AFS)?6 Table I11 shows structural param eters ofvarious lanthan ide hydrated trivalent cations determined by thesemethods. From this table one gains the impression that the valuedetermined for the coordination number does not depend so muchon the conce ntration or the co unterion but on the different ex-perimental methods.Wertz and ~ ~ - w o r k e r s ~ ~ * ~ ~ , ~ 'sed the assumption of Breen etal.39 that with increasing concen tration (1-3.5 m ) water isgradually substituted by chloride. They obtained a coordinationnumber of eight for La3+,Nd3+,and Gd3 +. In general, however,the association of lantha nide hyd rates with inorg anic anions isweak.4w2 Chloride anions may enter into the inner coordinationsphere at high concentrations, e.g. above 10N HC1.23*25*27.31neof the main hypotheses is due to S pedding and co-workers whointerpreted the nonregular change in aquo ion partial molarvolumes as evidence for a d ecrease of th e coord ination numberalong the lanthanide series.38,4345These conclusions were con-firm ed by X -ray investigations on LnC13 s o l ~ t i o n s ~ ~ ~ ~ ~ *nd byneu tron d iffraction on N dC13 and DyC13 solutions.l8qZ8Recentneutron diffraction" and EX AFS studies26 onfirm a decreaseof the coordination number along the series. Using a theoreticalelectrostatic m odel, M iyakaw a et a1.2 calculated the differenceof the hydration free energies at room temperature between[Ln(H20)9]3+ nd [Ln(H20)8]3+.Their results also support thehypothesis of a decreasing coordination number from nine to eightwith a transition region ranging from Pm3+ o Gd3+.2Molecu lar dynamics investigations on LaC13 have shown aconcentration-dependent hydration nu mber for the La3+ ion,decreasing from 12 at infinite dilution to 10.2 a t 2 m concen-tration.46 In this study all interactions were assumed to be pairwiseaddi tive with the exception of the water-water poten tial which,in addition, contained intramolecular three-body contributionsin the form of bending and stretch-tretch coupling terms.46 Theresulting coordination number is unexpectedly high compared tothe results from the diffraction methods. According to the prcacntINDO , results these findings may be due to th e absence of an0 - L a 4 bending potentia l. INDO/ 1 model investigations on[Ce( H2 0)2] 3+ nd (H 20 )2 or angles between 60' and 180'


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Kotzian and R W h290 The Journal of Physical Chemistry, Vol. 96, No. 18, 1992

La)+

Pr'+Nd3+

Sm3+

Eu3+Gd"

Tb3+

Dy3+

Er3+

Tm3+Y 3+LU3+

2.0, 3.811.74, 2.10, 2.672.663.803.311.90.50, 0.85, 1.732.851.433.233.613.231.430.85, 2.663.49

3.292.381 o3.540.95, 1.37, 3.051.333.630.313.61

9.138.0 *0.38.0 0.28.0 *0.29.228.909.58.08.5 *0.29.98.88 *0.39.38.38.69.97.68. 0 *0.28.188 *0.37.57.931.4 *0.58.17.9 0.28.198 0.37.86.56.38.128 O87.977.7

2.582.58 0.0052.48 f .022.48 *0.022.542.512.512.412.482.422.4742.414 0.0052.452.4502.432.402.412.372.412.409 *0.0052.392.402.37 * 0.022.372.392.372.369 *0.0052.342.32.32.362.332.33 0.022.342.31

C1- (5.0)C I O i , SCO~*-c1- (4.7)Br- (4.8)c1- (4.97)C1- (4.89)CIO,c1- (4.9)c1-c1- (4.9)c1- (4.9)C104-, Se0:-C104-c1- (4.9)c10,-c1- (4.5)C 1 O iCI- (4.8)C1- (4.82)C104-, SCO,~-C104-C1- (4.85)CI-C104-c10;c1-, c1- (4.79)c10;, s c o 4 2 -c l o d -C1- (4.6)I- (5.2)c1- (4.79)C104-C1-, C1OiC1- (4.78)C104-

