May 2014

# What we can teach with hybrid orbitals

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Alberto Moniz, Streetsville Secondary School, Streetsville ON

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> Chemistry has a method of making progress which is uniquely its own and which is not understood or appreciated by non-chemists. Our concepts are often ill-defined, our rules and principles full of exceptions, and our reasoning perilously near being circular. Nevertheless, combining every theoretical argument available, however shaky, with experiments of many kinds, chemists have built up one of the great intellectual domains of mankind and have acquired great power over nature, for good or ill.

> E. B. Wilson1

The value of teaching hybrid orbitals has been the topic of recent articles in the Journal of Chemical Education2,3,4 and in this publication.5 Grushow argues that the concept of hybrid orbitals is outdated, with very few valid applications in contemporary chemistry, and only ingrains an incorrect understanding of bonding which students will have to overcome in future learning. In contrast, Landis, Weinhold and Tro contend that a hybrid orbital approach, as a component of valence-bond (VB) theory, is still properly used by contemporary chemists to model electron densities and bonding, and that introducing these concepts does not get in the way of the future learning of students, but provides a secure foundation for more advanced work. It is clear from this discussion that the value of localised models of chemical bonding is still an open question. As a high school teacher, I do not feel qualified to contribute to this debate among professional chemists, but I would like to argue that making our students aware that such debates exist in contemporary science is essential in shaping a deeper and more authentic view of the nature of science in our students.

Despite their shortcomings, hybrid orbitals should not be taught as merely a flawed and simplified story we tailor to the limited powers of the teenaged mind. Just getting students through with a fairy tale understanding of chemical bonding robs us of an opportunity to expose them to some profound lessons in the nature and development of the modern science of chemistry. This point is well made by Nivaldo Tro:

> Chemical bonding is probably the only place in the curriculum where we teach multiple models for a single phenomenon. This exercise, if done correctly, teaches students a valuable lesson about the nature of scientific models. (Tro in reference 4, page 567)

The best reason to teach hybrid orbitals, as a component of Linus Pauling’s VB theory, is to compare and contrast it with Lewis structures and the delocalized, molecular orbital understanding of bonding. One of the most important goals in science education should be to demonstrate that science is not the static, black and white body of knowledge found in the average textbook. Instead of classifying different models as simplistically right or wrong, we need to help our students compare alternative scientific perspectives in terms of strengths and weaknesses. This approach encourages higher order thinking, deepens understanding and engages students with a more open, dynamic portrayal of science as the vital human endeavour it is. The teaching of chemical bonding is a unique opportunity in the science curriculum to achieve these goals, but this approach requires an awareness of the logical and historical underpinnings of the different models.

Students first encounter chemical bonding with Lewis dot diagrams and structures.6 G.N. Lewis first conceived of these diagrams in 1902 as a teaching tool for undergraduates, but his theory of valence continued to evolve during the subsequent 20 years with the introduction of Bohr’s model of the atom and the development of quantum mechanics (Gavroglu in reference 1, page 48). These humble diagrams, with their surprisingly powerful electron dot patterns, allow us to predict the valence of elements plus the formulae and structures of a large number of simple compounds which, with the introduction of VSEPR theory, leads to the inference of molecular geometries and polarities. It gives us the octet rule, and a way of introducing the formation of ionic and molecular compounds. And most importantly, it gives us the concept of the localized, directional, shared electron pair bond. All this from a non-mathematical, pre-quantum mechanical model largely based on empirical patterns of valence.

