Should Hybrid Orbitals Sell the Farm and Move to Florida?

An interesting controversy has emerged in the Journal of Chemical Education this month, following a paper by Grushow calling for the retirement of the hybrid orbital concept from the chemistry curriculum. The flurry of rebuttals that followed Grushow’s letter are an excellent summary of current thought about the relationship between canonical, delocalized molecular orbitals and localized MOs. The latter, although derived qualitatively from hybrid atomic orbitals, are just as legitimate as the canonical MOs that result from traditional quantum chemical calculations. A wonderful description of the idea with just the right amount of math has been provided by Hilberty, Volatron, and Shaik.

An important point of almost all of the rebuttals is that the traditional photoelectron spectroscopy argument in support of canonical MOs (and arguing against localized MOs) is totally bogus. I mention this particular aspect of the debate because I learned something myself! The traditional argument goes that because methane possesses two different ionization energies, its filled MOs must sit at two different energy levels. The two different ionization energies observed are the result of pulling an electron from MOs of two different energies. Hilberty et al. and DeKock + Strickwerda both point out that localized MO theory may be used with success to explain the two different ionization energies—and that the premises of those who claim otherwise are false. From Hilberty:

The reasoning of those people eager to retire the LMO model, is as follows: since the [Hybrid Atomic Orbital] model puts four electron pairs into four equivalent localized orbitals…then extracting an electron from anyone of these four orbitals should always cost the same energy, leading to a single unique ionization potential (IP). The error in this reasoning is simple: it completely ignores the quantum mechanical requirement that any wave function must match the symmetry of the molecule.

Hilberty goes on to illustrate that when the localized MO approach is applied to this problem, although the filled MOs of CH₄ all reside at the same energy, the MOs of ionized CH₄⁺ must bear two different symmetries and sit at two different energies. Hence, two ionization energies should be expected on the localized MO model as well.

Deslauriers, Schelew, and Wieman vs. “Hard Science”

Science education is the angsty teenager of the scientific research field. Assaulted on all sides with strict demands from the “patriarchal” hard sciences, education research holds its ground by echoing cries of “you don’t understand me!” and basing its claims on past literature, much of which was probably subject to the same criticisms that present-day educational research is! Where does the vicious cycle end?

A little background first—as regular readers of my blog may be vaguely aware (assuming these “readers” exist), Science has begun to include science education studies in its pages lately. This is a very good thing. Not only does it put important research in the spotlight, it also attracts science educators to the journal, and an army of science educators who read Science is much better than one that does not! A recent educational research paper by Deslauriers, Schelew, and Wieman published in the pages of Science made some sweeping claims about improved learning in a large physics class thanks to a course intervention based on the idea of “deliberate practice.” Exam scores and attendance were both higher in the section that used deliberate practice; the “old school” section’s scores and attendance were lower. The sections were “matched” using several metrics, including the Brief Electricity and Magnetism Assessment and Colorado Learning Attitudes about Science Survey. Matched sections, differing only in the presence or absence of deliberate practice…everything seems peachy, right?

Not according to Derting et al. and Torgerson, who both wrote letters to Science criticizing the study. The bulk of Torgerson’s argument is that the study is not properly controlled, and does not take into account teacher effects (maybe the control group teacher just sucks in general, in addition to using “bad, old school” methods), selection bias, whether students knew they were being treated differently, etc. Derting et al. echo many of these points. One of their more intriguing ideas in common is that, really, the original study is the equivalent of a “single data point,” or a clinical trial involving a single placebo patient and a single treatment patient. Replication, echo the throngs of hard scientists, is needed.

The original authors responded by supplying evidence that their experimental design was good enough to be generalized. Randomized, hyper-controlled trials are not, they claim, necessary in collegiate science courses. Teacher personalities tend to not affect the amount of learning that occurs in collegiate courses (?!). Finally, they raise the point that replications of their experiment may introduce ethical issues, as investigators should expect to replicate their result, which would involve putting the control group at an intrinsic disadvantage.

Where to fall on this debate? It’s tough for me to decide. Both sides advance good arguments. Theoretical ideas and educational psychology research do support the practices used by the experimental section from the original paper. It would have been very bad if the authors’ results had not supported this existing literature, and what they did was almost certainly good from an educational perspective. However, like a sparrow sitting on a giant’s shoulder, the work does little to advance the field of physics education. There are some very subtle issues at play in the classroom, not all of which can be addressed by sweeping labels like “deliberate practice” and even “active learning.” Practical ideas that real educators can take away are hard to find in the paper, and that lowers its value. It’s a shame, because one can tell that their hearts are in it, but the long-term usefulness of the work just doesn’t stand up to scrutiny! The most valuable literature in education (at least to me) has always been the stuff with the most practical value. This paper will at best fade away and be remembered as little more than a blip on the radar—and at worst have a negative effect on the practicing scientist’s view of education research.

Academic Performance and Concept Maps

“Mildly creepy yet thorough, with a number of ‘duh’ moments.”

That’s how I’d describe the Journal of Chemical Education’s latest cross-university look at the factors that influence academic performance in organic chemistry courses from Szu et al. Creepily, the researchers asked student volunteers to keep a diary of their daily studying activities, asking them to indicate at the resolution of fifteen minutes “when and where they were studying, with whom, and what materials they used.” As is so often the case (see my recent micoach lament), this rather invasive data produced some of their most interesting results. Does the data-supported conclusion that “higher-performing students study earlier, not more” constitute something interesting in an absolute sense? I’ll let you be the judge. To me it was a “duh” moment—staying ahead of course material means that concepts make more sense when hearing them for the “first” time.

