Molecular orbital studies of the electronic structure of lanthanide and actinide complexes—III chemical bonding and satellite structure in the X-ray photoelectron spectrum of uranium dioxide

L inort,, nucl ('hem Vol 41, pp. 693~699 Pergarnor~ Press l i d . 1979 Printed in Great Britain

MOLECULAR ORBITAL STUDIES OF THE ELECTRONIC STRUCTURE OF LANTHANIDE AND ACTINIDE COMPLEXES--Ill CHEMICAL BONDING AND SATELLITE S T R U C T U R E IN T H E X-RAY P H O T O E L E C T R O N SPECTRUM OF URANIUM DIOXIDE JACQUES WEBER and VLADIMIR A. GUBANOVt Department of Chemistry, University of Geneva, 30 quai Ernest-Ansermet, 1211 Geneva 4, Switzerland

(Received 19 June 1978; receivedfor publication 8 August 1978) Abstract--Using the multiple scattering Xa method, molecular orbital calculations of the electronic structure of UP= are performed by considering a cubic (UOsf z- cluster. It is shown that the typical features of the uranium 5/" shell in such complexes are well reproduced in the calculations.The greater part of the chemical bonding in UP2 is predicted to be due to covalent interactions between US./and O2p electrons. Then, a separate SCF calculation is performed for the 4/ ionized configuration of the cluster in an attempt to understand the satellite structure observed as accompanyingthe 4/photoelectron signals. The calculations suggest that the satellites originate from an interatomic shake-up process involvingthe predominantlyO2p and U5f molecular orbitals. INTRODUCTION clusters and heavy metal compounds[7,8, 14-17]. The As the most common actinide compounds, uranium choice of this model in a molecular cluster calculation of oxides and fluorides have been extensively studied in UP2 is further justified by the very good agreement recent years by both experimental[I-6] and existing between augmented-plane-wave (APW) band theoretical[7-11] techniques in an attempt to understand structure[18] and MS Xa molecular results[19] obtained their chemical bonding and electronic properties. There for the compounds VO and VN. is no doubt that the physico-chemical properties of Uranium dioxide crystallizes in the fluorite structure these compounds are connected to a large extent with with eighffold metal-ligand coordination; therefore we the behavior of their 5f electrons, and this explains the consider a cubic cluster (UPs) '2- representative of the current interest in theoretical models allowing an solid. In the first part of this work, the ground state adequate description of valence and 5f electron bands. electronic structure of the cluster is calculated and the It has recently been shown [11] that a molecular cluster 'bonding properties are discussed. Then, using the same approach, based either on the spin unrestricted Hartree- technique as in part II of this series[16], an attempt is Fock-Siater or the relativistic Dirac-Slater model, can be made to explain the satellite structure observed reasonably used for the determination of the electronic recently[5] as" accompanying the U4f photoelectron structure of ThO2 and UP2. This conclusion is a bit spectrum: a new calculation is performed on a "hole surprising since it was generally thought that band struc- state" of the cluster corresponding to the U4f n3 ture calculations would be required for such compounds configuration (i.e. the ground state of the 4f-ionized due to the partly itinerant nature of their 5f cluster). In both calculations, an electronic propulation electrons[12]. Furthermore, an analysis of the results of analysis is made which allows us to estimate the relaxRef. [I1] reveals a large similarity between relativistic ation charge transfer occuring during ionization and and non-relativistic results as far as valence and low- finally to suggest an explanation for the origin of satellite lying unoccuppied molecular orbitals (MO) are concern- structure. ed. In view of these interesting results, we found it worthwhile to undertake a thorough study of bonding CALCULATION PARAMETERS properties and satellite structure in the X-ray photoelecThe (UPs)~2- cluster is assumed to be cubic with a bond length tron spectrum (XPS) of uranium dioxide using another du-o = 2.37/~ taken from the UP2 lattice constant[20]. The SCF version of the non-relativistic Hartree-Fock-Slater MS Xa model used in the present calculations has been model. In contrast with the non-self-consistent field dis- described in detail elsewhere[13,21,22] and it does not need crete variational Xa (non-SCF DV Xa) method used in further development here. However, some computational details Ref. [11], we use here the SCF version of the multiple as well as the choice of the calculation parameters deserve some scattering Xa (MS Xa) method [13]. Even though this comments. The values of atomic coordinates and MS Xa parameters are technique rests on the rather crude approximation of a presented in Table 1. The value of the a exchange parameter ,of "muffin-tin" potential, it has recently been shown to lead uranium is 2/3, corresponding to the theoretical heavy atom to an electronic structure and related properties in good limit[23], whereas the a appropriate for oxygen is taken from the agreement with experiment for many types of large calculations of Schwarz[24]. A weighted average of the atomic values is chosen for the a value in the interatomic (intersphere) ?Permanent address: Institute of Chemistry, Ural Science and extramolecular (outer sphere) regions. Concerningthe choice Center, Academy of Sciences, Sverdlosk GSP-169, U.S.S.R. of the radii of muffin-tinspheres, it has recently been found in tINC Vol 41, No. 5--F

