IChEAmistry

Anyone told you chemistry was complicated? That the concepts were difficult to put together in your mind? And that to learn it you’ll need a master craftsman (or craftswoman) to help you put it together akin to building craftsman-style furniture? What if you didn’t need any of that? What if you could receive a package of parts, open it up, follow the instructions, and build your own knowledge of chemistry? Maybe it’s just like putting together IKEA furniture. Anyone can do it!

 

I confess that as a computational chemist and having poor hands in lab, I’m similarly challenged when it comes to IKEA furniture. I can put it together, but not very well. One of my chairs is still a little shaky. But by and large everything holds together and is functional.

 

Could we turn learning chemistry into something IKEA-like? Can we break down the concepts into bite-sized pieces and build the framework step-by-step? Can you be guided through the process by an instructor? In a sense, that’s how I design my chemistry classes – to help students digest smaller bits of material and get practice working through problems aimed at helping them grasp the concepts. But if I have such a program in place, does one need the human instructor? Could the process be automated with an instruction manual that’s simple enough to follow such that every student can “teach themselves” chemistry?

 

In my dreams, I call this IChEAMistry. I figure K and the “hard” Ch are similarly enunciated. I’ve even hacked together an imitation logo with not quite the right font (IKEA changed Verdana to Noto two years ago) and not quite the right colors from my eyeballing it. Maybe I need a lowercase leading “i”! Needless to say, this program has not gotten off the ground. I haven’t started looking for venture capital funding even though I can handwavingly claim that I will use machine learning to optimize an appropriate algorithm based on student data from my classes as a training set. And since I’ve taught two thousand students or so over the course of my career, maybe I’ve got some decent data.

 

What I’m presenting as a fantasy, someone else will try to sell you as a reality. Not too long ago, we had the robot tutor in the sky. And yes, one of their products was chemistry. While that venture hasn’t quite worked out, I assure you there will be others who will claim to have improved on the problems of the previous approaches. Will this be successful? For a self-motivated student who can learn on their own, it’s possible. We’ve had correspondence courses for a long time, and I opine that it’s possible to replicate that experience with a computer algorithm. Regular assessments run by the algorithm can check if the student has learned the material. Digital badges could be issued. Nothing wrong with any of that. Someone might even accredit the work. We already accept results from standardized multiple-choice computer graded exams such as CLEP or AP for chemistry, provided the student gets a high enough score.

 

Will this work for the majority of students? I don’t know. My guess is that a few of my students could sufficiently hack their way through IChEAmistry. But most of them will flounder. But is it because they’re not used to the system? If an IKEA-like approach was employed in the earlier grades, maybe this could work? I shudder at the thought since I think younger children should have as much human contact and guidance as possible. Maybe the IChEAmistry approach is centered around group work and activity? That introduces its own complications.

 

If launched at the introductory level, will IChEAmistry provide a sufficient foundation for students who want to pursue further courses in that subject? Maybe. As it is, many of my students in P-Chem seem to have trouble remembering what they learned in G-Chem. An appropriately-timed iChEAmistry “booster” just before P-Chem would likely be helpful. Could one construct an iChEAmistry version of P-Chem? Conceivably. Although venture capital funding would be less forthcoming. The killer app of tech dreams is one that will get widespread use. Lots of students take G-Chem. Much fewer take P-Chem.

 

I have a feeling that an education system using IChEAmistry will be impoverished compared to having a human instructor who you can interact with in close quarters. It’s a feeling that may or may not be justified. But I suspect a revolution is coming whether we like it or not that will continually divide the haves from the have-nots. “Elite” education will continue to have expert human tutors, such as the rich and the royal of yestercenturies were accustomed to. For the rest, you hardscrabble whatever you can get to survive. IChEAmistry might be a reality yet. Tech entrepreneurs will surely argue for the best-of-both-worlds hybrid approach where humans and algorithms cooperate to provide an enhanced education for all. But if we follow the money, I think the future looks more dystopian despite the bright cheery colors of my IChEAmistry logo.

