Application of the Covalent Bond Classification Method for the

Article pubs.acs.org/jchemeduc

Application of the Covalent Bond Classification Method for the Teaching of Inorganic Chemistry Malcolm L. H. Green† and Gerard Parkin*,‡ †

Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR, United Kingdom Department of Chemistry, Columbia University, New York, New York 10027, United States

‡

S Supporting Information *

ABSTRACT: The Covalent Bond Classification (CBC) method provides a means to classify covalent molecules according to the number and types of bonds that surround an atom of interest. This approach is based on an elementary molecular orbital analysis of the bonding involving the central atom (M), with the various interactions being classified according to the number of electrons that each neutral ligand contributes to the bonding orbital. Thus, with respect to the atom of interest (M), the ligand can contribute either two (L), one (X), or zero (Z) electrons to a bonding orbital. A normal covalent bond is represented as M−X, whereas dative covalent bonds are represented as either M←L or M→Z, according to whether the ligand is the donor (L) or acceptor (Z). A molecule is classified as [MLlXxZz] according to the number of L, X, and Z ligand functions that surround M. Not only does the [MLlXxZz] designation provide a formal classification of a molecule, but it also indicates the electron configuration, the valence, and the number of nonbonding electrons on M. As such, the classification allows a student to understand relationships between molecules, thereby increasing their ability to conceptualize and learn the chemistry of the elements. KEYWORDS: First-Year Undergraduate/General, Second-Year Undergraduate, Graduate Education/Research, Inorganic Chemistry, Analogies/Transfer, Covalent Bonding, Main-Group Elements, Nonmetals, Organometallics

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INTRODUCTION The carbon atoms in the vast majority of stable organic molecules have a valence1 of four and possess an octet2−4 configuration. These two simple facts allow a student to inspect complex organic molecules and obtain insight as to whether the molecule is chemically reasonable. In contrast, such simple rules do not exist for the other elements of the periodic table, which routinely form compounds in which the atom may possess either an array of electronic configurations (also referred to as electron counts or electron numbers), valence states, or both. Consider, for example, the elements that are adjacent to carbon in the periodic table, namely boron and nitrogen: boron forms a variety of trivalent compounds in which it may have either an octet configuration (e.g., H3BNH3) or a sextet configuration (e.g., Me3B),5 whereas nitrogen forms compounds in which it is either trivalent (e.g., NH3) or pentavalent (e.g., HNO3). The situation is exacerbated for transition metals, which may form compounds in which a given metal exhibits a variety of different valence states and electronic configurations. Traditionally, efforts to classify inorganic compounds have focused on the oxidation state6 of the element of interest, that is, the charge that resides on the atom after cleaving all bonds (other than homonuclear bonds) in a heterolytic manner. It is, however, becoming increasingly apparent that the oxidation state formalism has shortcomings that result from ambiguities due to either (i) the noninnocent nature of some ligands7 or (ii) the © XXXX American Chemical Society and Division of Chemical Education, Inc.

application of different procedures for assigning oxidation states, as discussed in more detail below. In large part, the problems encountered in the use of oxidation states to classify covalent compounds result from the fact that it is an approach that forces ionic character on a compound that may have little such nature. Here, we describe a more appropriate method for categorizing covalent compounds, namely the “Covalent Bond Classification (CBC)”,8 which does not attempt to force an ionic description upon a covalent molecule, but rather classifies a molecule according to the nature of the ligands that surround the element of interest (M).9

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OXIDATION STATE ASSIGNMENTS AND AMBIGUITIES Oxidation states are of widespread use as a simple classification system that has been described by Seddon and Seddon as the “Dewey Decimal Classification of inorganic chemistryif the rules are applied, a number is obtained”.10 However, beyond the classification, Seddon and Seddon question “Does oxidation state have a chemical significance? A number is always obtained does it mean anything?”10 The latter point is particularly pertinent in view of the ambiguity in the assignment of oxidation states.

A

dx.doi.org/10.1021/ed400504f | J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

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application of procedure (B),15,19−21 although it is less commonly invoked than that for the cation. Thus, depending upon the preference of an author, the cycloheptatrienyl ligand has been assigned charges of +1,16,17 −1,22 and −3.15,19−21 Applying these possibilities to (η5-C5H5)Ti(η7-C7H7), the oxidation state of titanium may be assigned values of either 0, +2, or +4 (Figure 3)! Figure 1. Two different procedures for assigning charges to ligands for the determination of oxidation states. In method A, the pair of electrons in the covalent bond are transferred to the more electronegative partner, whereas in method B, the pair of electrons are transferred such that the ligand, Y, adopts a closed shell configuration. In many cases, the two procedures assign the same charge to Y, but in some cases, the two procedures assign different charges, which therefore results in ambiguous oxidation states. Furthermore, in view of the existence of different electronegativity (χ) scales, ambiguity may also result if using only method A.

In this regard, a fundamental problem in the assignment of oxidation states is that there exists more than one method for allocating charges to ligands (Figure 1). For example, the charge on a ligand may be derived by either (A) removing the ligand such that the shared pair of electrons is transferred to the more electronegative atom11 or (B) removing the ligand in a closed shell configuration;12 for both of these methods, an exception is that bonds between the same element are broken homolytically. Although one often obtains the same charges regardless of which approach one uses, situations arise in which the outcomes are different,8b,13 thus rendering any interpretation questionable. Consider, for example, the η7-C7H7 cycloheptatrienyl ligand in 5 (η -C5H5)Ti(η7-C7H7).14,15 Application of the electronegativity procedure (A) assigns both carbocyclic rings as anions, that is, [C5H5]− and [C7H7]−, because carbon is more electronegative than titanium. On the other hand, if one were to apply the closed shell procedure (B), the cyclopentadienyl ligand is assigned as an anion, [C5H5]−, whereas the cycloheptatrienyl ligand is assigned as a cation, [C7H7]+ (Figure 2).16,17 The assignment of different

Figure 3. Ambiguity in the oxidation state of titanium in (η5-C5H5)Ti(η7-C7H7) depending on the charge assigned to the cycloheptatrienyl ligand.

