Skinny Core

I just returned from a LABSIP workshop. What is LABSIP? Lowering Activation Barriers to Success In P-Chem. While the acronym doesn’t roll off the tongue, I find the name amusing. Then again, I once gave a talk at a chemistry conference titled “Getting Over the Curve”, a subtle reference to the same “energy diagrams” that those of us who teach P-Chem agonize over, because our students are frequently confused by the graph axes among other things.

 

The workshop was a blast. There was plenty of nerdy P-Chem humor. I met old friends and acquaintances, and made new ones. It was a targeted small in-person workshop with just 25 invited participants with a packed schedule. I was not involved in organizing it, and was able to fully enjoy the time without worrying about administrative details. In today’s blog post, I will discuss one of the activities we attempted: Can we agree on and distill a “skinny core” list of topics that should be in physical chemistry courses?

 

Before this in-person group meeting, there had been a Zoom meeting with a few hundred participants. From the AllOurIdeas online polling system (here are the Quantum results), the group found that there was actually a good consensus on what the community of physical chemists thought was important in a potential two course outlay dubbed Quantum and Thermo. One of our jobs in the small workshop was to hash out a “skinny core” that provided a guideline for instructors who teach a wide variety of P-Chem courses. Some of us teach the standard two-semester sequence for chemistry majors. Others teach it in three-quarters. Others squeeze it into two. Yet others teach a one-semester grab bag that includes both broad areas. Some teach P-Chem for engineers, or biochemists, or some other subgroup.

 

What should the core ideas be? We came up with an initial set which still needs more discussion, refinement and editing. Eventually it will be published by LABSIP and hopefully this provides a service to the community of P-Chem instructors regardless of the flavor of our classes. A little later in the post, I will reveal my personal version for the Quantum half based on the discussions I participated in. It does not reflect the group consensus although there is significant overlap. I’m teaching Quantum in the upcoming fall semester so this exercise felt timely for me.

 

As chemists, we want students to learn how the quantum world applies to chemical questions; this means we are interested in things at the scale of atoms and molecules. Solving the Schrodinger (wave) equation is at the heart of quantum chemistry. This requires learning about eigenvalue equations and using operators. It also means coming to grips with the strange nature of quantum measurement, the ideas of wave-particle duality, and the Heisenberg Uncertainty Principle. As instructors, many of us use both historical and more recent research to highlight what’s cool about the quantum, but we don’t all use the same examples.

 

In my opinion, what science does to elucidate how the natural world works, is to build models. Models, by their very nature, cannot capture all aspects of a complex system. But by constructing a model, we can test our understanding of nature, make predictions, and thus refine our theories. In P-Chem, these models are grounded in mathematics. There was very broad consensus that as chemists we should cover the particle-in-a-box, harmonic oscillator, and hydrogen atom models. Some of us discuss the rigid rotor as an additional model, others fold it into the hydrogen atom or cover particle-in-a-ring models. Everyone agreed that there should be some mention of electron spin. We also agreed that one should go beyond the hydrogen atom and discuss models relevant to chemistry where the Schrodinger equation cannot be solved exactly. Thus approximate methods and their accompanying theories and models should be included. I think all of us covered at least the helium atom and the Born Oppenheimer approximation, i.e., cases with multiple electrons and multiple nuclei respectively. For me, that’s a core that covers 7-10 weeks, suitable for a half-semester or quarter-long quantum course. Most of us include a bit of spectroscopy, but I think it could also be done in a separate course (e.g. P-Chem lab).

 

Here’s an outline of my semester-long quantum course. My version of the skinny core is in bold, what I think is common consensus but I left out of the core is in italics, and things where there is less agreement is in unaccented text. As a computational chemist who is also interested in chemical bonding, there are certain things I want the students to appreciate in my Quantum course that are unique to me, and these optional items are also in unaccented text. (In my early days, I taught computational chemistry as an elective, but I have pivoted to origin-of-life which is a topic of broader interest to students.) Our LABSIP group did not specify an order that topics should be covered; I think there are different ways to skin the quantum cat, so the following order is my own. It’s somewhat close to a “traditional” sequence, but there are good reasons for doing so to take advantage of topics building on each other.

 

·      Dawn of the Quantum (bits of history)

·      De Broglie Hypothesis and the Heisenberg Uncertainty Principle

·      The Bohr Atom

·      Classical wave equation (to teach some differential equations)

·      Schrodinger Equation and Particle-in-a-Box models

·      Operators, Expectation Values, Commutators

·      Postulates of Quantum Mechanics, wavefunction properties

·      Quantum Tunneling

·      Harmonic Oscillator model

·      Infrared Spectroscopy, Normal Modes, Anharmonicity

·      Rigid Rotor Model, Rotational Spectra, Rovibrational Coupling

·      Spherical Harmonics and the Hydrogen Atom model; Atomic Orbitals

·      Electron Spin, Term Symbols

·      Helium Atom and the Variational Principle

·      Alternative Orbital Wavefunctions, Basis Sets, Hartree-Fock Theory

·      Perturbation Theory

·      Pauli Exclusion Principle

·      Multi-Electron Atoms and Hund’s Rule

·      Born Oppenheimer Approximation, Molecular Hydrogen Cation Model

·      Molecular Orbital Theory (Diatomics)

·      Electronic Transitions, Franck-Condon Principle

·      Polyatomics and Hybridization Theory

·      Huckel Theory

·      Advances in Valence Bond Theory (beyond the 2c-2e Heitler-London bond)

 

Whew! We get through a lot, but I hope at the end of the course, the students have a newfound appreciation for the importance of the quantum to fundamental questions in chemistry, and that what we call the chemical “bond” is a strange beast that’s largely imaginative (although grounded in different theories). I’ve rearranged my course over the 20+ years I’ve taught P-Chem. Topics such as group theory, lasers, NMR spectroscopy, have rotated in and out. I expect my class will continue to evolve, and I think that’s a good thing. But I also expect to preserve the skinny core.