Effective Atomic Number and Valence-Shell Electron-Pair Repulsion

Chapter 15

Effective Atomic Number and Valence-Shell Electron-Pair Repulsion 60 Years Later

Downloaded by PENNSYLVANIA STATE UNIV on July 23, 2013 | http://pubs.acs.org Publication Date: November 4, 1994 | doi: 10.1021/bk-1994-0565.ch015

Michael Laing Department of Chemistry, University of Natal, Durban 4001, South Africa It is now 60 years since Sidgwick showed that the stoichiometry of many coordination compounds could be deduced from his Effective Atomic Number formalism and almost 40 years since Gillespie showed that the geometric structure of compounds of the main group elements could be correctly predicted from his Valence Shell Electron Pair Repulsion approach. These two seemingly independent approaches to bonding and structure can be combined. One observes that a simple form of the VSEPR rules will also correctly give the geometry of a large number of transition metal complexes if these compounds obey the ΕΑΝ formalism. The Beginnings In 1934 Nevil Vincent Sidgwick published a paper in which he established the well-known Effective Atomic Number rule for the bonding and stoichiometry of transition metal carbonyl compounds (7). For the metals of even atomic number Z , he observed that i f each carbonyl group bonded to the metal atom is considered to "donate" two electrons to the metal atom (in its oxidation state of zero), then the sum of the atomic number, Z , of the metal plus two times the number of C O groups attached to it equals the atomic number of the next heavier inert gas. This worked beautifully for the 3d metals, i.e., Cr in Cr(CO) , Fe in Fe(CO) , and N i in Ni(CO) . A l l had an Effective Atomic Number of 36, Ζ of krypton. This idea was quickly extended to deal with transition metals with odd atomic numbers and to groups that donated one or three electrons, e.g., M n in M n ( C O ) (to give a Μη—Mn covalent bond) and Co in Co(CO) (NO) and Fe in Fe(CO) (NO) in which the N O molecule contributed 3 electrons. Six years later Sidgwick published a famous paper based on his Bakerian Lecture (2). In this truly remarkable paper he described how the shape of the molecule of a simple molecular compound of a nonmetallic element is determined by the number of bonds, hence pairs of electrons, surrounding the central atom. 6

5

4

2

3

10

2

0097-6156/94/0565-0193$08.00/0 © 1994 American Chemical Society In Coordination Chemistry; Kauffman, G.; ACS Symposium Series; American Chemical Society: Washington, DC, 1994.

2

194

COORDINATION CHEMISTRY

Molecules with four pairs of electrons are tetrahedral, e.g., CC1 , molecules with five pairs are trigonal bipyramidal, e.g., P F , and molecules with six pairs are octahedral, e.g., S F . This new idea contradicted the widely accepted Octet Rule of Langmuir (3) and Lewis (4); the molecules did not have octets, nor did they have closed electron shells of 18 electrons as did the atoms of the heavier inert gases and the metal atoms in the carbonyl compounds that obey the ΕΑΝ rule. 4

5

6


V S E P R is Born Thus was laid the foundations for the famous Quarterly Review published in 1957 by the two Rons, Gillespie and Nyholm (5), a paper that has had a greater influence on the teaching of structural chemistry at undergraduate level than any other publication during the past 40 years. Not only did it summarize the advances over the 20 years since Sidgwick and Powell's original ideas, but it also led to the development of what was to become the VSEPR method for deducing and rationalizing the structures of molecules. Moreover, the new ideas now encompassed molecules with mixed double and single bonds, e.g., S 0 C 1 , as well as giving a rationale for molecules with one or more lone pairs of electrons, e.g., S F , IC1 , and I F , and an internally self-consistent explanation of the shapes of the A B molecules of the main group elements, e.g., C F , S F , and X e F (6-10). By a strange coincidence, it was exactly 30 years ago that the ACS held its 144th National Meeting in Los Angeles — 31 March to 5 April, 1963 (11). On the Tuesday morning Ron Gillespie gave a presentation of his newly developed "VSEPR Theory of Directed Valency" (Abstract No 15, page 7E, Division of Chemical Education). He was severely attacked by R. E . Rundle (Abstract No 17, page 8E), who declared that the VSEPR approach was too naive and that the only approach to molecular structure was by the "more exact" Molecular Orbital method. After some discussion, Ron Gillespie then said, "Xenon hexafluoride has just been prepared (by Malm et al.; Abstract No 26, page 10K). You predict the shape of the molecule, and I will predict the shape. Then when the structure is determined, we will see who is correct" (12). We all know the result. History has proved that Ron Gillespie was correct. Bartell's infrared study subsequently showed that X e F is NOT a perfect octahedron in the gas phase, as Rundle had predicted from the M O method, but has a distorted structure as was predicted by the VSEPR formalism (13). This correct prediction was described by Ron Gillespie in his contribution to the Werner Centennial Symposium at the 152nd American Chemical Society National Meeting held in New York, September 12 16, 1966 (14). Why the VSEPR approach should be so successful has been muchly discussed; whether the electron pairs are truly similar in energy and whether they repel by either simple electrostatic forces or by the Pauli Exclusion principle (15). In his comparison of the VSEPR "points-on-a-sphere" formalism with results of Molecular Orbital computations of potential energy surfaces, Bartell concluded that "the VSEPR model somehow captures the essence of molecular behavior" (16). 2

