The Concept of Oxidation States in Metal Complexes

In the Classroom

The Concept of Oxidation States in Metal Complexes Dirk Steinborn Institut für Anorganische Chemie, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle, Kurt-Mothes-Straße 2, Germany; [email protected]

The concept of oxidation states is one of the most powerful heuristic concepts in chemistry. It plays an important role in teaching chemistry. To assign oxidation numbers (ON) of atoms in molecules, most textbooks and journal articles present a set of hierarchical rules. These sets can be quite complex (up to 16 rules to construct computer driven expert systems) but, in any case, are incomplete and suffer from an increasing number of exceptions (1). An alternative way is to go “back to the roots” of the concept and to assign oxidation numbers of atoms in molecules on the basis of their Lewis structures. This system of splitting shared electrons in covalent bonds heterolytically (2), according to certain principles (see below), is less frequently explained in textbooks. Thus, from the Lewis structure of a molecule, with knowledge of the electronegativities of elements, oxidation numbers can be assigned. In doing this it is obvious that the concept of oxidation states can be more than bookkeeping of electrons to balance oxidation–reduction reactions. Furthermore, limitations of the concept will be obvious in cases where the electronic structure of a molecule cannot properly be described by one Lewis structure. Historical Survey Originally, the valency of an atom was thought to be a fundamental atomic property that was constant and invariable (Kekulé, around 1860). The principle of constant valence numbers was successfully applied in the second half of the 19th century for carbon compounds in organic chemistry. However, it proved to be wrong in inorganic chemistry (3). For instance, contrary to experimental results lower valent metal halides had to be formulated as dimers (Figure 1) to maintain fixed valencies for metals. Thus, it was recognized that valency is not an inherent property of an atom, as for instance, the atomic mass is. Atoms may have variable valencies (“valence numbers”) that are indicated in the names of compounds by terminations such as “-ous” and “-ic” (e.g., ferrous, ferric). Later on valence numbers were placed as Roman numerals in parentheses (Stock’s method; ref 4 ), which is still used today. The progress in understanding chemical bonding and oxidation–reduction reactions resulted in the need to distin-

FeCl2

FeCl3 Cl

Cl Fe Cl

Fe

Fe Cl

Cl Cl Cl

SnCl2

SnCl4 Cl

Cl Sn Cl

Cl

Cl

Sn

Sn Cl

Cl

Cl

Figure 1. Formulas of iron and tin chlorides according to the principle of fixed valencies for iron (trivalent) and tin (tetravalent).

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guish between stoichiometric and electrochemical valencies and to define oxidation numbers. Pauling described this concept in the 1947 edition of his book General Chemistry (5) as follows: “The oxidation number of an atom is a number which represents the electrical charge which the atom would have if the electrons in a compound were assigned to the atoms in a certain way.” This way of assignment can be described for atoms in covalent compounds of known structures as “... the charge remaining on the atom when each shared electron pair is assigned completely to the more electronegative of the two atoms sharing it. A pair shared by two atoms of the same element is split between them” (5). Furthermore, Pauling also states that in compounds whose structures are uncertain, the oxidation numbers may be calculated from a reasonable assignment of oxidation numbers to the other elements in the compounds. Basic Considerations The oxidation number of an atom in a molecule is defined as the charge of that atom if the molecule would consist of (monatomic) ions that may also be neutral atoms. Cleavage of molecules into (hypothetical monatomic) ions has to be based on the polarity of covalent bonds. Electrons in polar covalent bonds are assigned to the more electronegative atom whereas those in nonpolar covalent bonds are equally shared between the bonded atoms. From this definition three statements follow: (i) Oxidation numbers are charges of hypothetical monatomic ions that cannot be measured experimentally, in principle; (ii) Assignment of oxidation numbers of atoms in a molecule is based on its electron distribution represented by an actual Lewis structure. Ambiguities may arise when the electronic structure of a molecule cannot be properly described by only one Lewis structure or when the polarity of a covalent bond to be split is not known; and (iii) The concept in this simple form is limited to molecules whose electronic structure can be described by appropriate Lewis structures. In some cases this may not be possible, for example, in cluster compounds and in compounds with electrons in highly delocalized molecular orbitals. To assign oxidation numbers of atoms in molecules, the relevant Lewis structures have to be drawn. An integral feature of (complete) Lewis structures are the formal charges of atoms. These are charges of hypothetical monatomic ions obtained by homolytic cleavage of all covalent bonds. On the other hand, heterolytic cleavage of polar covalent bonds and homolytic cleavage of nonpolar bonds (as described above), result in formation of monatomic ions whose charges define the oxidation numbers of atoms in a molecule. Thus, formal charges and oxidation numbers reflect the two hypothetical borderline cases of electron distribution in a molecule, namely the “pure covalent” and the “pure electrostatic” view of polar covalent bonds, respectively. From these definitions it follows

