A New "Bottom-Up" Framework for Teaching Chemical Bonding

Research: Science and Education

A New “Bottom-Up” Framework for Teaching Chemical Bonding Tami Levy Nahum,* Rachel Mamlok-Naaman, and Avi Hofstein Department of Science Teaching, Weizmann Institute of Science, Rehovoth 76100, Israel; *[email protected] Leeor Kronik Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel

Chemical bonding theory is central to an understanding of general chemistry (1–3). Clearly, the rigorous framework for understanding chemical bonding is given by quantum mechanics. As famously noted by Dirac in 1929 (4), shortly after the formulation of the theory, The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known.

Almost eighty years after Dirac’s observation, the prevalent teaching approach to chemical bonding and related ideas is still not rooted within a uniform conceptual framework. Instead, a plethora of bond models and bond types, the inter-relations among which are often poorly understood by students, are presented. The limitations and inaccuracies inherent in this approach, as manifested in many standard chemistry textbooks, have been examined extensively in the chemistry education literature (3, 5–11). Obviously, teaching chemistry, at either the high school or the university level, from a strictly formal quantum mechanical perspective is not only impractical, but also undesirable. However, one can still seek an intuitively appealing framework that, on the one hand, is well rooted in formal theory and, on the other hand, can treat all chemical bonds on an equal footing (12, 13). We strongly believe that the diversity

properties

ionic matter

covalent matter

molecular matter

metallic matter

ionic bonds

covalent bonds

molecular bonds

metallic bonds

intermolecular bonds

van der Waals forces

intramolecular bonds (covalent bonds)

hydrogen bonds

Figure 1. A schematic illustration of the traditional approach for teaching chemical bonding.

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of bonding mechanisms and variety of “chemical tools”, such as valence bond (VB) and molecular orbital (MO), are essential for chemical “intuition” and creativity. However, it is possible to show how this diversity arises from a small number of fundamental principles instead of presenting it as a large number of disparate concepts. In this article, we discuss what we view as some of the more problematic aspects of the traditional approach for teaching bonding. We then suggest that these can be alleviated by adopting a new “bottom-up” approach that rationalizes all bonds and structures based on a small set of underlying assumptions. Finally, we briefly discuss our initial experiences with this teaching approach. Difficulties in the Traditional Approach The traditional approach to teaching chemical bonding can be succinctly characterized by the illustration given in Figure 1. As discussed by Sproul (8) and Hurst (3), many general chemistry textbooks and courses classify matter into four major categories—ionic, covalent, molecular, and metallic—based on macroscopic physical properties (e.g., boiling and melting points, electrical conductivity, water solubility, etc.). Chemical bonding in each category is discussed and used to rationalize the properties of that category. Thus, different types of bonds are both presented as and used as different entities emanating from different bonding models. Partly, chemical bonding is presented in the above manner for historical reasons1 (3). Indeed, chemistry developed early on by collecting a comprehensive set of empirical observations and by attempting to find order in the observations by means of various classification schemes. Bonding models, often spectacularly successful, then arose as part of a natural attempt to rationalize the classification. New, increasingly refined bonding models were then simply added to the existing ones in many textbooks. However, generally speaking the historical perspective is not necessarily the pedagogical one. Specifically, the stratal structure of bonding models is problematic because students are easily confused by multiple theories of the same phenomenon (3, 14, 15), especially when each of the theories is mostly heuristic in nature. Another reason for the widespread use of the traditional approach is that it provides (relatively) clear-cut definitions that facilitate instruction, provide a “sense of security” for the students, and allow for an efficient evaluation process based on clear-cut answers to well-defined questions (16). Unfortunately, these advantages, which are not necessarily consistent with the

Journal of Chemical Education • Vol. 85 No. 12 December 2008 • www.JCE.DivCHED.org • © Division of Chemical Education


ultimate learning goals (7, 17) are sometimes attained at the price of over-simplification and over-generalization, which have been shown to be pedagogical learning impediments (18). First, the presentation of each bond type as a different entity that belongs to a specific category (see Figure 1) does not foster a deeper understanding of chemical bonds. Specifically, it may obscure the important notion of a unified rationalization of all chemical bonds based on underlying principles. Second, over-emphasis of the four “ideal” categories is misleading and may actually hinder the learning process. While the “ideal” classification is not without merit, we now know that many important groups of modern materials simply cannot be “forced” into one of the rigid categories. In the following, we illustrate some limitations of this rigid approach with specific examples.