In view of the fact that the actual bonding in the molecule is independent of the charges that are assigned to the ligands, it is evident that the derived oxidation state is of limited utility in compounds such as (η5-C5H5)Ti(η7-C7H7). Indeed, in view of such ambiguities, IUPAC recommends that oxidation numbers not be included in the nomenclature of organometallic compounds.23 It is, therefore, clear that discussions pertaining to covalent compounds would benefit from an alternative classification system, as described below.

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COVALENT BOND CLASSIFICATION In addition to the ambiguity of oxidation state assignments, another concern with the application of oxidation states pertains to its use to infer properties of a covalent molecule. Specifically, because the oxidation state approach reduces the description of a covalent molecule to the value of the charge on an isolated atom, with no ligands attached, it is evident that the oxidation state assignment can provide only very limited insight into the nature of the molecule itself. In contrast, the Covalent Bond Classification (CBC),8 as described in detail below, evaluates the nature of a molecule by identifying the number and types of bonds that surround the element of interest (M). Thus, by evaluating the intact molecule, the classification provides more information concerned with the nature of the compound than that which is provided by the mere numerical value of an oxidation state. Adopting the view that the bonding in many covalent molecules can be represented in terms of 2-center-2-electron bonding interactions, there are three possible scenarios that describe the construction of these bonds in a molecular orbital sense, as illustrated in Figure 4. Thus, with respect to the central element of interest (M), the neutral ligand can contribute either two (L), one (X), or zero (Z) electrons to the bonding orbitals. The classification of ligands as L-, X-, or Z-type, as featured in a variety of textbooks,24 is now well established, and some simple examples of these ligands are provided in Table 1. Normal covalent bonds are represented as M−X, whereas dative covalent bonds8d,25 are represented as either M←L or M→Z, according to whether the ligand is the donor (L) or acceptor (Z). Note that, in addition to using an arrow, the dative bond can also be represented as a line with formal charges,26 that

Figure 2. Frontier orbital occupations for the cycloheptatrienyl ligand in different charged states. Note that only [C7H7]+ and [C7H7]3− have closed shell configurations.

charges for the cyclopentadienyl and cycloheptatrienyl ligands when using the closed shell procedure (B) is a consequence of the fact that, whereas the closed shell form of C5-symmetric [C5H5] is the aromatic (4n + 2) 6 π-electron monoanion, the closed shell form of C7-symmetric [C7H7] is the aromatic six πelectron monocation.18 The C7-symmetric planar [C7H7]− monoanion is not an acceptable assignment for method B because it is an open shell paramagnetic species (Figure 2). The trianion [C7H7]3−, however, is a closed shell ten π-electron aromatic species and is, therefore, a valid assignment for the B



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Figure 4. The Covalent Bond Classification (CBC) of L, X, and Z ligands. Note that the ligands are always classified in their neutral forms. L-type ligands (2-electron donors) are identified as Lewis bases, X-type ligands (1-electron donors) as radicals, and Z-type ligands (0-electron donors) as Lewis acids.

Table 1. Classifications of Some Common Ligands Ligand

CBC description

Electron donor number

PR3 H R BR3 AlR3 η2-C2H4 η3-C3H5 η4-C4H6 η4-C4H4 η5-C5H5 η6-C6H6 η7-C7H7 η8-C8H8 κ3-TpR,R′ CO NO

L X X Z Z La LX L2a LX2 L2X L3a L2X3 L3X2 L2X La Xa (bent) X3 (linear) Z X2 LX2 X3 X (bent) LX (bent) L2X (linear) X2 (bent) LX2 (linear) X (pyramidal) LX (planar) X2 (Schrock alkylidene) La (Fischer carbene) X3

2 1 1 0 0 2 3 4 4 5 6 7 8 5 2 1 3 0 2 4 3 1 3 5 2 4 1 3 2 2 3

O

N OR

NR NR2 CR2 CR

Figure 5. Two alternative, but equivalent, representations for the dative bond in H3NBH3. Note that the representations are not resonance structures.

line with formal charges (as illustrated for H3NBH3 in Figure 5), correspond to exactly the same electronic structure and are not resonance structures.13 Ligands can be readily classified as L-, X-, or Z-type by consideration of some simple principles (Figure 4). For example, by virtue of the fact that they serve as electron pair donors, L-type ligands may be readily identified as neutral molecules that have available lone pairs and are Lewis bases, for example, H2O, H3N, and R3P. Correspondingly, Z-type ligands serve as electron pair acceptors and are, therefore, readily identified as neutral molecules that exist as Lewis acids, for example, BF3. Finally, because X-type ligands contribute only one electron to the bonding orbital, they correspond to neutral species that are radicals, for example, H•, Cl•, and H 3C • . Although many ligands coordinate to a metal center by a single covalent bond, a variety of multidentate ligands coordinate via more than one covalent bond. Such ligands are classified as [LlXxZz], where l, x, and z are the respective number of L, X, and Z functionalities that are associated with the frontier orbitals of the ligand in the geometry that corresponds to its binding mode. Some examples of multidentate ligands and their classifications are provided in Figure 6 and Table 1, from which it is evident that, in many cases, the classification can be simply derived by summing the individual bonding components that are implied by their valence bond representations. For example, the classification of benzene as an L3 donor ligand may be rationalized on the basis that each of the delocalized “double bonds” of an η6-benzene ligand may be conceptually viewed as an L donor akin to that of C2H4 (Figure 6). Likewise, the classification of η5-cyclopentadienyl as an L2X ligand can be rationalized on the basis that the cyclopentadienyl radical may be conceptually viewed as being composed of two “double bonds” (each of which is an L donor) and an alkyl radical

a

These classifications pertain to the primary bonding interactions. However, some ligands have relatively low energy empty orbitals such that, depending on the nature of the metal center, backbonding may provide an important supplement to the bonding. In such cases, the ligand should be classified with additional Z functions, the number of which would depend on the ligand. For example, extreme backbonding in an ethylene complex corresponds to a metallacyclopropane structure, such that the ligand is classified as LZ, which is equivalent to X2.

is, M−−L+ and M+−Z−. Despite their different appearances, the two representations of a dative bond, as either (i) an arrow or (ii) a C



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Figure 8. CBC description of oxo compounds. Depending on the atom to which it is attached, the oxygen can bind via either a single, double, or triple bond.