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that the sum of the formal charges over all the atoms of a molecule and the sum of the oxidation numbers over all the atoms of a molecule are equal to the total charge on the molecule. Neither of these charges reflect the real existing charge distributions in molecules. To get the charge distributions, the concept of partial or effective charges on atoms in molecules has to be applied. They can be derived from some spectroscopic measurements, such as photoelectron and Mössbauer spectroscopic measurements. However, usually, they are calculated quantum chemically by population analysis that partition the total charge among the atoms in molecules. Oxidation Numbers in Nonmetal Compounds Although several Lewis structures have to be considered for SO42− (Figure 2, structures 1a–c), the assignment of oxidation numbers is unambiguous. Owing to higher electronegativity of oxygen, χ(O) > χ(S), heterolytic cleavage of sulfur–oxygen bonds results in the formation of hypothetical O2 and S6+ ions (ON(O) = 2 and ON(S) = +6). This is not the case in the thiosulfate anion S2O32−: Consider the group electronegativities (6) χ(SO3) > χ(S), the sulfur–sulfur bond should be cleaved heterolytically as shown in Figure 2,

2−

O

O

S

O

O

S

2−

O O

O

S

O

etc.

O

O

O

2a

2b

2c

[MLx]n → Mz + x:Lm

O

O

1a

1b

1c

+2 +2

+2 +2

2−

S

O

S

2−

O

O

S

S

S

etc.

The oxidation number of the metal equals the charge n of complex minus the sum of the charges of all ligands (z = n − xm). In doing so, heterolytic cleavage of all ligands L from a metal complex results in a (monatomic) metal ion Mz (or neutral metal atom)1 whose ionic charge z defines the oxidation number of M in the complex [MLx]n. Examples are given in Figure 3.

+1 + 4 2−

O

O S

2−

O

S

ON(S): + 4 +1

S

S

O

S

O

O

3 ON: 0

S

Oxidation Numbers in Metal Complexes To assign oxidation numbers of all atoms in metal complexes, the same procedure as described above can be applied. However, frequently the oxidation numbers of central metals are the only ones of interest and therefore the following discussion will be restricted to these. Owing to the highly electropositive character of metals, electrons involved in metal–ligand bonds are assigned to the ligands. Thus, ligands (L) are cleaved off taking electrons from the M–L bonds with them:

O

O

O

2−

O

ON(S): + 4 0

O

+6

+6

ON(S): + 6

structures 2a–c, resulting in two different sets of oxidation numbers for sulfur atoms, ON(S): +4兾0 versus +2兾+2. An argument to favor the first set of oxidation numbers may be that the Lewis structure 2a does not involve a (p–d) π bond between third-row elements. This assignment also corresponds with the formation of thiosulfate from sulfite and sulfur and its decay in acidic solution yielding sulfur dioxide and sulfur. Oxidation of thiosulfate with iodine results in the formation of tetrathionate, 3, with oxidation numbers of +4 and +1 for the sulfur atoms. Thus, reaction 2 → 3 is understood as formal oxidation of terminal sulfur in S2O32− followed by S
S bond formation. SCN− (4), OCN− (5), and molecules like HC(O)NH2 (6) are given in the literature (1d) as examples where sets of oxidation-number rules failed to assign oxidation numbers. Oxidation numbers derived from the relevant Lewis structures using the heterolytic bond cleavage procedure are given in Figure 2. If the electronic structure of a molecule has to be described by a resonance hybrid of two or more (nearly) equivalent Lewis structures, then the mean values of oxidation numbers can be given. This may result in nonintegral oxidation numbers clearly indicating an extension of the original concept. Examples are the oxidation numbers of oxygen in the superoxo anion O2− (ON(O) = −1兾2) and the dioxygenyl cation O2+ (ON(O) = +1/2). Ambiguities in determining oxidation numbers from Lewis structures may arise when adjacent atoms have small electronegativity differences and when more than one Lewis structure has to be taken into account, also see the discussion in ref 2.