X R D (21)XR D (22)X R D (23, 24)X R D (25)X R D (21)X R D (21)E X A F S (26)X R D (27)N D (28)X R D (29)X R D (30)X R D (22)E X A F S (26)X R D (30)E X A F S (26)X R D (29)E X A F S (26)X R D (31)X R D (32)X R D (22)E X A F S (26)X R D (32)N D (18)E X A F S (26)ND(35)X R D (32)X R D (22)E X A F S (26)X R D (34)X R D (34)X R D (32)E X A F S (26)N D (35)X R D (32)E X A F S (26)

'Concentration of the solution (molal). bCoordina tion num ber. 'Distance of the oxygen atom to the central ion (angstroms). "Counterion an dits distance (angstroms) to the central ion. rMethods: XR D, X-ray diffraction; ND , neutron diffraction; EXA FS, extended X-ray adsorption finestructure.

1 - -

5Figure 2. Structures of lanthanide hydrates: tricappcd trigonal prism(l),dodecahedron ( t ) ,quare antiprism (3), cube (4), and bicappedtrigonal prism (5).suppo rt this hypothesis. Assuming a perfect icosahedral coor-dination shell, the *La43 angle is calculated to 63" ( L a 4distance: 261 A). In the case o f [ C C ( H ~ O ) ~ J ~ +he total energyat 63 O ligabout 1 eV above the minimum energy at 1200,whereasfor (H20)2 angle opening with respect to a fictitious center) anincrease in energy less than 0.1 eV is calculated.In the solid state all trivalent lanthanide ions can exist astricapped trigonal prismatic enneahydrates (see 1 in Figure 2)in the presence of trichlorosulfonate, ethyl sulfate, and b romate(tabulated in refs 37 and 38). Thedimmesto the capping waters(equatorial (eq.)) are longer than thosc to the prismatic (pr.)ligands, and both have the tendency to decrease with increasingatomic nu mber, a8 expected on the bnsisof the lanthanide con-traction. Th e increasing ratio d(L&;e4.)/d(Ln+,prr.) has beeninterpreted that trivalent lanthanide ions tend toward a lowercoordinrtionnumber with decreasing ionic radius." Hexahydratedampounds were obsesved for La", W+,ndE P n the prcacnceof perchlorate where the regular octahedral [Ln (H z0 )J3 + can

be Octah ydratcd chloride crystals only form in thepresence of a crown ether in low water content solvent mixtures.'8The preferential structures are the dodecahedron, the squ areantiprism, and the bicapped trigonal prism.According to th e exp erimenta l findings discussed above, tri-valent lan thanide ions are normally 8-fold or 9-fold coordinated.The structu re of an enneah ydrated complex is undoubtedly tha tof a tricapped trigonal prism 1 as depicted in Figure 2. Ourcalculation s are therefo re based on a model complex of the de-scribed geometry with C t o ond distan ces of 2.53 and 2.62 Afor the six prismatic and three equa torial (capping ) ligands, re-spectively. The angles between the molecular planes of the wa termolecules and the 3-fold molecular axis are chosen to 35" and90 for the prism atic and equatorial ligands, respectively. Thisimplies that all atoms of the th ree equa torial ligands lie in oneplane. Both angles are derived from IND O /l calculations. Allother structures used for the calculations are specified wheredeviations are made.In the case of a coordination number of eight, a dodecahed ronand a quadra tic antiprism are the dominant structures observed."We therefore considered the following four structures for thesolvation shell: a dodecahed ron 2 ( D u ) ,a quadratic antiprism3 (DU),cube 4 and a bicapped trigonal prism 5 (C,J.The structma arc sketched in Figure 2. The point group s@iedin paren theses reflect the highest possible symmetry when theplanes of the water ligand s are arrang ed appropriately . On th ebasis of INDO/ 1 calculatio ns which were performed to find theequilibrium distances of the four octahydrated structures, theCto istance was chosen to 2.53 A. The angles between thez xis and the vertical and equato rial ligands are 37" and 1 o" ,respectively. The Ce-0 distances for model complex 3 are 2.56A; the angles to the coordinate axes are kept at 45". For structure4 a Ce-0 bond distance of 2.57 A was used. I n the case of