Classification

I just finished reading Kate Crawford’s Atlas of AI. It is less about the nuts and bolts of A.I. (although there is some) and more about the ethics and implications of current and future use. Why an atlas? So that one can both zoom out for the broad view, but zoom in at some of the details, and see the intertwining. While the book roams through several different aspects, the question of who benefits and who is being taken advantage of comes up repeatedly. They may be tech workers, Uber drivers, criminals whose mugshots are stored in a database, mining companies, and more. The first paragraph of the book’s concluding chapter, “Power”, is a good summary of its contents:

 

Artificial Intelligence is not an objective, universal, or neutral computational technique that makes determinations without human direction. Its systems are embedded in social, political, cultural, and economic worlds, shaped by humans, institutions, and imperatives that determine what they do and how they do it. They are designed to discriminate, to amplify hierarchies, and to encode narrow classifications. When applied in social contexts… they can reproduce, optimize, and amplify existing structural inequities. This is no accident: AI systems are built to see and intervene in the world in ways that primarily benefit the states, institutions, and corporations they serve. In this sense, AI systems are expressions of power that emerge from wider economic and political forces, created to increase profits and centralize control for those who wield them.

 

These last several weeks, the media has been shining a spotlight on Facebook and its practices. Crawford’s analysis would have been spot-on, as would Zuboff’s, and many others who have sounded the alarm on the unregulated and extractive nature of A.I. and how it impinges on our lives whether we like it or not. We are entangled with machines and there’s no going back. As Roose warns, the question is whether we end up being machine-assisted or machine-managed. The latter is colonizing more area every day in the name of techno-efficiency. I’m not going down this rabbit-hole in today’s post. Instead I want to focus on Crawford’s statement of A.I. encoding narrow classifications. This is what Chapter 4 in Crawford’s book is about, and her main example is ImageNet.

 

How does one classify images to train an A.I.? Well, you need a training set. Lots of pictures and lots of cheap manual labor (via Amazon Mechanical Turk for instance) to attach labels to these pictures. Where do these labels come from? There’s WordNet, which classifies nouns in a particular taxonomy. Hierarchy is pre-built in a narrow way based on the classification system, and the training set further narrows the scope, not to mention implicit human biases in making classification choices.

 

One of my research projects involves training a program to calculate some molecular properties. I built the training set and have been playing around with a standard classification system that subdivides larger molecules into smaller fragments. This isn’t going so well, so I’ve been dreaming up some alternative classification systems that may do a better job “taming” the data. I’m sure my biases are affecting things in some way although likely not to the extent of present machine-learning face-recognition systems. Reading Crawford’s chapter on classification didn’t impact my research so much as make me think about chemistry and how I teach it.

 

As a so-called expert in chemistry, I have particular notions of how chemistry is organized; you might call these my “expert schema”. My goal is to help students move along the continuum from novice to expert by helping them build their schema. To do this, I have to classify things into categories so students can start to spot similarities and differences. The periodic table is an organizing schema of a sort. The division into elements that are metals or non-metals is a useful classifier. The model of atoms as balls connected by springs works well for covalent molecules with their directional bonds. I’ve used the general bond energy curve to help students think more broadly about how particles interact with each other. For that matter, helping students to think about energy requires a number of classifications.

 

Classification is by nature reductionist. This has its pros and cons. Reducing something that would otherwise seem very complicated with all sorts of things going on is very helpful to the novice learner. However, if the system isn’t merely complicated but complex, then the process of simplifying things via classification may throw out the baby with the bathwater. And chemistry is complex – at least I think so. I hope that in the upper-division classes of our curriculum, we guide students back through some of the complexity and help them to enrich their simplistic schema. This is the challenge of teaching chemistry, or any other complex subject material that one can’t just soak up by osmosis unconsciously. It takes a lot of effort on the part of the student to replace their folk-science understanding with the strangeness of nature.

