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A new definition of coordination number and its use in lanthanide and actinide coordination and organometallic chemistry
Poll'ht.dron Vol. 8. No. 20. pp. 2431 2437. 1989 Printed in Great Britain
I)277-5387/89 $3,00+.00 t 1989 Pergamon Press pie
A N E W D E F I N I T I O N OF C O O R D I N A T I O N N U M B E R A N D ITS USE IN L A N T H A N I D E A N D ACTINIDE C O O R D I N A T I O N A N D ORGANOMETALLIC CHEMISTRY* JOAQUIM MAR~ALOt and ANTONIO PIRES DE MATOS Departamento de Quimica, ICEN, L N E T I , P-2686 Sacav6m Codex, Portugal
(Received 13 Janua O, 1989; accepted 18 May 1989) Abstract--A steric coordination number of a ligand is defined, based on the solid angle comprising the van der Waals' spheres of the atoms of that ligand, as an alternative to the Jormal coordination number in discussing structural aspects of lanthanide and actinide coordination and organometallic compounds. The study of the bond lengths in 274 structurally characterized compounds of the lanthanides (including Sc and Y), in oxidation states II and III, and the actinides (Th and U), in oxidation states III and IV, was the basis to derive ligand effect&e radii which are discussed in relation to bonding, coordination geometries, metal ionic radii and oxidation states. Potential uses of the new definition of coordination number and of the ligand effective radii obtained in molecular structure comparison and bond length prediction are also discussed.
COORDINATION NUMBER-THE VARIOUS DEFINITIONS Werner's "'secondary valence" introduced one of the most important concepts of coordination chemistry, that of coordination number (CN), later defined as the number of donor atoms associated with the central atom in a compound, i In crystal chemistry the CN has been equally important and usually identified with the number of "nearest-neighbours" of a given central atom in a crystal. Rigorous definitions of CN in this field have been proposed by several authors to overcome the uncertainty in choosing the appropriate number of "nearest-neighbours". -~ With the advent of d-transition metal organo* Presented in part at the XXV1 International Conference on Coordination Chemistry, Porto, Portugal, 28 August-2 September 1988. t Author to whom correspondence should be addressed. ++The solid angles considered in this work are the "real" geometrical solid angles which correspond to the areas defined on a unit sphere centred on the metal atom by the cones comprising the van der Waals spheres of the atoms ofa ligand. The areas, which have different shapes according to the ligand, can be straightforwardly calculated either by numerical integration (using a simple BASIC program developed by J. P. Leal of our Department) or analytically, by partitioning the surfaces in spherical segments and spherical triangles whose areas can be easily calculated.
metallic chemistry, a new definition emerged to account for a whole new class of ligands and to be consistent with the 18-electron rule: this is the formal coordination number ( C N v ) - - t h e number of electron pairs involved in ligand-to-metal coordination. 3 In f-transition element compounds bonding is generally considered highly ionic in character and a unifying principle such as the 18-electron rule is lacking. The number, size and shape of the ligands are then major factors determining the structural features of lanthanide (Ln) and actinide (An) compounds, and a definition of C N based on geometrical principles appears to be more adequate than the CNF.
A NEW DEFINITION OF COORDINATION NUMBER Here we define the steric coordination number (CNs) of a ligand in a series of compounds, as the ratio of the solid angle comprising the van der Waals' spheres of the atoms of that ligand and the solid angle of a common ligand like chlorine, when placed at typical mean distances from the central metal atom. With this definition we can build up a catalogue of ligand's CNs and use them to obtain the CNs of a compound. In Table 1 we can find the CNs's of selected ligands, with solid angles computed either analytically or numerically:~ using Bondi's van der
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J. MAR(~ALO and A. PIRES DE MATOS
2432
Waals' radii, 4 average metal-ligand distances (for Ln and An) and typical geometries of the ligands. The main sources of error in the values of Table I are, on one hand, the van der Waals' radii, which having been derived from intermolecular contacts may not be adequate for intramolecular contacts,
and, more importantly, the geometries of the ligands which, in the individual structures may present different bendings, tiltings, etc. The CNs value defined here is related to other solid angle-based ligand steric parameters, like Tolman's cone angles, 5 extensively used in d-transi-
Table 1. Steric coordination numbers (CNs) of selected ligands Ligating atom
C
Ligand
CNs
HF, CI, Br, IBH3R (t) (b) (bb)
0.80 1.00 1.42 1.24 1.06
CCRCHCH5 PhPh-2,6-Me~ CH2Ph (90") (110 ~') (130 ~) Me 'Bu "BuCH2SiMe3/CH 2CMe3 CH(SiMe3) ;AllylCNR COT 2COT- 1,3,5,7-Me~ COT-I,3,5,7-Ph]COT-(CH_,)_~COT-(CH2)3 COT-(CH)]CpMeCpCsMe~ CsH4SiMe3 C 5H 3-1,3-(SiMe 3)., IndInd-l,4,7-Me~
1.24 1.22 1.26 2.01 1.72 1.39 1.25 1.06 1.50 1.18 1.42 2.24 1.81 0.98 3.44 3.53 3.72 3.46 3.47 3.49 2.04 2.14 2.49 2.34 2.60 2.28 2.50
f S-"PrSPhS THT BTME
P
PPh; PMe3 P(OCH2)3CEt DMPE
Ligating atom
N
O
1.22 1.33 1.18 1.85
1.45 1.06 0.93 2.01
t--tridentate, b--bidentate, bb--bridging bidentate.
