The Electronic Structure of Organometallic Complexes Involving f-Electrons, II1. Magnetic ..... which give the energies of the seven f-orbitals in terms of the Bn m ...
The Electronic Structure of Organometallic Complexes Involving f-Electrons, II1 Magnetic Susceptibility and Crystal Field Splitting
of Uranium(rV) - tetracyclopentadienide H . - D . AMBERGER a n d R .
D.
FISCHER
Institut für Anorganische Chemie der Universität Erlangen-Nürnberg B.
KANELLAKOPULOS
Institut für Heiße Chemie, Kernforschungszentrum Karlsruhe (Z. Naturforsch. 31b, 12-21 [1976]; received July 17, 1975)
Uranium-tetracyclopentadienide, Susceptibility, Model Calculations, Crystal Field Splitting Pattern, Electronic Structure Some significant features of the low-energy part of the crystal field ( = C F ) splitting pattern of the organometallic 5f 2 -system (^5-C5Hs)4U(IV) can be deduced from the temperature dependence of the magnetic susceptibility which has been measured on polycrystalline samples between 1.1 and 298 K . The results of model calculations performed independently on the basis of three different semi-empirical approaches are compatible with the deductions from the experiments and allow estimates of the sign and order of magnitude of quantities like the CF-splitting parameters B40 and Bö 0 viz. the (averaged) angular overlap parameters ea and e„ and of the valence state ionisation potential of the 5f-electrons. Anticipating a rather weakly perturbed tetrahedral CF, the observed magnetic properties may be satisfactorily simulated if the six lowest-lying first-order CF-states and one common scaling factor are accounted for. 1. Introduction The quasi-tetrahedral molecular structure o f the organometallic actinide complex uranium-tetracyclopentadienide, (?75-C5H5)4Ü(IV) = UCp 4 , which w a s p r o p o s e d b y FISCHER a n d HRISTIDU as e a r l y as
1962 2 - 3 has been recently confirmed b y BURNS 4-6 b y a detailed single crystal X - r a y study. Thus, each o f the t w o discrete UCp4-molecules composing the tetragonal unit cell (space group 142 m ) contains four equivalent, penta-hapto coordinated Cpligands, the appropriate rotational arrangements o f which give rise t o the molecular point symmetry S4*. I n view o f these results, the first attempt t o * As B U R N S has pointed out, the occurrence of equal quantities of the two S4-enantiomers would crystallographically correspond to one singular species with the molecular symmetry D2d 5 . Requests for reprints should be sent to Dr. H.-D. Institut für Anorganische Chemie der Universität Erlangen-Nürnberg, D-8520 Erlangen, Egerlandstraße 1, B R D . AMBERGER,
interpret the observed temperature dependence of the magnetic susceptibility ( = Sc) of the polycrystalline [ R n ] 5 f 2 -system** in terms of pure Tdsymmetry 7 is n o w subject t o improvement, although the basic conclusions concerning the origin of the isotropic : H - N M R shifts o f UCp4 in solution remain essentially unchanged 7 - 8 . The situation has been somewhat confused b y a subsequent Sc-study between T =2.6 and 100 K b y KARRAKER et al.9 who f o u n d Curie-Weissbehaviour up t o 25 K , but a practically temperature independent Sc ( = T I P ) between 60 and 100 K . W h i l e these authors have attempted to explain this unusual feature in terms o f Td-symmetry, arguing that a magnetically active electronic ground state b e closely followed b y a first excited, non-magnetic crystal field ( = CF)-state (zlE = 3 0 cm- 1 ), we have been unable t o construct any kind of CF-splitting ** The observation of Curie-Weiss-behaviour between T = 90 and 296 K , corresponding formally to 2.78 B.M. was originally associated with a simple two-electron spin-only system 2 - 3 .