693

694

JACQUES WEBER and VLADIMIR A. ,GUBANOV Table 1. Atomiccoordinates and MS Xa parameters for the cluster ( U O s ) 12- (atomicunits) a exchange parameter

sphere radlus

0.0

0.66667

2.9067

2.5858

0.74447

1.5720

2.5858

2.5858

0.74447

1.5720

-2.5858

-2.5858

2.5858

0.74447

1.5720

0(4)

2.5858

-2.5858

2.5858

0.74447

1.5720

0(5)

2.5858

2.5858

-2.5858

0.74447

1.5720

0(6)

-2.5858

2.5858

-2.5858

0.74447

1.5720

0(7)

-2.5858

-2.5858

-2.5858

0.74447

1.5720

0(8)

2.5858

-2.5858

-2.5858

0.74447

1.5720

Outer sphere

0.0

0.73583

6.0507

x

y

z

U

0.0

0.0

0(1)

2.5858

2.5858

0(2)

-2.5858

0(3)

I n t e r sphere

0.0

0.0

0.73583

this laboratory[25,26] that the use of overlappingspheres is not virtual 6tt. level in the same energy range. Indeed the adequate for clusters bearing an important negative charge since 5h. and 6t~. MO's share the 5f character as is shown by it leads to an electronic structure with the highest occupied the 87% total f contributions of these orbitals compared electronic levels located much too close to the continuum. with 94% for 2h.. Therefore the present calculations have been performed with An important question arises then: does the mixing non-overlapping ("touching") atomic spheres whose radii have between 5h. and 6tt. really mean that the 5f and 7p been determined according to the procedure described by Norman[27]: from the initial molecular charge distribution,con- orbitals are strongly hybridized in UO27 Or is that an structed by superposing atomic charge densities obtained for artifact of the calculations, as already observed in MS neutral atoms, the radii of atomic spheres containingthe atomic Xa calculations performed on clusters bearing an imnumber of electrons are determined. The ratio of these sphere portant negative charge[16, 2617 Even though one might radii is calculated,and the absolute values of the atomic radii are argue that hybridization is absent in 2t2. because metal calculated by dividing the bond length in this ratio. The outer s, p and d orbitals do not span this irreducible represensphere is chosen to be externally tangent. The stabilizingelec- tation, we think that the charge distribution associated trostatic fieldof the crystallineenvironmentis taken into account with this orbital is more reasonable and the second by use of a Watson sphere of the same radius as the outer sphere alternative should thus be retained. Indeed, there is little and bearing a charge of +12. Partial waves up to 1= 3 are included in the multiplescattering expansions in uranium sphere doubt that MS Xa boundary conditions are not entirely and extramolecularregion, and up to 1= I in oxygen sphere. The satisfactory for such clusters and the use of a highly frozen core approximationis not used: inner shell electrons are charged Watson sphere can induce spurious effects in the allowed to adjust their one-electron energies during the SCF •energy and nature of virtual levels. Furthermore, interprocedure, but they are constrained to conserve their atomic pretations of photoelectron data suggest that the 5f eleccharacter and to be entirely localized within the atomic spheres trons in UO2 are quite localized[l, 2, 5]. In Oh symmetry, ("thawed" core approximation).As spin-polarizationeffects are the 5f MO's belong to the A2., T~. and T2. irreducible not of primary importance in the chemical bonding of the representations. However, the present calculations were complex, all the calculations have been performed using the unable to give the exact position in the energy scale of non-spin-polarized version of the non-relativistic MS Xa the virtual 3a2. MO of this type due to its too high computer programs. energy, which probably locates it in the continuum. Nevertheless, it is interesting to point out that the orderRESULTS AND DISCUSSION ing obtained for the 5f orbitals in the present calculation: tt. ~ t2. ~ a2. is identical to that one deduced from (1) Ground state electronic structure The ground state electronic structure of the (UOs) *2- ligand field theory[28], contrarily to the DV Xa prediccluster is presented in Table 2. The 5h. orbital is the tion h . '~ a2. < h . [11]. Below these 5f levels, one finds the I3-O bonding band highest occupied MO (2 electrons) and it is practically degenerate with the unoccupied MO 2t2.. Examination which is built essentially from 02/, and some admixture of the charge distribution of these orbitals is interesting of U0d and 7s orbitals. Examination of Table 2 shows since it simultaneously reveals their degree of localiza- that the range of this bonding band extends from tion and their amount of hybridization with 6d, 7s and 7p les(-0.429Ry) to le.(-0.234Ry), i.e. the band width is orbitals, two questions of primary importance in the predicted to-be 2.7eV, in fak agreement with the discussion of the physical and chemical properties of experimental value of 1.8 eV[4]. Furthermore, the energy difference between the top of the bonding band and the uranium dioxide [1-5]. Both 5ft. and 2h. orbitals are essentially of metal 5f 5f level 5h. is calculated at 2.5eV, which compares type with very little oxygen contributions. However, quite well with the experimental estimates 3.3 eV[4] and there is a marked difference between them: whereas 2tz. 3.5 eV[1]. R is interesting to remark that in this respect is almost enitrely localized within the uranium sphere, the MS Xa and DV Xa models are in good agreement, 5tt. shows an important delocalization in the ex- since the corresponding DV Xa values for the U-O band tramolecular region. This is due to a strong mixing be- width and the USf-O2p energy difference are 2.0 and tween 5h. and a Rydberg orbital of T~. symmetry, 2.3 eV. A detailed examination of the charge distribution probably the U7p, as emphasized by the presence of the of the MO's belonging to the bonding band shows that

