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

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 according to the number and types of bonds that surround an of interest. This approach is based on an elementary analysis of the bonding involving the central atom (M), with the various interactions being classified according to the number of that each neutral 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←LorM→Z, according to whether the ligand is the donor (L) fi or acceptor (Z). A is classi ed as [MLlXxZz] according to the number of L, X, and Z ligand functions that surround M. Not only does fi fi the [MLlXxZz] designation provide a formal classi cation of a molecule, but it also indicates the con guration, the , 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, , Organometallics

■ INTRODUCTION application of different procedures for assigning oxidation states, The in the vast majority of stable organic molecules as discussed in more detail below. − have a valence1 of four and possess an octet2 4 configuration. In large part, the problems encountered in the use of oxidation These two simple facts allow a student to inspect complex states to classify covalent compounds result from the fact that it is organic molecules and obtain insight as to whether the molecule an approach that forces ionic character on a compound that may is chemically reasonable. In contrast, such simple rules do not have little such nature. Here, we describe a more appropriate Downloaded via SAINT EDWARD'S UNIV on July 28, 2020 at 16:59:18 (UTC). exist for the other elements of the , which routinely method for categorizing covalent compounds, namely the “ fi ” 8 form compounds in which the atom may possess either an array Covalent Bond Classi cation (CBC) , which does not attempt of electronic configurations (also referred to as electron counts to force an ionic description upon a covalent molecule, but rather See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. classifies a molecule according to the nature of the that or electron numbers), valence states, or both. Consider, for 9 example, the elements that are adjacent to carbon in the periodic surround the element of interest (M). table, namely and : boron forms a variety of trivalent compounds in which it may have either an octet ■ ASSIGNMENTS AND fi fi con guration (e.g., H3BNH3) or a sextet con guration (e.g., AMBIGUITIES Me B),5 whereas nitrogen forms compounds in which it is either 3 Oxidation states are of widespread use as a simple classification trivalent (e.g., NH ) or pentavalent (e.g., HNO ). The situation 3 3 system that has been described by Seddon and Seddon as the is exacerbated for transition , which may form compounds ff “Dewey Decimal Classification of inorganic chemistryif the in which a given exhibits a variety of di erent valence states 10 fi rules are applied, a number is obtained”. However, beyond the and electronic con gurations. fi “ Traditionally, efforts to classify inorganic compounds have classi cation, Seddon and Seddon question Does oxidation state 6 have a chemical significance? A number is always obtained focused on the oxidation state of the element of interest, that is, ”10 the charge that resides on the atom after cleaving all bonds (other does it mean anything? The latter point is particularly than homonuclear bonds) in a heterolytic manner. It is, however, pertinent in view of the ambiguity in the assignment of oxidation becoming increasingly apparent that the oxidation state states. formalism has shortcomings that result from ambiguities due to either (i) the noninnocent nature of some ligands7 or (ii) the Published: April 28, 2014

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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 − 22 − 15,19−21 η5 1, and 3. Applying these possibilities to ( -C5H5)Ti- η7 ( -C7H7), the oxidation state of 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 (χ) scales, ambiguity may also result if using only method A.