C

N

− 2 +1 +1 +2 −3 +1

− 2 + 4 −3

+ 2 −3 −

O

C

N

−

H

C

O

N 4

5

H

ON(M):

•

3+

7a

0

[CoH(CO)4 ] [Co(CO)4] − +1

+3

6

−1 0

0

[Co(NH3)6]

H

Figure 2. Oxidation numbers for some nonmetal compounds. The curved lines show heterolytic cleavage of the bonds and the straight vertical lines show homolytic cleavage of the bonds.

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Ligand charges:

−1 7b

7c

Figure 3. Oxidation numbers of metals in complexes.

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M–L interaction

n -ligands

π-ligands

σ-ligands

M–L σ bond Figure 4. Classification of ligands, L, in metal complexes. Orbital representations are shown schematically. Arrows are directed from the (filled) donor orbital to the (empty) acceptor orbital.

orbital type of L

n-donor (lone pair)

π-donor

σ-donor

M–L π bond

orbital type of L examples

none

π-donor

OH2, OR2,

O2−, F − , ...

π*-acceptor

−

NH3, H , ...

π*-acceptor

CO, NO, PF3, olefins, dienes, alkynes, aroη1-N , ... 2

matics, Cp −,

σ*-acceptor H

H

H , SiR3 , ...

η2-N2, ...

Ligands may be classified according to the types of orbitals used for metal–ligand bonds (Figure 4): ligand orbitals forming the σ M
L bonds may be non, π, or σ bonded resulting in formation of n, π, and σ complexes,2 respectively. Additionally, n ligands may act as π donors or as π acceptors. To stabilize binding of π and σ ligands, strengthening of metal–ligand bonds by π and σ back-donation, respectively, is usually necessary. These additional bondings may cause ambiguities in assigning the oxidation numbers of the central metals. n Ligands The vast majority of ligands are n ligands (e.g., NH3, py, MeCN, PR3, P(OR)3, H2O, Et2O, R2S, CO, F−, Cl−, HO−, O2−, RS−, S2−, and H−). Typical π-donating ligands are oxo (O2−) and fluoro (F−) ligands but this type of π bonding does not affect the assigning of oxidation numbers (Figure 5). This does not hold for π-acceptor ligands; CO is a typical example. Here the electrons forming the π M
L bonds are d electrons from the metal. As a result of the doubly degenerate LUMO of CO, there is the capacity for two π-type back-bonds. The increase of M
CO bond order is associated with the decrease of C
O bond order (Figure 6, 8a → 8b → 8c). Thus, Lewis structures 8b and 8c represent a metal in an oxidation number being two and four units, respectively, higher than that in 8a. Thus (formally) CO2 (8b) and

Lx M

Lx M ON(F)

O

Lx M

F

O −2

−2

ON(O)

Lx M

−1

F −1

Figure 5. Examples of π-donating ligands.

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CO4 (8c) ligands exist in these complexes. The ν(C
O) stretching frequencies for a series of mononuclear tetracarbonyl–metal complexes having a total of 18 valence electrons is shown in Figure 6 (7). Successive reduction gives rise to substantial lowering of the C
O stretching frequencies. The ν(C
O) in the “super-reduced” chromium species is in-between the typical C
O double and single bonds, where the CO ligands may be formulated as carbyne-like ligands. The number of π bonds formulated in Lewis structures (on which the determination of oxidation numbers is based) has to be in accord with the nine-orbital rule and the symmetry of orbitals.3 Furthermore, valence states of central atoms (ions) after (heterolytic) cleavage of all ligands have to be evaluated for proper assignment of oxidation states. Assignment of d10 valence electron configurations of M and oxidation numbers ranging from 0 (M = Ni) up to 4 (M = Cr) in complexes [M(CO)4]n (Figure 6) is consistent with all these aspects. Further instructive examples are nitrosyl complexes of transition metals (8). There are two types, “linear” complexes, M
N
O 160–180, and bent complexes, M
N
O 120– 140, with sp- and sp2-hybridized nitrogen atoms, respectively. Relevant Lewis structures are shown in Figure 7. Of particular interest is the lone electron pair on N in the bent complexes, 10a and 10b, which have σ symmetry and may not be included into the resonance of the π system. To choose appropriate oxidation numbers, experimental data are necessary on the bending of the M
N
O unit and on the extent of π back-donation. Owing to overlapping, IR spectroscopy cannot serve as a diagnostic tool for unambiguous structural assignments: Typical ranges of ν(N
O) in linear and bent NO complexes are 1600–1950 cm 1 and 1520–1720 cm 1 , respectively (for comparison, noncoordinated NO: ν(N
O) = 1878 cm1). The Fe
N
O angle in Na2[Fe(CN)5(NO)]2H2O is 178 and ν(N
O) = 1944 cm1. This clearly indicates a linear-type complex, FeΙΙ and a bound NO+ ligand. [IrCl(NO)(CO)(PPh3)2](BF4) is a bent-type complex, Ir
N
O 124 and ν(N
O) = 1680 cm–1. Hence, it has to be formulated as an IrIII complex having a bound NO− ligand. The classic “brown-ring” reaction