We do not teach Lewis diagrams because they are right, in many important ways they are not, but they are not merely heuristic tools to be discarded later on — indeed, structural formulae with lines representing the shared electron pair bond are ubiquitous in all of chemistry. We need to help our students appreciate the incredible predictive power of this utterly simple model and respect the genius behind it. But we also need to help students recognize its limitations. This is a chemist’s theory designed for the chemist’s need to predict bonding and structure. It fails as a physical theory to explain why and how bonding occurs and does not say anything about spectroscopic data, which was both the triumph and downfall of the Bohr model. Lewis, who was a leader in physical chemistry and recognized the importance of physics7 to chemistry, continued to modify his ideas until 1923 to better conform to Bohr’s atom.8 It is interesting to contrast the styles and commitments of these two scientists: the chemist and the physicist. Their theories were different because they had different perspectives and different goals: Lewis wanted to explain valence and bonding; Bohr was concerned with atomic structure and the hydrogen spectrum. In each case their work was influenced by the cultures of their respective disciplines and not merely by some abstract notion of a single, otherworldly, objective truth. It is this socio-historical background that is missing in our textbooks. In our rush to make things simple, we often perpetuate a view of science which is disconnected, unengaging and naïve — textbooks are where scientific curiosity and discovery go to die.

After a European tour where he immersed himself in the new quantum mechanics with many of the world’s leading physicists, Linus Pauling returned to Berkeley California in 1931 where he delivered his famous lecture series on “The Nature of the Chemical Bond” (Gavroglu in reference 1, page 61). The very important and pedagogically relevant case of how the carbon atom bonds to form methane will serve to illustrate his results. The ground state electronic configuration of carbon’s valence shell is 2s22p2, which — as I never tire of pointing out to my students — as a kind of discrepant event, does not provide the four equivalent, unpaired electrons necessary to form the methane molecule as predicted by its Lewis dot diagram. Pauling’s breakthrough, which actually came three years prior in 1928 (Servos in reference 8, page 290), was to realize that the 2s and 2p subshells were very close in energy, allowing for the combination of the wavefunctions into four equivalent hybrid orbitals. The higher energy of the hybrid orbital configuration would be more than compensated for by the lower energy of the molecule formed by their combination with the atomic wavefunctions of hydrogen. The result was the four equivalent, localised, shared electron pair bonds with tetrahedral geometry that all chemists know and love. Hybrid orbitals achieve this result because that was what they were designed to do. Pauling was a structural chemist and a pioneer in X-ray crystallography. As such, he was concerned with making the new quantum mechanics consistent with empirically known molecular structures, and he was entirely committed to the basic theory of valence and bonding developed by Lewis (Servos in reference 8, page 290 and Gavroglu in reference 1, page 64). Like Lewis before him, Pauling’s valence bond theory was influenced by his commitment to the goals and methods, that is, the culture of his discipline. When teaching this material, I make it a priority to draw connections between these different models and perspectives.

It is important to remember that hybrid orbitals (and orbitals in general) are not physical entities and that hybridisation is not a physical process as it is sometimes taught. When we speak of hybridisation or “orbital overlap” students can get the impression that entities are physically merging and changing into new forms when what is actually going on is the mathematical procedure of combining wavefunctions to create new wavefunctions that better describe the particular physical system of interest. The mathematics involved is far too advanced for the high school level, but that does not mean that we should give students the wrong impression by not stressing to them that this is a mathematical theory. And how exciting to realize that which wavefunctions are used and how they are combined is essentially a human choice, guided by empirical considerations and professional commitments. This is, of course, at the root of the controversy over hybrid orbitals in the first place.

Pauling’s valence bond theory was the application of quantum mechanics to Lewis’s model of localised chemical bonding. This links with the drawing of more advanced Lewis structures and the derivation of molecular geometry and polarity based on the VSEPR theory. And when we begin to explore these more advanced structures, we encounter the concept of resonance.9 Resonance was crucial to Pauling as it allowed him to explain the existence and unusual stability of benzene,10 but really it was an artifact of the theory’s greatest weakness. The valence bond and Lewis theories both assume that molecules result from atoms sharing bonding pairs of valence electrons in localised, directional bonds independently of the atoms’ other non-bonding electrons. A molecule is just the sum of its atoms and the distinct, chemical bonds that hold them together.