The Szu paper continues the recent trend (a fad of Gaga-esque proportions) to use concept maps to measure students’ conceptual understanding of a subject. I’m still not aboard the concept-map bandwagon, myself. Strangely, most human graders seem to treat concept maps like glorified open-response essays during the assessment process. How does it make sense to grade something containing discrete, explicit connections between concepts with a scale like “0 = total nonsense, 4 = scientifically complete”? It only makes sense when one “reads” a concept map as one would read an essay response, mentally talking out “[concept A] [verb expression] [concept B]” for each link. There must be a better way to grade these damn things!

Let me put on my Nostradamus cap for a second: visualization libraries for directed graphs on the web are not quite “there” yet, but once they get “there,” network analysis will bust onto the concept map scene in a big way. Humans aided by computer analysis of concept map networks will take education’s latest short-answer proxies to the next level as assessment tools. Right now, for instance, the distance between concepts is meaningless (related only to aesthetic concerns). Even basic network metrics, such as relative in- and out-degrees, are impossible to get a grip on visually. Can you imagine the incredible statistics educators could gain by pooling machine-readable concept maps from universities all over the country? It blows the mind!

Student Development as a Result of Science Courses

The most recent issue of Science contains an excellent editorial by David Asai on measuring student development through science education. He hits the nail on the head by identifying the key processes that students should be able to engage in after successfully completing an experience in science education. To some, the quip that “students of science should be able to apply the scientific method” may seem like a tautology, but it’s something educators must constantly remind themselves. Why? Because the body of content under the umbrella of “science” is so massive now that it’s easier than ever to fall into a rut of teaching to memorization. Quality not quantity, right?!

Anyway, back to Dr. Asai’s key competencies (lifted verbatim from Science 2011, 332 (6032), 895):

• Formulate a hypothesis
• Design a meaningful experiment
• Deal with uncertainty
• Critically evaluate evidence
• Engage in effective discourse

In other words, “do the scientific method”! Not quite a tautology when you see it broken up this way, right? What fascinates me is this question:

• How do we assess and look for these competencies meaningfully?

Teaching a lecture course of 200+, I can only dream of doing this on a formative basis. But the possibilities are endless if the manpower is there! The laboratory environment in particular is an interesting battle ground for this sort of assessment. For instance, in an advanced organic chemistry lab course I took in undergrad, we were given a set of reactants and reaction conditions and told “good luck have fun!” with only a lecture or two on the reaction for that experiment. Side products were reasonable and to be expected, so critical analysis was essential. We were judged on how well we evaluated evidence and established reasonable conclusions—not our yield of some “cookie cutter” product. This is the way science education should be!

Asian Dudes Talk White Power

Charges, excitons, and white organic LEDs

Happy April Fool’s Day! The linked article is a Chem. Soc. Rev. on controlling the properties of white OLEDs (for Jess and my mom: white lights made out of stuff containing carbon). Interesting stuff. Most of us chemists are probably familiar with the mobility problem for organic electronics—the fact that organic semiconductors tend to transport charge much worse than silicon. Improving OLED performance is more than just a matter of improving mobility, however, and managing charges and excitons within the active layers of OLEDs is a fundamental, deep way to improve OLED performance in a rational way. White OLEDs are particularly interesting, as they must span an extremely wide array of wavelengths and thus incorporate multiple active materials.

Emission in OLEDs occurs from excited states (excitons) of organic molecules. Excited states come in two flavors: singlets and triplets. Here’s the problem: excitation of organic molecules produces one singlet for every three triplets (on average), and only singlets can emit light efficiently! Emission happens via decay to a singlet ground state. The rule is “singlet-to-singlet OK, triplet-to-singlet NOT OK”. Triplets hang around until heat or some other non-emissive process kicks them back into a singlet state, or until they phosphoresce, which takes way too long for practical switching purposes (imagine turning on a light and waiting ten seconds for full brightness. Blah.). Some creative solutions have been devised to get around this problem, the most fundamental of which involves incorporating a heavy metal atom into the organic species, allowing violation of the rule and speeding up the triplet-to-singlet emissive process. In fact, considering the fact that triplets are longer lived and travel farther, you don’t even have to dope the entire device with metal—just place fluorescent materials close to the excitation site (to deal with singlets) and metal-doped phosphorescent materials farther away (to deal with triplets)! The singlets and triplets will separate spatially because of their differences in diffusion distances, and the triplets will travel farther. “Chromatography for excitons^TM!” In one cool application, different phosphors emitting different wavelengths of light are layered so that as triplets diffuse, multiple wavelengths of light are emitted, producing white light.

With regard to charges, an imbalance of negatively charged electrons and positively charged holes in an active layer can wreak havoc on device efficiency. Electrons and holes need to get together in order for LEDs to produce light. But most organic compounds treat electrons and holes differently, moving one along faster than the other…what to do?! Basically, existing solutions have relied on either helping the organic layer do what it can’t do on its own or slowing down what it does well. Either way, the way the material treats electrons and holes becomes more balanced.

Theories of WOLED operation are still in their infancy, say Wang and Ma, but this is clearly a fascinating area. My interest in organic electronics just got jump-started. Apologies to the blogosphere masters if I screwed anything up.