4

3

2

5

4

4

4

4

6

In Coordination Chemistry; Kauffman, G.; ACS Symposium Series; American Chemical Society: Washington, DC, 1994.

15. LAING

195

ΕΑΝ and Valence-Shell Electron-Pair Repulsion

The Application of VSEPR to Coordination Compounds


That such a simple model should yield such consistently correct predictions is remarkable. The question is: Is it applicable to compounds of transition metals? The answer is "Yes," if one limits the discussion to only those molecules that obey the ΕΑΝ rule. One observes an interesting, surprising — and beautiful — phenomenon. These molecules have geometric structures that appear to depend solely on the number of ligands that are bonded to the metal atom, i.e., the number of pairs of electrons in directed atomic orbitals: they obey a form of the VSEPR model. Carbonyl Compounds Consider first the simple carbonyl compounds of the 3d transition metals. N i ( C O ) is tetrahedral, Fe(CO) is trigonal bipyramidal, and Cr(CO) is octahedral. Their geometric structures appear to depend solely on the number of ligands that are bonded to the metal atom in accordance with the simplest VSEPR approach. The electrons NOT in the covalent metal—C bonds apparently play no role in determining the geometric structure; they behave as i f they were not there. These electrons are certainly not "lone pairs" in the VSEPR sense of having spatial influence; they seem to be "spherical" about the metal atom — structurally "inert" pairs. Yet there are 10 of these electrons in Ni(CO) , 8 in Fe(CO) and 6 in Cr(CO) . 4

5

6

4

5

6

Four Ligands As long as the different species obey the ΕΑΝ formalism, their geometries can be correctly predicted by the VSEPR model. Moreover, isoelectronic species are isostructural, independent of the charge carried. For example, Ni(CO) , [CoiCO)^-, [Fe(CO)4] -, Fe(NO) (CO) , MnCO(NO) , Co(CO) NO, and [Pd(PPh ) ] are all tetrahedral, all have 4 covalently bonded ligands and, it appears, have 10 d-electrons uninvolved in determining the shape. However, it is not only this class of compound that "fits. " A l l compounds of the type [ZnX (4-Rpyridine) ] (X = halogen; R = alkyl or aryl group), are tetrahedral. Similarly, both of the complex cations [Cu(I)(2,2-biquinoline^] and [Cu(I)(2,9 dimethyl-l,10-phenanthroline)2l are tetrahedral. Their commonality is ten 3d electrons, seemingly not involved in the bonding and certainly not affecting the geometry. 4

2

2

3

2

3

3

4

2

2

+

+

Five Ligands Isoelectronic and isostructural compounds with 5 ligands include Fe(CO) , Mn(CO) NO, [Mn(CO) r, [Ru(CO) (PPh )2], Fe(PF ) , [CoCl NO{P(CH ) } ], and the complexes formed between Co(I) and nitriles, e.g., [ C o ( N C M e ) ] . We now have in these compounds 8 d-electrons acting as disinterested spectators, while the five bonding pairs obey the VSEPR model and yield a trigonal bipyramidal geometry. 5

4

5

3

3

3

5

2

3

+

5


3

2

196


Six Ligands The classic case of octahedral geometry includes all possible types of complex, with the metal atoms in a variety of oxidation states : Cr(CO) , [V(CO) ]', M o ( P F ) , [ C o ( N 0 ) ( N H ) ] , [Co(CN)6] -, [Re(CO) Br], [RhCl (PPh ) ], [PtCl ] ", [ M n ( C O ) ] , and the isoelectronic [Co^CNJio] ', [IrCl(0 )CO(PMe3) ], and a host of others. Now it is only 6 d-electrons that are uninvolved. 6