This commitment to the idea of the localised chemical bond is what the physicist Robert Mulliken called the “ideology of chemistry” in 1935 (Gavroglu in reference 1, page 84). In a way that parallels the relationship between the models of Lewis and Bohr, but without the rapprochement, the controversy between VB theory and molecular-orbital (MO) theory can be similarly characterized as a clash of cultures between the chemical and the physical. Mulliken’s method treated each molecule as a unique system with its own set of molecular orbitals. The molecule is the result of the entire electronic structure of the system rather than the summation of the bonding atomic orbitals of each atom. This results in the possibility of electrons spanning more than just particular pairs of atoms — what is known as delocalized electrons. I teach the resonance structures of benzene as a discrepant event which is better understood by the delocalized bonding model of MO theory. Among its many advantages, MO theory is able to predict, as cited by both Mulliken and Grushow,2 spectroscopic data; but at the price of sacrificing any easy correspondence to the chemist’s concepts of valence and bonding. It is again the choice between the chemist’s concerns for bonding and structure versus the physicist’s commitment to the calculation of spectra and orbital energies. This is not just an issue for the high school curriculum, but a deep historical controversy that has lasted for almost ninety years.

As educators, we must be sensitive not only to the bare scientific content of the curriculum but also to the image of science that we implicitly portray to our students. The history of scientific ideas should be an integral part of our teaching as it gives our students the opportunity to develop a deeper and richer understanding of the subject. These ideas are not new, as this statement from the March 1979 issue of Chem 13 News attests: 11

> Knowing how the laws of chemistry came to be revealed, through insight, reasoning and logic of many minds, can lead to an enhancement of our own understanding and appreciation of this science.

But these considerations remain stubbornly and increasingly absent from our curricula and textbooks to the detriment of student understanding and engagement. By not allowing the history of science to inform our teaching we close off our subject from the dynamic human realm of the possible in favour of the rarefied, always existing knowledge of the textbook. This omission of context from our teaching in the name of simplification means that students are not given enough information and insight to construct any real understanding of the subject beyond a kind of rote surface knowledge that will get them through the hoops of the education system but is good for nothing else. Linus Pauling once said that “if you want to have good ideas you must have many ideas.”12 In the age of Google, when all the scientific content we could possibly teach is easily accessible everywhere to everyone, what is the value of the classroom experience? It must be to challenge students to do what no computer can — to think. By incorporating historical context into our lessons we expose students to the human reasoning, and controversies, behind the textbook facts. This opens up a space that makes the construction of deeper meaning by our students possible. Our lessons are more engaging, authentic and meaningful if we punctuate them not with periods, but with ellipses…

## References

1. Kostas Gavroglu, Ana Simões, Neither Physics nor Chemistry: A History of Quantum Chemistry. MIT Press, 2012, page 252.
2. Alexander Grushow, Is it Time To Retire the Hybrid Atomic Orbital? Journal of Chemical Education, 2011, 88, pages 860-862.
3. C.R. Landis, F. Weinhold, Comments on “Is it Time to Retire the Hybrid Atomic Orbital?” Journal of Chemical Education, 2012, 89, pages 570-572.
4. Nivaldo J. Tro, Retire the Hybrid Atomic Orbital? Not So Fast, Journal of Chemical Education, 2012, 89, pages 567-568.
5. Michael Jansen, Orbital hybridization — the stork, Chem 13 News. February, 2014. page 4.
6. Often it is Bohr diagrams that are taught first, but these should always be drawn with the same pairing pattern as Lewis diagrams to facilitate the teaching of bonding and valence.
7. Lewis was the author of the first paper published in the US on Einstein’s special relativity in 1908 (Gavroglu, 47).
8. John W. Servos, Physical Chemistry from Ostwald to Pauling. Princeton University Press, 1990, page 281.
9. I would also include the concept of formal charge which is essential for evaluating alternative Lewis structures.
10. Linus Pauling, Nature of the Chemical Bond, 2nd edition, Cornell University Press, 1948. page 129.
11. Quoted from Chem 13 News, February, 2014. Page 15.
12. Linus Pauling, quoted by Francis Crick. The Impact of Linus Pauling on Molecular Biology, Oregon State University Libraries, 1996. Accessed on March 11, 2014.

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