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Electronic Structure of Hydrated Cerium(II1)a)

00--5

g=-A

L5 40-

xz2 , yz2l&YZ ; , , 4 f , e z(x2( x2 - y q ,y2 ) zxy

xy, x2 - y2 23

- -- --50.- - == - -8

8 -

I -- - -- ,

- 8 - - - -- -

Figure 3. Schematic representation of the splittings of the 5d and the4f shell of Ce3+due to the interaction with the aquo ligands: (a) tri-capped trigonal prismatic coordination1 (DU ymmetry); (b) structures2-4.complex 5 the structural param eters of 1were used and only oneequatorial ligand was removed.Fdectronic St. The splittings of the 5d and the 4f shellsin the field of the nine aquo ligands (D31 ymm etry) is displayedschem atically n Figure 3a. The total splitting is 1.12 and 0.04eV for the Sd and the 4f orbitals, respectively. This differencereflects the compactness of the 4f shell which is influenced onlyto a small amoun t by the ligands. The splittings sketched in Figure3 reflect the field of the real ligan ds ( u and T interaction) andnot that of point charges like in a L F approach. The d g orbital(al) shows only a little interaction with the ligands whereas theorbitals d,, and dyz (e) pointin g toward the prism atic ligand sare repelled strongest. The energy orderin g of the 4f orbitals inthe enneahydrated complex is fH3+ < i < r(xlyt. fay < d+3y3


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7292 The Journal of Physical Chemistry, Vol. 96 , No. 18, 1992 Kotzian and Rbsch

I "lr 2st1LS+lL 2StlL@+%C$+%Ce,,ECeaq+EC$+

Figure 5. Electronicstates of the trivalent cerium atom and the hydratedmodel complex [CC (H ~O )~ ]~ +Dj h ymmetry) with and without spin-orbit interaction.energy differences between the Er (Im/I=2) and the E" (Imrl=1) states are 7/ 4 and 3/ 4 of the atomic spin-orbit constant, re-spectively. T he 4f states, on the othe r hand, provide an examplefor the other limiting situation where a large spin-orbit interactiondominates Over L F effects. Th is may be seen clearly by the smallL F splitting of the states 'F5/2 and 2F72. All relativistic statesare Krame rs doublets. In Figure S he iabeling of the relativisticstates is done according to th e n omen clature of double groups.52Comparing the calculated results with the experimental stateenergies, one finds the s pin-orbit splitting of t he spatially 2-foldE states underestimated. The spin-orbit coupling constant P ( 5 d )of 990 cm-' used for the calculatio n comp ares well with theexperimental value for Ce(IV) of 996 ~ m - l . ~ ~herefore, it is likelytha t a geo metrical distorsion away from the highly symm etricstructure causes an additional splitting. For this reason weperformed several model investigations where structural aspectsof the tricapped trigonal prism were varied, guided by informationon lanth anide solvation shells in the solid state.From X -ray investigations of several lanthanide salts a diskmionis h w n hat has not beenconsidered in the precedingcalculations.This is a rotation of the three equ atorial water ligands about the3-fold axis relative to the prism.47,53-56 his rotation entails asymmetry reduction from D3* o C3*. rotation by about 5 doesnot affect the band energies by more than abo ut 100 cm-'. Nosplitting of the degenerate E states w u r s in the nonrelativisticcase since the 3-fold rotation axis remains unaffected by thisstructure variation. Also the tilting of the H 2 0planes, mentionedpreviously, entails only a slight shift of t he excitations to higherenergies by about 100 cm-I. Furtherm ore, we varied the anglebetween the prismatic ligands and the main axis. With its re-duction the interaction of th e prism atic ligands with the orbitalsSd, and S d + z er ) decreases, too. This results in a smallerrepulsion and, therefore, a reduction of th e corresponding one-electron energy. Ultimately, one notes a lowering of the ZE' tateenergy. By varying this angle the second and third band (E3/2,E5/2)of the relativistic spectrum can be shifted. A qualitativelysimilar result may be achieved by varying the ratio of the equa-torial to th e prismatic bond distances. A s horter equatorial bondcauses a stronger repulsion of the e' orbitals and thu s a higher2Er-state energy. Similarly , the energy of the *Er r tate can beinfluenced by the d istance of the prismatic ligands.The geometry changes discussed above have no strong influenceon the degeneracy of the E states because they do not affect the3-fold axis of the polyhedron set up by the oxygen states. A largersplitting can only be obtained if the positions of the oxygen atoms