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H.-D. AMBERGER ET AL. • T H E ELECTRONIC STRUCTURE OF UCp4 pattern which would account for the experimental findings. In view of these apparent inconsistencies we have undertaken a complete re-examination of the temperature dependence o f the Sc of UCp4, which now covers the entire range f r o m 1.1 up to 298 K , and involves a particularly careful analysis of the lowtemperature range between 1.1 and 10 K . 2. Temperature Dependence of the Magnetic Susceptibility Metf (B.M.)2 5"
1 I mole \ 100"X. \crri3 J
o /
/
yff^ (a)
2- /
^
1
0
25
50
75
100
125
150
175
200
225
T(K)
Fig. 1. Temperature dependence of the reciprocal magnetic susceptibility y~x (a) viz. of the squared effective magnetic moment, /t2eff = 8^T (b). The circles correspond to the observed data, the two full-line curves to the best fit of the experimental findings calculated on the basis of Eq. (15). The curves (a) and (b) of Fig. 1 e m b o d y the results of a total of 105 measurements at 35 different temperatures of samples obtained from large, finely ground octahedral crystals of high-purity UCp4, a sample of which had also been subjected to the X - r a y study 5 . At each temperature, the magnetic field strength was varied between 2388 and 7959 A/cm*, but throughout the entire temperature range there was no evidence for a field dependence of the Sc. All the results have been corrected for the incremental diamagnetism of the U 4 + -cation and the four CsH^-anions. * According to 3 viz. 10 kOe.
As shown by curve (a), substantial T I P with X = 0.018 cm 3 /mole results at very low temperatures up to 11.5 K , thus immediately revealing the existence of a Zeeman-inactive CF-ground state, which can only contribute to the observed Sc via non-diagonal elements ( = N D E ) with respect to the magnetic field operator /9H(L + 2 S ) between its eigenfunction and those of low-lying excited states. The corresponding / u 2 e ff/T-diagram (b) confirms this since a relatively steep and strictly linear section of the curve extending up to 17 K is observed, which b y extrapolation towards T — 0 precisely intersects the coordinate origin**. The absence of any field dependence of the Sc, even at the lowest temperatures studied, is in full accordance with the assumption of a non-magnetic ground state and a T I P exclusively due to N D E ' s 1 0 . A b o v e 30 K , at least two and at most three different quasi-linear Curie-Weiss-sections*** are found as the temperature is increased in curve (a)****. This suggests that up to room temperature at least two excited CF-states become thermally populated 1 0 . The alternative graphic representation
Oy 3-
13
(b) is consistent with this view in that here, within the temperature ranges of the Curie-Weiss-sections no full linearity is apparent. A quasi-linear curve section above 210 K suggests that even up to room temperature second-order Zeeman-interactions between all of the thermally populated CF-states and at least one further, relatively low-lying but still practically unpopulated CF-state play a nonnegligible role. 3. General Crystal Field Considerations The optical absorption spectra of UCp4 are known t o be noticeable simpler than the corresponding spectra of all complexes of the type ( ^ - C s H s ^ U X ( X = C1, Br, B H 4 ) U , where the CFsymmetry cannot be higher than C3v, so that it may be deduced that the actual symmetry of the CF of UCp 4 should not deviate drastically f r o m Td. (Considering only the central ion and the ring normals, UCp4 belongs to the molecular point group Td 4 ). Therefore it seems tempting for a CF** ,"2efr - (3 • k/N/32) x ' T = 8.0 • x • T. *** According to x = C/(T—0). **** Linear curve sections are primarily found between T —21 and 83 K [C = 0.565 (cm 3 • grd)/(mole), 6 = —18°], between 195 and 298 K (C = 0.90, 0 = —100°) and possibly also between 100 and 177 K (C = 0.758, 0 = —53°).
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14
H.-D. AMBERGER ET AL. • THE ELECTRONIC STRUCTURE OF UCp4 14
treatment of UCp4 to adopt a CF-Hamiltonian of the form: HCF = HcF(Td) + Hcf(S4)
(1)
orbital reduction effects etc. might be too important to still maintain the LLW-formalism as a useful approximation 1 .
assuming a much stronger contribution from the strictly tetrahedral component H C F ( T < I ) than from the S4-component
E
E/ \ E
HCF(S4).