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Lx M

ON(M):

C

Lx M

C

O

CO

2−

Lx M

+2

0

Ligand:

Figure 6. Lewis structures and ν(C
O) stretching frequencies of some tetracarbonyl complexes. L is a neutral ligand.

O

CO

C

+4 −

CO4

8b

8a

O

CO

8c

C

C

O

O

(1000 –1300 cm–1)

νCO / cm-1

2000

1800

[Ni(CO)4]

[Co(CO)4]

−

1600

[Fe(CO)4] 2

−

[Mn(CO)4]3

to detect nitrate-ions results in formation of a bent-type complex, [FeIII(NO)(H2O)5]2+, and not a linear-type complex, [FeI(NO)(H2O)5]2+, as is usually quoted in undergraduate textbooks (9). Structurally similar metal complexes differing only in the number of electrons are also of interest with respect to assigning oxidation numbers. Such an electron variability has been found in an unusually broad range of phthalocyanine– metal complexes. As an example iron–phthalocyaninato complexes, [Fe(pc)]n (H2pc = phthalocyanine), are shown in Figure 8 (10). The question to be answered is whether the stepwise reduction of [Fe(pc)] results in reduction of the iron atom or of the ligand. The decision whether the additional electrons enters a metal-centered or a ligand-centered orbital can only be made on the basis of experimental investigations

Lx M ON(M):

N

O

Lx M

N

NO+

Ligand:

O

Ligand:

NO−

10a

−

(magnetic, Mössbauer, and ESR measurements) or on quantum chemical calculations. As shown in Figure 8, at first the central atom is reduced to Fe0 and is followed by reduction of the ligand up to pc4.

z

N

N

N

N

Fe

N

N

N

N

O

9c

N

LxM

O

+3

ON(M): +1

−

NO3−

9b

N

N

[Cr(CO)4]4

+3 NO−

9a

LxM

LxM

O

+1

−1

1400

NO3−

10b

Figure 7. Lewis structures of metal–nitrosyl complexes. L is a neutral ligand.

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complex

z ON(Fe) ligand

[FeBr(pc)] [Fe(pc)] Li[Fe(pc)]·4.5thf Li2[Fe(pc)]·5.5thf Li3[Fe(pc)]·8thf Li4[Fe(pc)]·9thf

1+ 0 1− 2− 3− 4−

+3 +2 +1 0 0 0

−

pc2 − pc2 2− pc − pc2 3− pc − pc4

Figure 8. Reduction of the iron–phthalocyanine complex.