Electronic structure of lanthanide and actinide complexes--IlI

695

Table 2. Groundstate valence energylevels (Rydbergs)and charge distribution of (UOE)~z-t Charge distribution

(per cent)

~U Orbital

Energy

"~

p

0 ~

~

~'~

Inter sph . . . .

Outer phere

42

6tlu

-0,022

34

16

8

2t2u

-0,0537

94

2

2

2

5flu

-O.O538

53

i

3

42

73

27

le u

-0.234

4flu

-0.241

Itlg

-0.258

3t2g

-0.287

2a2u

-0.303

3alg

-0.312

3flu

-0.330

2t2g

-0.366

it2u

-0.377

le

-0.429

g 2flu

17

3 19 5 3 6 4 3

-0.976

la2u

-1.334

it2g

-1.355

2alg

-1.360

itlu

-1.410

lalg

-2.018

1

76

12

63

21

13

58

12

II

61

25

9

54

33

10

59

34

1

56

32

8

48

40

9

6

7

i

i

82

14

3

80

17

2

75

19

2

69

iS

2

3

4

4

The hlg~lest occupied level is 5flu which aceomodates distribution

32

9

i

93

15

68

I

4 7

56

2 electrons.

The oxygen charge

refers to ~he charge contained in all the ligand spheres. The analysis

of charge distribution inside atomic spheres is made according to angular momentum contrlb~tions

to the total charge inside these spheres.

the major part of U-O bonding arises through the appreciable 5f contributions present in the 4t~, (17%) and 2a2, (19%) orbitals. On the other hand, participation of U6d and U7s in the bonding band is rather small: U6d contributes 3% in 3t2g, 6% in 2t2g and 3% in le~, whereas U7s contributes 5% in 3amg. Finally, one notices that there is no admixture of U7p in the bonding band. Examination of Fig. 1, which displays the contour levels of the 4tj.MO, shows the importance of the ~r(U-O) bonding. Indeed the covalent interactions between U5f and O2p electrons among the 4t,, and 2a~ MO's are the principal source of chemical bonding in the cluster. Thus, in addition to their important role in many physical properties of UO2 (magnetism, electrical conductivity, color)f1], which is due to the presence of their localized states near the Fermi energy of the solid, the 5f electrons of this compound are also responsible for most of the covalent metal-ligand interaction because, as shown by Veal and Lain [2] and the present calculations, part of the 5/electrons is transferred into the U-O bonding band. As expected, the low-lying valence levels of (UO~)~2- have respectively the following characters: metal 6p (2t,~), ligand 2s(lt,., 2a~g, l/2g, la2.) and metal 6s (la,s). It is seen in Table 2 that the crystal field splitting of the O2s band is rather large (1 eV), in agreement with the broad signal observed in the corresponding photoelectron spectrum[l]. Finally, the calculated energy difference between the centers of the U-O and O2s bands is 14.2eV, which compares well with the value of 16 eV deduced from their spectrum by Veal and Lam [ I]. As we have previously performed a similar calculation for the (La(III)O4)~- cluster[16], a comparison between