Table I. Correlation of some irreducible representations for the descent of symmetry: Td ->D 2 d -*S4. TD
D 2D
S4
Ai
AI 1
Am
AI BI
Ai BI
TI
A2 En
AN En
T2
B2 Ei
BII Ei
E
A strictly tetrahedral CF would split the ionic ground state 3 H4'* of the [ R n ] 5 f 2 -system U 4 + into four CF-states. Considering the correlation table (Table I) for the descent from Td- to S4-(t>{a Dad-) symmetry 12 , it appears reasonable to associate the three viz. four closely following CF-states already populated at room temperature with some tetrahedral parent states which are, moreover, almost accidentally degenerate. In Table II, the three particular situations are specified in which, according to the familiar Lea-Leask-Wolf ( = L L W ) diagram for the pure Russell-Saunders-state 3Ü4 (see Fig. 2) 13 a crossover of the two (or three) lowest CF-states can take place. However, the experimental /^eft-value for room temperature does not match any of the three theoretical /^eft-values which would correspond to the three particular values of the ratio B4°/B6° of the two CF-splitting parameters** if accidental degeneracy is required for the CF-states originating from the ideal RussellSaunders-term 3H4 only. It is therefore reasonable to assume that substantial "higher-order effects" such as J-mixing via the (necessarily strong) CF, * The prime signifies the somewhat idealized view adopted by using the Russell-Saunders-symbol 3 Hi. ** The parameters B n ° are defined by the following cubic Hamiltonian: H CF (Td) = B 4 0 £(O 4 0 + 5 0 4 4 ) + B 6 0y(O 6 °—21 0 6 4 ), where the 0« m -terms are angular momentum operators transforming like the corresponding spherical harmonics and ß, y are operator equivalent factors introduced by S T E V E N S 1 4 .
T1
•A\ -0.8
-OX
0
OX
0.8
x
Fig. 2. Lea-Leask-Wolf-diagram of the free ion state 3H4. Table II. Specification of zero-energy crossover points in the Lea-Leask-Wolf-diagram of the 3H4-manifold (from firs+-order CF-calculations). Accidental degeneracy of states E:T2
B4O/B6O 4.88
/t2eff
(B.M.) 2
7.872
AI:T 2
— 1.94
6.000
Ai:E:Ti
— 10.46
8.972
4. Model Calculations for Fictivc Td-Systems For a further examination whether the above assumption of some rather weakly perturbed and almost (accidentally) degenerate tetrahedral CFstates is compatible with the particular molecular geometry of UCp4, the ratio B4°/B6° was determined on the basis of various semi-empirical model concepts. T o begin with, the fictitious, strictly tetrahedral f 1 -system (^-CeHe^M was subjected to model calculations in terms of pure Td-symmetry which involved essentially the same procedures as outlined in full detail in a recent treatment of the sandwich complex uranoeene 1 . The radius of the circles circumscribing the Cö-rings was taken equal to that of the Cs-ring within a real Cpligand, and the distance MC was set equal to the known UC-value in UCp4 4 - The possibility of constructing two strictly tetrahedral but stereochemically non-equivalent conformers ***• * * * * *** Conformation A with CeHö-rings pairwise converging with corners. **** Conformation B with CeHß-rings pairwise converging with edges.
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15
H.-D. AMBERGER ET AL. • THE ELECTRONIC STRUCTURE OF UCp4 (which may be transformed into each other b y appropriate rotations about the six-fold axes of the cyclic ligands) has required a separate consideration of each conformer. In view of the current interest in the physical origin and significance of CF-parameter sets playing a dominant role in all parametrized models 15 we have chosen to adopt three different model conceptions for the evaluation of the ratio B4°/B6°: a) the electrostatic "point charge model" ( = EPC) 16 , b) the "angular overlap model" ( = AOM) 1 7 ' 1 8 and, c) a simple molecular orbital approach in terms of the Mulliken-Helmholz-Wolfsberg ( = M H W - M O ) method. Whilst the EPC represents the extreme view of purely electrostatic interactions, the AOM and the M H W - M O are modified versions of an alternative view involving essentially covalent interactions (based on the consideration of overlapping orbitals).
carbon atoms and the central metal ion ignoring, for the sake of simplicity, any ^-interaction within, and between, the cyclic ligands (vide infra). In the present case, where the ring-C-atoms will essentially employ their 2 p z -orbitals for covalent bonding we are restricted to A = a and n. B y appropriately accounting for the discrete geometries of the two possible Td-conformations, the two sets of equations which give the energies of the seven f-orbitals in terms of the B n m and of the e r values, respectively*, have been evaluated b y familiar methods 17 ' 18 - 20 . The CF-parameters of the two fictive model systems result as follows: conformation A : B 4 ° = — 0 . 2 7 8 e f f — 0.138e„ B 6 ° = —0.075 ea + 0.053 e„ conformation B : B 4 ° = —0.293 e a — 0.105 e„ B 6 ° - —0.088 e a + 0.024 e„
' (
'
Since the pairs of linear combinations in (4a) and (4 b) are so similar, the transition from the fictive f 1 -system to the two-electron system in question a) According to the EPC the CF-parameters B n ° has been carried out with Eq. (4 a) only. are given b y 1 6 : A tetrahedral CF splits the ionic RussellB n o = Ajj 0
