Molecular orbital studies of the electronic structure of lanthanide complexes. II. Ionization energies and satellite structure in inner shell photoelectron spectra of LaF3, CeF3, PrF3, NdF3, LaO45− and LaBr3

Chemical Physics 26 El9771 69-78 Q North-Holland-Publis~g CornParty

.

MGLECULAR ORBITAL STUDIES OF THE ELECTRONIC STRUCTURE OFLANTHANIDE COMPLEXES. ‘II. IONIZATION ENERGIES AND SATELLITE STRUCTURE IN LNNER SHELL PHOTOELECTRON SPECTRA OF LaF3, CeF-+ PrF3, NdF3, Laos- and LaBrj J. WEBER, I% BERTHOU and C.K. J@RGENSEN 5epfl?nent 0~C&zm&~, LI..iv~rs&y of Genevn, f2if Geneva #.5iviEze&nd Received 12 May 1977 ,

Using the &hipk scattering Xol method. ruolecularorbital calculations of the electronicstructure of the foliowingcomplexes are performed: LaFa, CeFa, PrFa, NdFa, NaOz- and LaBra. Is shown that the typica; features of the 4f shell in such mmplexes are well reproduced by the calculations. Furthermore the calculated ionization energies of LaFa, CeFa, PrFa and NdF3 are in good agreement with experiment on solids, which indicates that the multiple scattering Xo model is able to provide a reliable description of the electronic structure of rare earth compounds. Finally separate SCF calculations are performed for the 3d ionized contiiurations of the clusters in an attempt of understanding the satellite structure observed as accompanying the 3d photoelectron signals. The calculations demonstrate without doubt that the satellites originate from an interatomic shakeup process.

I. I~t~duction It is we11known that Iantbanide complexes exhibit a great number of interesting and unusual properties which have been investigated thoroughly during the last few years. As examples let us mention the luminescence oflanthanides [I], a phenomenon widely used in several applications, and the nature of chemical bonding in hmthanide compounds [2,3], a problem still lacking a general theoretical description. There is no doubt that reliable molecular orbital (MO) calculations of the electronic structure of Ianthanide complexes could provide a basis for an inte~re~tion and a qualitative unders~nd~g of some of these phenomena. At the present time the Hartree-Fock-Sister x0! method [4] is the only MO allelectron model which can be applied to such complexes and to Sf group compounds as well, either in the multiple scattering Xcc(MS Xor)version [5] or in the so-called discrete variational Xo (DV Xo) model [6], and the results obtained for lanthanide trifluorides [7], many1 ion [S] and actinide hexafluorides [9,10] are encouraging. We earlier reported in part I of this series [7] the pre~~ry results of MS Xa!c~culatio~ performed

for the clusters La(IfI)Fg, Ce(IV)Ff, Ce{HI)F3 and Yb(IIDF3, and showing that this mode1 is able to give a reasonably accurate description of the electronic structure of these lanthanide complexes and in the same time to provide a qualitative understanding of the sateIKe structure observed recently [I l-131 as accompanying the 3d photoelectron signals of the first four lanthanides. Indeed tire MS Xo results have shown that a large charge transfer relaxation occurs during 3d ionization in LaF, and CeF,, which ailc~s an interatomic shake-up process to take place, an

efectron being transferred from the ligands to the 4f shell. This result is in complete agreement with the qualitative expiration proposed in refs. [I I-13]. However, the calclitated satellite intensities and positions relative to their main signal were in rather poor agreement with experiment and this was attributed (i) to configuration mixing effects which are not included in this one-electron model and (ii) to the approximations inherent in the MS Xo method itself. It is fair to mention in fact that an accurate prediction of the features of satellite structure in photoelectron spectroscopy is a very delicate problem and quantitatively successful calculations in this HeId are very scarce 1141.