Figure 6. [LlXxZz] classifications of some common ligands as derived by summing the individual components that correspond to the valence bond representation. For example, a cyclopentadienyl ligand is classified as L2X because the Lewis structure contains two double bonds (L) and an alkyl moiety (X).

the bonding is supplemented by lone pair donation from the nitrogen to the metal (Figure 9).

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EQUIVALENT NEUTRAL CLASS After classifying the ligands attached to the element of interest, the molecule itself may be classified in the form [MLlXxZz]Q± by summing all the L, X, and Z functionalities, where Q ± is the charge on the molecule.28 This procedure is best performed by using a structure-bonding representation of the molecule in which the bonds to the neutral ligands are drawn explicitly as either normal covalent (M−X) or dative covalent (M←L and M→Z) and the appropriate charge is located on M.29 For example, the structure-bonding representations of [Co(NH3)6]3+, CoCl3(NH3)3, and [CoCl6]3− are illustrated in Figure 10, from which it is evident that these molecules are classified as [ML6]3+, [ML3X3], and [MX6]3−, respectively. At first glance, it would, therefore, appear that [Co(NH3)6]3+, CoCl3(NH3)3, and [CoCl6]3− belong to fundamentally different classes of molecules. However, the true relationship between these molecules is obfuscated by the fact that the molecules possess different charges. This issue is treated within the CBC method by formally localizing the Q± charge on the ligands, rather than on M, thereby reducing the [MLlXxZz]Q± assignment to its “equivalent neutral class” (ENC), as described below. Specifically, the reduction of [MLlXxZz]Q± to its equivalent neutral class is readily achieved by the application of some simple transformations (Figure 11), the most essential of which are (1) For cations, L+ → X and, if no L ligand is present, X+ → Z. (2) For anions, X− → L and, if no X ligand is present, L− → LX. (3) If the derived classification after performing these transformations contains both an L and a Z function, the classification is reduced further by using the transformation LZ → X2. Although a detailed explanation of the origin of these rules is provided in the Supporting Information, a simple rationalization is provided by recognizing that, for example, a positively charged 2-electron donor ligand is equivalent to a neutral 1-electron donor ligand, whereas a negatively charged 1-electron donor

(which is an X donor). However, although this simple aide memoire based on a valence bond representation of a ligand predicts the [LlXxZz] classification in many cases, there are situations in which it breaks down. In such cases, consideration of the frontier orbitals is essential to obtaining the correct representation. For example, analysis of the frontier orbitals of the η7-cycloheptatrienyl ligand indicates that is not classified as L3X but rather as L2X3 (Figure 7).27

Figure 7. Frontier orbitals for a variety of ligands indicating the L, X, and Z character of each orbital according to whether it is doubly occupied (L), singly occupied (X), or empty (Z). Note that the rule LZ→X2 (see the section Equivalent Neutral Class) must be applied to cycloheptatrienyl because Z is degenerate with the half occupied X orbital.

Although it is evident that multidentate ligands require representation by more than one L, X, or Z function, monodentate ligands may also be described by multiple functions. As an illustration, depending on the nature of M, the interaction of M with a single oxygen atom can be described as either a single, double, or triple bond, in which case the oxygen ligand is classified as either Z, X2, or LX2 (Figure 8). Examples of compounds that feature these different interactions are provided by amine oxides (R3N+O−), ketones (R2CO), and transition metal oxo compounds (LnM−O+), respectively. Other ligands that feature polyfunctional atoms include alkoxides, amides, and NO (Table 1). For example, the NR2 ligands in metal−amide compounds that feature a pyramidal nitrogen are classified as X, whereas those with a planar nitrogen are classified as LX because

Figure 9. X and LX classifications of an amide ligand according to whether it is pyramidal or planar. D



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Table 2. Definitions Pertaining to the CBC Method and the Equivalent Neutral Class Symbol L l X x Z z m VN LBN EN vn

Figure 10. [MLlXxZz] classifications of [Co(NH3)6]3+, [Co(NH3)3Cl3], and [CoCl6]3−. Note that all three compounds belong to the same equivalent neutral class, ML3X3, after applying the L+ → X and X− → L transformations, as appropriate.

Definition 2-electron donor function number of L functions 1-electron donor function number of X functions 0-electron donor function number of Z functions number of valence electrons on neutral M atom valence number VN = x + 2z ligand bond number LBN = l + x + z electron number (or electron count) EN = m + 2l + x number of electrons in “nonbonding” M orbitalsa n = m − x − 2z = m − VN

a n

v corresponds to dn for transition metal compounds.