Ligand
CNs
TPP:OEP 2HBPz~ HB(3,5-Me2Pz)~ H_,BPz_;Pz NEt~ NPh~ N(SiMe3);NCS NCR PzH py bipy N(CH2CH2)3CH NH3 TMED
4.68 4.30 2.90 3.55 1.92 1.54 1.67 1.79 2.17 0.90 0.79 0.89 1.19 1.74 1.38 0.79 2.22
O-'BuOPh
1.40 1.28 1.59 1.70
OPh-2,6-Me~ OPh-2,6-iPr_~ OPh-2,6-'Bu;acac-/dpm OH2 THF/OMe2 OEt., DME TPPO HMPA TPPA DMPA DMIBA/DMPVA DEPA DIPA DIPPA DIPIBA DMF DMSO DPSO TEU TMU
2.41 .95 L84 .21 .44 .78 .42 .51 .48 .26 .34 .31 .28 .37 .45 .15 1.14 1.25 1.24
1.18
A new definition of coordination number tion metal phosphine chemistry, in the original or modified versions, 6 or Bagnall and Li Xing-fu's solid angle factors,7 used with some success in discussing stability, stereochemistry and reactivity of Ln and An compounds. Other solid angle approaches to steric effects were made by several authors and include organic reactivity, 8 the stereochemistry of Sn 9 and Th t° complexes, stability of transition element compounds t t and cluster chemistry. ~2 T H E STERIC C O O R D I N A T I O N N U M B E R AND ./=TRANSITION E L E M E N T CHEMISTRY
Ligand effective radii--CNv versus CNs In this paper we are interested in using our definition of CN to discuss and extend Raymond's structural model for the bonding in organolanthanide and -actinide compounds. ~3 In his approach, based on the CNE, Raymond obtained linear correlations between different metal-ligand distances (namely Cp , COT-'- and N(SiMe3)2) and ionic radii for the metal ions taken from the widely used Shannon's table of ionic radii, ~4 concluding that an ionic model was adequate to describe the bonding in f-transition element compounds. The same approach was later used by Edelstein to study metal borohydride complexes ~5 although, in this case, some doubts could arise regarding the CNF values adopted for bidentate and tridentate
BH~. Several other authors have used Raymond's approach, namely Deacon et al. in discussing the structures of Ln complexes containing oxygen- or nitrogen-donor ligands, t 7 Since the publication of Raymond's paper, ftransition element chemistry has grown impressively from about four dozen structurally characterized Ln and An organo compounds to a few hundred structures on which the same type of analysis can be performed. In the following discussion we considered 274 structurally characterized Ln (including Sc and Y) and An (Th and U) coordination and organometallic compounds. The analysis is by no means exhaustive: uranyl compounds were not included,
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oligomeric or polymeric compounds were not considered except those involving bridging borohydride ligands, and compounds containing less-common ligands were also excluded. This left us with 16 Ln u, 99 Ln m, 15 An m and 144 An fv compounds, covering a wide range of coordination geometries. In spite of the large number of complexes studied, there was a special incidence of U compounds (46%) and a good span of ionic radii was not obtained, so, in most of the cases, good linear relationships of metal-ligand distances vs metal ionic radius could not be observed. Nevertheless, better correlations were obtained when using the ionic radii derived from the CNs. This led us to focus our discussion on liyand effective radii (REF), checking on the constancy and consistency of the values produced using CNF and CNs. The ligand effective radii are presented in Table 2 and were calculated in the following way : (a) Determination of CNF and CNs (from Table 1) for a given complex. (b) Direct interpolation or extrapolation of metal ionic radii (RJ from Shannon's table ~4 (or David's table 18 for Thm and U m in CN 8) for the CN's determined in (a) (Shannon's ionic radii, in the range of CN 6-9, that include the great majority of CNE and CNs of the compounds considered in this study, can be fitted with linear equations, for each metal and oxidation state, with correlation coefficients better than 0.99 ; Pauling's equation for the dependence of ionic radii on CN used by Raymond ~3 gives values that are not consistent with Shannon's values; some of the correlations of metal-ligand distances and ionic radii in Raymond's paper might have been affected by using this procedure). (c) When two or more identical ligands are coordinated, an average metal-ligand bond length dM_ L is obtained from the molecular structure of the compound. (d) Calculation of REF = dM__L--R i for each complex and each CN used (formal or steric). (e) Determination of the arithmetic mean of REF for each type of ligand ; the values in parentheses are the sample standard deviations.*
From the values in Table 2 it is clear that for most of the ligands considered the REI:'S obtained using the C N F have larger standard deviations, indicating a wider spread of the individual REF'S. For * A more rigorous determination of the mean REv'S instance, for L = alkyl, (REF)Frange from 1.34/~ could be made considering all independent bond lengths in UCp3("Bu) 19 to 1.63/~, in YbCI[CH(SiMe3)2]~, 2° in the different structures weighted by the corresponding while (REF)s for the same complexes are L46 and standard deviations, so that the more accurately determined bond lengths have a larger weight. However, for i.41 ~, respectively ; another example is NPh~- for the general purpose of this work, the simpler procedure which (REF)Fis 1.50/~ in U(NPh2)421 and 1.20 A in UCp3(NPh2), 22 while (REv)~ are 1.32 and 1.30/~,, followed above is quite reasonable.