textbooks metals are characterized by a set of common physical and chemical properties, for example, malleability, ductility, low ionization potential, and so forth. But the fact is that there is not even one chemical property common to all metals and there is a great variability of parameters in any other quantity, for example, brittleness, conductivity, boiling point, and so forth. Over-simplification occurs because many textbooks introduce a metallic bond as “metal ions floating in a sea of electrons”. This analogy is problematic because it presents the metallic bond as a bonding entity that is entirely different from the covalent one, whereas a more modern description views both types of bonds as involving “electron sharing”. The difference is again explained in terms of a continuum scale, this time involving the degree of electron delocalization (11).

Covalent versus Ionic Bonding Typically, covalent and ionic bonds are presented dichotomously, as “electron sharing” or “electron transferring” bonds, respectively. However, in heteroatomic systems, bonding is better described in terms of a continuum of a covalent–ionic “scale” (8, 17, 19). Furthermore, bonds are purely covalent between two identical atoms, but purely ionic bonds actually do not exist at all. The dichotomous presentation impedes the understanding of the more subtle “scale”.

Hydrogen and van der Waals Bonds In most textbooks, covalent and ionic bonds are described as “real” chemical bonds, whereas hydrogen and van der Waals bonds are often presented as “just forces” (9). Again this distinction is far too rigid. While the relative strengths of different types of bonds are, of course, very important, even “weak” bonds do indeed bond different chemical units and sub-units together and can have profound chemical consequences (17, 19), for example, in biochemistry. Therefore, a continuum scale is a more appropriate scientific description. Two related over-simplifications are the classification of hydrogen bonds as strictly intermolecular, whereas they are often intramolecular as well (e.g., 21), and the discussion of such bonds only when N, O, or F atoms are involved, whereas hydrogen bonds, albeit weaker or non-conventional, may occur with other atoms or groups as well (e.g., 22, 23). To summarize, we view the traditional approach that is characterized by clear-cut definitions and rigid distinctions as an insufficient basis for rationalization of current chemical knowledge. This problem can be amplified by traditional assessment methods, in which the superficial study of classification and “rules” by rote is rewarding to both students and teachers (16, 17). Despite this, the traditional general chemistry curriculum as a whole has by and large been taken for granted by science educators for over a century (15).

Electronegativity and Bond Polarity Because within the traditional approach bond polarity is essentially viewed as an additional characteristic of covalent bonds (3, 19), the important concept of electronegativity (EN) is only introduced in the context of polar covalent bonds and not as an integral part of bond-polarity concepts in general (13). EN differences between atoms are then used as an indication of whether compounds should be classified as ionic or covalent. However, EN differences are not the ultimate measure for predicting bond type (8). Indeed, cases of bonds between atoms with large EN differences that possess a significant covalent nature nevertheless are known experimentally (20). The Octet “Rule” Because it is simple to visualize and use, the octet “rule” is often presented as an obligatory condition for “proper” bonding. Thus, students often adopt the anthropomorphic notion of atoms “wanting” to possess “octets” or “full outer shells” and that chemical reactions occur to “allow” atoms to achieve this “natural desire” (9). But this causes some students to have difficulties in accepting anything that is not clearly explicable in “octet” terms, for example, hydrogen bonds or even covalent bonds or transition metal bonding not leading to “octets” (13). The octet rule is certainly a time-honored useful guideline and shall remain so. However, it is not an explanation for bond formation. For these reasons, Hurst (3) and Taber and Coll (19) suggested that an over-emphasized “octet framework” may actually impede higher-level learning process. Metallic Bonds The traditional discussion of metals and metallic bonds may involve both an over-generalization and an over-simplification. Over-generalization occurs because in many general chemistry