Table 3. Number of Valence Electrons Associated with the Neutral Transition Metal Atoms (i.e. the Group Valence).a Group 3

Group 4

Group 5

Group 6

Group 7

Group 8

Group 9

Group 10

Sc, Y, La

Ti, Zr, Hf

V, Nb, Ta

Cr, Mo, W

Mn, Tc, Re

Fe, Ru, Os

Co, Rh, Ir

Ni, Pd, Pt

3

4

5

6

7

8

9

10

Figure 11. Transformations for reducing [MLlXxZz]Q± to its equivalent neutral class. For cations, the order of priority is L+ → X and, if no L ligand is present, X+ → Z. For anions, the order of priority is X− → L and, if no X ligand is present, L− → LX. a

Note that the number of valence electrons is independent of their distribution within the nd and (n+1)s levels.

ligand is equivalent to a neutral 2-electron donor ligand. For example, coordination of a Cl− (i.e., X−) ligand to a metal center may be viewed analogously to coordination of NH3 (i.e., L). Applying these rules to [CoCl6]3−, CoCl3(NH3)3, and [Co(NH3)6]3+, each of the respective [MX6]3−, [ML3X3], and [ML6]3+ classifications are reduced to the same equivalent neutral class of ML3X3 (Figure 10). Thus, the CBC method indicates that each of these complexes belong to the same class of molecule. As a consequence, the central atoms in these complexes also have the same valence and electron count. Some examples of the derivation of the [MLlXxZz] classes for some metallocene complexes30 are illustrated in Figure 12.

nonbonding electrons (vn), and ligand bond number (LBN), as summarized in Table 2. For example, the electron number (i.e., the electron count) of M in MLlXxZz, is given by EN = m + 2l + x, where m is the number of valence electrons on the neutral M atom. The origin of this equation is simply that each L ligand contributes two electrons to the electron count of M, whereas each X ligand contributes one electron. The value of m is indicated by the periodic table group number,31 as illustrated for the transition metals in Table 3. Likewise, the valence number (VN) of M, that is, the number of electrons that the element uses in bonding, is VN = x + 2z and is often abbreviated to valence. The origin of this expression is that each X ligand requires the metal to contribute one electron to the M−X bond, whereas each Z ligand requires M to contribute two electrons to the M→Z bond. As such, the valence may be considered to be composed of two components: the x valence and the z valence. It should be noted that, in many cases, the

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INFORMATION EMBODIED IN THE MLLXXZZ CLASSIFICATION In addition to providing a simple classification of a covalent molecule, the MLlXxZz description also contains useful information pertaining to the nature of a molecule, such as the electron number (EN), valence number (VN), number of

Figure 12. [MLlXxZz] classifications of some metallocene compounds. E



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valence may be coincidentally equal to the oxidation state; however, the equivalence breaks down if, for example, homonuclear element−element bonds are present. As an illustration, the mercury centers of Hg(I) compounds, such as Hg2Cl2, are divalent due to the presence of a Hg−Hg bond. The number of nonbonding valence electrons on M (vn), as expressed by the value of n, is n = m − x − 2z = m − VN. For diamagnetic main group element compounds, this quantity is typically referred to as the number of lone pair electrons, whereas in transition metal chemistry, it is normally described as the dn configuration. A final quantity that may be derived from the MLlXxZz classification is the ligand bond number (LBN), which represents the effective total number of ligand functions surrounding M, and is defined as LBN = l + x + z. Although this quantity is not defined to be the coordination number,32 it is, in many cases, equivalent to the value that most chemists would assign as the coordination number.

Figure 15. CBC plot for nitrogen. The majority of compounds possess MX3 and MX3Z classifications (indicated by orange).

same valence, it is also worth noting that classes that are diagonally related (i.e., lower left to upper right) possess the same ligand bond number. Examination of these plots indicates that, although a variety of classifications are possible, each element generally adopts only a few of the available MLlXxZz classes. For example, the vast majority of isolated carbon compounds belong to the MX4 classification; the only other commonly encountered class for carbon is MLX2, as exemplified by molecules such as CO, RNC, and N-heterocyclic carbenes (Figure 16).34 Carbanions (R3C−)

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CBC PLOTS In view of the fact that the MLlXxZz classification of a molecule embodies information that relates to the electron count, the valence, the ligand bond number, and the vn configuration, it provides a better method for classifying a covalent compound than one based on oxidation state. Specifically, whereas a classification based on oxidation state is one-dimensional, one based on the MLlXxZz description is multidimensional. The distribution of MLlXxZz classes for a given element can be conveniently represented in a CBC plot33 of electron number versus valence, in which each box is occupied by a specific MLlXxZz class. CBC plots are characteristic of each element (M), as illustrated for boron, carbon, and nitrogen in Figures 13−15. Although it is self-evident that all classes in a given column have the same electron number and all classes in a given row have the

Figure 16. Examples of carbon compounds that belong to the class MLX2. The molecules are drawn using both the dative bond arrow (top) and with formal charges (bottom). Both representations are used in the literature and are equivalent.

Figure 13. CBC plot for boron. Only compounds with MX3 and MLX3 classifications (indicated by orange) are commonly observed.

Figure 17. Procedure for classifying [CH3]•, [CH3]+, and [CH3]−.

Figure 14. CBC plot for carbon. The majority of stable compounds possess MX4 classifications (indicated by orange); the other (blue) highlighted classes are less commonly observed and are often reactive intermediates.

also belong to the MLX2 classification, whereas other reactive intermediates, such as carbocations (R3C+), belong to MX2Z, while radicals (R3C•) belong to MX3, as illustrated in Figure 17. Whereas carbon has a strong preference for forming compounds that belong to the MX4 classification, nitrogen commonly forms compounds that belong to the MX3 and MX3Z classifications, and boron commonly forms compounds that belong to the MX3 and MLX3 classifications. Some illustrative examples of boron, carbon, and nitrogen compounds and their classifications are provided in Tables 4−6. As noted above, the vast majority of carbon compounds may be classified as MX4, of which simple tetrahedral molecules of the type CH4, CH2Cl2, CMe4, Me3CCl, Me2CCl2, MeCCl3, and CCl4 are illustrative. The observation that these compounds have the same classification is in accord with the facts that they are structurally similar and that the central carbon atom in each F



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Table 4. Representative Examples of [CH3]−, [CH3]+, [CH3]• Carbon Containing Molecules According to Their CBC Designation MX4 CH4 H2CCH2 HCCH CO2

MLX2

MX2Z

MX3

−

+

H3C•

H3C RNC CO

H3C

In contrast to the observation that main group elements such as boron, carbon, and nitrogen adopt only a few of the possible MLlXxZz classifications, the transition metals typically exhibit a large variety of classifications. For example, the CBC plot for organometallic compounds of iron is illustrated in Figure 18.8c

Table 5. Representative Examples of Boron Containing Molecules According to Their CBC Designation MX3

MLX3

BH3 B(CH3)3

H3BNH3 BH4−

Table 6. Representative Examples of Nitrogen Containing Molecules According to Their CBC Designation MX3

MX3Z

MX2

MX2Z

NH3 HNO2

NH4+ H3NBH3 HNO3

NO

NO2

Figure 18. CBC plot for organometallic iron compounds (key: orange, 71%; pink, 20%; gold, 7%; green, < 1%).