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J. MAR(~ALO and A. PIRES DE MATOS Table 2. Ligand effective radii (Rr~v) (/~) Ligating" atom
Ligand type
(REF)V
(REF) s
Borohydride (t)
1.33(8) 1.21(8) 1.56(6)
1.56(3) 1.49(4) 1.75(3)
1.42
1.65(5)
(b) (bb) Alkyl
C
Aryl Benzyl Alkenyl Alkynyl Allyl Cyclopentadienyl Cyclooctatetraene Isocyanide
Dialkylamide Disilylamide
N
Diarylamide Thiocyanate Pyrazolide Polypyrazolylborate (t) (b) Porphyrinate Nitrile Pyridine Bipyridyl Amine TMED NHs
Aryloxide Alkoxide fl-Diketonate Phosphine oxide O
Carbamide Sulphoxide Water Ether DME
F
Fluoride
N
O.S,
28 2 5
H L H
1.67
1
L
1.91(3)
8
H
19
H
1.45(8)
1.47(4)
1.27
1.44
1.46(17) 1.54(10) 1.35 1.26(2) 1.67(2) 1.66(7) 1.56(4) 1.56(4) 1.49(1) 1.63(33) 1.28
I
L
1.45(2) 1.54(3) 1.42 1.38(2) 1.71(1) 1.74(4) 1.66(3) 1.70(I) 1.62(7) 1.59(1) 1.41
4 6 1 2 2 103 23 9 2 2 1
H H H H H H L H L H L
1.39 1.43(7) 1.38(4) 1.35(21) 1.43(6) 1.28(3) 1.53(4) 1.46(4) 1.47(2) 1.48(6) 1.49(9) 1.41(5) 1.58 1.54 1.47 1.66(19) 1.44 1.41
1.12 1.27(2) 1.26(4) 1.31(1) 1.42(4) 1.39(1 ) 1.53(3) 1.47(4) 1.43(2) 1.60(5) 1.58(4) 1.50(2) 1.63 1.67 1.62 1.76(I) 1.50 1.47
1 9 3 2 17 3 11 2 4 14 8 3 1 1 1 2 1 1
H H L H H H H H H H H L H H L H H L
1.22( 11) 1.03 1.31(4) 1.33(7) 1.10 1.34(3) 1.37(6) 1.38(4) 1.37(12) 1.35(9) 1.52(26) 1.39(12)
1.09(4) 1.02 1.32(4) 1.28(4) 1.24 1.31(3) 1.32(6) 1.43(2) 1.45(6) 1.39(3) 1.60(1) 1.42(6)
13 1 21 20 1 18 2 11 37 7 2 3
H H H H L H H H H L H L
1.02
1.16
1
H
A new definition of coordination number
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Table 2--continued Ligating atom
(REF)V
(REF)s
1.82 1.87(7) 1.69(1) 2.04(14) 1.84(22)
1.83 1.99(2) 1.86(2) 2.07(4) 1.96(3)
1 3 2 7 4
H H L H L
1.67 1.69 1.83 1.70
1.70 !.74 2.10 1.85
1 1 1 I
H H H L
CI { Chloride
1.65(7) 1.51
1.65(4) 1.56
60 1
H L
Br
Bromide
1.81(8)
1.82(4)
14
H
I
Iodide
2.03(7)
2.05(5)
7
H
Ligand type Diarylphosphide Phosphine/Phosphite DMPE
Alkylthiolate Arylthiolate BTME Thioether
N
O.S.
N--number ofcompounds. O.S. H--Ln m and An Iv, O.S. L--Ln n and An"k t--tridentate, b--bidentate, bb--bridging bidentate.
respectively, in the same compounds. Other significant examples could be given, indicating the difficulties of the formal CN approach for dealing with sterically demanding ligands, especially those that formally donate one electron pair [e.g. N(SiMe3)_;-, NPh_;, OPh-2,6-'Bu_;, CH(SiMe3)_;-]. Another aspect which is apparent from Table 2 is that the REF values derived from the CNs have a relative ordering which is in closer agreement with what is expected from the sizes and bonding capabilities of the different coordinating atoms (e.g. (REF)F for C in alkyls is 1.45 /~, while for N in disilylamide it is i.43 ~, when one would expect a larger difference which is retained by the corresponding (REF)~ values, 1.47 and 1.27 ,~,).
Ligand effective radii--trends #7 (REv)s After showing some of the advantages of our definition of CN we will focus our attention now on (REF)~ and on some qualitative aspects that became apparent after studying such a large volume of structural data. The first aspect is that two sets of (REv)s had to be calculated for each type of ligand, one for Ln "~ and An ~v compounds and another one for Ln n and An m compounds. In fact, it was verified that REv'S obtained from this last group of compounds were systematically lower than the corresponding REv's obtained from Ln m and An jv compounds. The
reason for this can probably be found from Shannon's ionic radii 14which, having been derived from oxides and halides, were initially thought to be applicable to any kind of compound. This was later shown to be wrong and revised sets of ionic radii were reported for sulphides by Shannon 23 and for nitrides by Baur. 24 When comparing Shannon's oxide and sulphide sets, significant differences exist for the Ln and An ions, especially for Urn; Ri(6) = 1.025 /~ from oxides, Ri(7)= 0.99/~ and Ri(8) = 1.07/~ from sulphides. Other pertinent data concerning the size of the U vx ion result from the bond distances in structurally analogous compounds of U m and Ln w, for instance MCp3(THF), 25 which would place U m between Nd HIand Pr m (du_c = 2.79, du--o = 2.55/~, ; dpr-o = 2.80, dpr_ o = 2.56 and dNd---C= 2.78, dNd--O = 2.54/~,), while Shannon's oxide table gives a U m radius close to that of La m) (Ri(6) = 1.032 ~), and larger than the radii o f N d m (Ri(6) = 0.983 /~) and Pr nl (Ri(6) = 0.99/~). The differences between REF of compounds in higher and lower oxidation states might as well be attributed to covalency effects. Although these differences between (REEL are fairly constant for most of the ligand types in Table 2, significantly larger differences are seen for n-accepting ligands (isocyanide or phosphine). Incidentally, Andersen and co-workers have recently found evidence, based on structural data of isoleptic Ce H~ and U u'
2436
J. MAR(~ALO and A. PIRES DE MATOS
organometallic compounds, for the existence of n-back donation in the U m compounds containing isocyanide and phosphine or phosphite. 25 Another aspect is the s~nsitivity of the (REF)s values to the coordination geometry and to the relative repulsivities of the different positions in coordination polyhedra like the trigonal and pentagonal bipyramids (TBP and PBP), the capped octahedron (CO), the dodecahedron (DD) and the tricapped trigonal prism (TCTP). 26 As examples, we can refer to two U compounds, prepared in our laboratories, displaying CO geometries, where (REF)~ for the oxygen atoms of the capping T H F ligands are substantially larger than the mean value for that iigand in Table 2 (1.56 A in UCI3[HB(3,5Me2Pz)3](THF) 27 and 1.60 A. in UCI(OPh)2[HB (3,5-Me2Pz)3](THF). 28 The same happens in two closely related U compounds with PBP geometries, where (REF)~ for the O atoms of the TPPO ligands in equatorial positions are larger than the mean value in Table 2 (1.36 A, in UCI2(acac)2(TPPO) and 1.38 A, in UCpCl(acac)2(TPPO)29). This sensitivity to the position on the coordination polyhedron is more evident for neutral ligands and is reflected in the larger standard deviations of the corresponding (REF)s, when compared with the standard deviations of anionic ligands (e.g. ether and nitrile values in Table 2). The different behaviour of neutral and anionic ligands are not surprising as larger repulsions would be expected between anionic ligands which would then preferentially occupy the coordination positions with smaller repulsitivities. This also has implications on the metal-ligand distances in charged complexes and is more evident from some of the (REF)~ in anionic complexes. For example, in Er(NCS)36-, 3° (REF)s is 1.49 A,, significantly larger than the mean values for N C S - in Table 2; the same happens in UCI6- where, for the more accurate structural determination of this species,31 (REF)s is 1.73 A,, again substantially larger than the mean value for CI in Table 2.