A New “Bottom-Up” Framework Based on the above arguments, a need for a new framework, within which chemical bonding can be taught, is evident. Here, we present such a framework, where the traditional approach is substituted by a “bottom-up” approach based on fundamental principles. The development process of this framework was based on a collaborative work with leading chemistry teachers, chemical educators, and eminent research chemists (17). Our focus here is on a suitable curricular basis. Teaching strategies and assessment methods associated with this curriculum are of course of much practical importance, but as the curriculum clearly comes first (24), these will be discussed elsewhere. The general structure of our proposed framework is illustrated schematically in Figure 2. It is based on introducing salient properties of isolated atoms (stage 1), followed by a discussion of general principles of chemical bonding between

© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 12 December 2008 • Journal of Chemical Education

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Research: Science and Education bond length

stage properties

4

structures

3

bonds—a continuum approach

2

the chemical bond—fundamental principles

1

a single atom—elemental principles

Figure 2. A schematic illustration of a new “bottom-up” framework for teaching chemical bonding.

two atoms (stage 2). The general principles are then used to present the different traditional categories of chemical bonding as extreme cases of various continuum scales (stage 3). Equipped with this knowledge, students can then rationalize different structures (stage 4) and ultimately properties (stage 5), within a coherent picture. We emphasize that the general structure outlined in Figure 2 is in fact appropriate for different levels of chemistry students (from high school students to advanced undergraduate students), depending on the mathematical and physical rigor of the discussion. Here, we focus on high school studies, with occasional comments on first-year university instruction as well. Stage 1: A Single Atom Our suggested presentation begins with the description of a single atom. First, single atoms are the obvious “building blocks” of all chemical systems. Second, it is a relatively easy point to introduce two concepts that are key in subsequent discussion: Coulomb’s law and the wave nature of electrons. Coulomb’s law is central to chemistry because electrical interactions are overwhelmingly the dominant ones in the range and energy scale relevant to chemistry. However, Coulomb’s law is obviously not enough because quantum theory tells us that the picture of an electron orbiting a nucleus owing to an attractive force is not at all the same as the picture of, say, the moon orbiting the earth owing to an attractive force. Instead, understanding electrons requires that we consider their wave-like character. In other words, we immediately do away with the physically wrong and conceptually misleading analogy of electron behavior being the same as that of a classical billiard ball. Instead, we explain that electrons in atoms exist as fuzzy “probability clouds” of negative charge around the nucleus, which we call orbitals. At the high school level, this can be rationalized by means of a descriptive treatment of some experiments that rule out the “billiard ball” picture. At more advanced levels the justification can (and should!) be refined. This is also the appropriate point to introduce the important chemical concepts of shells and sub-shells as well as valence electrons. The discussion of single atoms can also be used to introduce electron spin and Pauli’s exclusion principle at a descriptive level.

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0

Internuclear Distance

Energy

5

bond energy

repulsive forces greater than attractive forces

the equilibrium point—the most stable bond length

attractive forces greater than repulsive forces

Figure 3. A schematic energy curve for any two atoms that interact.

However, it can also be deferred to a later point as students (and scientists) find quantum concepts difficult to digest at first encounter. At higher levels (but not the high school one), we recommend the introduction of Pauli’s exclusion principle in terms of the more general principle of anti-symmetric wavefunctions. (We note in passing that a particularly intuitive and appealing argument for simple wave function symmetry has been given by Bethe and Jackiw in ref 25). Stage 2: The Chemical Bond The primary purpose of this stage is to provide a qualitative description that is conceptually consistent with quantum mechanics but gives a clear, intuitive answer to the question which puzzles many students, “What really causes atoms to interact and form a chemical bond?” In this stage, we aim to convince students that there is nothing “mysterious” about chemical bond formation. Instead, we begin by introducing (or refreshing, depending on the amount of physics background) the concepts of energy and force and the relation between them. The understanding that nuclei are held together because of nucleus–electron attraction, which is a simple consequence of Coulomb’s law, is the first step towards a rational view of chemistry that is not based on rules of thumb, anthropomorphic concepts, and so forth. A crucial concept is that stability, in general, is obtained by minimizing energy (the distinction between energy and free energy is obviously important, but it can be discussed later on). Once this is understood, all chemical bonds, of any type, can be rationalized in terms of energy stabilization (i.e., bond energy) and all equilibrium interatomic distances (i.e., bond lengths) reflect positions where there is no net force on the nuclei, that is, attraction balances repulsion. The salient point to be emphasized at this stage is the relationship between Coulomb’s law and stability in terms of a balance of the various attractive and repulsive Coulomb potential energies, as well as the electron kinetic energy. In other words, the student should understand that chemical bonding is nothing but a consequence of Coulomb’s law, except that it is a non-trivial consequence because it is “cloaked” by the wave-like nature of the electron and the laws of quantum physics.