6

3

3

2

3

3

6

2

3

5

3

3

3

6

6

2

10

2

2


Nine Orbitals, Nine Ligands Given that in the transition metals there are 9 valence orbitals available for bonding, one s, three p, and five d (implying a maximum of 18 electrons which then obey the ΕΑΝ formalism), one can naively expect a maximum of 9 ligands covalently bonded to the metal atom. There is a classic case of such a complex whose geometry exactly fits what the VSEPR theory predicts: [ReH ] " — a tricapped trigonal prism. In this case there are no disinterested electrons; all pairs making up the ΕΑΝ rule are in the Re—Η bonds (or so it seems). 2

9

Eight Ligands In the field of large coordination numbers different geometries can be energetically very similar (77). This applies especially to coordination number 8. The atoms bonded to the metal can be arranged at the corners of a cube, as a square antiprism, or as a dodecahedron. The compound [Mo(CN) ] ' exemplifies this class and is dodecahedral, which the VSEPR would predict as very likely, but we are now stretching the theory to its very limit. This [ M L ] structure appears to have 2 electrons not involved in dictating the geometry. 4

8

8

Seven Ligands We have seen the cases of 0, 2, 6, 8, and 10 "disinterested" electrons; we now must consider the case of 4. This is the coordination complex with 7 ligands bonded to the metal, and, interestingly, this is the geometry where VSEPR founders, even for simple molecules like I F and X e F (78,79). What is the most favored geometry: "capped octahedral" (1, 3, 3); "capped trigonal prismatic" (1, 4, 2); "pentagonal bipyramidal" (1, 5, 1)? I F is (1, 5, 1); [NbF ] " and [TaF ] " are (1, 4, 2); [ZrF ] " and [ H f F ] ' are (1, 5, 1); and [ N b O F J ' is (1, 3, 3). There is clearly little to choose between the energies of the three idealized geometries. Moreover, none of these coordination complexes obey the ΕΑΝ rule. There are, however, several examples that do satisfy the ΕΑΝ formalism: [Mo(CN) ] " and [Re(CN) ] "; and [OsH4(PEt Ph) ] and [IrH (PEt Ph) ]. A l l of these complexes are pentagonal bipyramidal — the 4 unbonded electrons do not disturb the geometry, which is correctly predicted by the VSEPR approach. 7

6

2

7

3

7

7

3

7

5

7

2

7

3

4

7

2

3

5

2

2

Limitations Of course, the attainment of large coordination numbers is often limited by the


15.

bulk of the ligand, defined by its Cone Angle θ (20); and i f this is large enough, it alone will totally dominate the geometry of the complex. Two simple examples are: trigonal planar [Pd(PPh ) ], ligand Cone Angle θ = 145°, and linear [Pt{P(f-But) } ], ligand Cone Angle θ = 182°. These complexes do not obey the ΕΑΝ rule, but they have the simple geometry deduced from the VSEPR approach: two pairs, collinear; three pairs, trigonal planar. It is well at this stage to recall the basic premise of the VSEPR approach: the electron pairs are similar in energy and repel by either simple electrostatic forces or by the Pauli exclusion principle (75). Within the d-block transition metals, this implies that the 4s, 4p, and 3d electrons should be of similar energy if the model is to work. We know that this is not true, and certainly the energy differences will be greater for metals like Sc, T i , Zr, Zn, and Hg (27). Worse and different problems exist for the elements Rh, Ir, Pd, Pt, and Au, which exhibit the robust square planar 16-electron structure and which participate in oxidative addition and reductive elimination reactions. Similarly, the geometry of the common low-spin square planar d compounds of Ni(II) ( like Ni(DMG) and [Ni(CN) ] "), which do not obey the ΕΑΝ rule, cannot be deduced from the VSEPR approach. One might ask whether there are coordination complexes of the heavy base metals that simultaneously obey both the ΕΑΝ and VSEPR rules. This question is further complicated by the existence of the Inert Pair Effect (22, 23) — another concept coined by Sidgwick (24). Tetraethyllead cannot be correctly called a coordination compound although it does fulfill the ΕΑΝ formalism. There is one nice example that does satisfy the requirements: H g l " , the tetrahedral colorless complex formed by dissolving the brilliant orange, insoluble H g l in KI solution. Tetrahedral [ Z n ( N H ) ] and [Zn(CN) ] ' also fall into this category. 3