In the present work, MS X@results for the following trivalent lanthanide monomeric complexes are presented: L&3, Lao:-, LaBr3, CeF3, PrF3, NdF3. This choice of clusters will enable us firstly to make comparisons of the electronic structure of La(III) complexes with different Hgands, and secondly to make a combarative study of the trifluorides of the first four lanthanides. For all the complexes, the electronic structure of the ground state is reported together with an analysis of the charge density witbin the atomic spheres. Fu~he~ore we present in the case of Ianthsnide trifluorides a comparison of ionization energies calculated for valence and core levels with photoelectron data. Concerning the satellites accompanying the 3d photoelectron signals, estimates are made of their intensities, calculated using the model suggested by Larsson [15], and energy separations to their main signal.

2. Method of c&ulation and parameters Au objection fr~uen~y raised against the MS Xo mode1 is that it gives poor results for planar systems due to the ~adeq~cy of the muffm-tin appro~mat~on in such a case. However, the resulti obtained by Preston et al. [I61 for boron trihalides of D3u symmetry as well as our previous calculations [7] for planar J&$3 show that this objection is irrelevant for smah systems. As a matter of fact it is still possible to obtain satisfactory MS Xarresults for larger planar molecules like benzene [17,18] when choosing adequately

the cakulatioti par&neters.‘hr add&ion to the reason of simplicity, it is thus fully justified.tochoo~e in this study trihkide lanthauide clustek.of D&symmetry. As to L.aO~-, it is assumed to be regular tetrahedral. The bond distances used.in the cajculations have been deterinined aecord&g to the ionic radii values of Goldschmidt ‘et al. [I 91 for &aF3, Lao:- and LaBri; for.the other clusters, a scaling of the lanthanide radius has been made using the-data of Sinha [20], ~ch~automati~~y gives the cotiesponding bond distance when assuming an flanged iokic tidius~of the @and. The values of bond distances and b&X& parameters are presented in table 1. The atomic exchange parameters Q are those determined by Schwarz [21,22] using a Iinear interpolation for determkring the value appropriate for neodymium. A weiglrted average of the atomic values is chosen for the a: value in the interatomic region (i.e. three parts of fluorine to one part of lanthanum for LaF3). In the extramolecular region (i.e. outside the outer sphere), the a value appropriate for the &and is used. Ia MS Xrucalculations, the choice of appropriate

values for the radii of atomic spheres may be delicate since it is enlarged by the possibility of using overlapping, instead of “touching”, atomic spheres in an attempt of circumventing the limitations of the muffin&n approximation. Aa a matter of fact, the influence of this choice on the results has been recently investi&ed for various compounds by one of us 123-251, leading to the conclusion that, when modifying the sjheres radii, (non-uniform) shifts of the eiec-

Table 1 MSXp parametersand metal-l&and distances(d) bF3

Lao:-

L&r3

CeFa

PrFs

NdF3

2.46

2.46

3.10

2.41

2.4f

240

liand outer sphere intersphere

0.S9898 0.73732 0.73732 0.72724

0.69898 0.74447 0.74447 0.73537

0.69898 0.70606 0.70606 0.70429

0.69845 0.73732 0.73732 0.72760

0.69765 0.73732 0.73732 0.72740

0.69718 0.13732 0.73732

sphereradii (au) metal i&and outer sphere

2.82000 1.82879 6-47776

2.82000 1.82879 6.47776

3.14231 2.71592 8.57415

2.70296 1.85134 6.40564

2.73984 1.81446 6.36876

2.72G52 ‘. 1.81489 6.35029

(rvalues metal

0.72129

L Weberet

al./Mhecularorbital calcthtions

of hthanide

71

complexes

and extramolecular region, and up to I = 2 in ligand spheres. We do not use the frozen core approximation in any part of the calculation, but the lanthanide and ligand inner shell orbitals are “thawed” i.e. they conserve their atomic character and are constrained to be entirely localized within the atomic spheres, but they adjust their one-electron energies during the self-con&tent procedure. All the calculations are performed using the non-spin-polarized version of the non-relativistic MS XU computer progranis.