 

But perhaps how scientists look at the natural world is blinkered by the classification schemes we have used so we can comprehend it – or at least we think we do. And this reductionist approach may be part of why science seems both strange and alien, at least when you get into its intricacies. Conceptualization is tricky; I don’t quite understand how it works, and yet somehow I’ve acquired abstract ideas about chemistry that organize my knowledge. Somehow that passes for expertise; at least that’s how students classify me at the moment – the one who knows the stuff. Do I really? I’m not so sure.

The Mesocosm

As human beings, our particular size (in the meter range) strongly influences how we interact with other objects. Some are close to our size, and they are the touchstones by which we try to understand things that are much bigger or much smaller. Planets and stars fall into the ‘much bigger’ category: we might group them into the macrocosm. Amoebae and bacteria fall into the ‘much smaller’ category: they constitute the microcosm. A tennis ball or a chair, objects that we directly interact with – we can see, touch, and use such things – sit somewhere in between and with us are part of the mesocosm. That’s a human perspective, of course!

 

I’m slowly working my way through Philosophy in the Flesh, a tome by George Lakoff and Mark Johnson. They posit that we should recast philosophy in terms of three main points. The first three sentences in the book (appropriate for philosophers I suppose) encapsulate the story: “The mind is inherently embodied. Thought is mostly unconscious. Abstract concepts are largely metaphorical.” Lakoff and Johnson think the discoveries of cognitive neuroscience force us to rethink the basics of philosophy and reject the mind-body separation of Cartesian dualism. They think that the way we think (both conscious and unconscious) are highly influenced by our neural architecture, by biological evolution, and by how we interact with objects relative to our size and timeframe.

 

At the simplest level, we learn by what we see and what we can manipulate. In scientific terms, one might call this observation and experimentation. Babies and toddlers do this a lot. One might posit that as they explore their surroundings, they begin to conceptualize. And in some mysterious way, learning takes place. They begin to understand not just what they can see and touch, but as children grow older they are able to imagine what they cannot see and touch. Lakoff and Johnson might argue that human biology (and by extension, interacting with others in one’s environment) both shapes and limits the way the human thinking does its magic. When we go to school and learn about science, we might even have the opportunity to extend our scope beyond the mesocosm. The authors write:

 

One thing that science has done successfully in many cases has been to extend our basic-level capacities for perception and manipulation via technology. Instruments like telescopes, microscopes, and spectroscopes have extended our basic-level perception, and other technologies have expanded our capacities for manipulation. In addition, computers have enlarged our basic capacity for calculation. Such enhancements of basic bodily capacities extend the basic level for us, the level that is at the heart of embodied realism.

 

Embodied realism. That’s the two-word philosophical backbone of the book. The three instrumental ‘scopes’ mentioned made me think of astronomy, biology, and chemistry, respectively. Spectroscopy is at the heart of chemistry, which lengthscale-wise is in the nanocosm. We can’t see discrete entities as small as single atoms and molecules, but we can infer their structure based on measurements in the electromagnetic spectrum – the ‘spectra’ of the spectroscope. I’ve themed my G-Chem 1 classes around this idea: how we make visible the invisible!

 

Conceptually, though, the way we picture this nanocosm is by imagining blobs made up of balls connected by springs. The blobs are constantly in motion and may interact with one another depending on their properties. But the mind’s-eye picture is mesocosmic – I played pingpong as a child and that’s my picture of small balls. At one point, I even had a bunch of pingpong balls (both white and orange) in a transparent container that I would bring to class as a demo, shaking it around to demonstrate atoms of a gas bouncing off the walls of a container. (Now I just use computer animations.) But we can go further. Lakoff and Johnson write:

 

What fills out embodied realism, permitting us to move far beyond mere observation and manipulation… is the existence of conceptual metaphor, which allows us to conceptualize one domain of experience in terms of another, preserving in the target domain the inferential structure of the source domain. Mathematics allows us to model metaphorical theories and to calculate precisely inferences about literal basic-level categories. Such inferences can then be projected onto scientific subject matters to give explanatory accounts for existing data and to make predictions.

