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Home , Bond length, Single bond

Proc. Nati. Acad. Sci. USA Vol. 73, No. 12, pp. 4290-4293, December 1976

Metal-metal bond lengths in complexes of transition metals* (valence bonds/resonating bonds/metal carbonyls/spd hybrid orbitals) LINUS PAULING Linus Pauling Institute of Science and Medicine, 2700 Sand Hill Road, Menlo Park, California 94025 Contributed by Linus Pauling, October 12, 1976

ABSTRACT In complexes of the transition metals con- charge on each is close to zero (in the range-1 to +1), taining clusters of metal the cobalt-cobalt bond lengths when calculated with consideration of transfer and of are almost always within 1 pm of the single-bond value 246 pm given by the enneacovalent radius of cobalt, whereas most of the partial ionic character of covalent bonds as determined by the observed iron-iron bond lengths are significantly larger than the difference in electronegativity of the bonded atoms (ref. the single-bond value 248 pm, the mean being 264 pm, which 12, p. 98). corresponds to a half-bond. A simple discussion of the structures of these complexes based on spd hybrid orbitals, the electro- Cobalt complexes neutrality principle, and the partial ionic character of bonds between unlike atoms to the conclusion that The neutral cobalt atom has nine valence and nine spd between single bonds and no-bonds would occur for iron and bond orbitals, and can accordingly form nine covalent its congeners but not for cobalt and its congeners, explaining bonds without electron transfer. In the Co(CO)4 group eight the difference in the bond lengths. of the valences of the cobalt atom would be used in the four Co=C=;O bonds, leaving one valence, which can attach the An atom of a transition metal may form as many as nine cova- group to another atom, as in HCo(CO)4 (13), Hg[Co (CO)4]2 lent bonds, with use of nine hybrid spd bond orbitals (1). An (14), In[Co(CO)4]3 (15), and BrSn[Co(CO)413 (16). The group example is the [ReH9] ion in K2ReH9 (2), in which the nine Co(CO)3 can form three bonds, as in Sb4[Co(CO)3]4 (17), in Re-H bonds are formed by one of the three most stable sets which the and cobalt atoms lie at corners of inverse of nine spd orbitals. The transfer of two electrons from the tetrahedra and the Co-Sb bonds lie along the edges of the potassium atoms to the rhenium atom increases the number of distorted cube, with Sb-Co--Sb angle 74.3°, close to the value its valence electrons from 7 to 9, permitting it to become en- 73.15° for best spd bonds (ref. 12, p. 152). neacovalent. I formulated a set of single-bond enneacovalent All of the complexes listed in Table 1 involve trivalent radii for the transition metals on the basis of many reported Co(CO)3 groups. In Co2(CO)8 the two.Co(CO)3 groups are tied bond lengths (3). These radii decrease by steps of 1 pm from 126 together by a Co-Co bond and two bridging carbonyl groups, to 122 pm in the sequence Cr, Mn, Fe, Co, Ni, and the values each forming a with each of the cobalt atoms. In for the congeners Mo, Tc, Ru, Rh, Pd. and W, Re, Os, Ir, Pt are all of the other complexes there are tetrahedra of four atoms, respectively 13 pm and 14 pm larger. The value for Re, 139 pm, Co2C2 or Co3C, with single bonds along the six edges. A single and the customary value for H, 30 pm, to 169 pm for valence-bond structure can be assigned to each of these com- Re-H, in agreement with the observed value (2), 168 pm. plexes. Some contribution, however, is made also by other Similar agreement is found for many other bonds, including to the often observed many metal-metal bonds. For Co-Co, for example, the seven structures, corresponding hyperconju- pm, with five gation of groups with bond-angle