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←LorM→Z, according to whether the ligand is the donor (L) fi or acceptor (Z). A molecule 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 electron con guration, 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 ■ INTRODUCTION application of different procedures for assigning oxidation states, The carbon atoms 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 periodic table, 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 ligands 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 boron and nitrogen: boron forms a variety of trivalent compounds in which it may have either an octet ■ OXIDATION STATE 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 metals, which may form compounds ff “Dewey Decimal Classification of inorganic chemistryif the in which a given metal 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 © 2014 American Chemical Society and Division of Chemical Education, Inc. 807 dx.doi.org/10.1021/ed400504f | J. Chem. Educ. 2014, 91, 807−816 Journal of Chemical Education Article − 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 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 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.