Again, a detailed teaching strategy is beyond the scope of this article. However, we believe that, at least at the high school level, the above principles are best explained by considering the energy curve for two isolated atoms, as shown in Figure 3. Specifically, Figure 3 can be rationalized “step-wise” by realizing that, if there is any net gain of energy from bringing atoms together, there will be a region where, even though nuclei generally repel each other as they are both positive, there will be net attraction because the nucleus–electron attraction acts as an effective “glue” for the nuclei (we note in passing that at a more advanced level, it can be pointed out, or even shown, that the “gluing” effect is inherently quantum mechanical and is not always obtained if the system is treated classically; refs 5, 26, 27). If the atoms are close enough, there will be net repulsion. The equilibrium distance, namely, the bond length, is then simply the special point at which net attraction exactly offsets net repulsion and the bond energy is the net gain in energy obtained at this point, with respect to the well-separated-atoms limit. This is a stable equilibrium point because either increasing or decreasing the interatomic distance requires energy. Importantly, Figure 3 is general. It describes the relation between energy and internuclear distance for the H2 dimer as well as it describes the Li2 dimer, the NaCl heterodimer, or even the He2 dimer! Obviously, there is very much that separates H2 and He2. However, equipped with the understanding that all interatomic interaction is alike at least in some aspects, the student is now ready for a discussion of specific attraction mechanisms based on variety of “chemical tools”, that is, for stage 3. Stage 3: Bonds, A Continuum Approach One of the key goals of the proposed framework is to stress that a continuum scale exists between extreme cases of qualitatively different bonding scenarios. Having understood, in stage 2, the common denominator of all bonds, we can now rationalize some distinct bonding categories, as shown in Figure 4. Again, we find the example of a chemical bond in a diatomic molecule to be most instructive because of the focus on one bonding entity only. Perhaps the easiest bond to rationalize is the ionic one, where charge transfer results, effectively, in a cation and anion that attract each other as an obvious consequence of Coulomb’s law. Pure covalent bonds (such as H2 and Li2) are then rationalized in terms of electron-pair bonding, “charge sharing”, and orbital overlap (at higher levels an introduction to the concepts of the molecular orbital by means of a linear combination of atomic orbitals and bond order can be included). Once the concepts of ionic and covalent bond are internalized, we recommend stressing right away that the nature of most bonds is in fact partly covalent and partly ionic, that is, polar, as generally both “charge sharing” and “charge transfer” aid energy stabilization. We then further recommend that this continuum of bonding is immediately related to a continuum of bond strength, as shown in Figure 4. This continuum follows Pauling (28; p 100), who recognized that bonds between unlike atoms typically have greater bond energy than that of the average of the corresponding homoatomic bonds. Of course, it is important to add caveats—bond strength is not only a function of the degree of ionicity but also a function of atomic size and other factors.