are varied such that this 3-fold symmetry is broken. This ca n beachieved by enlongating the bond distance to one equatorial ligand(dissociation pathway), but this does not in crease the splittingsignificantly. Another possible distorsion is the symm etric tiltingof the triangles which form the top and th e bottom of the prism.Suc h a tilted prismatic coordination is found in the solid sta te forthe sulfato complexes [Nd2(S04)3(H20)4]-H20nd [Sm(S-04 ) 2 ( H z 0) 3 ] N H 4- H 20ith two and th ree water molecules in theinner shell, res pe cti ~e ly .~~n these solid-state systems one mightargu e that th e observed structure is a consequence of the differentinteraction of sulfato and water oxygen atoms with the metal.However, in the case of the cerium doped lanthanum ethyl sulfateenneah ydrate crystals, such a distorsion could be caused by thedifferent Ln -O eq uilibrium bond distances of La an d Ce.On the basis of a structure with a 4' tilting (angle between thetop or botto m norma l and the 3-fold axis), the energies of theSd-derived excited states were calcula ted (see Table 1). In thisCI procedure, all possible metal configu rations were taken intoaccount. The calculated energies approx imate he experimentalspectra very well, except for a uniform upward sh ift by less thanloo0 cm-I. The energy difference between the second and thirdstates is strongly influenced by the tilting angle. This splittingis too large compared to the value found in the crystal, bu t toosmallcompared to the value of the solution. Such a tilted structuremay be interpreted a s an intermediate between tricapped trigonalprism and monocapped square antiprismas' Apart from fluctu-ations, the average structure in solution seems o exhibit a similarg e o m e t r ~ . ~We refrained from applying further geometricalchanges and distorsions that m ight have led to better agree mentwith the exprimental spectra. In the case of the solution spectrum,an obvious extension of the present study would be to use moleculardynamics simulations to generate an ensemble of complexes withdiffering geom etry. The calculate d transition energies and os-cillator strengths would then be used to obtain a representationof the solution spectrum by a sui table averaging procedure.58 Ofcourse, this approach depends critically on an accu rate modelingof the stru cture of the h ydrated ion, i.e. on the availability of asuitable forc e field.Figure 1 shows a representation of the calculated spectrum usinga common Gau ssian broadening by 900 ~ m - ' . '~ l l excitationsfrom the *Fs,,-derived m olecular stat es are taken into accountand Boltzmann weighted corresponding to room temperature.Agreement between calculated and experim ental spectra is verysatisfactory which demonstrates that the calculated transitionmoments are also in good agreement with experiment.In solution an add itional band at an energy of 34 000 cm-' isobserved (see Figure 1). According to the IND O/S-C I resultspresented in Fig ure 4, the o ctacoordin ated species are th e likelycandid ates for causing this band. On the basis of IND O/ 1ground-state calculations for the fo ur octah ydrated cerium com-plexes ( C e O distance of 2.56 A), the cub ic structure is excludedbecause t lies highest in energy. Also, it has not yet been observedexperimentally. Of the three remain ing structures, the dodeca-hedron 2 is energetically favored. It is known from experiment3that with increasin g temperatu re the intensities of the first andsecond band decrease. This rules out structure 3 since it exhibitsexcited states with s ignificant transition probability in this energyregion. The two remain ing complexes 2 (dodecahedron) and 5(bicapped trigonalprism)exhibit the lowest transitions at energiesof 35 640 and 36 120 cm-', respectively. According to the rea-soning presented here, both these structu res have to be associatedwith the extra low-energy band found in the solution spectrumof hydrated Ce3+.Conclusions