trmic levels of sev&al eV or, in some cases, valence levc! cr&sings may occur. This emphasizes the need of performing test calculations with the MS XCY model in q attempt of &ding general rules of choosing the most adequate calculation parameters. In the case of lanthani~e cqmplexes, pr@oUs calculations [7] of the ionization energies of LaF3 have shown that nonoverlappixig (“touching”) atomic spheres, whose radii are determined according to the procedure described by Normti. [26], lead to a satisfactory agreement withphotoelectron data. Therefore this procedure is applied to all the complexes studied in this work, the only exception being LaOi- for which the radii of “touching” atomic spheres have been attributed the stie v&es as those of LaF3 because central atom and bond distances are unchanged in both complexes. An externally tangent outer sphere is used in each calculation. The stabilizing electrostatic field of the crystalline environment for the LaOi- cluster is taken into account by use of a Watson sphere of the same radius as the outer sphere and bearing a charge of 6. In all cases, partial waves up to I = 4 are included in the multiple scattering expansions in the lanthanide sphere

3. Results and discussion 3.1. Ground state electronic structure of the clusters The ground state electronic structure of the valence levels of LnF, (In = La, Ce, Pr,Nd) is presented in table 2. It is seen that the sequence of the levels is the same in the four complexes, with the 10e’ moleculai orbital as the highest 2p bonding one and the 4e” the lowest 4f antibonding one. The energy separation be-

Table 2 Ground state electronic energies (Rydbergs) of the valence levels of LnFs (Ln = La, Ce, Pr, Nd)

MO type a)

Symmetry

Occupancy

bF3

CzF3

PrF3

NdF3

Ln4f

1 ISI 2a> lie’ 6ai 4e”

0 0 0 0 0, 1,2,3 b)

-0.563 -0.570 -0.571 -0.573 -0.514

-0.590 -0.598 -0.599 -0.602 -0.602

-0.614 -0.621 -0.622 -0.625 -0.626

-0.630 -0.637 -0.638 -0.641 -0.642

FOP

10e’ 5a: la> 3e” 9e’ lOa\

4 2 2 4 4 2

-0.716 -0.125 -0.728 -0.731 -0.738 -0.742

-0.728 -0.740 -0.743 -0.745 -0.751 -0.7 55

-0.726 -0.738 -0.741 -0.743 -0.749 -0.755

Ln 5p

8e’ 4a:

4 2

-1.682 -1.689

-1.704 -1.712

-1.733 -1.741

-1.755 -1.764

F2s

9ai 7e’

2 4

-2.067 -2.080

-2.082 -2.095

-2.083 -2.095

-2.088 -2.101

Ln 5s

&i

2

-2.698

-2.759

-2.817

-2.873

a) Main atomic component of the corresponding MO. b)O&zupation is 0, 1,2,3, for LaFa, CeFa, PrFa, NdFa, respectively.