In this context, the concept of EN can be introduced early, and more importantly, naturally, as one way of quantifying the covalence–ionicity balance. As noted by Noy et al., “EN is an important part of the intuitive approach that helps chemists in understanding nature. In particular, it provides a measure to the uneven distribution of electrons among bound atoms and the probability of electron transfer among two unbound atoms (or molecules)” (29; p 3684). It is then natural to introduce hydrogen bonds, in terms of attraction between partial effective charges (positive, on the hydrogen atom that is bound to an atom that is part of an electron withdrawing group, and negative, on an electronegative atom or group), augmented by a weak covalent component (30–32). In this approach, however, we emphasize how this explains their specificity and directionality and that such bonds cover a fairly broad range of bond strengths and lengths, that is, have their own continuum scale. Finally, we recommend that van der Waals bonds are introduced, again via diatomic molecules. The He2 dimer—a large bond length, very weakly bound molecule (33)—can be used for introducing the concept of induced dipole–induced dipole interactions, which can be rationalized as yet another manifestation of Coulomb’s law. Here, it is easy to convince the student that a covalent bond cannot explain the bonding as there is no meaningful orbital overlap, the lack of which is rationalized in terms of the “filled” shells of the He atom (in advanced levels this can be related to the bond order). Finally, differences in the intermolecular interaction between dimer pairs, for example, ICl versus Br2, can be used to introduce dipole–dipole interactions. After the prototypical bonding scenarios have been introduced, several additional comments are important. First, it is important to understand that the traditional “intermolecular” versus “intramolecular” division, especially for hydrogen bonds, is superficial; if the relative scale of bond strengths is understood, one can understand that liquid water turns to gas by breaking hydrogen bonds even without this distinction. Second, it is essential to emphasize that the transition between covalent-polar bonds and hydrogen bonds is blurred, rather than sharp. Finally, it is also important to tell the students that many chemists prefer not to use the word “bond” for van der Waals interactions, as they prefer to reserve this term for specific, directional interactions. It is important to make sure the students understand this distinction, irrespective of the semantics chosen.

ionic bonds polar bonds covalent bonds hydrogen bonds van der Waals bonds

Increasing Bond Strength Figure 4. A schematic continuous scale of bond strengths.


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At an advanced level, other specific bonding scenarios, for example, charge-shift bonding (34), can be discussed, with an emphasis on how they too can be rationalized as special cases of the general principles. Stage 4: Structures Once bonding is understood, the relevant key ideas immediately explain different molecular structures. Here, one can introduce a variety of concepts, depending on the level of detail and depth sought. Valency is clearly one concept of much importance. Atomic valence shell and periodicity properties can then be discussed (35) Through valency, Lewis dot diagrams (36) can be rationalized and the “octet rule” can then be presented as a guideline (as opposed to mandatory rule) with respect to electron pairing, together with other shell rules, for example, an 18-electron rule or a “rule of 12” for transition metals (13). Importantly, one can then distinguish between molecules that are “physically stable” (i.e., nuclei at equilibrium) and molecules that are “chemically stable”, for example, with respect to addition of more atoms (e.g., by comparing CH, CH2, CH3, and CH4). This then ties in the knowledge garnered so far with the tools that we like to call “chemical intuition” that are obviously of much value in chemistry. Simple models, such as the valence shell electron pair repulsion (VSEPR) theory can then be introduced and used (likely mainly in the context of organic compounds). If desired, ideas of molecular orbital calculations in general, and possibly those of density functional theory (DFT; ref 37) in particular, can be introduced, at least at the “philosophical” level, at this stage. It can then be explained that DFT provides both a solid basis for chemical concepts (38) and a practical computational tool for chemical predictions. Once molecular structures are understood, one can introduce giant structures, that is, structures that do not possess welldefined sub-units. Importantly, these need to be understood using the same set of principles. For ionic giant structures, this provides a perfect opportunity to explain the difference between, for example, HF and NaCl. Because HF is not as ionic as NaCl (~40% versus ~80% ionicity, respectively), it is reasonable that HF does not form an ionic giant structure whereas NaCl does. For metallic giant structures, metallic bonding is introduced at this stage as essentially covalent bonding with delocalized electrons. This introduces yet another continuum scale—that of electron delocalization, obtained when bringing together a large number of metal atoms (11). At this stage, we recommend to emphasize the relation between bonding type and structure as much as possible. Stage 5: Properties Finally, the stage is set for a detailed discussion of the interrelation between bonding, structure, and properties—a key issue in chemistry. We do not discuss this in detail, despite its great importance, as there are obviously many possibilities and as a detailed discussion is clearly outside the scope of the present manuscript. We only emphasize that the tools acquired so far really do allow for linking the macroscopic and sub-microscopic points of view in a logical fashion.

