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Jacob Schaefer was a physical chemistry researcher who developed methods for studying complex solid materials using solid-state nuclear magnetic resonance. After his 1964 doctorate he worked at Monsanto, then joined Washington University in 1986. His contributions included cross-polarization magic-angle spinning with Edward O. Stejskal and rotational-echo double resonance with Terry Gullion.^[ref]

The materials in the 1976 cross-polarization magic-angle spinning demonstration made the method's reach tangible. They included polysulfone, ebony wood and a cylinder cut from an ivory billiard ball. Schaefer's father and grandfather were billiards champions; a familiar object became a specimen for measuring carbon-13 responses in a complex solid. Combining polarization transfer with magic angle spinning made weak and broadened solid-state responses much more accessible.^[ref]

REDOR addresses another measurement problem. Magic angle spinning averages interactions that broaden spectra, but some of those interactions carry structural information. Appropriately timed radio frequency pulses restore sensitivity to NMR dipolar coupling between different nuclear species. Comparing a reference echo with a deliberately dephased echo then probes that coupling, with structural interpretation supplied by a suitable spin model.^[ref]

Schaefer reproduced a laboratory record from 29 May 1987 in which Gullion measured carbon-13 spectra of nitrogen-15-labelled alanine. Carbon remained at natural isotopic abundance. The record compares full and dephased echoes at a carbon frequency of $50.3\mathrm{MHz}$, using magic angle spinning at $3.2\mathrm{kHz}$ and 10 rotor periods of dipolar evolution. The corresponding duration isThe reproduced record does not give sample mass or number of accumulated scans. Later use of XY8 NMR phase cycling suppressed pulse-train amplitude and phase errors, enabling measurements of weaker couplings over longer pulse trains.^[ref]

Rotational-echo double resonance, or REDOR, is a solid-state nuclear magnetic resonance method that reintroduces sensitivity to NMR dipolar coupling during magic angle spinning. Rotor-synchronized pulses acting on a second nuclear species interrupt the averaging of the interaction. Comparison with a matched reference echo reveals coupling-dependent dephasing; dipolar recoupling makes a normally suppressed interaction experimentally useful.^[ref]

Write $S_0$ for the full reference echo and $S$ for the echo measured with the dephasing pulse pattern. A common normalized readout isFor invented matched signals $S_0=100$ and $S=60$, the dephasing is0.40. This does not mean that40 percent of the nuclei are missing. The pulses change the coherent echo, and converting its attenuation into an internuclear distance requires an appropriate spin model and experimental calibration.

The early alanine record reproduced in Jacob Schaefer's retrospective is unusually concrete. It compares full and dephased carbon-13 echoes of nitrogen-15-labeled alanine, recorded by Terry Gullion on29May1987 at a carbon resonance frequency of50.3MHz. Dipolar evolution lasted ten rotor periods at3.2kHz spinning. The authors used an isolated-pair calculation and an isotropic powder average to choose pulse placements.^[ref]

An original timing calculation gives $10/(3200{\mathrm{s}}^{-1})=3.125\mathrm{ms}$ for those ten rotor periods. That is a duration derived from the reported settings, not a newly inferred pulse width. The retrospective explicitly says the sample weight and accumulated scan count were not recorded, so those details cannot be reconstructed from its spectrum.^[ref]

Because the dephasing experiment can involve many refocusing pulses, NMR pulse errors can mimic or obscure coupling-dependent changes. XY8 phase routing helped control off-resonance distortions in long REDOR pulse trains. Reference matching, pulse quality and a suitable model remain necessary even when the normalized dephasing is easy to calculate.^[ref]

Terry Gullion is a physical chemist whose work develops solid-state nuclear magnetic resonance. With Jacob Schaefer, he developed rotational-echo double resonance, or REDOR, which restores sensitivity to heteronuclear NMR dipolar coupling in a spinning solid. His first-person retrospective describes the method as a way to measure couplings and infer structural information.^[ref][ref]

Institutional profile: www.chemistry.wvu.edu/directory/professors/terry-gullion

The physical problem is that magic angle spinning suppresses interactions that broaden spectra but can also remove useful structural information. REDOR uses controlled pulse timing to reintroduce a selected interaction. A paired acquisition compares a reference signal $S_0$ with a dephased signal $S$ under matched conditions. Varying the evolution time supplies more information than a single intensity difference.^[ref]

For an original arithmetic example, $S_0=100$ and $S=72$ give fractional dephasing $(S_0-S)/S_0=0.28$. This does not directly mean that 28 percent of the atoms occupy a particular state. Structural inference requires an appropriate spin model, evolution times and controls on the acquisition. The example shows the inferential step that Gullion's method makes possible: a controlled change in a spectrum can encode an otherwise hidden interaction.