strain (the Co-C-Co angle reported values (Table 1) lie between 245 and 252 in [CCo3(CO)9]2 is 77.5°, much less than the unstrained tetra- of them 247 pm, and average 247 pm. These values suggest that hedral value, 109.5°), and in consequence the C-C bond RI, the single-bond of enneacovalent cobalt, length is decreased below the single-bond value, 154 pm, usu- be given the value 123.5 pm, which is very close to the value in that it was assigned, 123 pm. On the other hand, striking dis- ally to about 140 pm (137 pm [CCo3(CO)g]2). agreement with the values of the radii is found for Fe-Fe, Tricarbonylcobalt sulfides and selenides Ru-Ru, Os-Os, Mn-Mn, and Re-Re. Thus, for Fe-Fe the reported bond lengths in complexes that might be expected to Cobalt complexes containing or have a different have structures with single bonds between iron atoms range structure from those containing . The reported values from 240 to 280 pm, with an average of 260 pm, much larger of the Co-Co , 264 pm in SCo3(CO)9 (18), 262 pm than the value 2R1 for iron, 248 pm. in SeCos(CO)9 (19), and 253 pm in [SCos(CO)7h2S2 (20) (for four I have found that valence-bond theory provides a simple bonds; 247 pm for the other two), are significantly larger than explanation of the observed constancy of the lengths of the expected. The increase over the single-bond value 246 pm may bonds formed by cobalt atoms with one another and the vari- be attributed to resonance with a structure involving a cobalt- ability of those formed by iron and manganese and their con- sulfur . The observed Co-S bond length, 214 pm, geners. Moreover, the theory also explains the fact that com- is 11 pm less than that expected for a single bond, and equal to plexes containing clusters of cobalt, rhodium, or iridium atoms within 1 pm to the value for a bond with n = 4/3, corre- are usually less stable and harder to synthesize than those con- sponding to a single bond to each of two cobalt atoms and a taining clusters of atoms of iron or manganese or their conge- double bond to the third. The cobalt-cobalt bonds would then ners. The argument depends largely on the electroneutrality have n = 2/3 (two single bonds resonating among three posi- principle (ref. 12, p. 172), which states that the resultant electric tions), giving a bond length of 257 pm, in approximate agree- ment with the observed values. For the complex SFeCo2(CO)9, * Publication no. 64 from the Linus Pauling Institute of Science and with an FeCo2 ring in place of the Co3 ring, a structure can be Medicine. assigned with three single bonds between the metal atoms, as 4290 Downloaded by guest on September 26, 2021 Chemistry: Pauling Proc. Natl. Acad. Sci. USA 73 (1976) 4291

Table 1. Cobalt-cobalt bond lengths Table 2. Iron-iron bond lengths Co-Co Complex Fe-Fe (pm) Ref. Complex (pm) Ref. Fe3(CO)9 246 24 Ph2C2Co2(CO)6 247 4 (C6H5C2C6H,)2Fe3(CO)8, 243 25 [HC2Co2(CO)6, 3As 247 5 black C6Co8(CO)24 247 6 (C6HC2C6H,)2Fe3(CO)., 246, 259 25 OC[CC03(CO)j] 247 7 violet H3CC[Co(CO)3 ]3 247 8 PhCCo3(CO)6C6H3Me3 245 9 (AsCH3)4Fe2(CO)6 268 26 [CCo3(CO)9]2 245 9 CHP(CH3)2Fe2(CO)5 263 27 [Co6(CO)15 249 10 (CH,)2Fe2(CO)3SO2 259 28 Co2(CO)8 252 11 [C.H4Si(CH3)2CH4]Fe2(CO)4 251 29 Fe3(CO)1 IP(C6H,)3 257, 268, 271 30 well as the 4/3 bonds to sulfur (with one Fe-C=-O+). If it Fe5(CO)15C 264 31 contributes equally with the first structure, which lacks one of [Fe6(CO)16C] 267 32 the three metal-metal single bonds, the metal-metal bond COP(C6H. )3PtFe2(CO)6 278 33 length would be 6 pm less [n = 5/6 rather than n = 2/3; difference of -60 pm X log n (21)]. The bond lengths for vation in some Fe2 complexes, such as (AsCH3)4Fe2(CO)6 (26). SFeCo2(CO)9 and SeFeCo2(CO)9 are in fact reported to be 9 (In this complex each