APPLICATIONS OF CNs AND (REr)s The two main uses for the quantities presented in Tables 1 and 2 are molecular structure comparison and bond length prediction. In the first application, the (REF)s in Table 2 may serve as references in discussing a new structure, by comparison with the (REF)s determined, as described before, for each ligand in the new complex. This enables us to see if we are in the presence of a "well-behaved" compound or if there are any unusual bond lengths and, in a certain way, try to explain its origin, for instance, in coor-
dination geometry, covalency effects, intra- or intermolecular contacts or uncertainties in the structural determination. The second application is obvious and, of course, dependent on the uncertainties of the values in Tables I and 2. The procedure is simple : (a) Determination of the CNs of the complex in question from the values in Table 1. (b) Determination of the metal ionic radius by interpolation or extrapolation from Shannon's table. ' 4 (c) Determination of metal-ligand distance by adding the appropriate (REF)s value from Table 2 to the value obtained in (b). (d) Introduction of corrections accounting for relative repulsivities in the expected coordination polyhedron (from ref. 26). C O N C L U D I N G REMARKS The CNs introduced above was shown to account for the general structural features of Ln and An compounds. The influence of steric effects on the bond lengths of a particular compound is, of course, more subtle, requiring a detailed analysis of the available structural data. Such a study is being undertaken, as well as extensions of the model to include uranyl complexes, new ligands and oligomeric compounds. Acknowledgements--The authors are grateful to Jo~o Paulo Leal for computer programs and many helpful discussions. The authors thank Dr N. Edelstein for encouragement. Supplementary material. A list of the compounds studied (with references) is available from the authors.
REFERENCES 1. N.N. Greenwood and A. Earnshaw, Chemistry of the Elements, pp. 1068-1069. Pergamon Press, Oxford (1984). 2. R. Hoppe, Angew. Chem. Int. Ed. Engl. 1970, 9, 25; G. O. Brunner, Acta Crvst. 1977, 33A, 226; S. S. Batsanov, Russ. d. Inory. Chem. 1977, 22, 631 ; F. L. Carter, Acta Crvst. 1978, 34B, 2962; M. O'Keeffe, Acta Cryst. 1979, 35A, 772. 3. J. P. Collman, L. S. Hegedus, J. R. Norton and R. G. Finke, Principles and Applications aJ Organotransition Metal Chemistry, pp. 24-30. University Science Books, Mill Valley, California (1987). 4. A. Bondi, J. Phys. Chem. 1964, 68, 441. 5. C. A. Tolman, Chem. Rev. 1977, 77, 313.
A new definition of coordination number 6. C. A. McAuliffe, in Comprehensh,e Coordination Chemistl3' (Edited by G. Wilkinson, R. D. Gillard and J. A. McCleverty), Vol. 2, pp. 1012-1029. Pergamon Press, Oxford (1987). 7. K. W. Bagnall and Li Xing-fu, J. Chem. Soc., Dalton Trans. 1982, 1365; R. D. Fischer and Li Xing-fu, J. Less-Common Met. 1985, 112, 303 ; Li Xing-fu, Shen Tian-gi, Guo Ao-ling, Shun Guang-li and Sun Pengnian, Inor9. Chim. Acta 1987, 129, 227 and following papers in the same issue; Li Xing-fu and Guo Aoling, Inor9. Chim. Acta 1987, 131, 129: Li Xing-fu and Guo Ao-ling, Inor9. Chim. Acta 1987, 134, 143. 8. W. T. Wipke and P. Gund, J. Am. Chem. Soc. 1976, 98, 8107; J. I. Secman, J. W. Viers, J. C. Schug and M. D. Stovall, J. Am. Chem. Soc. 1984, 106, 143. 9. R. E. Zahrobsky, J. Am. Chem. Soc. 1971, 93, 3313. 10. A. J. Smith, Proceedinys o] the 11 ~'''" Journbes des Acthrides, p. 64. Jesolo, Italy (1981). 11. E. B. Lobkovskii, J. Struct. Chem. 1983, 24, 224; E. B. Lobkovskii, J. Organomet. Chem. 1984, 277, 53. 12. D. M. P. Mingos, Inor9. Chem. 1982, 21,464. 13. K.N. Raymond and C. W. Eigenbrot Jr, Accts Chem. Res. 1980, 13, 276. 14. R. D. Shannon, Acta OTst. 1976, 32A, 751. 15. N. Edelstein, Inor9. Chem. 1981, 20, 297. 16. T. J. Marks and J. R. Kolb, Chem. Retd. 1977, 77, 263. 17. G. B. Deacon. P. I. Mackinnon, T. W. Hambley and J. C. Taylor, J. Oryanomet. Chem. 1983, 259, 91 ; G. B. Deacon, B. M. Gatehouse, S. N. Platts and D. L. Wilkinson, Aust. J. Chem. 1987, 40, 907.