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π Ligands The electron balance of π-donor–π-acceptor ligands has to be handled in the same way as for n-donor–π-acceptor ligands. As an example, in Figure 9 the two relevant Lewis structures 11a and 11b are shown for an η2-ethene complex (11). Exceptionally high π back-donation results in increasing the oxidation number of the metal by two units (n versus n + 2) and reducing the ligand (C2H4 versus C2H42−). 11a represents a π ethene and 11b a metallacyclopropane complex. Real electronic structures of all η2-ethene complexes (11) have to be described as resonance hybrids, as they are a weighted average of these two canonical forms. To ascribe oxidation numbers means to decide which formula contributes most to the resonance hybrid. This decision has to be based on experimental data, especially the information gained about the coordination induced lengthening of the olefinic C
C bond and the degree of back bending of the substituents on olefinic carbon atoms (Figure 10). Zeise’s salt, K[PtCl3(η2-C2H4)]H2O, is the classic example of a π-ethene complex, C
C 1.375(4) Å and α = 16.2 (11), with a small degree of back-donation only as comparison with uncoordinated ethene, C
C 1.339 Å and α = 0, shows. On the other hand, X-ray structural analyses of [Os(CO)4(η2-C2H4)] and mer-[W(CO)3(η2-C2H4)(η4-nbd)] (nbd = norbornadiene) exhibit metallacyclopropane structures (12), where the C
C bonds, 1.49(2) and 1.48(1) Å, respectively, in the η2-C2H4 ligands are nearly as long as that in cyclopropane, 1.512 Å. Analogously, η2-alkyne complexes (Figure 9, structure 12) have to be considered as resonance hybrids between πalkyne (12a) and metallacyclopropene (12b) complexes.4 Diphenylacetylene, for example, forms complexes of both types as shown by the following complexes (13): cis[Pt(C 6 F 5 ) 2 (η 2 -PhC⬅CPh) 2 ], C
C 1.203(7) Å and [WCl2(η2-PhC⬅CPh)L(PMe3)2], L = CO, C
C 1.341(6) Å; L = PMe3, C
C 1.33(2) Å. Designation of these complexes as “π-diphenylacetyleneplatinum(II)” and “tungsta(IV)cyclopropene” is justified by comparison the C
C bond lengths in the complexes with those in noncoordinated diphenylacetylene, 1.21 Å, and 1,2-diphenylcyclopropene, ≈1.34 Å. σ Ligands Oxidative addition reactions of dihydrogen to low-valent metal complexes yielding dihydridometal complexes are very common and may proceed in a concerted mechanism with η2-H2 complexes as intermediates (Figure 11, structures 13–15). Such complexes have been isolated and fully characterized spectroscopically and structurally (14). These are the prototypes of σ complexes. As a result of the exceptionally low donor strength of H2, stable dihydrogen complexes will not exist without a substantial degree of donation of d electrons of the metal atoms into the antibonding σ* H
H orbital. However, balance is important; a too great extent of back-donation results in breaking the underlying σ H
H bond and oxidative addition occurs, yielding 15. η2-H2 complexes 14 have to be represented by the two Lewis structures 14a and 14b.5 The first isolated stable complex was [W(CO)3(η2-H2){P(i-Pr)3}2] (Kubas, 1984) exhibiting a significantly longer H
H bond than in free H2,

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CH2 Lx M

CH2

:

Lx M

CH2

ON(M):

CH2 Lx M

CH2

0

CH2

+2 C2H42 −

C2H4

Ligand:

11a

11

R

R C

R C Lx M

11b

Lx M

: C

C

R

R

C Lx M

R

0

ON(M):

+2 C2R22 −

C2R2

Ligand:

12a

12

C

12b

Figure 9. η2-Ethene and η2-alkyne metal complexes. L is a neutral ligand.

back bending

α

R

R2

R2

R

C

C

elongation

M

C R

R

C

R2

R2

free

front view

coordinated side view

Figure 10. Schematic showing of the coordination induced C
C bond elongation and back bending of the R groups in η2-olefin complexes.

H

H Lx M + H2 ON(M):

Lx M

Lx M H

H

0

+2

13

14

15 H

H Lx M

Lx M

H

H ON(M):

0

+2

14a

14b

Figure 11. Oxidative addition of dihydrogen to low-valence metal complexes via η2-dihydrogen complexes. L is a neutral ligand.

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VSEPR model

molecular formula

topological formula

Lewis structure(s)

Figure 12. Concepts of Lewis structures and oxidation numbers in teaching molecular chemistry (above) with SO2 as an example (below).

electronegativity

geometric structure electronic structure formal charges oxidation numbers

S O

SO2

O

S

O

O

O

S

etc.