the main features of results obtained for lanthanum and uranium oxides is interesting as it reveals the most important differences between lanthanides and actinides. As expected, the participation of the f-band in metaliigand bonding band is different in the two complexes. In (LaO,)5-, the 4/participation in the La-O band is 9% at the most and generally of the order of 2 to 3% (Table 4 of Ref. [16]). ,In (UOs) ~2-, the present results indicate that the largest 5/ character of the bonding orbitais is about 20%, which emphasizes again the well-known fact that actinide compounds are more covalent than lanthanide ones because the spatial extent of the radial part of the 5f orbital is larger than that of the 4[. On the other hand, the localization of both 4/and 5/ MO's in their metal sphere is predicted to be approximately tl~e same: about 90% on average for (UOs) ~2- and 95% for (LaO4)5-. This result confirms the general assumption that 5f electrons in UO2 are only slightly less localized than 4/ electrons in La203; it is thus justified to treat them in the molecular cluster approach instead of the energy-band model. (2) Satellite structure accompanying the U4f photoelectron spectrum It has recently been reported by various authors[5,6, 29-31] that a satellite structure is obserw~d as accomanying the 4[ photoelectron signals of U(IV) compounds. Both 4fTt2 and 4f~12 signals exhibit these satellites which lie at higher energy (5--8eV) than the main peaks and which are generally attributed to an interatomic shake-up, an electron being transferred from the O2p band to some unoccupied or partly occupied level of uranium during 4/ionization. Indeed the detailed

696

JACQUES WEBER and VLADIMIR A. GUBANOV

...,-.

/' j.o i" t 3.-"" 4

/

,...•

:/,. !4..... 1"~.,~

i',,

2

:.,2"

t

\

•

i /"

I

•

...... 4'

{

"\

".

':::.~;-,.

%',.,

x,

,

:f -~

............

..."

Fig. 1. Wavefunctioncontours of the 4tt, MO plotted in a plane midwaybetween the xz and yz planes. Contour values of 0, 1, 2, 3 and 4 are equal to 0, 0.0025, 0.007, 0.025 and 0.07 (electrons/bohr3)1~. The total region plotted covers 10x 10bohrs2. analysis of their UO2 photoelectron data made by Pireaux et al. [5] and the MS Xa calculations performed on ThO2 (Sf° configuration) by Bancroft et al.[32,33] both conclude that this phenomenon originates from shake-up. Furthermore, the same interpretation has been confirmed recently by our MS Xa calculations in the analogous case of the satellites to 3d photoelectron signals of the first four lanthanides[16]. It was thus of interest to undertake similar calculations for UO2 (i.e. for the (UOs) 12- cluster) in an attempt to confirm this interpretation and to make suggestions as to the type of excitations involved in this interatomic shake-up. The necessary condition for an interatomic shake-up process to take place is an important deformation of the electronic density of the complex during 4f ionization. When we want to make conspicuous such as phenomenon from theoretical calculations, we have to perform, in addition to the ground state calculation, a new SCF calculation of the 4f ionized configuration. Then, by comparing charge distributions, it is possible to estimate the importance of electron reorganization during ionization. Table 3 presents the electronic structure of the (UOs) '2- cluster after 4f ionization, i.e. the "ground state" of the complex with configuration 4f135f 2. The highest occupied orbital is now 2t2~ which accomodates the two 5f electrons. It is seen that the nature of this MO is the same as in the un-ionized