iron atom forms single bonds with the pm and 4 pm, average 6.5 pm, less than those for their Co3 other iron atom, an atom, and one carbonyl group, and analogues (19). This straightforward explanation of the observed double bonds with an arsenic atom and two carbonyl differences in these analogous complexes illustrates the value groups.) of the valence-bond theory. With a larger cluster of iron atoms there are additional Iron possibilities of resonance, in that the iron-iron no-bond can complexes resonate among the alternative iron-iron positions. This extra The iron atom has eight valence electrons, and might use them resonance stabilizes the no-bond structures and increases their in forming double bonds with four carbonyl groups, to give the contribution, thus decreasing n and increasing the iron-iron compound Fe(CO)4. It could still, however, attach another bond length. One complex, (C6H5)3P(CO)PtFe2(CO)8, with carbonyl group by a single bond, formed with an electron do- iron-iron distance 278 pm, n = 1/3, has been reported (33). The nated into its ninth spd orbital by this group, -C=O+, giving square planar platinum atom, with ligands CO and P(C6H5)3, the stable complex Fe(CO)5. The Fe(CO)4 group, with one forms single bonds with the two iron atoms at the normal bond -CO+ and enneacovalent iron, can form two single bonds with length of 260 pm. The value 1/3 for the iron-iron bond number other groups, as in [Cl(C5H5N)Hg]2Fe(CO)4 (22), and the corresponds to equal resonance of the Fe-Fe bond and the two Fe(CO)3 group can form four single bonds with other groups, no-bond structures. as in (C6H5C)4Fe(CO)3 (23), in which the iron atom is bonded to the four carbon atoms of the cyclobutane ring. In Fe2(CO)9 Manganese complexes (24) the two Fe(CO)3 groups are held together by three bridging Manganese, with seven valence electrons, can become en- carbonyls and an Fe-Fe single bond. The Fe-Fe bond length, neacovalent by the transfer of two electrons to it by two 246 pm, is close to the single-bond value. Nearly the same C=O+ groups or other electron-donating groups, such as values, 243 pm and 246 pm, are found in the black and violet -PR3+ or -AsR3+. In HMn(CO)5, for example, the manga- isomers of the iron carbonyl diphenylacetylene complex for nese atom forms single bonds with the atom and two those pairs of iron atoms with three Fe-C-Fe bridges, carbonyl groups, as well as double bonds with three carbonyl whereas the value for the pair without these bridges in the violet groups. Because of its smaller amount of double-bond character isomer has a bond length of 259 pm (25). It is in fact only rarely (60%) and its 1 pm larger value of R1, the manganese-carbonyl that the iron-iron bond length in complexes with composition bond length, 184.7 pm (34), is somewhat larger than the values such that single Fe-Fe bonds are expected is close to the sin- for iron and cobalt. The single-bond Mn-Mn distance 252 pm gle-bond value of 248 pm. In a compilation of 26 values greater is observed in one complex, carbonyl-bishexafluoroisopropyl- than 252 pm, I obtained a mean of 264 pm. Representative idenamidohexacarbonyldimanganese (35), in which the man- complexes are listed in Table 2. There is no doubt that in these ganese-manganese bond is bridged by two amido complexes the bonds between iron atoms usually have lengths atoms and one carbonyl group. In most dimanganese com- greater than the length for a single bond, 248 pm. plexes, however, the manganese-manganese distance is very If for some reason the bond number n were less than 1, the large. In [Mh(CO)5]2, with no bridging groups, its value is 293 bond length would be greater: 252 pm for n = 3/4, 259 pm for pm (36), and in the ion [(CO)3Mn(N3)3Mn(CO)3]-, with