I

-0.733 -0.743 -0.746 -0.747 -0.753 -0.760

We!% 1Oe’ gd.4e” decreases,when going from LaF, to NdF~,.~~~~ indicates that the complexes become .: moreandm_ore covalent along the l~~~ide~~e~es. ‘- It cari’also be noted that for ah the clusters the five4f a&bonding levels he very close to one another in energy, with the result that they .shmdd form a very narrow band in solid i~~~ide ffuorides, as is the case in rare earth metals [27]. The width of the 2p’ vaFence band comes out larger than that of the 4f from these MS Xcrcalculations, the explanation being that 2p electrons are much more delocalized than 4f electrons. The electronic structure of the chrsters disprayed in tabie 2 is thus very reasonable, the only. problem being related to an accurate p~d~ction of the position of the 4fband relative to the 2p. As in rare earth metals f27], the position of the 4f band seems to be somewhat sensitive to the calculation parameters and, as discussed below, there is some evidence that the ~tibond~g character of the 4forbitaIs is sligbtiy ~d~restimated in the present cakulations (i.e. the 4f band is predicted to lie too close in energy to the Zp Oll-t$. In t&de 3 is represented the distribution of electronic charge of 4f and Zp vabmce level of LnF3 (Ln = La, Ce, Pr, Nd). The outer sphere (i.e. the ext~oIe~~r~ region is omitted in this analysis since itincludes in each case a nestle amount ofcharge.~x~ation of tabIe 3 is interesting because it reveals immediately the typical property of extreme locahzation of the 4f electrons. Indeed their molecular orbitah are between 90% and 100% localized in the fanthanide sphere, which is in complete agreement with the eondnsion of Gschneidner [ZJ; in trivalent cerium, prasaody~um and neo‘dymium the 4f electrons are mainly “‘atomic-like” and participate in the chemicai bonding by en amounr of a few percent at the most. On the other hand, the electrons of the bonding 2p moIecular orb&k are much more delocalized over the all cluster as seen from table 3; their charge di~dbution analysis reveals a non-ne~~ble 4f component in the l~~~ide sphere and a substantial delocabzation in the intersphere mgion. As elsewhere reported for transition metal complexes [18], this is a typical result for bonding omitah and the amonnt of charge in the intersphere region can be used as a qu~tative criterion for estimating the bonding or ~~ban~g character of mo.lecuIar orbit&. This is a ratbet nice exampIe of the pecbsgogical value of the MS Xa model; the muffin-tin partitioning,

13

J.- Weber et aL/Molecular orbital mlculations of lanthantde complexes

&to. atomic sphkres ana interatomic region allows in some cases an interp&atioli:of the-results in terms of &her simpk he&al concep&. Another interesting observation.t& be done from tb6 results displayed in table 3 is the monotonous increasing of the 4f component dfjhe bonding orbitals when going from LaF, to NdF,, which confirms the interpretation of an increikng covaleky along this se&+. The ground state electronic structure and charge distribution of upper valence levels for Lao&- are presented in table 4. It is seen that because of the large negative charge of the cluster the MO levek lie at higher energy (i.e. closer to the continuum) than in the fluorides. This certainly explains the presence of a Rydberg orbital in the same energy range as the antibonding orbitals and which strongly mixes with the 4f MO of a1 symmetry. This ls undoubtedly an artifact of the calculations since.the two orbitals 9al and 1Oal are calculated as having roughly the same 4f component and as being largely delocalized in intersphere and outersphere regions, which is in contradic-

tion with the extreme localization of the other4f molecular orbitals. Taking apait this slight disagreement and the shift in orbital energies, the general features of the . MS XCY results obtained for Lao:- are similar to those of the lautbanide trifluorides. In table 5 we present the ground state electronic structure and charge distribution of upper valence levels for La&,. When comparing with Lal!,, it is seen that the sequence of symmetry orbitals among p bonding and 4f antbonding levels is the same in both compounds, but the energy separation between the e’ highest bonding and errlowest antibonding molecular orbitals is much smaller in LaBr3 than in LaF3. This is due to the fact that bromine ligands are more reducing than fluorine ones and it results further in a larger covalency between ligaud and central ion in LaBr3, as can be inferred from the larger 4fcomponents in the bonding orbitals of this complex when compared with LaF,. Thus these MX XCY results indicate that electron transfer transitions, due to an electronic excitation from a ligand p orbital to the 4f shell, should occur at lower energies

Table 4 Ground state electronic eneties (Rydbergs) and distribution of electronic charge a) of valence levels of ~a@MO type b,

Symmetry

occupancy

Energy

Charge distribution 4fC)

2p d)

Ie)