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18. F. David, J. Less-Common Met. 1986, 121, 27. 19. G. Parego, M. Cesari, F. Forina and G. Jugli, Acta Cr.vst. 1976, 32B, 3034. 20. J. L. Atwood, W. E. Hunter, R. D. Rogers, J. Holton, J. McMeeking, R. Pearce and M. F. Lappert, J. Chem. Soc., Chem. Commun. 1978, 140. 21. J. G. Reynolds, A. Zalkin, D. H. Templeton and N. M. Edelstein, Inor9. Chem. 1977, 16, 1090. 22. R. E. Cramer, U. Engelhardt, K. T. Higa and J. W. Gilje, Organometallics 1987, 6, 41. 23. R. D. Shannon, in Structure and Bondin 9 in Crystals (Edited by M. O'Keet'e and A. Navrotsky), Vol. 2, pp. 53-70. Academic Press, New York (1981). 24. W. H. Baur, Cryst. Rev. 1987, 1, 61. 25. J. G. Brennan, S. D. Stults, R. A. Andersen and A. Zalkin, Inor#. Chim. Acta 1987, 139, 201; Oryanometallics, 1988, 7, 1329. 26. D. L. Kepert, Inorganic Stereochemistry. Springer, Berlin (1982). 27. R. G. Ball, F. Edelmann, J. G. Matisons, J. Takats, N. Marques, J. Marqalo, A. Pires de Matos and K. W. Bagnall, lnor9. Chim. Acta 1987, 132, 137. 28. N. Marques, A. Domingos, J. Marqalo, A. Pires de Matos, J. Takats and K. W. Bagnall, J. Less-Common Met. 1989, 149, 271. 29. C. Baudin, P. Charpin, M. Ephritikhine, M. Lance, M. Nierlich and J. Vigner, J. Organomet. Chem. 1988, 345, 263. 30. J. L. Martin, L. C. Thompson, J. L. Radonovich and M. D. Glick, J. Am. Chem. Soc. 1968, 90, 4493. 31. M. R. Caira, J. F. De Wet, J. G. H. Du Preez and B. J. Gellatly, Acta Crvst. 1978, 34B, 1116.
I)277-5387/89 $3,00+.00 t 1989 Pergamon Press pie
A N E W D E F I N I T I O N OF C O O R D I N A T I O N N U M B E R A N D ITS USE IN L A N T H A N I D E A N D ACTINIDE C O O R D I N A T I O N A N D ORGANOMETALLIC CHEMISTRY* JOAQUIM MAR~ALOt and ANTONIO PIRES DE MATOS Departamento de Quimica, ICEN, L N E T I , P-2686 Sacav6m Codex, Portugal
(Received 13 Janua O, 1989; accepted 18 May 1989) Abstract--A steric coordination number of a ligand is defined, based on the solid angle comprising the van der Waals' spheres of the atoms of that ligand, as an alternative to the Jormal coordination number in discussing structural aspects of lanthanide and actinide coordination and organometallic compounds. The study of the bond lengths in 274 structurally characterized compounds of the lanthanides (including Sc and Y), in oxidation states II and III, and the actinides (Th and U), in oxidation states III and IV, was the basis to derive ligand effect&e radii which are discussed in relation to bonding, coordination geometries, metal ionic radii and oxidation states. Potential uses of the new definition of coordination number and of the ligand effective radii obtained in molecular structure comparison and bond length prediction are also discussed.
COORDINATION NUMBER-THE VARIOUS DEFINITIONS Werner's "'secondary valence" introduced one of the most important concepts of coordination chemistry, that of coordination number (CN), later defined as the number of donor atoms associated with the central atom in a compound, i In crystal chemistry the CN has been equally important and usually identified with the number of "nearest-neighbours" of a given central atom in a crystal. Rigorous definitions of CN in this field have been proposed by several authors to overcome the uncertainty in choosing the appropriate number of "nearest-neighbours". -~ With the advent of d-transition metal organo* Presented in part at the XXV1 International Conference on Coordination Chemistry, Porto, Portugal, 28 August-2 September 1988. t Author to whom correspondence should be addressed. ++The solid angles considered in this work are the "real" geometrical solid angles which correspond to the areas defined on a unit sphere centred on the metal atom by the cones comprising the van der Waals spheres of the atoms ofa ligand. The areas, which have different shapes according to the ligand, can be straightforwardly calculated either by numerical integration (using a simple BASIC program developed by J. P. Leal of our Department) or analytically, by partitioning the surfaces in spherical segments and spherical triangles whose areas can be easily calculated.
metallic chemistry, a new definition emerged to account for a whole new class of ligands and to be consistent with the 18-electron rule: this is the formal coordination number ( C N v ) - - t h e number of electron pairs involved in ligand-to-metal coordination. 3 In f-transition element compounds bonding is generally considered highly ionic in character and a unifying principle such as the 18-electron rule is lacking. The number, size and shape of the ligands are then major factors determining the structural features of lanthanide (Ln) and actinide (An) compounds, and a definition of C N based on geometrical principles appears to be more adequate than the CNF.
A NEW DEFINITION OF COORDINATION NUMBER Here we define the steric coordination number (CNs) of a ligand in a series of compounds, as the ratio of the solid angle comprising the van der Waals' spheres of the atoms of that ligand and the solid angle of a common ligand like chlorine, when placed at typical mean distances from the central metal atom. With this definition we can build up a catalogue of ligand's CNs and use them to obtain the CNs of a compound. In Table 1 we can find the CNs's of selected ligands, with solid angles computed either analytically or numerically:~ using Bondi's van der
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J. MAR(~ALO and A. PIRES DE MATOS
2432
Waals' radii, 4 average metal-ligand distances (for Ln and An) and typical geometries of the ligands. The main sources of error in the values of Table I are, on one hand, the van der Waals' radii, which having been derived from intermolecular contacts may not be adequate for intramolecular contacts,
and, more importantly, the geometries of the ligands which, in the individual structures may present different bendings, tiltings, etc. The CNs value defined here is related to other solid angle-based ligand steric parameters, like Tolman's cone angles, 5 extensively used in d-transi-
Table 1. Steric coordination numbers (CNs) of selected ligands Ligating atom
C
Ligand
CNs
HF, CI, Br, IBH3R (t) (b) (bb)
0.80 1.00 1.42 1.24 1.06
CCRCHCH5 PhPh-2,6-Me~ CH2Ph (90") (110 ~') (130 ~) Me 'Bu "BuCH2SiMe3/CH 2CMe3 CH(SiMe3) ;AllylCNR COT 2COT- 1,3,5,7-Me~ COT-I,3,5,7-Ph]COT-(CH_,)_~COT-(CH2)3 COT-(CH)]CpMeCpCsMe~ CsH4SiMe3 C 5H 3-1,3-(SiMe 3)., IndInd-l,4,7-Me~
1.24 1.22 1.26 2.01 1.72 1.39 1.25 1.06 1.50 1.18 1.42 2.24 1.81 0.98 3.44 3.53 3.72 3.46 3.47 3.49 2.04 2.14 2.49 2.34 2.60 2.28 2.50
f S-"PrSPhS THT BTME
P
PPh; PMe3 P(OCH2)3CEt DMPE
Ligating atom
N
O
1.22 1.33 1.18 1.85
1.45 1.06 0.93 2.01
t--tridentate, b--bidentate, bb--bridging bidentate.