cluster, whereas 5tlu is no longer mixed with the Rydberg UTp orbital due to the stabilization of all levels resulting from 4f ionization, which emphasizes our previous conclusion that the mixing effect predicted in the ground state was an artifact of the calculation. Because of this orbital stabilization effect, the MS X~z calculations of the 4f ionized cluster are able to predict the positions in energy of many more virtual orbitals: the 3a2,, MO is of 5f type, 4atg and 6hu are probably the U7s and U7p orbitals, whereas 2e~ and 4t~ correspond to U6d. It is a bit surprising that the last four orbitals have a charge distribution without any metal sphere contribution, but this may be ascribed to the large delocalization of these orbitals and the poor boundary conditions of the model. Nevertheless, these virtual orbital energies provide a useful information for the discussion of satellite positions. Another feature which emerges from a comparison between Tables 2 and 3 is that 4f ionization results in a large increase in 5f participation in the U-O bonding band: the 5f character of 4tl. is 28% in the 4f ionized cluster as compared with 17% in the un-ionized complex, and the corresponding figures for 2a2u are 30 and 19%. This shows undoubtedly that a large charge transfer relaxation towards the 5f shell takes place during ionization. As to energy positions of the various levels, the gap between U-O bonding and 5f bands is narrowed to

697

Electronic structure of lanthanide and actinide complexes--Ill Table 3. Valence energy levels (Rydbergs) and charge distribution of the (UO8)" cluster with configuration 4/'35f2t Charge distribution

( per cent)

j U ~S

p

0 d

f

s

p

Inter

Outer

sphere

sphere

Orbital

Energy

4t2g

-O.164

7

4

2e

-0.215

I0

12

78

14

16

68

g 6tlu

-O.257

i

i

4alg

-0.338

I

28

67

3a2u

-0.360

71

21

3

5

5tlu

-0.410

75

15

4

6

2t2u

-0.432

93

4

2

1

le

-0.523

73

27

u 4flu Itlg

4

89

-0.538

28

-0.547

3t2g

-0.570

3alg

-0.598

2a2u

-0.603

3flu

-0.616

2t2g

-0.653

It2u

-0.665

le g 2tlu

-O.712

la2u

-1.623

It2g

-1.645

2alg

-1.651

itlu

-1.697

lalg

-2.309

3 5 30 6 6 7 3

-1.260

76

65

21

62

26

7

51

ii

8 8

contributions

II

54

32

59

34

i

56

31

6

SO

40

7

6

7

I

1

82

14

3

80

17

2

76

18

2

70

18

2

2

4

4

94

2 electrons.

The oxygen charge

distribution refers to the charge contained in all the ligand spheres. of charge distribution

7

9

I

The highest occupied level is 2t2u which aceomodates

14 32

i

4 6

51 68

The analysis

inside atomic spheres is made according to angular momentum

to the total charge inside these spheres.

1.2eV through inner-shell ionization, whereas in the same time the U-O band width remains practically unchanged: 2.6 eV. Table 4 presents the total electronic charges in the various regions of the cluster before and after 4[ ionization, together with an estimation to the total 5f population in the uranium sphere on the basis of an analysis of the angular momentum contributions of the occupied bonding and antibonding MO's. It is seen that the considerable charge transfer relaxation which takes place during 4/ionization leads to an increase in the electronic charge in the metal sphere. This underlines the. specific role of the 5./ shell: ejection of a 4/ electron modifies strongly the potential of valence electrons and favors an important charge transfer (1.36 electrons) from the ligands to the 5f shell. These results are very similar to those obtained in the LaO2- case[16], which shows the strong analogy between the 4[ shell in lanthanum oxide and the 5[ shell in uranium oxide. Thus, there is no doubt that the satellite structure in UO2 originates also from an interatomic shake-up due to O2p~U5./ excitations. Another conclusion which emerges from Tables 2 and 3 is that the charge transfer relaxation which occurs during 4./ ionization is directed only towards the U5/ shell, excluding any participation of U7s, 7p, 6d orbitals in this phenomenon. Indeed the participation of the latter orbitals in the U-O bonding MO's remains constant during ejection of the 4./electron.