In this regard, a fundamental problem in the assignment of Figure 3. Ambiguity in the oxidation state of titanium in oxidation states is that there exists more than one method for η5 η7 allocating charges to ligands (Figure 1). For example, the charge ( -C5H5)Ti( -C7H7) depending on the charge assigned to the cycloheptatrienyl ligand. on a ligand may be derived by either (A) removing the ligand such that the shared pair of electrons is transferred to the more In view of the fact that the actual bonding in the molecule is electronegative atom11 or (B) removing the ligand in a closed independent of the charges that are assigned to the ligands, it is shell configuration;12 for both of these methods, an exception is evident that the derived oxidation state is of limited utility in that bonds between the same element are broken homolytically. compounds such as (η5-C H )Ti(η7-C H ). Indeed, in view of Although one often obtains the same charges regardless of which 5 5 7 7 such ambiguities, IUPAC recommends that oxidation numbers approach one uses, situations arise in which the outcomes are 8b,13 not be included in the nomenclature of organometallic different, thus rendering any interpretation questionable. 23 compounds. It is, therefore, clear that discussions pertaining Consider, for example, the η7-C H cycloheptatrienyl ligand in 7 7 to covalent compounds would benefit from an alternative (η5-C H )Ti(η7-C H ).14,15 Application of the electronegativity 5 5 7 7 classification system, as described below. procedure (A) assigns both carbocyclic rings as anions, that is, − − [C5H5] and [C7H7] , because carbon is more electronegative ■ COVALENT BOND CLASSIFICATION than titanium. On the other hand, if one were to apply the closed shell procedure (B), the cyclopentadienyl ligand is assigned as an In addition to the ambiguity of oxidation state assignments, − another concern with the application of oxidation states pertains anion, [C5H5] , whereas the cycloheptatrienyl ligand is assigned fi as a cation, [C H ]+ (Figure 2).16,17 The assignment of different to its use to infer properties of a covalent molecule. Speci cally, 7 7 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 Figure 2. Frontier orbital occupations for the cycloheptatrienyl ligand in ff + 3− molecules can be represented in terms of 2-center-2-electron di erent charged states. Note that only [C7H7] and [C7H7] have closed shell configurations. 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 charges for the cyclopentadienyl and cycloheptatrienyl ligands element of interest (M), the neutral ligand can contribute either when using the closed shell procedure (B) is a consequence of two (L), one (X), or zero (Z) electrons to the bonding orbitals. fi the fact that, whereas the closed shell form of C5-symmetric The classi cation of ligands as L-, X-, or Z-type, as featured in a π 24 [C5H5] is the aromatic (4n +2)6 -electron monoanion, the variety of textbooks, is now well established, and some simple π closed shell form of C7-symmetric [C7H7] is the aromatic six - examples of these ligands are provided in Table 1. 18 − − electron monocation. The C7-symmetric planar [C7H7] Normal covalent bonds are represented as M X, whereas monoanion is not an acceptable assignment for method B dative covalent bonds8d,25 are represented as either M←Lor because it is an open shell paramagnetic species (Figure 2). The M→Z, according to whether the ligand is the donor (L) or 3− π trianion [C7H7] , however, is a closed shell ten - (Z). Note that, in addition to using an arrow, the dative aromatic species and is, therefore, a valid assignment for the bond can also be represented as a line with formal charges,26 that

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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 . Table 1. Classifications of Some Common Ligands

Ligand CBC description Electron donor number

PR3 L2 HX 1 RX 1 Figure 5. Two alternative, but equivalent, representations for the dative BR3 Z0 bond in H3NBH3. Note that the representations are not AlR3 Z0structures. η2 a -C2H4 L 2 η3 -C3H5 LX 3 η4 a -C4H6 L2 4 η4 line with formal charges (as illustrated for H3NBH3 in Figure 5), -C4H4 LX2 4 η5 correspond to exactly the same electronic structure and are not -C5H5 L2X5 13 η6 a resonance structures. -C6H6 L3 6 fi η7 Ligands can be readily classi ed as L-, X-, or Z-type by -C7H7 L2X3 7 η8 consideration of some simple principles (Figure 4). For -C8H8 L3X2 8 κ3 R,R′ example, by virtue of the fact that they serve as -Tp L2X5 fi a donors, L-type ligands may be readily identi ed as neutral CO L 2 molecules that have available lone pairs and are Lewis bases, NO Xa (bent) 1 for example, H2O, H3N, and R3P. Correspondingly, Z-type X3 (linear) 3 ligands serve as electron pair acceptors and are, therefore, OZ 0 readily identified as neutral molecules that exist as Lewis acids, X2 2 for example, BF . Finally, because X-type ligands contribute LX 4 3 2 only one electron to the bonding orbital, they correspond NX 3 • • 3 to neutral species that are radicals, for example, H ,Cl,and OR X (bent) 1 • H C . LX (bent) 3 3 Although many ligands coordinate to a metal center by L X (linear) 5 2 a single covalent bond, a variety of multidentate ligands NR X (bent) 2 2 coordinate via more than one covalent bond. Such ligands LX (linear) 4 2 are classified as [L X Z ], where l, x,andz are the respective NR X (pyramidal) 1 l x z 2 number of L, X, and Z functionalities that are associated with LX (planar) 3 the frontier orbitals of the ligand in the geometry that CR X (Schrock alkylidene) 2 2 2 corresponds to its binding mode. Some examples of multi- La (Fischer carbene) 2 dentate ligands and their classifications are provided in Figure 6 CR X3 3 a fi and Table 1, from which it is evident that, in many cases, the These classi cations pertain to the primary bonding interactions. classification can be simply derived by summing the individual However, some ligands have relatively low energy empty orbitals such bonding components that are implied by their valence bond that, depending on the nature of the metal center, backbonding may representations. provide an important supplement to the bonding. In such cases, the fi ligand should be classified with additional Z functions, the number of For example, the classi cation of as an L3 donor which would depend on the ligand. For example, extreme backbonding ligand may be rationalized on the basis that each of the in an complex corresponds to a metallacyclopropane delocalized “double bonds” of an η6-benzene ligand may be con- fi structure, such that the ligand is classi ed as LZ, which is equivalent ceptually viewed as an L donor akin to that of C2H4 (Figure 6). fi η5 to X2. Likewise, the classi cation of -cyclopentadienyl as an L2X ligand can be rationalized on the basis that the cyclopentadienyl is, M−−L+ and M+−Z−. Despite their different appearances, the may be conceptually viewed as being composed of two two representations of a dative bond, as either (i) an arrow or (ii) a “double bonds” (each of which is an L donor) and an alkyl radical

