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NMR True Confessions

I must admit, with a great deal of humility, that I've never taken an NMR myself. NMRs were always handled by my TA's in undergrad. Provided my chemistry was clean, the NMRs always came back nice and neat, with huge signal-to-noise and no indication of any difficulty with actually obtaining the spectrum. I naturally assumed, then, that taking NMRs was a simple matter of dropping in the sample, turning on the magnet, setting parameters, clicking START and kicking back.

Of course, to quote Garson Hampfield, "that's not how it works." NMR works because application of a uniform magnetic field to a sample polarizes nuclear spins in the sample "with" and "against" the field lines, and the energy difference between these two states is directly proportional to the strength of the magnetic field felt by each nucleus (which in turn depends on the electronic environment around each nucleus). The problem? Applying a perfectly uniform magnetic field to a sample turns out to actually be kinda tough, and magnetic field gradients in the sample can lead to line broadening and distortion of spectra. The process of canceling out any magnetic field gradients in the sample (via the application of fields from "shim coils") is called "shimming."

The study of magnetic field gradients in NMR samples has led to some fascinating results. The exponent of the field variation with position is called the "order" of the gradient. First-order gradients can be constructed from the three Cartesian directions x, y, and z, which correspond conceptually with the atomic p orbitals. An arbitrary second-order quadratic gradient can be made from five independent first-order gradients, reminiscent of the five d orbitals. Seven independent third-order gradients (analogous to the seven f orbitals) form a basis for every possible cubic third-order gradient. Adjustable shim coils that can compensate for the "basis gradients" of a certain order can thus cancel out all possible gradients of that order. Shim coils up to and including fifth-order are now common on spectrometers. Gradients can also be distinguished by their direction relative to the axis of rotation of the sample--gradients aligned with the rotation axis are "spinning," and those that aren't are "non-spinning."

Low-order gradients (first- and second-order) tend to affect the entire vertical profile of an NMR peak, while high-order gradients affect only the bottoms of peaks. Even-order gradients skew a peak asymmetrically, causing buildup of signal on one side of the peak or another, while odd-order peaks cause symmetrical line broadening. These frequency-domain effects correspond to characteristic distortions of the free induction decay signal, essentially the time-dependent NMR signal.

The integral of a particular sample peak is constant, but because peak asymmetry and line broadening cause the area under the curve to "leak" away from the frequency of peak signal, they cause a reduction of peak height. The basic idea of adjusting low-order shim coils, then, is to maximize the peak height of a standard, really strong singlet peak (TMS or CHCl₃ in deuterated acetone, for example). Higher-order shims are actually best adjusted using multiplets, because the bottom-widening effect is amplified by the closely spaced peaks. Ortho-dichlorobenzene is often used.

Gerald Pearson of Iowa has written an extremely informative (albeit a bit ancient) guide to shimming superconducting NMRs.

Sunday Evening Random Fact

Kentucky's only chemistry Nobel laureate, William Lipscomb, is a regular presenter at the Ig Nobel awards "for achievements that first make people laugh, then make people think." He's the guy on the far left in the picture.

He's now a professor at Harvard. See? People from Kentucky aren't all bad...

Metal Carbene Chemistry

I'm beginning to wonder if I chose the wrong school...Northwestern straight-up dominated Purdue this week to move to 6-1. Who would've thought? This has been a rough couple of weeks for sports fans in the C-U area, begun by the Cubs' abysmal playoff performance and capped by an embarrassing UI homecoming loss to Minnesota. At least Ron Zook seems to be taking it well!

Every organic chemist is at least mildly familiar with the chemistry of metal carbenes, complexes containing a metal-carbon double bond. Their propensity to do [2+2] cycloadditions and retro-[2+2] processes renders them ideal for olefin metathesis, a process that was deemed Nobel-worthy in 2005. Although a metal-carbon double bond may look somewhat mystical at first, demystifying metal carbenes is certainly possible.