Larsson[34] has reported a model for estimating the intensities of shake-up satellites associated with charge transfer relaxation. According to this model, each shakeup excitation from a bonding to an antibonding MO has an intensity relative to the main peak h/Io given by L/lo = (d - n)

sin2 (~ -"O)/cos 2 (~:- r/)

(1)

where d is the maximum number of electrons which the antibonding MO can accomodate and n is the ground state occupation number of this MO. The angles s¢ and are defined from the MO coefficients of the bonding orbitals obtained in SCF calculations before (h) and after (h') 4[ ionization: h = usr

sin ,/+ ULCOS"O

(2)

h' = u~i

sin ~ + uc sin ~:

113)

ust and UL being the orthogonal U5/and O2p symmetry orbitals, respectively. As shown by Larsson[34], L]Io increases with relaxation charge transfer (i.e. if sin2 ~sin2 rt is large) but decreases with 5f occupancy in the neutral ground state (i.e. if r/is small). It is thus possible to use the results of Tables 2 and 3 to estimate the angles rt and ~ and then by using eqn (1) the intensities of the satellites corresponding to O2p~U5./ shake-up excitations are calculated. The results are presented in

698

JACQUES WEBER and VLADIMIR A. GUBANOV Table 4. Total electronic charges in the various regions of the cluster before and after 41 ionization Before 4f i o n i z a t i o n

After 4f i o n i z a t i o n

89.806

89.949

T o t a l charge i n uranium sphere oxygen sphere

interatomic region extramolecular r e g i o n

7.202

7.187

16.829

16.572

3.752

2.983

3.88

5.24

3f p o p u l a t i o n i n metal sphere

Table 5. Calculated intensities and energy separations for the various O2p ~ USf shake-uptransitions in UO2 tt Transition

Is/Io f

AE (eV)

3tlu--->5tlu

0.03

2.8

4tlu.->5tlu

0.II

1.7

it2u--->2t2u

0.02

3.2

2a2u---~3a2u

0.03

3.3

t

Intensity ratio of satellite to main peak.

tt

Energy splitting between satellite and main peak.

Table 5 together with an estimation of the energy separation between satellite and main peak obtained simply by taking the difference of the corresponding orbital energies calculated for the 4f ionized cluster. In principle, a transition state calculation[35], taking into account orbital relaxation effects, should be performed to estimate this energy separation, but a test-calculation has shown these effects to be negligible in the UOz case. Finally, let us notice that the other possible shake-up excitations: O2p ~ U 7 s , 7p or 6d have zero intensities according to our calculations, since there is no charge transfer relaxation towards U7s, 7p and 6d shells during 4f ionization and thus ~ = ~:. It is seen in Table 5 that four orbital channels are leading to a possible O2p--* USf shake-up excitation. In complete agreement with the results obtained by Bancroft et al. [33] for ThO2, both intensities and energy separations predicted for UO2 are rather small. I t is interesting to compare these results with experiment: Pireaux et al. [5] report the presence in the U4f photoelectron spectrum of UO2 of three satellites lying at higher energies than the main peak and located respectively at 5.8, 8.2 and 16 eV when referred to the parent U4f line. As suggested in Ref. [5], the satellite at 16 eV is most probably due to an electron energy loss process since it is located at a much too high energy to be interpreted as an O2p-~ U5f shake-up and according to the present calculations the other possible shake-up transitions have pi'aetically zero intensity. Concerning the two satellites at low energy, we suggest that both of them are due to O2p--, USf shake-up, even though our calculations underestimate the energy separations, which

has already been noticed in our (LaO,) ~calculations[16]. The structure at 5.8eV in the experimental spectrum could thus be due to an overlap of the four satellites described in Table 5, their overall intensity being qualitatively in agreement with the measurements of Pireaux et al. [5]. As to the second satellite observed at 8.2 eV, it could originate from a significant splitting of the O2p-~USf shake-up transitions due to spinpolarization effects. Indeed the calculations of Gubanov et al.[ll], whose results are very similar to ours, show that whereas spin-polarization effects are negligible for the U-O bonding band, they lead to a splitting of roughly 2.5 eV for USf orbitals. This indicates that two groups of equally allowed O2p -~ USf electronic transitions, occuring respectively between MO's of a and/t spin, will be predicted in a spin-polarized calculation, with excitation energies separated by 2 to 3 eV, in agreement with the experimental energy difference of 2.4eV between the first two satellites. Furthermore, such an explanation is coherent with the case of ThO:, whose corresponding spectrum exhibits only one low energy satellite at 7.2 eV: spin-polarization effects are absent in ThO2[11] and thus the two groups of shake-up transitions coincide. Therefore, in spite of the approximations inherent to the model used, the present calculations are able to provide a reasonable interpretation of the satellite structure accompanying the 4f photoelectron spectrum of UO2. Acknowledgement--The Computer Center of University of Geneva is gratefully acknowledgedfor a grant of computer time.