 

This is especially true for the tougher parts of chemistry. I teach P-Chem, much dreaded classes for chemistry and biochemistry majors. The math is heavy-going. Many students struggle through the course. But the mathematics is uncannily powerful, and allows us to access abstract ideas that seem so far out of the realm of what we can see and touch in the mesocosm. That’s part of what makes math challenging once you leave the familiar realms of counting objects to more abstract relations. Yet mathematical models have their limitations like any other model. And what is a model, if not a way to represent something outside the mesocosm to the human mind built evolutionarily to interact within the mesocosm and yet be able to have thoughts outside it.

 

If there’s one thing in particular, outside of balls and springs, that I ask students to conceptualize in my chemistry classes, it is energy diagrams. Higher up means more energy and reduced stability. I gesticulate frequently in class and my arms move up and down to embody this idea. Lower down means lower energy and being in a more stable state. To break a chemical bond, the system moves up in energy. The chemical system must receive energy from the outside to break bonds. Conversely, and non-intuitively, making a chemical bond moves the system down in energy. Energy flows out of the system. Energy is conceptually protean and abstract, but we can count it and keep track of it.

 

I’d like to think that teaching again in-person and using bodily motions as part of my explanations helps student learning. Not so easy to do via online learning, but I suppose I could make videos of myself. I still feel that something is lost in translation through the flat screen, but I’d be hard-pressed to tell you exactly what that is. I’d like to think there’s something particular apt in learning person-to-person physically in the same space and sharing the mesocosm directly!

 

P.S. Interested in the osmocosm? See here.

Seven Years

Potions for Muggles is seven years old! Amazingly, I’m still writing. In the early years, I felt that my writing was improving, but more recently I feel I’ve reached stasis. Perhaps I haven’t stretched myself by trying to learn some new things about the art and craft of writing. This is something I need to ponder.

 

I haven’t spent much time writing about magic and science lately. Although I tried to revive this by reading Terry Pratchett’s original Discworld series parlayed into the Science of Discworld, I ultimately did not find it as interesting. So, I’m on the lookout for some potentially new and interesting fiction that will spark creative themes. I haven’t yet searched in earnest.

 

Quite a number of posts were related to new teaching protocols related to the Covid-19 global pandemic. I did learn some new tricks, but I’ve mostly reverted to the old storehouse of pedagogy I’ve built up over the years. Teaching remotely or masked was not as bad I as anticipated, but I still prefer face-to-face and personally meeting and chatting with my students with as few barriers as possible (masks and Zoom boxes, primarily).

 

There were more posts than usual about my research-related thoughts on non-equilibrium thermodynamics, kinetics, and living systems. Much of this stemmed from reading challenging scientific papers and books that are more obscure, but I think there are some very interesting nuggets that have helped me progress in thinking about the age-old question: “What is life?”

 

And yes, a large portion of my posts are still about books and articles that I’ve read. Going out less because of the pandemic means staying at home and reading more. Not a bad thing, necessarily.

 

As with every new year, I don’t make resolutions or predictions. Maybe I’ve grown old, a little jaded, a little less expectant, but perhaps I’m also more comfortable in my routine and where I am in life. Supposedly I’m a little past the lowest dip in the happiness curve, but I frankly can’t tell.

 

It’s nice to take a moment to reflect when reaching a milestone of sorts. I don’t have anything Halloween-themed to say, but since I just finished Lewis Structures in my G-Chem classes this past week, here’s my Quest for a Stable BOO!

Extra Life

I enjoy Steven Johnson’s books – a blend of history, science, and creativity, that strikes just the right balance for my reading interests. His latest book, Extra Life, is subtitled: “A short history of living longer”. Average global life expectancy has only recently risen significantly over the past century thereabouts, especially as infant/child mortality has reduced, among many other improvements in medicine, public health, and work safety. 

 

There is a chapter that recaps the masterful story Johnson tells in the book that made him famous, The Ghost Map – whereby several unsung heroes traced the outbreak of cholera in the East End of London to a contaminated water source. But there are several other interesting stories. I was familiar with the role of Mary Montagu and variolation – which then led to vaccination, one of the most important advances in public health. I’d heard of W.E.B. DuBois’s work in Philadelphia, although Johnson provided a number of details I wasn’t aware of. I did not know about the work of Nancy Howell among the !Kung tribe in the Kalahari – a very fascinating read.