Complexes with an electron-withdrawing heteroatom attached to the double bond are known as "Fischer carbenes." They behave, to a first approximation, like carbonyl compounds...the double-bound carbon is electrophilic, and the whole metal fragment just acts like a carbonyl oxygen! The substitution of Fischer carbenes is easily changed by adding a nucleophile through a transesterification-esque process. Deprotonation generates an enolate-type species that can perform aldol reactions, alkylation, Michael reactions, etc. Fischer carbenes are unique, however, for their ability to perform cyclopropanation of double bonds, a reaction that bare organic carbenes are famous for. One of the generally accepted mechanisms is somewhat odd; nucleophilic attack by the olefin on the carbene generates a zwitterionic intermediate reminiscent of the famous "tetrahedral intermediate" of carbonyl chemistry, then the cyclopropane is liberated by attack of the remaining carbon-metal bond on the positive olefin carbon. [2+2] reactions under similar conditions tend to give olefin metathesis products, not cyclopropanes, so choosing an adequate olefin partner is important.One of the most intriguing reactions of chromium carbenes is the Dotz reaction, the regioselective conversion of a chromium carbonyl vinyl carbene and an alkyne into a substituted phenol. Extensions of this reaction can generate highly substituted aromatic systems. There you go; the lesser known side of a giant of organic chemistry, the metal carbene!

On Teaching Chemistry: Volume 1

This is an excerpt from some of my recent insomnia-induced ramblings on teaching chemistry.

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What’s the best way to teach chemistry? This question has as many answers as there are students of chemistry. Educators pat themselves on the back for inventing terms like “visual learners,” “mathematically inclined,” and the like, but the truth is, the way one learns is a hopelessly complicated function of personality. Some are averse to learning outright; some gravitate towards it. Some require a deadly serious classroom environment to absorb information; others find themselves more comfortable in a light-hearted environment. Naturally then, presenting chemistry in a way that appeals to every student in a classroom is an exercise in futility.

This doesn’t mean that the development of a teaching philosophy should exclude considerations of the nature of your average, everyday college student, of course. Because most college students are living in the same campus environment, generalizations can be (and always are, at least subconsciously) made by educators concerning their students. Giving the edge to nurture over nature, we can look to the average college campus to draw conclusions about its average denizen, the American college student in the twenty-first century.

Today’s vast media landscape has a profound effect on college students. When advertising first caught hold in America in the first half of the twentieth century, some were suspicious that it was bringing about the slow stupefying of the American public (many still are). As the number of media outlets expanded through the 1900s, advertising was there every step of the way to finance the ventures of those excited about presenting their product to America through a novel medium. Print, radio, television, and now the Internet have thus become inundated with advertisements on a daily basis. College students, along with every other American equipped with a pair of good eyes, are now daily subjected to hundreds of messages attempting to persuade them to buy this or that product or service. How can professors, who are “selling” a “product” that won’t improve one’s sex life, provide entertainment, or make one’s life easier in any way, shape or form, compete with modern advertisers?

This begs the question of whether professors are responsible for “selling” their material in the first place. To a first approximation, the professor’s material has already been bought and paid for on the first day of class. Any failure of the student to learn the material is thus a bad economic decision on their part, and no reflection of the professor’s innate ability. And yet if this model were realistic, we’d have no way to distinguish good professors from bad ones! Teaching would become an enterprise quickly turned over by administrators to books, computers, or robots. Education is more than just the material presented—when you buy a book, you pay for material; when you pay for college, you pay to learn. And persuading a student to learn at all is the first step in giving them the education they paid for.

That said, you can’t fault a student for not caring about the overarching goals of a field of study. If after sufficient exposure a student doesn’t care about the fundamental nature of materials and how to transform them, even the world’s greatest chemistry professor can’t help him out. The interesting problem for the frustrated professor, on the other hand, is figuring out what exactly constitutes “sufficient exposure.” Getting bogged down in justifying one’s field during lecture is a sign of weakness that today’s students will, I must harshly admit, ravenously exploit; at the same time, diving directly into the esoterica of molecular structure and reactivity is unlikely to capture many imaginations. Where does the position of this equilibrium lie?

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More to come...