3


197

ΕΑΝ and Valence-Shell Electron-Pair Repulsion

LAING

3

2

8

2

2

4

2

4

2

2+

3

4

2

4

Is There a Straightforward Theoretical Explanation? There is no facile explanation for the success of the ΕΑΝ formalism (25) nor for the apparently self-consistent geometric behavior of the various coordination complexes described above. The relationship between total electron count, number of bonded ligands, number of non-bonding electrons and molecular geometry is complex and has been discussed at length (26-29). To tease a full understanding out of all the data, self-consistent as well as contradictory, is to hope for too much. One could of course say: "This is NOT the VSEPR theory at all. It is solely a steric or electrostatic scheme that happens to work on this carefully chosen group of coordination compounds." However, where there are no sterically active lone pairs, surely this is precisely what the simplest version of the VSEPR formalism is. What is remarkable is that so simple a model, originally designed solely for covalent bonded compounds of nonmetals, should succeed for so many coordination complexes of transition metals! The only requirement for the success of this particular form of the VSEPR approach seems to be that the compounds obey the ΕΑΝ rule. We inorganic coordination chemists will be forever grateful for this combination of the visionary ideas of Nevil Vincent Sidgwick and the painstaking development of these ideas by Ron Gillespie that has given to us this remarkable pair of valuable tools — ΕΑΝ and VSEPR.


198


Literature Cited


1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Sidgwick, Ν. V.; Bailey, R. W. Proc. Roy. Soc. 1934, 144, 521-537. Sidgwick, Ν. V.; Powell, H. M . Proc. Roy. Soc. A. 1940, 176, 153-180. Langmuir, I. J. Am. Chem. Soc. 1919, 41, 868. Lewis, G. N. J. Am. Chem. Soc. 1916, 38, 762. Gillespie, R. J.; Nyholm, R. S. Quart. Revs. Chem. Soc. 1957, 11, 339380. Gillespie, R. J. J. Chem. Educ. 1963, 40, 295-301. Gillespie, R. J. J. Chem. Educ. 1970, 47, 18-23. Gillespie, R. J. Molecular Geometry; Van Nostrand: London, 1972. Gillespie, R. J.; Hargittai, I. The VSEPR Model of Molecular Geometry; Allyn and Bacon: Boston, 1991. Gillespie, R. J. Chem. Soc. Revs. 1992, 59-69. Collected Abstracts, 144th National ACS Meeting, Los Angeles, 31 March to 5 April, 1963; American Chemical Society: Washington, 1963. Laing, M . I was present at the presentation by Ron Gillespie and remember well the discussion and his prediction that XeF "will NOT have a perfect octahedral geometry." Gavin, R. M . ; Bartell, L. S. J. Chem. Phys. 1968, 48, 2466. Gillespie, R. J. In Werner Centennial; Advances in Chemistry Series No. 62; Kauffman, G. B., Symposium Chairman; American Chemical Society: Washington, 1967; pp 221-228. Bader, F. W.; Gillespie, R. J.; MacDougall, P. J. J. Am. Chem. Soc. 1988, 110, 7329-7336. Bartell, L. S. J. Am. Chem. Soc. 1984, 106, 7700-7703. Kepert, D. L. In Comprehensive Coordination Chemistry; Wilkinson, G., Ed.; Pergamon: Oxford, 1987; Vol 1, pp 31-107. Boggess, R. K.; Wiegele, W. D. J. Chem. Educ. 1978, 55, 156-158. Burbank, R. D.; Jones, G. R. J. Am. Chem. Soc. 1974, 96, 43-48. Tolman, C. A. Chem. Rev. 1977, 77, 313-348. Mitchell, P. R.; Parish, R. V. J. Chem. Educ. 1969, 46, 811-814. Pyykkö, P.; Descaux, J.-P. Acc. Chem. Res. 1979, 12, 276-281. Pyykkö, P. Chem. Rev. 1988, 88, 563-594. Sidgwick, Ν. V. The Chemical Elements and Their Compounds; Clarendon Press: Oxford, 1950; pp 287, 481, 617, 795. Chu, S. Y.; Hoffmann, R. J. Phys. Chem. 1982, 86, 1289-1297. Burdett, J. K. Molecular Shapes; John Wiley: New York, 1980; pp 170238. N.B. page 171: "... the VSEPR approach does not work for transition metal species." This statement is most certainly true for the high-spin compounds of the 3d-series for which the crystal field theory is usually invoked and also for the many unusual or transient species like Fe(CO) and Cr(CO) which do not obey the ΕΑΝ formalism. Albright, Τ. Α.; Burdett, J. K.; Whangbo, M . H. Orbital Interactions in Chemistry; John Wiley: New York, 1985; pp 277-338. Mingos, D. M . P.; Hawes, J. C. Structure and Bonding 1985, 63, 1-63. Mingos, D. M . P.; Zhenyang, L. Structure and Bonding 1990, 72, 73111. 6

13. 14.

15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

4

5

27. 28. 29.

RECEIVED March 15, 1994


Effective Atomic Number and Valence-Shell Electron-Pair Repulsion

Recommend Documents