0.82(1) versus 0.74 Å. The ν(H
H) stretching frequencies in dihydrogen complexes are typically lowered by more than 1000 cm1 compared with free H2. Furthermore, there are η2-H2 complexes with elongated H
H bonds, 1.2–1.4 Å; for example, [ReH5(η2-H2)(PR3)2], that have to be described in terms of resonance theory by a higher contribution of canonical form 14b. Concluding Remarks To apply the concept of oxidation numbers means electrons that are shared between atoms in molecules are assigned to a specific atom. From this it follows that oxidation numbers, in general, do not reflect the “properties” of atoms in molecules but the concept is used to systematize chemistry. Furthermore, inherent in this concept is that there may be alternative assignments of oxidation numbers to atoms of a molecule (as it happens quite often in metal complexes). To select the “best” set of oxidation numbers may be—within certain limits—arbitrary and may also depend on the application one is interested in. If need be, experimental information (structural data, results from IR, Raman, or Mössbauer measurements) and theoretical calculations have to be considered. To do so, the concept of oxidation states is complementary to other “rules” (like the 18-electron rule) already in use. Furthermore, the concept proved to be a valuable framework to systematize and to analyze coordination compounds structurally and electronically (15). The concept of oxidation states is embedded in the teaching process of molecular chemistry for early chemistry students as shown in Figure 12. Starting from molecular formulas (giving the composition of molecules) via topological formulas6 (representing the constitution of molecules, that

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O

trigonal planar (C2v symmetry) VSEPR: O-S-O ca. 120° exper.: O-S-O 119.5° S sp2 hybridized - delocalized (O-S-O) π system - lone pair of S has σ symmetry

ON(S) = +4 ON(O) = – 2

is, the connectivity of atoms in molecules) the Lewis formulas are derived. They show the pattern and numbers of bonds and nonbonding electrons or electron pairs and play a central role to the understanding of molecular chemistry. Lewis formulas give a first insight into geometric structures (by applying the VSEPR model) and electronic structures of molecules as well. Homolytic and heterolytic cleavage of covalent bonds are indicated via the formal charges and the oxidation numbers the (hypothetical) borderline cases. These are the “pure covalent” and “pure electrostatic” views of covalent bonds, respectively. From the didactical point of view this is the most informative way for students to understand the underlying principles of the concept of oxidation states7 and the model character of oxidation numbers. This view neither overestimates the meaning nor reduces the concept to a formal numerical tool for bookkeeping electrons in reduction–oxidation reactions. This is especially true when the electronic structure of a molecule can only be properly described by a resonance hybrid. By evaluating the oxidation numbers in all relevant resonance forms, the students will recognize directly the model character of the concept and get a sense of the limitations of the concept. Thus students will learn where no oxidation numbers should be given at all because they are meaningless or where alternative sets of oxidation numbers should be discussed to understand different aspects of electronic structures of molecules under consideration. For the formal bookkeeping of electrons in redox equations, it may also be enough to give a reasonable set of oxidation numbers without detailed analysis of small differences in electronegativities of bonding partners or of π-bonding effects. This also holds for all molecules that cannot be properly described by Lewis structures.

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Acknowledgments

Literature Cited

I am indebted to Rudolf Taube (Halle) for stimulating discussions, to Amanda Elliott (Loghborough) for language polishing, and to the Fonds der Chemischen Industrie for financial support.