CBC plots of this type present a large amount of factual information. For example, examination of Figure 18 indicates that the vast majority of organometallic iron compounds are classified as either ML5 (20%), ML4X2 (71%), or ML3X4 (7%), and this information is useful when evaluating the significance and novelty of certain molecules. For example, consider the [tris(pyrazolyl)hydroborato]iron t carbonyl compound [PhTpBu ]Fe(CO) (Figure 19).36 In

molecule is tetravalent. However, the oxidation state of the central carbon atom in these molecules varies widely: CH4 (−4), CH2Cl2 (0), CMe4 (0), Me3CCl (+1), Me2CCl2 (+2), MeCCl3 (+3), and CCl4 (+4). This large range of eight units of oxidation state is striking given the general similarity of these molecules, such that one has to question the perceived significance and utility of these values.1,35 For example, the large range of oxidation states could be taken to suggest that the molecules at the extremes are effective oxidizing or reducing agents. However, CH4, with an oxidation state of −4, is not a well-known reducing agent, and CCl4, with an oxidation state of +4, is not widely used as an oxidizing agent. It is, therefore, clear that, from the perspective of either their structure or reactivity, the assignment of a large range of oxidation states is not warranted for these compounds. By extension, inferring the oxidizing and reducing nature of metal complexes on the basis of oxidation state assignments may sometimes be misguided. For example, rather than acting as oxidizing agents, high oxidation state compounds, such as the W(VI) and Re(VII) complexes W(PR3)3H6 and Re(PR3)2H7, are capable of reducing organic substrates by virtue of the presence of hydride ligands. Although the chemistry of carbon is dominated by the MX4 class of molecules, there are two common classes for boron, namely MX3 and MLX3, as illustrated in Table 5 and Figure 13. In this regard, while it is evident that molecules such as BH3 and [BH4]− are structurally and electronically different, in accord with the respective MX3 and MLX3 classifications, the oxidation states of boron in these compounds are the same (+3). Thus, in this case, the oxidation state assignment provides no insight into the fact that BH3 and [BH4]− are fundamentally different in terms of their electronic structure. With respect to nitrogen chemistry, the two common classes are MX3 and MX3Z, as illustrated by NH3 and [NH4]+ (Table 6 and Figure 15). Despite these different classifications, the oxidation states of nitrogen in NH3 and [NH4]+ are the same (−3), which thereby provides another illustration of how the oxidation state fails to capture the fundamental difference in the electronic structures of these two molecules.

t

Figure 19. Molecular structure of [PhTpBu ]Fe(CO). The lines are only intended to show connectivity and are not intended to be a structuret bonding representation. [PhTpBu ] is an L2X donor ligand.

terms of oxidation state, the iron in this molecule is classified as Fe(I), which is the same as that in the well-known cyclopentadienyl iron compound [CpFe(CO)2]2.5 Therefore, on the basis of oxidation state, it would appear that there is t nothing unusual about [PhTpBu ]Fe(CO) because Fe(I) carbonyl compounds are precedented. However, examination of the CBC plot for iron (Figure 18) indicates that monomeric t [PhTpBu ]Fe(CO), with a classification of ML3X, represents a novel class of monovalent iron carbonyl compound. [CpFe(CO)2]2, on the other hand, belongs to the well-known 18electron class of ML4X2 molecules.8d It is important to emphasize that although a CBC plot may indicate the distribution of compounds, it does not explain why a particular class of compound is common because the classification does not incorporate a sufficiently detailed view of the bonding. Likewise, the oxidation state alone cannot be used to explain why certain classes of molecule are stable. Thus, while a CBC plot is a useful guide, it should not be inferred, for example, that any molecule belonging to the most popular class G



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Figure 20. Comparison of the neutral ligand method and the oxidation state method for determining electron count. Note that the neutral ligand method involves fewer mathematical steps because it does not require determination of the oxidation state.

Although the electron count obtained by the CBC method is necessarily equivalent to that obtained by invoking oxidation states38 (when performed correctly), the latter approach mathematically involves more steps, as illustrated for (η5C5H5)Ti(η7-C7H7) in Figure 20. In view of the greater number of steps, the oxidation state method is more susceptible to incorporation of errors. For example, a student may correctly identify the number of valence electrons associated with the neutral atom but could incorrectly determine the number of electrons associated with the oxidation state. In such a case, the overall derived electron count will be incorrect. Likewise, a student could determine the correct number of valence electrons associated with an oxidation state, but then use an incorrect number of electrons for the ligand if it may be classified more than one way. As an illustration, to determine the electron count for a molecule such as (η5-C5H5)Ti(η7-C7H7), a student could assign a charge of −3 to the η7-C7H7 ligand to determine the oxidation state of the titanium and the corresponding number of valence electrons but then use the electron donor number that is associated with the cation [C7H7]+, thereby resulting in an incorrect electron count. The neutral ligand approach that is utilized by the CBC method is, therefore, a necessarily simpler and more direct approach for determining the electron count.

in a CBC plot will be stable, nor that one which belongs to an unpopular class will be unstable.