Ligand
CNs
TPP:OEP 2HBPz~ HB(3,5-Me2Pz)~ H_,BPz_;Pz NEt~ NPh~ N(SiMe3);NCS NCR PzH py bipy N(CH2CH2)3CH NH3 TMED
4.68 4.30 2.90 3.55 1.92 1.54 1.67 1.79 2.17 0.90 0.79 0.89 1.19 1.74 1.38 0.79 2.22
O-'BuOPh
1.40 1.28 1.59 1.70
OPh-2,6-Me~ OPh-2,6-iPr_~ OPh-2,6-'Bu;acac-/dpm OH2 THF/OMe2 OEt., DME TPPO HMPA TPPA DMPA DMIBA/DMPVA DEPA DIPA DIPPA DIPIBA DMF DMSO DPSO TEU TMU
2.41 .95 L84 .21 .44 .78 .42 .51 .48 .26 .34 .31 .28 .37 .45 .15 1.14 1.25 1.24
1.18
A new definition of coordination number tion metal phosphine chemistry, in the original or modified versions, 6 or Bagnall and Li Xing-fu's solid angle factors,7 used with some success in discussing stability, stereochemistry and reactivity of Ln and An compounds. Other solid angle approaches to steric effects were made by several authors and include organic reactivity, 8 the stereochemistry of Sn 9 and Th t° complexes, stability of transition element compounds t t and cluster chemistry. ~2 T H E STERIC C O O R D I N A T I O N N U M B E R AND ./=TRANSITION E L E M E N T CHEMISTRY
Ligand effective radii--CNv versus CNs In this paper we are interested in using our definition of CN to discuss and extend Raymond's structural model for the bonding in organolanthanide and -actinide compounds. ~3 In his approach, based on the CNE, Raymond obtained linear correlations between different metal-ligand distances (namely Cp , COT-'- and N(SiMe3)2) and ionic radii for the metal ions taken from the widely used Shannon's table of ionic radii, ~4 concluding that an ionic model was adequate to describe the bonding in f-transition element compounds. The same approach was later used by Edelstein to study metal borohydride complexes ~5 although, in this case, some doubts could arise regarding the CNF values adopted for bidentate and tridentate
BH~. Several other authors have used Raymond's approach, namely Deacon et al. in discussing the structures of Ln complexes containing oxygen- or nitrogen-donor ligands, t 7 Since the publication of Raymond's paper, ftransition element chemistry has grown impressively from about four dozen structurally characterized Ln and An organo compounds to a few hundred structures on which the same type of analysis can be performed. In the following discussion we considered 274 structurally characterized Ln (including Sc and Y) and An (Th and U) coordination and organometallic compounds. The analysis is by no means exhaustive: uranyl compounds were not included,
2433
oligomeric or polymeric compounds were not considered except those involving bridging borohydride ligands, and compounds containing less-common ligands were also excluded. This left us with 16 Ln u, 99 Ln m, 15 An m and 144 An fv compounds, covering a wide range of coordination geometries. In spite of the large number of complexes studied, there was a special incidence of U compounds (46%) and a good span of ionic radii was not obtained, so, in most of the cases, good linear relationships of metal-ligand distances vs metal ionic radius could not be observed. Nevertheless, better correlations were obtained when using the ionic radii derived from the CNs. This led us to focus our discussion on liyand effective radii (REF), checking on the constancy and consistency of the values produced using CNF and CNs. The ligand effective radii are presented in Table 2 and were calculated in the following way : (a) Determination of CNF and CNs (from Table 1) for a given complex. (b) Direct interpolation or extrapolation of metal ionic radii (RJ from Shannon's table ~4 (or David's table 18 for Thm and U m in CN 8) for the CN's determined in (a) (Shannon's ionic radii, in the range of CN 6-9, that include the great majority of CNE and CNs of the compounds considered in this study, can be fitted with linear equations, for each metal and oxidation state, with correlation coefficients better than 0.99 ; Pauling's equation for the dependence of ionic radii on CN used by Raymond ~3 gives values that are not consistent with Shannon's values; some of the correlations of metal-ligand distances and ionic radii in Raymond's paper might have been affected by using this procedure). (c) When two or more identical ligands are coordinated, an average metal-ligand bond length dM_ L is obtained from the molecular structure of the compound. (d) Calculation of REF = dM__L--R i for each complex and each CN used (formal or steric). (e) Determination of the arithmetic mean of REF for each type of ligand ; the values in parentheses are the sample standard deviations.*
From the values in Table 2 it is clear that for most of the ligands considered the REI:'S obtained using the C N F have larger standard deviations, indicating a wider spread of the individual REF'S. For * A more rigorous determination of the mean REv'S instance, for L = alkyl, (REF)Frange from 1.34/~ could be made considering all independent bond lengths in UCp3("Bu) 19 to 1.63/~, in YbCI[CH(SiMe3)2]~, 2° in the different structures weighted by the corresponding while (REF)s for the same complexes are L46 and standard deviations, so that the more accurately determined bond lengths have a larger weight. However, for i.41 ~, respectively ; another example is NPh~- for the general purpose of this work, the simpler procedure which (REF)Fis 1.50/~ in U(NPh2)421 and 1.20 A in UCp3(NPh2), 22 while (REv)~ are 1.32 and 1.30/~,, followed above is quite reasonable.