Rydberg La4f

lOal 2t1 11tz 9at

0 0 0 0

-0.097 -0.125 -0.129 -0.145

1.06 5.75 5.69 0.78

0.02 0.03 0.01 0.01

0.25 0.10 0.23 0.70

0.62 0.01 0.04 0.49

0 2p

lot, 8al ItI

-0.318 -0.334 -0.338 -0.363 -0.366

0.10 0.18 0.15 0.09 -

1.07 0.35 1.07 0.96 0.63

0.98 0.29

3e

6 2 6 6 4

0.36 0.13 0.22 0.32 0.16

8tz

6

-1.228

7al 7t2

2 6

-1.378 -1.419

6al

2

-2.256

9t2

LaSP 0 2s

La 5s

1.37 1.53 1.18

a) Analysis made according to anguku momentum contributions in the various regions of the cluster. For unoccupied orbitals the analysis deals with holes instead of electrons b)Main atomic component of the corresponding MO. c, 4f charge distribution in lanthanum sphere. d, 2p charge distribution in one oxygen sphere (multiply by four for total 2p’distrihution). e, Intersphere region.. . f) Outer sphere.

74.

--..

:

J. Weber et al./Molecularorbital

calculntiork if lmithnnkle complgres

:. :

.. Y

Table5

Grtiund Gate electronic ~I&+

(Rydbergs)

_

and distribution

..

of electronic charge a) of

,. : .-

Va&e

kV&

..

Of klh~,

i ~. >

. . .,

: MO

type

La4f

b)

Symmetry

OCCUPancy

Energ;..

Ch&& distri~$~on .. 4fC) -4pd)

liai 5a; 2Oe’ 9a; 8e”

0 0 0 0 0

-0.508 -0.512 -0.513 -0.515 -0.516

l.Si 1.86 3.78 1.93 3.88

19e’ 8a;

4 2

-0.579 -0.581

4ai 7e” 18e’ 166,

2 4 4 2

-0.582 -0.584 -0.596 -0.605

Br4s

17e’ 15a;

4 2

-1.423 -1.428

LaSp

7a”

16’e’

2 4

-1.706 -1.712

14a,

2

-2.692

Br4p

La 5s

.i. ;_\I : +) .-;

-0.04 -. 0.04 0.05 0.01 0.02

hods 0.03 0.07 0.03 0.05

0.15 0.05

i.03 0.52

0170 0.38

0.13

o.jo1.02 0.97 0.46

0.35 0.78 0.60 0.27

0.10

0.13 0.24

.-

..

._

,’

: a) Analysis made according to angular momentum contributions in the various regions of the cluster. For unoccupied orbit& the analysis deals with holes instead of electrons. b, Main atomic component of the corresponding MO. ‘)4f chage distriblrtion in lanthanum sphere. d, 4p charge distribution in one bromine sphere (multiply by three for total distniution). e, Intersphere region.

in LaBr3 than in LaF, and tbis is in agreement with the conclusions of Blasse [I 1. Using the electronic structure of these lanthanide complexes, it-is pokible to calculate, among other properties, their ionization energies and electronic excitation energies, which provides an easy way of estimating the validity of the model by allowing direct comparisons with experiment. As for ionization energies, the values presented in the next section for the lanthanide trifluorides indicate that the electronic structure of fklly occupied levels is reasonably well described by the MS Xor method. Concerning electronic excitation

energies, which should give indications about the degree of accuracy of the electronic structure of partially occupied and unoccupied valence levels, prelimimiry results obtained for CeF, show that the 4f antibonding levels are predicted to lie too close in energy to the 2p band, with the result that the electron transfer ab-

sorption band (resulting from a transition from the

highest filled bonding MO to the partly filled 4f shell) is calculated to be at a lower energy than the 4f + Sd transitioils. As there is every reason to believe from an analysis of the absorption spectra [I,281 that in trivalent cerium complekes the first aliowed transition is of 4f + 5d type, the position of the 4f band as calculated by MS Xa must be questioned. h a matter of fact the position of the 4f band is gomewhat sensitive to the calculation parameters and by using overlapping atomic spheres, it is possible tq shift this band towards the Rydberg Sd levels and to obtain thus a first akowed transition of 4f+ Sd type, i&agreement with experimerk A full account of MS X&calculafjo@s of the. electronic excittifion en&j&s in CeF, wlbe-reported elsewhere [5!9]. --