 

Johnson takes great pains to repeat one of his main points – that such “discoveries” or “improvements” came about through the concerted effort of many people, not just a lone genius. This is apparent in his story about pasteurization. We’ve heard of Louis Pasteur, but perhaps not about the many other folks who were key to its widespread use. We’ve heard of Alexander Fleming and penicillin, but if not for many others, not much would have come out of his serendipitous discovery. It’s the network of people that push for change that ultimately led to large segments of humankind being able to enjoy longer, perhaps, healthier lives. Johnson also shines a light on the role of data and statistics in all of this – I liked how his examples highlighted this aspect.

 

What I was really interested in was what Johnson had to say about transhumanism and the quest to extend life significantly further than what seem to be the present limits. Our bodies are programmed to die after some time – it’s built into our biology or at least we and many other organisms have evolved to reproduce offspring and then die ourselves in the hope that the children are able to repeat the feat in the next generation. Johnson touches on the topic in the last bit of his epilogue. There isn’t much groundbreaking on the scientific front, I’m sorry to say, which is why the popularity of sci-fi and fantasy in plumbing this topic will continue – Voldemort notwithstanding. Maybe there will be some sort of strange merging of mind and machine, and transhumans live in virtual reality. Then the bonus of classic video games will finally become reality: Extra Life!

 

P.S. Two of Johnson’s other books, I’ve recently blogged about: Wonderland and How We Got to Now.

Learning Machines

Over the years I’ve read secondary sources referring to Alan Turing’s famous 1950 paper (“Computing Machinery and Intelligence”, Mind, 1950, 59, 433-460) but only last week did I finally read the original paper. It opens with the question: “Can machines think?” and sets out the principles from what is now well-known as “The Imitation Game” (also a title on a recent movie biopic on Turing). After describing his thoughts on why the answer would be a carefully-qualified “yes, in the not-so-distant future”, Turing also takes time to answer possible objections to his position.

 

Today’s post is not about Turing machines or whether machine intelligence can sufficiently mimic human intelligence, but focuses on the last section of the article, “Learning Machines”, in line with my interests in teaching and learning. It begins with an objection to his thinking machine: a “machine can only do what we tell it to do”. Turing responds by proposing the setup for a nuclear reaction: If the setup of an “atomic pile” is sub-critical, firing a neutron at the pile causes some change but does not lead to a sustained chain reaction. But if it has reached “critical mass” (of fissile material), bombarding neutrons will trigger the chain reaction. Turing wonders whether this is an analogy for how the human mind learns.

 

I find this analogy interesting. Suppose there are some students who have learned some chemistry or did the reading beforehand, and a combination of some knowledge and its rudimentary organization prepares the mind to learn something new in a sustained way. Suppose there are other students who aren’t sufficiently prepared (they’re still in the “subcritical” domain). Then when encountering the lesson in class, things click for some students such that they really “get it” while for others, the lesson seems to make sense but is not enduring and they can look back at their notes with little or no understanding. I’ve certainly encountered both groups in my classes, and likely a continuum of “partial-understanding” cases in between.

 

The situation is more pronounced when the subject material is conceptually difficult, unfamiliar, abstract, mathematical, or all of the above. Chemistry spans all these categories. Since introductory chemistry and physical chemistry are classes I’ve taught almost every year for twenty years, I can attest that incoming students who had a strong secondary school chemistry preparation do well and struggle less in the introductory classes. No surprises there. They’ve seen some of the material before and therefore have “critical” background and content knowledge, although in many cases not well organized (i.e., they know a bunch of useful yet isolated facts). In physical chemistry, the students are on the same footing conceptually, but those who are much more comfortable with mathematical language and equations, are significantly more successful. For those who are not, the math bogs them down from grasping the abstract conceptual material in a sustained way.