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Figure 8. CBC description of oxo compounds. Depending on the atom fi Figure 6. [LlXxZz] classi cations of some common ligands as derived by to which it is attached, the can bind via either a single, double, or summing the individual components that correspond to the valence . bond representation. For example, a cyclopentadienyl ligand is classified as L2X because the contains two double bonds (L) and the bonding is supplemented by donation from the an alkyl moiety (X). nitrogen to the metal (Figure 9). ■ EQUIVALENT NEUTRAL CLASS (which is an X donor). However, although this simple aide After classifying the ligands attached to the element of interest, memoire based on a valence bond representation of a ligand fi Q± fi the molecule itself may be classi ed in the form [MLlXxZz] by predicts the [LlXxZz] classi cation in many cases, there are summing all the L, X, and Z functionalities, where Q ± is the situations in which it breaks down. In such cases, consideration of charge on the molecule.28 This procedure is best performed by the frontier orbitals is essential to obtaining the correct using a structure-bonding representation of the molecule in representation. For example, analysis of the frontier orbitals of which the bonds to the neutral ligands are drawn explicitly as the η7-cycloheptatrienyl ligand indicates that is not classified as − ← 27 either normal covalent (M X) or dative covalent (M L and L3X but rather as L2X3 (Figure 7). M→Z) and the appropriate charge is located on M.29 For example, the structure-bonding representations of 3+ 3− [Co(NH3)6] , CoCl3(NH3)3, and [CoCl6] are illustrated in Figure 10, from which it is evident that these molecules are fi 3+ 3− classi ed as [ML6] , [ML3X3], and [MX6] , respectively. fi 3+ At rst glance, it would, therefore, appear that [Co(NH3)6] , 3− ff CoCl3(NH3)3, and [CoCl6] belong to fundamentally di erent 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, Q± rather than on M, thereby reducing the [MLlXxZz] assignment to its “equivalent neutral class” (ENC), as described below. fi Q± Speci cally, the reduction of [MLlXxZz] 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, Figure 7. Frontier orbitals for a variety of ligands indicating the L, X, and L− → LX. Z character of each orbital according to whether it is doubly occupied fi (L), singly occupied (X), or empty (Z). Note that the rule LZ→X (see (3) If the derived classi cation after performing these 2 transformations contains both an L and a Z function, the the section Equivalent Neutral Class) must be applied to cyclo- fi heptatrienyl because Z is degenerate with the half occupied X orbital. classi cation is reduced further by using the trans- → formation LZ X2. Although a detailed explanation of the origin of these rules is Although it is evident that multidentate ligands require provided in the Supporting Information, a simple rationalization representation by more than one L, X, or Z function, is provided by recognizing that, for example, a positively charged monodentate ligands may also be described by multiple 2-electron donor ligand is equivalent to a neutral 1-electron functions. As an illustration, depending on the nature of M, the donor ligand, whereas a negatively charged 1-electron donor interaction of M with a single oxygen atom can be described as either a single, double, or triple bond, in which case the oxygen fi ligand is classi ed as either Z, X2,orLX2 (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, Figure 9. X and LX classifications of an amide ligand according to whereas those with a planar nitrogen are classified as LX because whether it is pyramidal or planar.

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Table 2. Definitions Pertaining to the CBC Method and the Equivalent Neutral Class

Symbol Definition L 2-electron donor function l number of L functions X 1-electron donor function x number of X functions Z 0-electron donor function z number of Z functions m number of valence electrons on neutral M atom VN valence number VN = x +2z LBN ligand bond number LBN = l + x + z EN electron number (or electron count) EN = m +2l + x fi 3+ Figure 10. [MLlXxZz] classi cations of [Co(NH3)6] , [Co(NH3)3Cl3], n “ ” a 3− v number of electrons in nonbonding M orbitals and [CoCl6] . Note that all three compounds belong to the same n = m − x − 2z = m − VN + − equivalent neutral class, ML X , after applying the L → X and X → L a 3 3 vn corresponds to dn for compounds. transformations, as appropriate.