L Weber et al.~iUoIecufr orbitd cetculatidnsof

3.2. -Ionization energies of LaF3, CeF3, PrFx and NdF3 A comparison between MS Xo ionization energies calculated for the valence and core levels of IaP,, CeF3, PrF3 and NdF3 by means &the transition state procedure [30] (i.e. taking into account the major part of electronic relaxation effects) and corresponding photoelectron data [31 J is presented.in table 6. The

overall agreement between calculated values and experiment is very satisfactory for both valence and inner shell binding energies, especially when taking into account that for heavy elements it is generally diffIcult to describe adequately exchange Interactions of both valence and core electrons with an unique atomic value of the parameter cy. When looking at the lanthanide 4f and 5p binding energies, it is seen that they are overestimated in the calculations, but this effect is larger for J_aF3 and CeFa than for PrF, and

NdF,. Thus, the 4f binding energy is predicted to be roughly the same (a12 eV) in CeF,, PrF,, NdF,, whereas corresponding experimental values are 8, IO, 12 eV. However, the lanthanlde 3d ionization energies are predicted very accurately by the MS Xo model and this is gratifying when taking into account the approximations inherent to the method. When examining the results of table 6 as a whole, it Seems that they provide a good a posteriori justification of our choice of calculation parameters, while indicating in the same time the degree of accuracy in one-electron energies it is possible to expect from such calculations on rare earth complexes. Table 6 Calculated and experimental ionization Level a)

Ln4f FOP Ln sp F2s Ln 5s Ln4d Ln 4p -Ln 3d

energies

LaFa

ientirmde

75

complexes

3.3. &tellite structure accompanying the 3d photoelectron signals of the complexes It has recently been reported by Berthou et al. [13] that the satellites accompanying the 3d photoelectron signals of the first four lanthanides, and lying at higher energy (from 3.0 to 4.5 eV) than the main peak, vary considerably in intensity in both cases of complexes of(i) different lanthanides with the same ligands and (ii) of a given lanthanide in different ligand environments. As examples let us mention that intensity ratios of satellite to main peak are 028,0.60, 1.0, 1.0 in solid I.aF,, CeF,, PrF,, NdF,, respectively, whereas they are 0.8 1 and 1.63 in I.a,O, and LaBr3 [13]. There is little doubt that these satellites are due to an interatomic shake-up, an electron being transferred from the ligands to the 4f shell during 3d ionization, as was previously assumed [l l-131 and recently confirmed [7] by our MS Xa calculations performed on LaF, and CeF,. It is therefore interesting to undertake similar calculations for the other complexes of the series meirtioned above in order to know if the interatomic shake-up phenomenon is still at the origin of the satellite structure and if, by using the model of Larsson [IS] for calculating satellite intensities, it is possible to explain such large variations in intensities. The necessary condition for an interatomic shake-up process to take place is an important deformation of the electronic density of the complex during 3d ionization. When we want to make conspicuous such a

of LnFp (Ln = La, Ce, Pr, Nd). All energies are in eV PrF3

CeF3

NdF3

Cal&b)

exp.@

CdC.

exp.

CdC.

exp.

C&Z.

-

-

12.9 26.6 31.4 40.5 111.6 199.2 854.3

13.5 23.7 34.4 40.4 111.0 203.2 850.8

11.9 13.2 26.9 31.8 41.3 117.1 208.1 906.3

WI 12.9 23.6 34.0 42.5 115.3 213.3 898.8

12.1 13.1 27.3 31.7 42.1 122.4 216.9 950.2

lo(?) 13.7 24.1 34.1 44.3 121.6 223.8 947.8

12.2 13.3 27.6 31.8 42.9 127.7 225.8 999.8

exp.