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J. MAR(~ALO and A. PIRES DE MATOS Table 2. Ligand effective radii (Rr~v) (/~) Ligating" atom
Ligand type
(REF)V
(REF) s
Borohydride (t)
1.33(8) 1.21(8) 1.56(6)
1.56(3) 1.49(4) 1.75(3)
1.42
1.65(5)
(b) (bb) Alkyl
C
Aryl Benzyl Alkenyl Alkynyl Allyl Cyclopentadienyl Cyclooctatetraene Isocyanide
Dialkylamide Disilylamide
N
Diarylamide Thiocyanate Pyrazolide Polypyrazolylborate (t) (b) Porphyrinate Nitrile Pyridine Bipyridyl Amine TMED NHs
Aryloxide Alkoxide fl-Diketonate Phosphine oxide O
Carbamide Sulphoxide Water Ether DME
F
Fluoride
N
O.S,
28 2 5
H L H
1.67
1
L
1.91(3)
8
H
19
H
1.45(8)
1.47(4)
1.27
1.44
1.46(17) 1.54(10) 1.35 1.26(2) 1.67(2) 1.66(7) 1.56(4) 1.56(4) 1.49(1) 1.63(33) 1.28
I
L
1.45(2) 1.54(3) 1.42 1.38(2) 1.71(1) 1.74(4) 1.66(3) 1.70(I) 1.62(7) 1.59(1) 1.41
4 6 1 2 2 103 23 9 2 2 1
H H H H H H L H L H L
1.39 1.43(7) 1.38(4) 1.35(21) 1.43(6) 1.28(3) 1.53(4) 1.46(4) 1.47(2) 1.48(6) 1.49(9) 1.41(5) 1.58 1.54 1.47 1.66(19) 1.44 1.41
1.12 1.27(2) 1.26(4) 1.31(1) 1.42(4) 1.39(1 ) 1.53(3) 1.47(4) 1.43(2) 1.60(5) 1.58(4) 1.50(2) 1.63 1.67 1.62 1.76(I) 1.50 1.47
1 9 3 2 17 3 11 2 4 14 8 3 1 1 1 2 1 1
H H L H H H H H H H H L H H L H H L
1.22( 11) 1.03 1.31(4) 1.33(7) 1.10 1.34(3) 1.37(6) 1.38(4) 1.37(12) 1.35(9) 1.52(26) 1.39(12)
1.09(4) 1.02 1.32(4) 1.28(4) 1.24 1.31(3) 1.32(6) 1.43(2) 1.45(6) 1.39(3) 1.60(1) 1.42(6)
13 1 21 20 1 18 2 11 37 7 2 3
H H H H L H H H H L H L
1.02
1.16
1
H
A new definition of coordination number
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Table 2--continued Ligating atom
(REF)V
(REF)s
1.82 1.87(7) 1.69(1) 2.04(14) 1.84(22)
1.83 1.99(2) 1.86(2) 2.07(4) 1.96(3)
1 3 2 7 4
H H L H L
1.67 1.69 1.83 1.70
1.70 !.74 2.10 1.85
1 1 1 I
H H H L
CI { Chloride
1.65(7) 1.51
1.65(4) 1.56
60 1
H L
Br
Bromide
1.81(8)
1.82(4)
14
H
I
Iodide
2.03(7)
2.05(5)
7
H
Ligand type Diarylphosphide Phosphine/Phosphite DMPE
Alkylthiolate Arylthiolate BTME Thioether
N
O.S.
N--number ofcompounds. O.S. H--Ln m and An Iv, O.S. L--Ln n and An"k t--tridentate, b--bidentate, bb--bridging bidentate.
respectively, in the same compounds. Other significant examples could be given, indicating the difficulties of the formal CN approach for dealing with sterically demanding ligands, especially those that formally donate one electron pair [e.g. N(SiMe3)_;-, NPh_;, OPh-2,6-'Bu_;, CH(SiMe3)_;-]. Another aspect which is apparent from Table 2 is that the REF values derived from the CNs have a relative ordering which is in closer agreement with what is expected from the sizes and bonding capabilities of the different coordinating atoms (e.g. (REF)F for C in alkyls is 1.45 /~, while for N in disilylamide it is i.43 ~, when one would expect a larger difference which is retained by the corresponding (REF)~ values, 1.47 and 1.27 ,~,).