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ADVANTAGES OF THE CBC METHOD In addition to providing a classification of molecules that reflects both the structure and electronic nature of a molecule, the CBC method offers several other advantages over the oxidation state approach, as detailed below. All Ligands Are Classified in Their Neutral Form

In view of the fact that all ligands are categorized in their neutral forms, one does not have to remember any rules about the charges assigned to ligands. One only needs to examine the neutral form of the ligand in order to establish the electron configuration of the donor atom. In general, (i) a radical corresponds to an X ligand, (ii) a molecule with an octet configuration and at least one lone pair corresponds to an L ligand (i.e., a Lewis base), and (iii) a molecule with a sextet configuration corresponds to a Z ligand (i.e., a Lewis acid). Thus, rather than having to resort to tables of electronegativity values (of which there are many), one can identify the nature of the donor by using simple chemical principles involving the construction of a Lewis representation. Multidentate ligands can be classified by a simple extension of this approach.

Assignment of dn Configuration

Electron Counting Is Simpler

The assignment of the dn configuration (i.e., the number of electrons in metal-based nonbonding and metal−ligand antibonding orbitals), as predicted by the CBC method, corresponds closely to the results of theoretical calculations.13 In contrast, methods based on oxidation state assignments predict incorrect dn configurations for molecules that feature either metal−metal bonds or interactions with Lewis acids because they fail to take into account the true nature of the bonding. For example, the existence of a metal−metal bond requires each metal to contribute an electron to the bond, and this interaction is neglected in the oxidation state assignment. Likewise, the coordination of a metal to a Lewis acid requires the metal to donate a pair of electrons, thereby reducing the dn configuration, an effect that is not captured by the oxidation state approach if the ligand is simply assigned a neutral charge.13

Since all ligands are classified in their neutral forms, a student does not have to (i) remember the charges assigned to ligands, (ii) remember the number of electrons that the different charged forms of the ligand may donate or accept, (iii) determine the oxidation state of the element of interest, or (iv) determine the number of valence electrons corresponding to the oxidation state of the element of interest. The electron count is simply the sum of the number of valence electrons of the element of interest (m) plus those provided by the neutral ligands (Σ ligand electrons) adjusted by the charge on the molecule (eq 1)37 EN = m + Σ ligand electrons − Q±

(1)

Thus, all that is necessary to determine the electron count is a knowledge of the number of valence electrons of the atom of interest (as illustrated in Table 3 for the transition metals) and the number of electrons that the neutral ligand can donate (which is obtained, in general, from a simple Lewis structure of the neutral ligand and is provided for some common ligands in Table 1). In this regard, within the context of the CBC method, a cyclic ηn-CnHn ligand donates n electrons, which is simpler to commit to memory than having to remember that an anionic η5C5H5 ligand donates 6 electrons, an η6-C6H6 ligand donates 6 electrons, and an η7-C7H7 ligand donates either 6, 8, or 10 electrons, depending upon the oxidation state formalism that is employed.

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SUMMARY The CBC method is an approach that is based on an elementary molecular orbital analysis of metal−ligand bonding and, thereby, provides a means for classifying covalent molecules in their intact state. In contrast, the oxidation state approach merely ascribes a charge to an isolated atom after all ligands have been removed. Thus, whereas a classification based on oxidation states may be viewed as one-dimensional, that based on the CBC method is multidimensional because the [MLlXxZz] classification provides the valence, the electron count, and the ligand bond number. H