11.9(?) 15.0 25.7 34.1 126.4 991.5

a) Valence levels are labelled according to their main atomic component. b, When necessary, the mean values of the correspond& Dab levels are taken. c) For all the complexes. experimental values are taken from ref. [31]. For Ln p and d levels, a weighted average of the spin-orbit doublets is reported.

phen~~~n~~ from theO&C;?l

cdOuIaticj*, it is ._ XKXX&S~‘~~perf& t&sqmmt~ SC6 cakulations;one for.the-ground s&of the cltiter and another

for the’3d i&&d configuration. Thenby comparing electronic densities, it ispossible to estimate the im&&&~ of~electron reorganization during ionization. Table 7 presents the total electronic charges inthe varloiis .mgions of the clusters before and after 3d ionization; together with an estimation of the total 4f population in the metal sphere on the basis of &L anatysis of the angular momentum contributions of the occupied bonding and antibonding molecular orbitals. It is seen that indeed.there is a considerable charge transfer relaxation accompany~g the inner shell ionization. The total charges in metal sphere are larger after ionizati& than before, i.e. after having removed an inner shell electron from that sphere (?>.This result can be surprising at a first glance, but it ls easily explained by the specific role of the 4f shell in these compounds [12]; ejection of a 3d election modifies strongly the potential of the valence electrons and favors an important charge transfer from the ligands to the 4f shell. Examination of table 7 shows that there is a net transfer of 1. I-l.4 eiectrons to the 4f shell, depending on the cluster considered. It is interesting to notice that this transfer occurs about equaIIy at the expanse .of the charge in interatomic region and ligand spheres, which means that the bonding p orbit& are completely modiiied during 3d ionization. On the basis of the results displayed in table 7, it is possible to say that for all the lanthanide compounds studied in the present work there is a large charge transfer relaxation accompanying 3d ionization and that the satellite structure originates thus mainly from interatomic shake-up. It remains now to be seen if, by using an appropriate theoretical model, it is possible to explain the large difference in intensities of these satellites among the different compIexes. La&on {15] has reported a model for ~timating the intensities of shake-up satellites associated with large transfer relaxation. According to this model, each bonding-antibonding pair of molecular orbitals of the same symmetry (the shake-up obeying the selection rule of being monopolar, it is not necessary to take into account the pairs of orbitah of different symmetries) contributes to the overall intensity ratio of satellite to main peak by an amount

fpo=(d - n)sin2(S. - q}/cos2(s. - ?&

(1)

-.

J. Weber et aL/MoIecularorbital calculationsof hnthantie complexes

. where d is the maximtim number of eIectrons which --the titibonding MO can accqmadate.and n is the ground state occupa+ itimber of this M&The tigies [ and 11 .are.defined from the MO coefficients of the bonding orbit& obtained in SCF calculation before (h) and after (h’) 3d ionization: k = [email protected] q -+u, coslj,

(2)

h’=U4@~+ULc0s~,

(3)

UQfand U, being the orthogonal 4f lanthanide and ligand p symmetry orbitals respectively. As we have seen that partial 4f Populations are larger after 3d ionization than before, we have 5 > 9 and the amount of charge transfer relaxation for this bonding-antibonding pair is sin’f - sin2q. As shown by Larsson and Lopes de Siqueira [32], the satellite intensity is not proportional to the amount of charge relaxation, and for a given amount qfcharge transferred it is stronger when the 4f population-is small before ionization. A qualitative interpretation of eq. (1) is thus that the intensity increases with relaxation charge transfer (i.e. if sin2{ - sin2~ is large) but decreases with 4f occupancy in the neutral ground state (i.e. if n is small). Using the results of separate SCF calculations performed for the un:ionized and 3d ionized clusters it is possib!e tb estimate the angles 9 and 5 for each pair of bonding-antibondiig MO (belonging to the same symmetry) by doing an electronic distribution analysis of the charge in lanthanide sphere, and then, by using expression (l), we are able to calculate the intensity of the shake-up satellite resulting from an excitation from this bonding MO to the corresponding antibonding MO. The energy separation between satellite and main peak is obtained by a transit+ state calculation of the corresponding electronic excitation in the 3d ionized cluster. As in each cluster all the satellites resulting from the possible orbital channels are found to lie practically at the same energy value, it is allowed to simply sum up their partial intensities in order to obtain the overall intensity, and the results are presented in table 8. Examinatidn of table 8 shows that for each cluster

II

Table 8 Satellite intensities and positions (eV) relative to their main. signal .