Ligand effective radii--trends #7 (REv)s After showing some of the advantages of our definition of CN we will focus our attention now on (REF)~ and on some qualitative aspects that became apparent after studying such a large volume of structural data. The first aspect is that two sets of (REv)s had to be calculated for each type of ligand, one for Ln "~ and An ~v compounds and another one for Ln n and An m compounds. In fact, it was verified that REv'S obtained from this last group of compounds were systematically lower than the corresponding REv's obtained from Ln m and An jv compounds. The
reason for this can probably be found from Shannon's ionic radii 14which, having been derived from oxides and halides, were initially thought to be applicable to any kind of compound. This was later shown to be wrong and revised sets of ionic radii were reported for sulphides by Shannon 23 and for nitrides by Baur. 24 When comparing Shannon's oxide and sulphide sets, significant differences exist for the Ln and An ions, especially for Urn; Ri(6) = 1.025 /~ from oxides, Ri(7)= 0.99/~ and Ri(8) = 1.07/~ from sulphides. Other pertinent data concerning the size of the U vx ion result from the bond distances in structurally analogous compounds of U m and Ln w, for instance MCp3(THF), 25 which would place U m between Nd HIand Pr m (du_c = 2.79, du--o = 2.55/~, ; dpr-o = 2.80, dpr_ o = 2.56 and dNd---C= 2.78, dNd--O = 2.54/~,), while Shannon's oxide table gives a U m radius close to that of La m) (Ri(6) = 1.032 ~), and larger than the radii o f N d m (Ri(6) = 0.983 /~) and Pr nl (Ri(6) = 0.99/~). The differences between REF of compounds in higher and lower oxidation states might as well be attributed to covalency effects. Although these differences between (REEL are fairly constant for most of the ligand types in Table 2, significantly larger differences are seen for n-accepting ligands (isocyanide or phosphine). Incidentally, Andersen and co-workers have recently found evidence, based on structural data of isoleptic Ce H~ and U u'
2436
J. MAR(~ALO and A. PIRES DE MATOS
organometallic compounds, for the existence of n-back donation in the U m compounds containing isocyanide and phosphine or phosphite. 25 Another aspect is the s~nsitivity of the (REF)s values to the coordination geometry and to the relative repulsivities of the different positions in coordination polyhedra like the trigonal and pentagonal bipyramids (TBP and PBP), the capped octahedron (CO), the dodecahedron (DD) and the tricapped trigonal prism (TCTP). 26 As examples, we can refer to two U compounds, prepared in our laboratories, displaying CO geometries, where (REF)~ for the oxygen atoms of the capping T H F ligands are substantially larger than the mean value for that iigand in Table 2 (1.56 A in UCI3[HB(3,5Me2Pz)3](THF) 27 and 1.60 A. in UCI(OPh)2[HB (3,5-Me2Pz)3](THF). 28 The same happens in two closely related U compounds with PBP geometries, where (REF)~ for the O atoms of the TPPO ligands in equatorial positions are larger than the mean value in Table 2 (1.36 A, in UCI2(acac)2(TPPO) and 1.38 A, in UCpCl(acac)2(TPPO)29). This sensitivity to the position on the coordination polyhedron is more evident for neutral ligands and is reflected in the larger standard deviations of the corresponding (REF)s, when compared with the standard deviations of anionic ligands (e.g. ether and nitrile values in Table 2). The different behaviour of neutral and anionic ligands are not surprising as larger repulsions would be expected between anionic ligands which would then preferentially occupy the coordination positions with smaller repulsitivities. This also has implications on the metal-ligand distances in charged complexes and is more evident from some of the (REF)~ in anionic complexes. For example, in Er(NCS)36-, 3° (REF)s is 1.49 A,, significantly larger than the mean values for N C S - in Table 2; the same happens in UCI6- where, for the more accurate structural determination of this species,31 (REF)s is 1.73 A,, again substantially larger than the mean value for CI in Table 2.
APPLICATIONS OF CNs AND (REr)s The two main uses for the quantities presented in Tables 1 and 2 are molecular structure comparison and bond length prediction. In the first application, the (REF)s in Table 2 may serve as references in discussing a new structure, by comparison with the (REF)s determined, as described before, for each ligand in the new complex. This enables us to see if we are in the presence of a "well-behaved" compound or if there are any unusual bond lengths and, in a certain way, try to explain its origin, for instance, in coor-
dination geometry, covalency effects, intra- or intermolecular contacts or uncertainties in the structural determination. The second application is obvious and, of course, dependent on the uncertainties of the values in Tables I and 2. The procedure is simple : (a) Determination of the CNs of the complex in question from the values in Table 1. (b) Determination of the metal ionic radius by interpolation or extrapolation from Shannon's table. ' 4 (c) Determination of metal-ligand distance by adding the appropriate (REF)s value from Table 2 to the value obtained in (b). (d) Introduction of corrections accounting for relative repulsivities in the expected coordination polyhedron (from ref. 26). C O N C L U D I N G REMARKS The CNs introduced above was shown to account for the general structural features of Ln and An compounds. The influence of steric effects on the bond lengths of a particular compound is, of course, more subtle, requiring a detailed analysis of the available structural data. Such a study is being undertaken, as well as extensions of the model to include uranyl complexes, new ligands and oligomeric compounds. Acknowledgements--The authors are grateful to Jo~o Paulo Leal for computer programs and many helpful discussions. The authors thank Dr N. Edelstein for encouragement. Supplementary material. A list of the compounds studied (with references) is available from the authors.
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18. F. David, J. Less-Common Met. 1986, 121, 27. 19. G. Parego, M. Cesari, F. Forina and G. Jugli, Acta Cr.vst. 1976, 32B, 3034. 20. J. L. Atwood, W. E. Hunter, R. D. Rogers, J. Holton, J. McMeeking, R. Pearce and M. F. Lappert, J. Chem. Soc., Chem. Commun. 1978, 140. 21. J. G. Reynolds, A. Zalkin, D. H. Templeton and N. M. Edelstein, Inor9. Chem. 1977, 16, 1090. 22. R. E. Cramer, U. Engelhardt, K. T. Higa and J. W. Gilje, Organometallics 1987, 6, 41. 23. R. D. Shannon, in Structure and Bondin 9 in Crystals (Edited by M. O'Keet'e and A. Navrotsky), Vol. 2, pp. 53-70. Academic Press, New York (1981). 24. W. H. Baur, Cryst. Rev. 1987, 1, 61. 25. J. G. Brennan, S. D. Stults, R. A. Andersen and A. Zalkin, Inor#. Chim. Acta 1987, 139, 201; Oryanometallics, 1988, 7, 1329. 26. D. L. Kepert, Inorganic Stereochemistry. Springer, Berlin (1982). 27. R. G. Ball, F. Edelmann, J. G. Matisons, J. Takats, N. Marques, J. Marqalo, A. Pires de Matos and K. W. Bagnall, lnor9. Chim. Acta 1987, 132, 137. 28. N. Marques, A. Domingos, J. Marqalo, A. Pires de Matos, J. Takats and K. W. Bagnall, J. Less-Common Met. 1989, 149, 271. 29. C. Baudin, P. Charpin, M. Ephritikhine, M. Lance, M. Nierlich and J. Vigner, J. Organomet. Chem. 1988, 345, 263. 30. J. L. Martin, L. C. Thompson, J. L. Radonovich and M. D. Glick, J. Am. Chem. Soc. 1968, 90, 4493. 31. M. R. Caira, J. F. De Wet, J. G. H. Du Preez and B. J. Gellatly, Acta Crvst. 1978, 34B, 1116.