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elements or transition elements, in either a general inorganic chemistry course or one focusing on organometallic chemistry. (10) The Chemistry of Ruthenium; Seddon, E. A., Seddon, K. R., Eds.; Elsevier: New York, 1984; Chapter 2. (11) (a) Pauling, L. General Chemistry; Freeman: San Francisco, 1947; p 173. (b) Pauling, L. The Modern Theory of Valency. J. Chem. Soc. 1948, 1461−1467. (c) Summerville, D. A.; Jones, R. D.; Hoffman, B. M.; Basolo, F. Assigning Oxidation-States to Some Metal Dioxygen Complexes of Biological Interest. J. Chem. Educ. 1979, 56, 157−162. (12) (a) Nyholm, R. S.; Tobe, M. L. The Stabilization of Oxidation States of the Transition Metals. Adv. Inorg. Chem. Radiochem. 1963, 5, 1−40. (b) Lewis, J.; Nyholm, R. S. Metal-Metal Bonds in Transition Metal Complexes. Sci. Prog. (London) 1964, 52, 557−580. (c) Nyholm, R. S. Magnetism, Bonding and Structure of Coordination Compounds. Pure Appl. Chem. 1968, 17, 1−19. (d) Jean, Y. Molecular Orbitals of Transition Metal Complexes; Oxford University Press: New York, 2005; p 13. (e) Elschenbroich, Ch. Organometallics, 3rd ed.; Wiley-VCH: New York, 2006; p 478. (13) Parkin, G. Organometallics 2006, 25, 4744−4747. (14) van Oven, H. O.; de Liefde Meijer, H. J. Cyclopentadienylcycloheptatrienyltitanium. J. Organomet. Chem. 1970, 23, 159−163. (15) Green, M. L. H.; Ng, D. K. P. Cycloheptatriene and -enyl Complexes of the Early Transition Metals. Chem. Rev. 1995, 95, 439− 473. (16) (a) Elschenbroich, Ch.; Salzer, A. Organometallics, 2nd ed.; WileyVCH: New York, NY, 1992; p 358. (b) Spessard, G. O.; Miessler, G. L. Organometallic Chemistry; Prentice Hall: Upper Saddle River, NJ, 1996; p 44. (17) For specific examples, see: (a) Dauben, H. J.; Honnen, L. R. πTropenium-Molybdenum-Tricarbonyl Fluoroborate. J. Am. Chem. Soc. 1958, 80, 5570−5571. (b) King, R. B.; Stone, F. G. A. π-Cyclopentadienyl-π-Cycloheptatrienyl Vanadium. J. Am. Chem. Soc. 1959, 81, 5263−5264. (c) Andréa, R. R.; Terpstra, A.; Oskam, A.; Bruin, P.; Teuben, J. H. He(I) and He(II) Photoeletron Spectra of Some Mixed Sandwich Compounds of Titanium, Zirconium and Hafnium. J. Organomet. Chem. 1986, 307, 307−317. (d) Gourier, D.; Samuel, E. EPR, ENDOR, and Optical Absorption Studies on the Electrochemically Produced Cycloheptatrienylcyclopentadienyltitanium [(η5-C5H5)Ti(η7-C7H7)] Anion Radical. Inorg. Chem. 1988, 27, 3018−3024. (e) Vogler, A.; Kunkely, H. Charge Transfer Excitation of Organometallic Compounds Spectroscopy and photochemistry. Coord. Chem. Rev. 2004, 248, 273−278. (18) The cation, [C7H7]+, is commonly referred to as tropylium and is well known to exist as, for example, the tetrafluoroborate salt, [C7H7][BF4]. (19) Janiak, C. Klapötke, T. M.; Hans-Jürgen Meyer, H. J.; Reidel, E. Moderne Anorganische Chemie; De Gruyter: Berlin, Germany, 2003. (20) (a) Glockner, A.; Tamm, M. The Organometallic Chemistry of Cycloheptatrienyl Zirconium Complexes. Chem. Soc. Rev. 2013, 42, 128−142. (b) Tamm, M. Synthesis and Reactivity of Functionalized Cycloheptatrienyl-Cyclopentadienyl Sandwich Complexes. Chem. Commun. 2008, 3089−3100. (c) Tamm, M.; Bannenberg, T.; Frohlich, R.; Grimme, S.; Gerenkamp, M. Mono- and Dinuclear Molybdenum Complexes with Sterically Demanding Cycloheptatrienyl Ligands. Dalton Trans. 2004, 482−491. (d) Wang, H. Y.; Xie, Y. M.; King, R. B.; Schaefer, H. F. Bis(cycloheptatrienyl) Derivatives of the First-Row Transition Metals: Variable Hapticity of the Cycloheptatrienyl Ring. Eur. J. Inorg. Chem. 2008, 3698−3708. (e) Wang, H. Y.; Xie, Y. M.; Silaghi-Dumitrescu, I.; King, R. B.; Schaefer, H. F. The Mixed Sandwich Compounds C5H5MC7H7 of the First Row Transition Metals: Variable Hapticity of the Seven-Membered Ring. Mol. Phys. 2010, 108, 883−894. (f) Menconi, G.; Kaltsoyannis, N. Nature of the Transition Metal - Cycloheptatrienyl bond. Computational Studies of the Electronic Structure of [M(η7-C7H7)(η5-C5H5)] (M = Groups 4− 6). Organometallics 2005, 24, 1189−1197. (21) (a) Bahl, J. J.; Bates, R. B.; Beavers, W. A.; Launer, C. R. Cycloheptatrienyl and Heptatrienyl Trianions. J. Am. Chem. Soc. 1977, 99, 6126−6127. (b) Miller, J. T.; Dekock, C. W. Facile Formation of the

As such, the CBC method provides a more useful approach to the classification of covalent molecules than does one based on oxidation states. Finally, we note that the CBC method also affords a means to compare the chemistry of different elements, evaluate the types of ligands that favor specific [MLlXxZz] classes, and discuss reaction mechanisms.8,10

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ASSOCIATED CONTENT

S Supporting Information *

Worksheets to help students practice the concepts and an orbital based explanation for rules used to obtain the equivalent neutral class. This material is available via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*G. Parkin. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS G. P. thanks the National Science Foundation (CHE-1058987) for support. REFERENCES

(1) The valence of an atom is the number of electrons that it has used in bonding. See: Parkin, G. Valence, Oxidation Number, and Formal Charge: Three Related but Fundamentally Different Concepts. J. Chem. Educ. 2006, 83, 791−799. (2) (a) Lewis, G. N. Valence and The Structure of Atoms and Molecules; The Chemical Catalog Company: New York, 1923. (b) Lewis, G. N. The Chemical Bond. J. Chem. Phys. 1933, 1, 17−28. (3) (a) Langmuir, I. Types of Valence. Science 1921, 54, 59−67. (b) Langmuir, I. The Structure of Atoms and the Octet Theory of Valence. Proc. Natl. Acad. Sci. U. S. A. 1919, 5, 252−259. (4) Jensen, W. B. Abegg, Lewis, Langmuir, and the Octet Rule. J. Chem. Educ. 1984, 61, 191−200. (5) Abbreviations: Me = CH3, R = alkyl, Cp = C5H5, TpR,R′ = HB(C3N2HRR′)3. (6) Some authors use the phrase “formal oxidation state”, although it is not clear how this is meant to differ from that of “oxidation state”. (7) (a) Butin, K. P.; Beloglazkina, Y. K.; Zyk, N. V. Metal Complexes with Non-Innocent Ligands. Russ. Chem. Rev. 2005, 74, 531−553. (b) Kaim, W.; Schwederski, B. Non-innocent Ligands in Bioinorganic Chemistry-An Overview. Coord. Chem. Rev. 2010, 254, 1580−1588. (c) Kaim, W. The Shrinking World of Innocent Ligands: Conventional and Non-Conventional Redox-Active Ligands. Eur. J. Inorg. Chem. 2012, 343−348. (d) Luca, O. R.; Crabtree, R. H. Redox-active Ligands in Catalysis. Chem. Soc. Rev. 2013, 42, 1440−1459. (e) Kaim, W. Manifestations of Noninnocent Ligand Behavior. Inorg. Chem. 2011, 50, 9752−9765. (8) (a) Green, M. L. H. A New Approach to the Formal Classification of Covalent Compounds of the Elements. J. Organomet. Chem. 1995, 500, 127−148. (b) Green, M. L. H. An Introduction to the Chemistry of Molybdenum. In Molybdenum: An Outline of its Chemistry and Uses; Braithwaite, E. R., Haber, J., Eds.; Elsevier: Amsterdam, 1994; Chapter 2. (c) Parkin, G. Classification of Organotransition Metal Compounds. In Comprehensive Organometallic Chemistry III; Crabtree, R. H., Mingos, D. M. P., Eds.; Elsevier: Oxford, 2007; Vol. 1, Chapter 1. (d) Green, J. C.; Green, M. L. H.; Parkin, G. The Occurrence and Representation of Three-Centre Two-Electron Bonds in Covalent Inorganic Compounds. Chem. Commun. 2012, 48, 11481−11503. (e) Covalent Bond Classification. http://www.covalentbondclass.org/. (9) The material described herein can be introduced when first describing coordination chemistry, whether it be that of the main group I