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

Group Group Group Group Group Group Group Group 3 4 5 6 7 8 9 10 Q± Figure 11. Transformations for reducing [MLlXxZz] to its equivalent Sc, Ti, V, Cr, Mn, Fe, Co, Ni, neutral class. For cations, the order of priority is L+ → X and, if no L Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, ligand is present, X+ → Z. For anions, the order of priority is X− → L and, La Hf Ta W Re Os Ir Pt if no X ligand is present, L− → LX. 345678910 aNote 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 nonbonding electrons (vn), and ligand bond number (LBN), as may be viewed analogously to coordination of NH3 (i.e., L). summarized in Table 2. 3− Applying these rules to [CoCl6] ,CoCl3(NH3)3,and For example, the electron number (i.e., the electron count) of 3+ 3− [Co(NH3)6] , each of the respective [MX6] , [ML3X3], and MinMLX Z , is given by EN = m +2l + x, where m is the 3+ fi l x z [ML6] classi cations are reduced to the same equivalent number of valence electrons on the neutral M atom. The origin of neutral class of ML3X3 (Figure 10). Thus, the CBC method this equation is simply that each L ligand contributes two indicates that each of these complexes belong to the same class of electrons to the electron count of M, whereas each X ligand molecule. As a consequence, the central atoms in these contributes one electron. The value of m is indicated by the complexes also have the same valence and electron count. periodic table group number,31 as illustrated for the transition Some examples of the derivation of the [MLlXxZz] classes for metals in Table 3. 30 some complexes are illustrated in Figure 12. 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 ■ INFORMATION EMBODIED IN THE MLLXXZZ often abbreviated to valence. The origin of this expression is that CLASSIFICATION each X ligand requires the metal to contribute one electron to the In addition to providing a simple classification of a covalent M−X bond, whereas each Z ligand requires M to contribute two → molecule, the MLlXxZz description also contains useful electrons to the M Z bond. As such, the valence may be information pertaining to the nature of a molecule, such as the considered to be composed of two components: the x number (EN), valence number (VN), number of and the z valence. It should be noted that, in many cases, the

fi Figure 12. [MLlXxZz] classi cations of some metallocene compounds.

811 dx.doi.org/10.1021/ed400504f | J. Chem. Educ. 2014, 91, 807−816 Journal of Chemical Education Article 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,isn = 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. fi A nal quantity that may be derived from the MLlXxZz fi Figure 15. CBC plot for nitrogen. The majority of compounds possess classi cation is the ligand bond number (LBN), which represents fi the effective total number of ligand functions surrounding M, and MX3 and MX3Z classi cations (indicated by orange). is defined as LBN = l + x + z. Although this quantity is not defined to be the ,32 it is, in many cases, equivalent same valence, it is also worth noting that classes that are to the value that most chemists would assign as the coordination diagonally related (i.e., lower left to upper right) possess the same number. ligand bond number. Examination of these plots indicates that, although a variety of ■ CBC PLOTS classifications are possible, each element generally adopts only a fi few of the available MLlXxZz classes. For example, the vast In view of the fact that the MLlXxZz classi cation of a molecule embodies information that relates to the electron count, the majority of isolated belong to the MX4 n fi classification; the only other commonly encountered class for valence, the ligand bond number, and the v con guration, it fi carbon is MLX2, as exempli ed by molecules such as CO, RNC, provides a better method for classifying a covalent compound 34 − than one based on oxidation state. Specifically, whereas a and N-heterocyclic carbenes (Figure 16). Carbanions (R3C ) 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 Figure 16. Examples of carbon compounds that belong to the class the same electron number and all classes in a given row have the 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 MX and MLX 3 3 • + − classifications (indicated by orange) are commonly observed. Figure 17. Procedure for classifying [CH3] , [CH3] , and [CH3] . fi also belong to the MLX2 classi cation, whereas other reactive intermediates, such as carbocations (R C+), belong to MX Z, • 3 2 while radicals (R3C ) belong to MX3, as illustrated in Figure 17. Whereas carbon has a strong preference for forming fi compounds that belong to the MX4 classi cation, nitrogen commonly forms compounds that belong to the MX3 and MX3Z classifications, and boron commonly forms compounds that fi belong to the MX3 and MLX3 classi cations. 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 fi be classi ed as MX4, of which simple tetrahedral molecules of the Figure 14. CBC plot for carbon. The majority of stable compounds type CH4,CH2Cl2, CMe4,Me3CCl, Me2CCl2, MeCCl3, and fi possess MX4 classi cations (indicated by orange); the other (blue) CCl4 are illustrative. The observation that these compounds have highlighted classes are less commonly observed and are often reactive the same classification is in accord with the facts that they are intermediates. structurally similar and that the central carbon atom in each