Cluster

LaF3 CeF3 PrF3 NdFB Lao:LaBr3

Es-E0 b,

f,lIo a) CaIC.d

exp.d)

cak. e)

exp.d)

0.42 0.37 0.32 0.30 0.52 0.40

0.28 0.60 1.0 1.0. 0.81 1.63

1.1 1.1 0.9 0.9 1.4 0.6

3.9 3.5 3.4 3.3 4.2 3.6

a) Intensity ratio of satellite to main peak. b, Energy splitting between satellite and main peak. c) Calculated as the sum of the intensity ratios of satellites resulting from each orbital channel. d)Average value of the 3ds/z and 3d,/, signals of ref. [ 131 measured in solids, including LazO3. e, Average value of the splittings of each orbital channel calculated by the transition state method.

tioned that the calculated energy separation between bonding and antibonding levels is underestimated in the un-ionized clusters and therefore in the 3d ionized complexes also. However it is interesting to remark that the experimental trend of Es - E, along the series J_aPj, CeF3, PrF3, NdF3, and LaF3, Lao:L&r3 is reproduced in the calculations; the splitting decreases when going from LaF, to NdF, ‘whereas, when compared with LaF3, it is larger for LaOi- and smaller for LaBr3. This is an encouraging result as it shows that the MS Xa model is able to predict correctly the variations in one-electron energies along these series of lanthanide complexes. As for intensities, it is seen in table 8 that there is poor agreement between theory and experiment, even from a qualitative point of view. The calculated intensities decrease slowly when going from LaF3 to

the shake-up satellite is predicted to lie at higher energy than the main peak, in agreement with experiment, but the energy separaeqns between satellite and main

NdF, whereas the experimental values increase strongly along this series, and similarly the experimental trend in the series LaF3, Lao:-, LaBr3 is not reproduced in the calculations. Let us mention briefly some possible reasons for so large discrepancies. It seems to us that the main reason for the failure of the prediction lies in the fact that we use here a one-electron model without including any configuration mixing

peak come out much too small in the calculation. This is not a surprising result since we have already men-

effects which have been shown recently [14] to be essential for an accurate prediction of satellite intensi-

.. ties in photoelectron s~eetrosco~y. Another possibility is to in&minate theapproximations inherent in the MS Xtirnodel itseLf since in the model proposed by Earsson [IS] satellite intensities are stmngiy dependent ORthe quality of the wa~functions. However, we have seen in the case ofCeF3 [29] that, when changing the calctdation parameters, the composition of the molecular orbitals is practically unchanged, on the other hand the intensities calculated for IS,, Gel?,, PrFs and PdFs are in agreement with the electronic structure of the ciusters; the covalency increases along this series (and so does 11>whiIe the amount of relaxation charge.transfer is roughly corrstant, which explains the slight decrease in calculated intensities. As a matter of fact one may ask what could be the differences in electronic structures of I.aF3 and NdF, c~c~ated in a one-electron model which would produce so large variations in satellite intensities. Among the possible factors tiecting the calculation of intensities and which have been neglected in the present work, let us mention the possibility of two-electron shake-up excitations, but their contribution has been shown [ 1.51to be of little importance in t~sition metat complexes; and multipiet structure effects in CeF3, PrFS, NdFj , but a recent cakmlatio~ performed for metallic praseodymium and neodymium f333 has shown that they lead to a satellite structure of low intensity. It seems thus that whereas the ptisent c~cuIatio~ provide a qu~ta~ve unde~t~d~g of the presence of satellites, an accurate prediction of their intensity requires more sophisticated calculations allowing introduction of configuration interaction effects. Acknowledgement The Computer Center of the University of Geneva is gratefuhy acknowledged for a grant of computer time.

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