 

Can we imagine a machine with enough “background” knowledge learn something in a new way going beyond the rules of its programming? Can it make new rules? Does the concept of “critical” content apply and if so, how? I’m not sure, although I can imagine it following the tropes of sci-fi sentient machines. But is there a more fundamental limitation in machines that humans can transcend?

 

Turing provides an intriguing analogy. In a parenthetical statement, he writes: “Mechanism and writing are… almost synonymous”. The context is imagining a machine that is child-like, in the sense of its capacity to learn. One can imagine an educational “program” being fed to the machine that moves it from child-brain to adult-brain, assuming that the brain is like blank sheets of paper that can be filled with writing. Since machines are by nature mechanistic, introducing a program by writing data into memory is certainly what computers do. But this doesn’t get around the seeming divide between syntax and semantics. If you don’t comprehend a language, it’s all syntax to you. But to those who understand it, the language acquires meaning – it signifies something, i.e., the symbols truly symbolize!

 

All this makes me think of assessment. How do we assess if a student has learned something? On an exam, I (the examiner) ask questions, and the student provides answers. Assuming a written exam, I read the syntax of the students and decide if the semantics of that syntax corresponds to understanding. This is trickier than it looks. First, consider the two extremes. A student who leaves it blank or writes irrelevant nonsense clearly has not demonstrated knowledge. A student who nails the answer carefully and critically, in my interpretation, has demonstrated learning. But for the majority of students, I get something in between – a partial, somewhat garbled understanding. Perhaps some learning has taken place, but perhaps it’s a data dump, such that you might expect from a machine search.

 

What gets the student from partial understanding to more complete understanding? There must be a refinement process that goes on. Exactly how that happens in the human mind is less than clear. One can imagine machines going through refinement algorithms of some sort as part of machine learning. But by using the word “algorithm” have I unwittingly restricted the process to be mechanistic in a way dissimilar to how humans learn? I’m not sure. If complexity, by definition, cannot be simulated by an algorithm, then perhaps there are some types of learning that a machine cannot attain. Machines can learn simple things, complicated things, but not complex things. If chemistry isn’t merely complicated but complex, a machine can’t learn chemistry in the same way a human can.

 

A final tidbit from Turing’s paper is his suggestion that randomness be included in the algorithm for learning to take place. This is a messy and far-ranging topic, but my brief thought on the matter is that it allows us to simulate an anticipatory system that can adapt to changing environmental conditions. Biology features control systems via feedback and feedforward loops, and one can imagine a machine doing something similar. Perhaps that’s where the critical line lies. But it’s possible that the gulf between semantics and syntax cannot be bridged even if the imitation might fool us more than once.

Exceptions: Who Cares?

I got annoyed at myself while teaching my General Chemistry classes this past week. I had a meta-moment or an epiphany while I was going through the motions of explaining some observed chemistry-related factoids. I’m good at explaining this stuff because I’ve spent a lot of time thinking about it, not just at the superficial level but a little more deeply. But even as I was talking in class, a part of my mind was questioning why I was doing so. Is this factoid or its explanation even important? At the General Chemistry level? At some point, I transitioned into saying that the rest of the explanation was beyond the purposes of the class, but I would be happy to discuss the subject at length in office hours. I don’t think the students noticed my frustration with myself; but then again no one has come by my office to query me about the finer points yet.

 

Today’s rant is about exceptions-to-the-rule that showed up this past week in my General Chemistry classes. With some examples, I will briefly state the general rule, why the general rule is important, the exceptions, and then rhetorically pose the question “Who Cares?” Finally, I will muse about some situations where one might care about the answer.

 

To write the ground state electronic configuration of an atom, one can mechanically use two rules: place electrons in the lowest energy orbitals first, and each orbital can only accommodate two electrons. (They’re called the “aufbau” and “Pauli” principles respectively.) Why is this important? Chemistry is all about what electrons are doing in an atom. Knowing something about their arrangement allows us to describe chemical structure and reactivity. Why the ground state? Under standard conditions, electrons arrange themselves to be in the most stable state which has the lowest energy – what we call the ground state. But there are exceptions. For example, chromium’s valence electron configuration is 4s¹3d⁵ in its ground state rather than the expected 4s²3d⁴ if you followed the two rules. There are less-than-satisfactory “explanations” for these provided in the typical G-Chem textbook, but I say: Who Cares?