The structure of th e lan thanum enneahydrated complexes hasbeen determined by diffraction methods to be a tricapped trigonalprism in crystals. In solution a continuou s decrease of the co-ordination number from an average of about nine to abo ut eighthas been postulated along the lanthan ide series. In this paper wehave focused on the cerium hy drated complex to eluc idate thestruc ture of the coord ination shell. In this case the transitions


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Electronic Structure of Hydrated Cerium(II1)to the excited 5d states lie in th e experimentally accessible energyregion below 50000 cm-l. Th e Ce 5d orbitals interact muchstronger with the w ater ligands due to their g reater radial extensioncompared to the 4f shell. Therefore, the resulting excited statesare ideal candidates for studying the coordination geometry.The model complex [Ce(H20)I3 served as a start for thedescription of the metal ligand interaction. There, the bond isformed through a dative interaction from the H 2 0 u (2al) andr (19) one pairs and to a lower extent of the H- 0 bonding orbital1b l. Th e only valence electron of th e formally trivalent ceriumion does not participate in th e bonding due to the compactnessof the 4f shell. Th e IN DO /S- CI calculations were based onvarious structures known for lan thanid e coordination compounds:for a coordination number of nine on the tricapp ed trigonal prismand for a coordination num ber of eight on the dodecahed ron, thequadratic antiprism, the cube, and the bicapped trigonal prism.The calculations showed that the five main bands observed ex-perimentally cannot be explained on the basis of the octa-coordinated model complexes. This result confirms previousassumptions and interpretation^.',^ But according to our calcu-lations, a distorsion of the tricapped trigonal prismatic structurehas to be invoked in order to reproduce the splitting patte rn ofthe spectrum. Th e additional band observed in the solutionspectrum has been attribute d to a dissociative product of theenneahyd rated complex in ag reement with earlier assumptions?.60This could be either a fully dissociated and relaxed complex ofthe dodecahed ral structure or a d issociative complex of the bi-capped trigonal prismatic struc ture with a loose contact of theninth ligand.Th e present calculations have shown that for lanthanide com-plexes an accu rate description of the spectra is now av ailable onan MO-based IND O-C I approach.4d In contrast to previousinvestigations on the basis of the L F theory, we presented a unifiedapproach to the cerium hydrated compounds with different co-ordination numbers. In addition, an accurate calculation of thetransition energies including spin -orbit in teraction and of transitionprobabilities is possible. With this formalism at hand, moredetailed theoretical investigations of solution spectra should befeasible in combination with m olecular dynamics simulations (thelatter including a 0-L n- O bending potential). In this way, apreferred coordination and/or an ensemble average over variouscoordination structures could be generated for which CI calcu-lations are to be performed in order to simulate the solutionspectrum.

Acknowledgment. We thank Prof. S. P.Sinha for helpfuldiscussions during his visit in Garching. This work has beensupported by the Deutsche Forschungsgemeinschaft, by the Fondsder Chemischen Industrie, and by the Bund der Freunde der TUMiinchen.References and Notes

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Kotzian, M. and Roesch, N., (1992) Electronic Structure of Hydrated Cerium(III)