1. (a) Eggert, A. A.; Middlecamp, C.; Kean, E. J. Chem. Inf. Comput. Sci. 1990, 30, 181. (b) Birk, J. P. J. Chem. Educ. 1992, 69, 294. (c) Calzaferri, G. J. Chem. Educ. 1999, 76, 362. (d) Holder, D. A.; Johnson, B. G.; Karol, P. J. J. Chem. Educ. 2002, 79, 465. 2. (a) Kauffmann, J. M. J. Chem. Educ. 1986, 63, 474. (b) Woolf, A. A. J. Chem. Educ. 1988, 65, 45. (c) Packer, J. E.; Woodgate, S. D. J. Chem. Educ. 1991, 68, 456. 3. Werner, A. Neuere Anschauungen auf dem Gebiete der Anorganischen Chemie; Vieweg: Braunschweig, Germany, 1920. 4. Stock, A. Angew. Chem. 1919, 32, 373. 5. Pauling, L. General Chemistry; Freeman: San Francisco, CA, 1947; p 173. 6. Mullay, J. Struct. Bond. 1987, 66, 1. 7. (a) Ellis, J. E. Adv. Organometal. Chem. 1990, 31, 1. (b) Beck, W. Angew. Chem. 1991, 103, 173. 8. (a) Mingos, D. M. P.; Sherman, D. J. Adv. Inorg. Chem. 1989, 34, 293. (b) Johnson, B. F. G.; Haymore, B. L.; Dilworth, J. R. In Comprehensive Coordination Chemistry; Wilkinson, G., Gillard, R. D., McCleverty, J. A., Eds.; Pergamon: Oxford 1987; Vol. 2, p 99. 9. Wanat, A.; Schneppensieper, T.; Stochel, G.; van Eldik, R.; Bill, E.; Wieghardt, K. Inorg. Chem. 2002, 41, 4. 10. Taube, R. Pure Appl. Chem. 1974, 38, 427. 11. Love, R. A.; Koetzle, T. F.; Williams, G. J. B.; Andrews, L. C.; Bau, R. Inorg. Chem. 1975, 14, 2653. 12. (a) Bender, B. R.; Norton, J. R.; Miller, M. M.; Anderson, O. P.; Rappé, A. K. Organometallics 1992, 11, 3427. (b) Grevels, F.-W.; Jacke, J.; Betz, P.; Krüger, C.; Tsay, Y.-H. Organometallics 1989, 8, 293. 13. (a) Usón, R.; Forniés, J.; Tomás, M.; Menjón, B.; Fortuno, C.; Welch, A. J.; Smith, D. E. J. Chem. Soc., Dalton Trans. 1993, 275. (b) Clark, G. R.; Nielson, A. J.; Rae, A. D.; Rickard, C. E. F. J. Chem. Soc., Dalton Trans. 1994, 1783. (c) Nielson, A. J.; Boyd, P. D. W.; Clark, G. R.; Hunt, P. A.; Hursthouse, M. B.; Metson, J. B.; Rickard, C. E. F.; Schwerdtfeger, P. A. J. Chem. Soc., Dalton Trans. 1995, 1153. 14. (a) Kubas, G. J. Acc. Chem. Res. 1988, 21, 120. (b) Crabtree, R. H. Angew. Chem. 1993, 105, 828. 15. Cotton, F. A.; Wilkinson, G.; Murillo, C. A.; Bochmann, M. Advanced Inorganic Chemistry; Wiley: New York, 1999. 16. (a) Nyholm, R. S.; Tobe, M. L. Adv. Inorg. Chem. Radiochem. 1963, 5, 1. (b) Taube, R. In Internationales DöbereinerKolloquium; Bolck, F., Ed.; University Press: Friedrich-Schiller University of Jena, Germany, 1981; p 73.

Notes 1. When we do not allow a rearrangement of electrons, then we get the valence state of Mz in the complex. If there is more than one reasonable possibility of (formal) cleavage of the ligands then the valence states of M in the alternatives may be inspected to find out what might be the more plausible oxidation number in this instance (16). 2. Of particular interest is the designation of the σ complex. This is a complex where a ligand donates electrons from a σ bond into an empty metal orbital, as in the case of complexes of dihydrogen (see Figure 11 for an example). Before complexes of this type were known, one could only distinguish between n and π complexes; typically in this case the former ones were frequently named as σ complexes. 3. Transition metals have nine valence orbitals [5(n – 1)d + 1ns + 3np; n is the principal quantum number]. Hence, Lewis structures that make use of more than nine orbitals are not valid. Furthermore, the number of π bonds has to be in accord with orbital symmetry. 4. This is a simplified picture in that owing to the orthogonal π bonds alkynes may act as four-electron donors and as fourelectron acceptors. 5. Taking into consideration that resonance structures are defined as alternative representations of the electronic configuration of a fixed set of nuclei, it will be evident that formula 14b (representing one of the two canonical forms of an η2-H2 complex 14) has another meaning different from Lewis structure 15 (representing a real existing dihydrido complex). 6. In topological formulas two atoms are connected by a line when a bond between them exists, irrespective of the bond type. Hence, these lines do not represent electron pairs as it is the case in Lewis structures. 7. Experience shows that students who have mastered writing a Lewis formula of a molecule are capable of assigning the oxidation numbers correctly in most cases. On the other hand, students who fail to draw a Lewis formula of a molecule successfully often fail to correctly use a set of hierarchical oxidation number rules. Instructors can check tutorials for the treatment of S2O82− as a useful example .

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