three n = 2/3,266 pm for n = 1/2, and 277 pm for n = 1/3 (21). The bridging nitrogen atoms of the azido groups, it is 289 pm (37). explanation of the long bonds is that the iron atoms can be either These values correspond to bond number about 1/4, indicating enneacovalent or octacovalent, permitting resonance among a large amount of resonance to the no-bond structures. several valence-bond structures. For a fragment of a complex The transfer of two electrons to a manganese atom is made the principal structure is +O=C-Fe--Fe-C-=O+, with compatible with the electroneutrality principle by the rather each iron atom enneacovalent, and the other structures are of large amount of ionic character, 22%, of the manganese-carbon type O=C-Fe- Fe-CO+, with one iron atom octacovalent bond. The explanation of the special stability of the enneaco- and the iron-iron bond missing. If the principal structure is valent structure in the complex with Mn-Mn bond length 252 given twice the weight of each of the other two, the iron-iron pm is not evident, but it may be the hyperconjugating effect bond would have a length of 266 pm. This agrees with obser- of the CF3 groups, which stabilize the Mn-N bridging bonds Downloaded by guest on September 26, 2021 4292 Chemistry: Pauling Proc. Natl. Acad. Sci. USA 73 (1976) (Mn-N bond length 201 pm, as compared with 208 pm in the bond length, 266 pm, corresponds to n = 0.83 and the Ru-Ru ion with bridging azido groups). bond length, 287 pm, to n = 0.61. Complexes of the heavier transition metals Other metal-metal bonds The observed metal-metal bond lengths for ruthenium and Multiple bonds, including quadruple bonds, are sometimes osmium are similar to those for iron, in that they range from formed between atoms of transition metals. The bond lengths the value for n = 1 to about that for n = 1/2. The single-bond for these bonds have been discussed in an earlier article (3). value 274 pm for Ru-Ru is found, for example, in [(C5H5)- In some complexes it is likely that the nine bond orbitals of (CO)2Ru]2, in which there are two bridging carbonyl the enneacovalent transition-metal atom are not equivalent and groups (38), and the value 293 pm (n = 0.48) is found in do not have the same value of the covalent radius R1. This [(CH3)2GeRu(CO)3]3, in which the dimethylgermanyl groups possibility can be illustrated by the complexes M06Cl8Cl4(OH2)2 bridge the edges of the Ru3 triangle (39). A representative os- and Mo6Cl8(OH)4(OH2)2 (43). Each atom has mium complex is Os3(CO)12, with osmium-osmium bond ligancy 9 and can be considered to have covalence 9. Eight lengths of 288 pm, n = 0.63, and no bridging groups (40). atoms lie out from the centers of the faces of the Mo6 The complexes of rhenium are similar to those of manganese. octahedron. Each molybdenum atom may be described as The rhenium-rhenium bond length in [(CO)5Re]2 (no bridging forming four single covalent bonds with the adjacent molyb- groups), 302 pm (36), corresponds to n = 0.40, somewhat larger denum atoms, four with the bridging chlorine atoms, and the than the value for [(CO)5Mn]2. ninth, along its 4-fold axis, with Cl, OH, or OH2. These bonds The only reported complexes of rhodium in which there are contribute just enough electrons to make the molybdenum Rh-Rh bonds are those in which there is a cyclopentadienyl atoms enneacovalent, and if the bonds to chlorine and ligand attached to each rhodium atom, giving the possibility have an average of 601% ionic character, the molybdenum atom of resonance to structures with multiple bonds. No cluster would have zero electric charge. The observed Mo-Cl bond complexes of iridium have been reported. Clusters of rhodium lengths (axial 243 pm, bridging, n = 2/3, 