REFERENCES 1. B. W. Veal and D. J. Lam, Phys. Rev. B10, 4902 (1974). 2. B. W. Veal and D. J. Lain, Phys. Lett. 49A, 466 (1974). 3. B. W. Veal, D. J. Lam, W. T. Carnal1 and H. R. Hoekstra, Phys. Rev. !112,5651 (1975). 4. J. Verbist, J. Riga, J. J. Pireaux and R. Caudano, J. Electron Spectr. 5, 193 (1974). 5. J. J. Pireanx, J. Riga, E. Thibaut, C. Tenret-No~l, R. Candano and J. Verbist, Chem. Phys. 22, 113 (1977). 6. J. J. Pireaux, N. Martensson, R. Didriksson,K. Siegbahn,J. Riga and J. Verbist, Chem. Phys. Lett. 46, 215 (1977). 7. D. H. Maylotte, R. L. S. Peters and R. P. Messmer, Chem. Phys. Left. 38, 181 (1976). 8. M. Boring and J. W. Moskowitz, Chem. Phys. Lett. 38, 185 (1976). 9. D. D. Koelling,D. E. Ellis and R. J. Bartlett, J. Chem. Phys. 65, 3331 (1976). 10. B. I. Kim, H. Adachi and S. lmoto, Chem. Left. 109 (1977).

Electronic structure of lanthanide and actinide complexes--IIl ! 1. V. A. Gubanov, A. Rosen and D. E. Ellis, Sol. State Comm. 22, 219 (1977). !2. A. J. Freeman and D. D. Koelling, The Actinides: Electronic Structure and Related Properties (Edited by A. J. Freeman and J. B. Darby, Jr.), p. 51. Academic Press, New York (1974). ~3. K. H. Johnson, Advan, Quantum Chem. 7, 143 (1973). ~4. K. H. Johnson, Ann. Rev. Phys. Chem. 26, 39 (1975); and references therein. 15. J. Weber, Chem. Phys. Lett. 45, 261 (1977). 16. J. Weber, H. Berthou and C. K, Jcrgensen, Chem. Phys. 26, 69 (1977); and references therein. !7. J. Weber, M. Geoffroy, A. Goursot and E. Penigault, J. Am. Chem. Soc. 100, 3995 (1978). 18. A. Neckel, P. Rastl, R. Eibler, P. Weinberger and K. Schwarz, J. Phys. C9, 579 (1976). 19. V. A. Gubanov and J. Weber, to be published. 20. I. Narai-Szabo, Inorganic Crystal Chemistry. Academia Kiado, Budapest (1%9). 21. J. C. Slater, Quantum Theory o.f Molecules and Solids. McGraw-Hill, New York ~1974).

6,99

22. J. B. Danese and J. W. D. Connolly, J. Chem. Phys. 61, 3063 (1974). 23. K. Schwarz, Theoret. Chim. Acta 34, 225 (1974). 24. K. Schwarz, Phys..Rev. BS, 2466 (1972). 25. J. Weber, Chem. Phys. Lett.40, 275 (1976). 26. J. Weber and H. Bill,Chem, Phys. Left. 52, 562 (1977). 27. J. G. Norman, J. Chem. Phys. 61, 4630 (1974). 28. C. K. J~rgensen, R. Pappalardo and H. H. Schmidtke, J. Chem. Phys. 39, 1422 (1%3). 29. G. C. Allen, J. A. Crofts, M. T. Curtis, P. M. Tucker, D. Chadwick and P. J. Hampson, J. Chem. Soc. (Dalton Trans.) 12, 12% (1974). 30. C. K. J~rgensen, Struct. Bonding 24, I (1975). 31. C. Miyake, H. Sakurai and S. Imoto, Chem. Phys. Left. 36, 158 (1975). 32. G. M. Bancroft, T. K. Sham. and S. Larsson, Chem. Phys. Lett. 46, 551 (1977). 33. G. M. Bancroft, T. K. Sham. J. L. Esquivel and S. Larsson, Chem. Phys. Lett. 51, 105 (1977). 34. S. Larsson, J. Electron Spectr. 8, 171 (1976). 35. J. C. Slater, Advan. Quantum Chem. 6, 1 (1972).