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Practical Advantages of the New Framework: Preliminary Results In our opinion, the proposed new framework overcomes a major difficulty in the traditional approach by removing the artificial division between different types of bonding. Instead, a variety of bonds are introduced to the students from a continuum point of view. Furthermore, a gradual exposure of the main concepts and ideas, in five stages, allow us to overcome the dichotomous classification without falling into the trap of over-simplifications and over-generalizations. Most importantly, we believe that such a framework facilitates the attainment of two important objectives: (i) preventing pedagogical impediments for further studies and (ii) fostering the understanding that molecular species and bonding scenarios that textbooks often designate as “exceptions” can, in fact, be rationalized by the same small number of principles used to rationalize the “regular cases”. We believe that our approach may enhance the students’ understanding of bonding and foster them to think scientifically. However, we are also aware of its weakness—using abstract theoretical ideas right from the start may prove difficult for some students. In the academic year 2006 we started a preliminary implementation of an experimental teaching unit that was developed based on the above ideas. At present, this unit has been tested in ten 11th grade classes and more research is clearly needed. However, preliminary input from both teachers and students is encouraging—they ask creative questions, they start to think! We end this article by quoting one teacher and one student. These quotes strongly enhance our own faith in the presented approach. Teacher: I loved the idea that I can teach and explain all bonds based on a uniform model. Starting from submicroscopic ideas and moving up to the material world improved the students’ learning and thinking. Student: The continuum scale of bonds helped me to understand…last year the teacher said: ‘it’s one of the two’ (covalent/ionic)…

In 2009, the new program will be implemented in all 11th grade chemistry classes, which is possible because the educational system in Israel is centralized. We plan to conduct a full scale procedure, assessing both the teaching and learning, and to report broader and statistically sound field results in due course. Summary We believe that the traditional curriculum for teaching bonding is insufficient and to some extent inaccurate. There is a need for a coherent conceptual model for all bonds that is consistent with present scientific knowledge and that provides the student with the proper intellectual infrastructure for further studies. In this article, we presented a general model for bonding that can be presented at different levels of sophistication depending on the student’s level and needs. This is achieved without sacrificing the benefits of traditional qualification of different bond



types as this qualification is presented along a continuum scale of chemical bonding. The pedagogical strategy for teaching this model is a “bottom-up” one, starting with basic principles and ending with specific properties. It is our hope that its use could reduce the use of over-simplifications and over-generalizations and remove learning impediments so as to improve students understanding of the nature of chemical bonds. Acknowledgments We thank Richard N. Zare (Stanford University) for illuminating discussions and encouraging this approach to understanding (and teaching) chemical bonding. We also thank Roald Hoffmann (Cornell University) and Sason Shaik (Hebrew University) for their valuable and inspiring comments on the ideas expressed in this article. Note 1. Personal communication with Roald Hoffmann, Dec 23, 2004.

Literature Cited 1. Fensham, P. Concept Formation. In New Movements in the Study and Teaching of Chemistry; Daniels, D. J., Ed.; Temple Smith: London, 1975; pp 199–217. 2. Gillespie, R. J. Chem. Educ. 1997, 74, 862–864. 3. Hurst, O. J. Chem. Educ. 2002, 79, 763–764. 4. Dirac, P. A. M. Proc. Roy. Soc. Lond. A 1929, 123 (792), 714–733. 5. Ashkenazi, G.; Kosloff, R. Chem. Educator 2006, 11, 66–76. 6. Justi, R.; Gilbert, J. Models and Modeling in Chemical Education. In Chemical Education: Towards Research-Based Practice; Gilbert, J. K., Jong, O. D., Justy, R., Treagust, D. F., Van Driel, J. H., Eds.; Kluwer: Dordrecht, Netherlands, 2002; pp 47–68. 7. Taagepera, M.; Arasasingham, R.; Potter, F.; Soroudi, A.; Lam, G. J. Chem. Educ. 2002, 79, 756–762. 8. Sproul, G. J. Chem. Educ. 2001, 78, 387–390. 9. Taber, K. S. Int. J. Sci. Educ. 1998, 20, 597–608. 10. Hawkes, S. J. J. Chem. Educ. 1996, 73, 421–423. 11. Myers, R. T. J. Chem. Educ. 1979, 56, 712–713. 12. Weinhold, F. J. Chem. Educ. 1999, 76, 1141–1146. 13. Weinhold, F.; Landis, C. R. Valency and Bonding: A Natural Bond Orbital Donor–Acceptor Perspective; Cambridge University Press: Cambridge, 2005. 14. Henderleiter, J.; Smart, R.; Anderson, J.; Elian, O. J. Chem. Educ. 2001, 78, 1126–1130.