255 pm) correspond or iridium thus seem to be less stable than those of ruthenium to R1 = 149 pm, with the correction for the difference in elec- and osmium, presumably because of the absence of the stabi- tronegativity (ref. 12, p. 229), and the smaller value 132 pm is lizing effect of the resonance between the normal valence-bond given by the observed Mo-Mo distance 264 pm. The average structure and the various no-bond structures described above. of these values, 140.5 pm, is close to the enneacovalent value The same decreased stability applies also to cluster complexes of R1, 140 pm. A reasonable explanation of the difference be- of cobalt, which are observed only with a much smaller variety tween the two values of R1 is that the Mo-Mo bonds make use of structures than for those of iron. of a set of four spd orbitals fQr each atom that are best suited to bond formation and have a smaller value of R1, and that the Bonds between unlike transition-metal atoms other five bonds, which have only 40% covalent character, are We have discussed the lengthening of iron-iron bonds in terms formed by the remaining bond orbitals, with a larger value of of resonance between the structures +O=C-Fe--Fe- R1. The value of 132 pm for R 1 for the four best spd orbitals is C(=O+ and +OmC-Fe Fe-=C=O. In the second structure close to that for the six best, 130 pm, given by the observed bond the electron pair of the iron-iron bond has moved to the second length in molybdenum metal (ref. 12, p. 403), in which the carbonyl group, changing the formal charge of the first iron atoms have covalence 6. atom from +1 to 0, values that are compatible with the elec- troneutrality principle because of the partial ionic character of the iron-carbon bonds. Analysis of the problem shows that 1. Pauling, L. (1975) "Valence-bond theory of compounds of transition metals," Proc. Natl. Acad. Sci. USA 72,4200-4202. this sort of resonance is unlikely, however, for bonds between 2. Abrahams, S. C., Ginsberg, A. P. & Knox, K. (1964) "Transition iron (or ruthenium or osmium) and cobalt, rhodium, or iridium, metal-hydrogen compounds. II. The crystal and molecular which are enneacovalent without electron 'transfer. For ex- structure of potassium rhenium hydride, K2ReH9," Inorg. Chem. ample, in CsHsRhFe3(CO)ll (41) there is a tetrahedral RhFe3 3,558-567. group. In resonance of the. sort Rh-Fe-C=-O+ to Rh+ 3. Pauling, L. (1975) "Maximum-valence radii of transition metals," Fe-=C=O, an electron would be removed from Rh, giving Proc. Natl. Acad. Sci. USA 72,3799-3801. it an added positive charge. The resultant positive charge of the 4. Sly, W. G. (1959) "The molecular configuration of dicobalt octacovalent atom of rhodium would then be greater than 1, hexacarbonyldiphenylacetylene," J. Am. Chem. Soc. 81, 18- however, because in addition to the electron transferred to the 20. 5. Bird, P. H. & Fraser, A. R. (1970) "Preparation and crystal iron carbonyl group some negative charge is removed from the structure of tris(hexacarbonyldicobalt-7r-ethynyl)arsine: rhodium atom to its ligands (which in general are more elec- [(CO)6Co2C2H]3As," Chem. Commun. 681-682. tronegative than the transition metals) by the partial ionic 6. Dellaca, R. J. & Penfold, B. R. (1971) "Structural studies of de- character of the bonds. The no-bond structure for Rh-Fe- rivatives of methinyltricobalt enneacarbonyls. V. Crystal struc- (also Co-Fe, Os-Fe) is accordingly incompatible with the ture of hexacarbonoctacobalt tetracosacarbonyl, Co8(CO)24C6," electroneutrality principle, and in consequence we rule out the Inorg. Chem. 10, 1269-1275. no-bond structures, and expect these metal-metal bonds to have 7. Allegra, G., Peronaci, E. M. & Ercoli, R. (1966) "Synthesis and the single-bond lengths. The observed value of the Fe-Rh crystal structure of bis(tricobaltenneacarbonyl)acetone. An ap- bond length in this complex is in fact 260 pm, exactly equal to plication of a new method of sign determination," Chem. the sum of the single-bond radii. The resonance to the no-bond Commun. 