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Cycloheptatrienyl Trianion by Lanthanide Andactinide Ions. J. Organomet. Chem. 1981, 216, 39−48. (22) (a) Collman, J. P.; Hegedus, L. S.; Norton, J. R.; Finke, R. G. Principles and Applications of Organotransition Metal Chemistry; University Science Books: Mill Valley, CA, 1987; p 26. (b) Crabtree, R. H. The Organometallic Chemistry of the Transition Metals, 4th ed., Wiley: New York, 2005; p 43. (c) Demerseman, B.; Dixneuf, P. H.; Douglade, J.; Mercier, R. A Novel Organometallic Phosphine Ligand Containing Titanium(II), (η5-C5H5)Ti(η7-C7H6PPh2), and Related Heterobimetallic Complexes: X-Ray Structure of (η5-C5H5)Ti(η7C7H6PPh2)Mo(CO)5·C6H5HCH3. Inorg. Chem. 1982, 21, 3942−3947. (23) Salzer, A. Nomenclature of organometallic compounds of the transition elements (IUPAC Recommendations 1999). Pure Appl. Chem. 1999, 71, 1557−1585. (24) (a) Molecular Orbitals of Transition Metal Complexes; Jean, Y., Ed.; Oxford University Press: Oxford, U. K., 2005. (b) Organometallic Chemistry and Catalysis; Astruc, D., Ed.; Springer: New York, 2007. (c) Organometallic Chemistry; Spessard, G. O., Miessler, G. L., Eds.; Prentice-Hall: Upper Saddle River, NJ, 1996. (d) Inorganic Chemistry, 5th ed.; Miessler, G. L., Fischer, P. J., Tarr, D. A., Eds.; Prentice-Hall: Upper Sadle River, NJ, 2014. (e) The Organometallic Chemistry of the Transition Metals; 5th ed.; Crabtree, R. H., Ed.; Wiley-Interscience: Hoboken, NJ, 2009. (f) Organotransition Metal Chemistry: From Bonding to Catalysis; Hartwig, J., Ed.; University Science Books: Sausalito, CA, 2010. (g) reference 10. (25) Haaland, A. Covalent versus Dative Bonds to Main Group Metals, a Useful Distinction. Angew. Chem., Int. Ed. Engl. 1989, 28, 992−1007. (26) The formal charge is the charge remaining on an atom when all ligands are removed homolytically. See ref 1. (27) A closely related example of a multifunctional ligand that features a Z function is provided by linear NO, for which the classification becomes a X3. See Landry, V. K.; Pang, K.; Quan, S. M.; Parkin, G. Tetrahedral Nickel Nitrosyl Complexes with Tripodal [N3] and [Se3] Donor Ancillary Ligands: Structural and Computational Evidence that a Linear Nitrosyl is a Trivalent Ligand. Dalton Trans. 2007, 820−824. (28) A “chemputer” to obtain the [MLlXxZz] classification of molecules is presently available on the World Wide Web at http://winter.group. shef.ac.uk/chemputer/mlxz.html. (29) ηn-Coordination of cyclic ligands such as cyclopentadienyl and benzene is, for pictorial convenience, normally represented as a line to the centroid. In such cases, one needs to evaluate the nature of the interactions on an individual basis (see Table 1). (30) Majoral, J. P.; Zablocka, M. Zirconate Complexes: Multifaceted Reagents. New J. Chem. 2005, 29, 32−41. (31) For groups 1−10, the value of n is equal to the group number, whereas for groups 11−18, the value of n is equal to the last digit of the group number. (32) Although commonly used, the term “coordination number” is ambiguous. For example, the coordination number of Cr in (η6C6H6)2Cr may be considered to be 12, 6, or 2. See reference 8c. (33) Since z = 0 for most compounds, this distribution is often simply referred to as an “MLX” plot. (34) Jacobsen, H.; Correa, A.; Poater, A.; Costabile, C.; Cavallo, L. Understanding the M-(NHC) (NHC = N-heterocyclic carbene) Bond. Coord. Chem. Rev. 2009, 253, 687−703. (35) Calzaferri, G. Oxidation Numbers. J. Chem. Educ. 1999, 76, 362− 363. (36) Kisko, J. L.; Hascall, T.; Parkin, G. The Synthesis, Structure, and Reactivityt of Phenyl Tris(3-tert-butylpyrazolyl)borato Iron Methyl, [PhTpBu ]FeMe: Isolation oft a Four-Coordinate Monovalent Iron Carbonyl Complex, [PhTpBu ]FeCO. J. Am. Chem. Soc. 1998, 120, 10561−10562. (37) Note that the expression EN = m + 2l + x can also be used to determine the electron count once the equivalent neutral class is obtained (Table 2). (38) This method is often called the “ionic counting method”. However, this term is not particularly appropriate because some ligands are considered to be neutral (e.g., NH3).

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Application of the Covalent Bond Classification Method for the

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