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− + • Table 4. Representative Examples of [CH3] , [CH3] , [CH3] In contrast to the observation that main group elements such Carbon Containing Molecules According to Their CBC as boron, carbon, and nitrogen adopt only a few of the possible fi Designation MLlXxZz classi cations, the transition metals typically exhibit a large variety of classifications. For example, the CBC plot for MX4 MLX2 MX2ZMX3 8c − + • organometallic compounds of is illustrated in Figure 18. CH4 H3C H3C H3C  H2C CH2 RNC HCCH CO


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


BH3 H3BNH3 − B(CH3)3 BH4

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

MX3 MX3ZMX2 MX2Z NH NH + NO NO 3 4 2 Figure 18. CBC plot for organometallic iron compounds (key: orange, HNO2 H3NBH3 71%; pink, 20%; , 7%; green, < 1%). HNO3 CBC plots of this type present a large amount of factual molecule is tetravalent. However, the oxidation state of the information. For example, examination of Figure 18 indicates central carbon atom in these molecules varies widely: CH (−4), 4 that the vast majority of organometallic iron compounds are CH Cl (0), CMe (0), Me CCl (+1), Me CCl (+2), MeCCl 2 2 4 3 2 2 3 classified as either ML (20%), ML X (71%), or ML X (7%), (+3), and CCl (+4). This large range of eight units of oxidation 5 4 2 3 4 4 and this information is useful when evaluating the significance state is striking given the general similarity of these molecules, and novelty of certain molecules. such that one has to question the perceived significance and 1,35 For example, consider the [tris(pyrazolyl)hydroborato]iron utility of these values. t 36 carbonyl compound [PhTpBu ]Fe(CO) (Figure 19). In 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 t complexes on the basis of oxidation state assignments may Figure 19. Molecular structure of [PhTpBu ]Fe(CO). The lines are only sometimes be misguided. For example, rather than acting as intended to show connectivity and are not intended to be a structure- But oxidizing agents, high oxidation state compounds, such as the bonding representation. [PhTp ]isanL2X donor ligand. W(VI) and Re(VII) complexes W(PR3)3H6 and Re(PR3)2H7, are capable of reducing organic substrates by virtue of the presence terms of oxidation state, the iron in this molecule is classified of ligands. as Fe(I), which is the same as that in the well-known 5 Although the chemistry of carbon is dominated by the MX4 cyclopentadienyl iron compound [CpFe(CO)2]2. Therefore, class of molecules, there are two common classes for boron, on the basis of oxidation state, it would appear that there is But namely MX3 and MLX3, as illustrated in Table 5 and Figure 13. In nothing unusual about [PhTp ]Fe(CO) because Fe(I) this regard, while it is evident that molecules such as BH3 and carbonyl compounds are precedented. However, examination − ff [BH4] are structurally and electronically di erent, in accord of the CBC plot for iron (Figure 18) indicates that monomeric fi But fi with the respective MX3 and MLX3 classi cations, the oxidation [PhTp ]Fe(CO), with a classi cation of ML3X, represents a states of boron in these compounds are the same (+3). Thus, in novel class of monovalent iron carbonyl compound. [CpFe- this case, the oxidation state assignment provides no insight into (CO)2]2, on the other hand, belongs to the well-known 18- − ff 8d the fact that BH3 and [BH4] are fundamentally di erent in electron class of ML4X2 molecules. terms of their electronic structure. It is important to emphasize that although a CBC plot may With respect to nitrogen chemistry, the two common classes indicate the distribution of compounds, it does not explain why a + are MX3 and MX3Z, as illustrated by NH3 and [NH4] (Table 6 particular class of compound is common because the and Figure 15). Despite these different classifications, the classification does not incorporate a sufficiently detailed view + oxidation states of nitrogen in NH3 and [NH4] are the same of the bonding. Likewise, the oxidation state alone cannot be (−3), which thereby provides another illustration of how the used to explain why certain classes of molecule are stable. Thus, oxidation state fails to capture the fundamental difference in the while a CBC plot is a useful guide, it should not be inferred, for electronic structures of these two molecules. example, that any molecule belonging to the most popular class