549-550. 8. Sutton, P. W. & Dahl, L. F. (1967) "The molecular structure of structure +O-C-Fe Fe-=C="O is, however, permitted, and Co3(CO)9CCH3. A tricyclic organocobalt complex containing the observed value of the iron-iron distance in the same com- a metal-coordinated triply bridging aliphatic carbon atom," J. plex, 258 pm, corresponds ton = 0.68, i.e., to 32% contribution Am. Chem. Soc. 89,261-268. of this structure. 9. Brice, M. D., Dellaca, R. J., Penfold, B. R. & Spencer, J. L. (1971) For the similar FeRu3 tetrahedron in H2FeRu3(CO)13 (42), "X-ray crystal and molecular structures of three methinyl tri- however, there is no such restriction. The observed Fe-Ru cobalt enneacarbonyl derivatives," Chem. Commun. 72-73. Downloaded by guest on September 26, 2021 Chemistry: Pauling Proc. Natl. Acad. Sci. USA 73 (1976) 4293

10. Albano, V., Chini, P. & Scatturin, V. (1968) "Crystal and mo- 28. Churchill, M. R. & Kalra, K. L. (1973) "Crystallographic studies lecular structures of new cobalt carbonyl clusters," Chem. on sulfur dioxide insertion compounds. V. Elucidation of the Commun. 163-164. of cis-u-carbonyl-A-(sulfur dioxide)-bis 11. Sumner, G. G., Klug, H. P. & Alexander, L. E. (1964) "The crystal (,r-cyclopentadienylcarbonyliron), cis-(r-C5H5)2Fe2(CO)3(SO2)," structure of dicobalt octacarbonyl" Acta Crystallogr. 17, 732- Inorg. Chem. 12,1650-1656. 742. 29. Weaver, J. & Woodward, P. (1975) "Crystal and molecular 12. Pauling, L. (1960) The Nature of the (Cornell structure of di-At-carbonyl-cds-,u-(1-5-n: 1'-5'-n-dicyclopentadi- University Press, Ithaca, New York), 3rd ed. enyldimethylsilane-bis(carbonyliron)(Fe-Fe)," J. Chem. Soc. 13. Natta, G. & Corradini, P. (1953) "Struttura di alcuni composti Dalton Trans. 1439-1443. carbonilici del cobalto," Atti Accad. Naz. Lincei Sez. 2a 15, 30. Dahn, D. 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A. & Woodward, P. (1970) structure of Fe(CO)3(C6H5C2C6H5)2," Acta Crystallogr. 18, "Germanium complexes of ruthenium and osmium dodecacar- 614-617. bonyls: metal-metal heterocycles: crystal structure of 24. Powell, H. M. & Ewens, R. V. G. (1939) "The crystal structure [Me2GeRu(CO)3]3," Chem. Commun. 1477-1478. of iron enneacarbonyl," J. Chem. Soc. 286-292. 40. Corey, E. R. & Dahl, L. F. (1962) "The molecular and crystal 25. Dodge, R. P. & Schomaker, V. (1965) "The molecular structures structure of OS3(CO)12," Inorg. Chem. 1, 521-526. of two isomers of Fe3(CO)8(C6H5C2C6H5)2," J. Organometal. 41. Churchill, M. R. & Veidis, M. V. (1970) "X-ray crystallographic Chem. 3, 274-284. determination of the structure of (7r-C5H5)RhFe3(CO)I1: a tet- 26. Gatehouse, B. M. (1969) "The crystal structure of rahedral metal cluster derivative with a crowded co-ordination [Fe(CO)3]2(AsCH3)4; a compound with a noncyclic tetrameth- surface," Chem. Commun. 1470-1471. yltetra-arsine ligand," Chem. Commun. 948-949. 42. Gilmore, C. J. & Woodward, P. (1970) "The crystal and molecular 27. Vahrenkamp, H. (1973) "Metallorganische Lewis-Basen. XVIII. structure of H2FeRu3(CO)13: a tetrahedral iron-ruthenium hy- Kristallstruktur von Fe2(CO)5C5H5P(CH3)2, einem Komplex mit dridocarbonyl," Chem. Commun. 1463-1464. Metall-Metall-Bindung, Carbonyl- und Phosphin-Bruicke," J. 43. Brosset, C. (1945) "Structure of complex compounds of bivalent Organometal Chem. 63, 399-406. molybdenum," Ark. KIemi, Mineral. Geol. A20, no. 7, 1-16. Downloaded by guest on September 26, 2021