 

There’s a third rule mentioned when it comes to writing ground state electron configurations known as Hund’s Rule: When you place more than one electron in orbitals of the same energy, put the electrons in separate orbitals and keep them spin-aligned where possible. Why is this important? Having electrons in separate orbitals is useful when we discuss covalent chemical bonds as the overlap of singly-occupied orbitals from when two atoms approach each other. Thus, knowing this helps us understand chemical structure and reactivity. There’s also an explanation why the electrons should be spin-aligned But: Who cares?

 

After students learn to write ground state electron configurations of neutral atoms, we move on to ions. Once again, learning this is useful to subsequently describe chemical structure and reactivity of ions. Generally, ions follow the same rules as neutral atoms except when you get to the transition metals. An example exception to the rule: For d-block atoms, when removing electrons, remove the valence s electrons before the seemingly “higher energy” d electrons. Once again, there is an explanation. And once again: Who cares?

 

Once we can write electron configurations for atoms and ions, we can discuss several useful trends across the periodic table. For example, the first ionization energy of an atom decreases down a column and increases across a row. Why is this useful? Knowing the trends tells you that the bottom left corner of the periodic table (Francium) has the lowest ionization energy, and the top right corner (Helium) has the highest ionization energy. This allows you to classify elements into two broad categories: metals and non-metals. Those two categories can then broadly be used to classify three types of chemical bonds (metallic, ionic, covalent) and relate these to the macroscopic properties of compounds. It’s one of the most useful classifications in chemistry. But there are exceptions to the ionization energy trend. Going across a row, there are two kinks. I wrote a previous post examining this (which I assign as optional reading for the curious student). With regard to this exception: Who Cares?

 

What made me annoyed about these exceptions is that their inclusion in the textbook and on typical standardized exams results primarily in a mechanism to identify students who know the exceptions and can (somewhat vaguely) articulate them. The explanations in G-Chem textbooks for these cases are incomplete at best and downright misleading at worse. If that’s all we use them for – as a way to separate the A from the B students – then I for one would prefer to jettison them. Who Cares?

 

Who might actually care? The inorganic chemist might. When you’re delving into the details of transition metals, detailed knowledge of electron configurations and spin states are important. The curious student might. What makes chemistry interesting is that while the general rules are a powerful way of organizing knowledge, there are all sorts of intriguing exceptions that give chemistry its unique unruly flavor. The messy details become very interesting if you’re really into chemistry! In my classes, I regularly include little tidbits outside of the standard syllabus in the hope I will intrigue students into wanting to explore the subject more. I want students to be surprised by chemistry!

 

The Pauli Exclusion Principle is one such under-utilized concept. It’s not just an esoteric rule about quantum numbers – it gets at the heart of what keeps fundamental particles distinct, and yet indistinguishable when they “switch” places and you can’t tell the difference. It’s why humans can’t walk through brick walls even though atoms are mostly empty space – a demonstration I do every year after which I throw in a tidbit about quantum tunneling. It explains the shape of molecules through VSEPR theory. It’s both strange and surprising. I try to tell students this every year. Not sure if they believe me.

 

I haven’t decided what to do about the exceptions I’ve mentioned when I teach first-semester G-Chem again (next Fall semester). I’ve made my peace with including orbitals in G-Chem, since they are quite interesting and useful in discussing some of the nuances of electronic structure. But I’m no longer as interested in, for example, students memorizing exactly how to draw the five d-orbitals transformed in Cartesian space. I wonder what else I will get annoyed by as we progress through the semester. Last Fall, I was just trying to not screw up and do the best I can for my students while teaching remotely. But now I have more bandwidth to think a little more carefully about what’s important and why we should care about some particular concept as a foundation for learning chemistry.