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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. in a CBC plot will be stable, nor that one which belongs to an Although the electron count obtained by the CBC method is unpopular class will be unstable. necessarily equivalent to that obtained by invoking oxidation states38 (when performed correctly), the latter approach ■ ADVANTAGES OF THE CBC METHOD mathematically involves more steps, as illustrated for (η5- C H )Ti(η7-C H ) in Figure 20. In view of the greater number In addition to providing a classification of molecules that reflects 5 5 7 7 of steps, the oxidation state method is more susceptible to both the structure and electronic nature of a molecule, the CBC incorporation of errors. For example, a student may correctly method offers several other advantages over the oxidation state identify the number of valence electrons associated with the approach, as detailed below. neutral atom but could incorrectly determine the number of All Ligands Are Classified in Their Neutral Form electrons associated with the oxidation state. In such a case, the In view of the fact that all ligands are categorized in their neutral overall derived electron count will be incorrect. Likewise, a forms, one does not have to remember any rules about the student could determine the correct number of valence electrons charges assigned to ligands. One only needs to examine the associated with an oxidation state, but then use an incorrect neutral form of the ligand in order to establish the electron number of electrons for the ligand if it may be classified more configuration of the donor atom. In general, (i) a radical than one way. As an illustration, to determine the electron count η5 η7 corresponds to an X ligand, (ii) a molecule with an octet for a molecule such as ( -C5H5)Ti( -C7H7), a student could − η7 configuration and at least one lone pair corresponds to an L assign a charge of 3 to the -C7H7 ligand to determine the ligand (i.e., a Lewis base), and (iii) a molecule with a sextet oxidation state of the titanium and the corresponding number of configuration corresponds to a Z ligand (i.e., a Lewis ). Thus, valence electrons but then use the electron donor number that is + rather than having to resort to tables of electronegativity values associated with the cation [C7H7] , thereby resulting in an (of which there are many), one can identify the nature of the incorrect electron count. The neutral ligand approach that is donor by using simple chemical principles involving the utilized by the CBC method is, therefore, a necessarily simpler construction of a Lewis representation. Multidentate ligands and more direct approach for determining the electron count. can be classified by a simple extension of this approach. Assignment of dn Configuration Is Simpler The assignment of the dn configuration (i.e., the number of Since all ligands are classified in their neutral forms, a student electrons in metal-based nonbonding and metal−ligand does not have to (i) remember the charges assigned to ligands, antibonding orbitals), as predicted by the CBC method, (ii) remember the number of electrons that the different charged corresponds closely to the results of theoretical calculations.13 forms of the ligand may donate or accept, (iii) determine the In contrast, methods based on oxidation state assignments oxidation state of the element of interest, or (iv) determine the predict incorrect dn configurations for molecules that feature number of valence electrons corresponding to the oxidation state either metal−metal bonds or interactions with Lewis acids of the element of interest. The electron count is simply the sum because they fail to take into account the true nature of the of the number of valence electrons of the element of interest (m) bonding. For example, the existence of a metal−metal bond plus those provided by the neutral ligands (Σ ligand electrons) requires each metal to contribute an electron to the bond, and adjusted by the charge on the molecule (eq 1)37 this interaction is neglected in the oxidation state assignment.

± Likewise, the coordination of a metal to a Lewis acid requires the EN=+Σm ligand electrons − Q (1) metal to donate a pair of electrons, thereby reducing the dn configuration, an effect that is not captured by the oxidation state Thus, all that is necessary to determine the electron count is a approach if the ligand is simply assigned a neutral charge.13 knowledge of the number of valence electrons of the atom of interest (as illustrated in Table 3 for the transition metals) and SUMMARY the number of electrons that the neutral ligand can donate ■ (which is obtained, in general, from a simple Lewis structure of The CBC method is an approach that is based on an elementary the neutral ligand and is provided for some common ligands in molecular orbital analysis of metal−ligand bonding and, thereby, Table 1). In this regard, within the context of the CBC method, a provides a means for classifying covalent molecules in their intact ηn cyclic -CnHn ligand donates n electrons, which is simpler to state. In contrast, the oxidation state approach merely ascribes a commit to memory than having to remember that an anionic η5- charge to an isolated atom after all ligands have been removed. η6 fi C5H5 ligand donates 6 electrons, an -C6H6 ligand donates 6 Thus, whereas a classi cation based on oxidation states may be η7 electrons, and an -C7H7 ligand donates either 6, 8, or 10 viewed as one-dimensional, that based on the CBC method is fi electrons, depending upon the oxidation state formalism that is multidimensional because the [MLlXxZz] classi cation provides employed. the valence, the electron count, and the ligand bond number.