15. de Vos, W.; Pilot, A. J. Chem. Educ. 2001, 78, 494–499. 16. Levy Nahum, T.; Hofstein, A.; Mamlok-Naaman, R.; Bar-Dov, Z. Chem. Educ: Res. Prac. Eur. 2004, 5, 301–325. 17. Levy Nahum, T.; Mamlok-Naaman, R.; Hofstein, A.; Krajcik, J. Sci. Educ. 2007, 91, 579–603. 18. Taber, K. S. Sci. Educ. 2005, 89, 94–116. 19. Taber, K. S.; Coll, R. Bonding. In Chemical Education: Towards Research-Based Practice; Gilbert, J. K., Jong, O. D., Justy, R., Treagust, D. F., Van Driel, J. H., Eds.; Kluwer: Dordrecht, Netherlands, 2002; pp 213–234. 20. Woicik, J. C.; Nelson, E. J.; Kronik, L.; Jain, M.; Chelikowsky, J. R.; Heskett, D.; Berman, L. E.; Herman, G. S. Phys. Rev. Lett. 2002, 89, 1–4 (077401). Woicik, J. C.; Yekutiel, M.; Nelson, E. J.; Jacobson, N.; Pfalzer, P.; Klemm, M.; Horn, S.; Kronik, L. Phys. Rev. B 2007, 76, 1–6 (165101). 21. Özen, A. S.; De Proft, F.; Aviyente, V.; Geerlings, P. J. Phys. Chem. 2006, 110, 5860–5868. 22. Naaman, R.; Vager, Z. J. Chem. Phys. 1999, 110, 359–362. 23. Nakanaga, T.; Buchhold, K. Chem. Phys. 2002, 277, 171–178. 24. Goedhart, M. J. Chem. Educ. 2007, 84, 971–976. 25. Bethe, H. A.; Jackiw, R. Intermediate Quantum Mechanics, 3rd ed.; Benjamin Cummings: San Francisco, 1986; pp 20–25. 26. Teller, E. Rev. Mod. Phys. 1962, 34, 627–631. 27. Kurth, S.; Perdew, J. P. Int. J. Quant. Chem. 2000, 77, 814–818. 28. Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell University Press: Ithaca, NY, 1967. 29. Noy, D.; Fiedor, L.; Hartwich, G.; Scheer, H.; Scherz, A. J. Am. Chem. Soc. 1998, 120, 3684–3693. 30. Martin, T.; Zygmunt, S. Nat. Struc. Bio. 1999, 6, 403–406. 31. Steiner, T.; Desiraju, G. Chem. Commun. 1998 (8), 891–892. 32. Gilli, P.; Bertolasi, V.; Ferreti, V.; Gilli, G. J. Am. Chem. Soc. 1994, 116, 909–915. 33. Lohr, L. L.; Blinder, M. J. Chem. Educ. 2007, 84, 860–863. 34. Hiberty, P. C.; Megret, C.; Song, L.; Wu, W.; Shaik, S. J. Am. Chem. Soc. 2006, 128, 2836–2843. 35. Bent, H.; Weinhold, F. J. Chem. Educ. 2007, 84, 1145–1146. 36. Lewis, G. L. J. Am. Chem. Soc. 1916, 38, 762. 37. Koch, W.; Holthausen, M. C. A Chemist’s Guide to Density Functional Theory, 2nd ed.; Wiley-VCH: Weinheim, Germany, 2001. 38. Geerlings, P.; De Proft, F.; Langenaeker, W. Chem. Rev. 2003, 103, 1793–1874.

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A New "Bottom-Up" Framework for Teaching Chemical Bonding

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