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As such, the CBC method provides a more useful approach to the elements or transition elements, in either a general inorganic chemistry classification of covalent molecules than does one based on course or one focusing on . oxidation states. Finally, we note that the CBC method also (10) The Chemistry of Ruthenium; Seddon, E. A., Seddon, K. R., Eds.; affords a means to compare the chemistry of different elements, Elsevier: New York, 1984; Chapter 2. fi (11) (a) Pauling, L. General Chemistry; Freeman: San Francisco, 1947; evaluate the types of ligands that favor speci c [MLlXxZz] classes, and discuss reaction mechanisms.8,10 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.; ■ ASSOCIATED CONTENT Basolo, F. Assigning Oxidation-States to Some Metal Dioxygen Complexes of Biological Interest. J. Chem. Educ. 1979, 56, 157−162. *S Supporting Information (12) (a) Nyholm, R. S.; Tobe, M. L. The Stabilization of Oxidation Worksheets to help students practice the concepts and an States of the Transition Metals. Adv. Inorg. Chem. Radiochem. 1963, 5, 1−40. (b) Lewis, J.; Nyholm, R. S. Metal-Metal Bonds in Transition orbital based explanation for rules used to obtain the equivalent − neutral class. This material is available via the Internet at Metal Complexes. Sci. Prog. (London) 1964, 52, 557 580. (c) Nyholm, R. S. Magnetism, Bonding and Structure of Coordination Compounds. http://pubs.acs.org. Pure Appl. Chem. 1968, 17,1−19. (d) Jean, Y. Molecular Orbitals of Transition Metal Complexes; Oxford University Press: New York, 2005; p ■ AUTHOR INFORMATION rd 13. (e) Elschenbroich, Ch. Organometallics,3 ed.; Wiley-VCH: New Corresponding Author York, 2006; p 478. − *G. Parkin. E-mail: [email protected]. (13) Parkin, G. Organometallics 2006, 25, 4744 4747. (14) van Oven, H. O.; de Liefde Meijer, H. J. Cyclopentadienylcyclo- Notes heptatrienyltitanium. J. Organomet. Chem. 1970, 23, 159−163. The authors declare no competing financial interest. (15) Green, M. L. H.; Ng, D. K. P. Cycloheptatriene and -enyl Complexes of the Early Transition Metals. Chem. Rev. 1995, 95, 439− ■ ACKNOWLEDGMENTS 473. (16) (a) Elschenbroich, Ch.; Salzer, A. Organometallics,2nd ed.; Wiley- G. P. thanks the National Science Foundation (CHE-1058987) VCH: New York, NY, 1992; p 358. (b) Spessard, G. O.; Miessler, G. L. for support. Organometallic Chemistry; Prentice Hall: Upper Saddle River, NJ, 1996; p 44. ■ REFERENCES (17) For specific examples, see: (a) Dauben, H. J.; Honnen, L. R. π- (1) The valence of an atom is the number of electrons that it has used in Tropenium-Molybdenum-Tricarbonyl Fluoroborate. J. Am. Chem. Soc. bonding. See: Parkin, G. Valence, Oxidation Number, and Formal 1958, 80, 5570−5571. (b) King, R. B.; Stone, F. G. A. π-Cyclo- Charge: Three Related but Fundamentally Different Concepts. J. Chem. pentadienyl-π-Cycloheptatrienyl Vanadium. J. Am. Chem. Soc. 1959, 81, Educ. 2006, 83, 791−799. 5263−5264. (c) Andrea,́ R. R.; Terpstra, A.; Oskam, A.; Bruin, P.; (2) (a) Lewis, G. N. Valence and The Structure of Atoms and Molecules; Teuben, J. H. He(I) and He(II) Photoeletron Spectra of Some Mixed The Chemical Catalog Company: New York, 1923. (b) Lewis, G. N. Sandwich Compounds of Titanium, Zirconium and Hafnium. J. The . J. Chem. Phys. 1933, 1,17−28. Organomet. Chem. 1986, 307, 307−317. (d) Gourier, D.; Samuel, E. (3) (a) Langmuir, I. Types of Valence. Science 1921, 54,59−67. EPR, ENDOR, and Optical Absorption Studies on the Electrochemi- (b) Langmuir, I. The Structure of Atoms and the Octet Theory of η5 cally Produced Cycloheptatrienylcyclopentadienyltitanium [( -C5H5)- Valence. Proc. Natl. Acad. Sci. U. S. A. 1919, 5, 252−259. η7 − Ti( -C7H7)] Anion Radical. Inorg. Chem. 1988, 27, 3018 3024. (4) Jensen, W. B. Abegg, Lewis, Langmuir, and the . J. Chem. (e) Vogler, A.; Kunkely, H. Charge Transfer Excitation of Organo- Educ. 1984, 61, 191−200. R,R′ metallic Compounds and photochemistry. Coord. Chem. (5) Abbreviations: Me = CH3, R = alkyl, Cp = C5H5,Tp = − ′ Rev. 2004, 248, 273 278. HB(C3N2HRR )3. + “ ” (18) The cation, [C7H7] , is commonly referred to as tropylium (6) Some authors use the phrase formal oxidation state , although it is and is well known to exist as, for example, the tetrafluoroborate salt, not clear how this is meant to differ from that of “oxidation state”. [C7H7][BF4]. (7) (a) Butin, K. P.; Beloglazkina, Y. K.; Zyk, N. V. Metal Complexes (19) Janiak, C. Klapötke, T. M.; Hans-Jürgen Meyer, H. J.; Reidel, E. 2005 − with Non-Innocent Ligands. Russ. Chem. Rev. , 74, 531 553. Moderne Anorganische Chemie; De Gruyter: Berlin, Germany, 2003. (b) Kaim, W.; Schwederski, B. Non-innocent Ligands in Bioinorganic (20) (a) Glockner, A.; Tamm, M. The Organometallic Chemistry of Chemistry-An Overview. Coord. Chem. Rev. 2010, 254, 1580−1588. Cycloheptatrienyl Zirconium Complexes. Chem. Soc. Rev. 2013, 42, (c) Kaim, W. The Shrinking World of Innocent Ligands: Conventional 128−142. (b) Tamm, M. Synthesis and Reactivity of Functionalized and Non-Conventional -Active Ligands. Eur. J. Inorg. Chem. 2012, − Cycloheptatrienyl-Cyclopentadienyl Sandwich Complexes. Chem. 343 348. (d) Luca, O. R.; Crabtree, R. H. Redox-active Ligands in − Catalysis. Chem. Soc. Rev. 2013, 42,1440−1459. (e) Kaim, W. Commun. 2008, 3089 3100. (c) Tamm, M.; Bannenberg, T.; Manifestations of Noninnocent Ligand Behavior. Inorg. Chem. 2011, Frohlich, R.; Grimme, S.; Gerenkamp, M. Mono- and Dinuclear − Molybdenum Complexes with Sterically Demanding Cycloheptatrienyl 50, 9752 9765. − (8) (a) Green, M. L. H. A New Approach to the Formal Classification Ligands. Dalton Trans. 2004, 482 491. (d) Wang, H. Y.; Xie, Y. M.; of Covalent Compounds of the Elements. J. Organomet. Chem. 1995, King, R. B.; Schaefer, H. F. Bis(cycloheptatrienyl) Derivatives of the 500, 127−148. (b) Green, M. L. H. An Introduction to the Chemistry of First-Row Transition Metals: Variable of the Cyclohepta- − Molybdenum. In Molybdenum: An Outline of its Chemistry and Uses; trienyl Ring. Eur. J. Inorg. Chem. 2008, 3698 3708. (e) Wang, H. Y.; Xie, Braithwaite, E. R., Haber, J., Eds.; Elsevier: Amsterdam, 1994; Chapter 2. Y. M.; Silaghi-Dumitrescu, I.; King, R. B.; Schaefer, H. F. The Mixed (c) Parkin, G. Classification of Organotransition Metal Compounds. In Sandwich Compounds C5H5MC7H7 of the First Row Transition Comprehensive Organometallic Chemistry III; Crabtree, R. H., Mingos, D. Metals: Variable Hapticity of the Seven-Membered Ring. Mol. Phys. M. P., Eds.; Elsevier: Oxford, 2007; Vol. 1, Chapter 1. (d) Green, J. C.; 2010, 108, 883−894. (f) Menconi, G.; Kaltsoyannis, N. Nature of the Green, M. L. H.; Parkin, G. The Occurrence and Representation of Transition Metal - Cycloheptatrienyl bond. Computational Studies of η7 η5 − Three-Centre Two-Electron Bonds in Covalent Inorganic Compounds. the Electronic Structure of [M( -C7H7)( -C5H5)] (M = Groups 4 Chem. Commun. 2012, 48, 11481−11503. (e) Covalent Bond 6). Organometallics 2005, 24, 1189−1197. Classification. http://www.covalentbondclass.org/. (21) (a) Bahl, J. J.; Bates, R. B.; Beavers, W. A.; Launer, C. R. (9) The material described herein can be introduced when first Cycloheptatrienyl and Heptatrienyl Trianions. J. Am. Chem. Soc. 1977, describing coordination chemistry, whether it be that of the main group 99, 6126−6127. (b) Miller, J. T.; Dekock, C. W. Facile Formation of the

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Cycloheptatrienyl Trianion by 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 η5 η7 Containing Titanium(II), ( -C5H5)Ti( -C7H6PPh2), and Related η5 η7 Heterobimetallic Complexes: X-Ray Structure of ( -C5H5)Ti( - · − C7H6PPh2)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. “ ” fi (28) A chemputer to obtain the [MLlXxZz]classi cation 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 (η6- C6H6)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 Reactivity of Phenyl Tris(3-tert-butylpyrazolyl)borato Iron Methyl, t [PhTpBu ]FeMe: Isolation of a Four-Coordinate Monovalent Iron t 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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