NMR Without Magnets

Nuclear Magnetic Resonance (NMR) is an important tool in analyzing the structure of organic compounds, and, its relative, Magnetic Resonance Imaging (MRI) is used in medical diagnosis.

Nuclear Magnetic Resonance (NMR) depends on the fact that many atomic nucleii possess spin and their own dipolar magnetic fields. During conventional NMR spectroscopy these nuclei are lined by a strong external magnetic field, then knocked off axis by a burst of radio waves. The rate at which each kind of nucleus then wobbles, or precesses, is unique and identifies the element. For example, a hydrogen-1 nucleus (a lone proton) precesses four times faster than a carbon-13 nucleus (6 protons and 7 neutrons).

Being able to detect these signals depends first of all on being able to detect net spin. If the sample were to have as many spin-up nuclei as spin-down nuclei it would have zero polarization, and the signals would cancel out. But since the spin-up orientation requires slightly less energy, a population of atomic nuclei usually has a slight excess of spin ups, if only by a few in a million.

The lines in a typical NMR spectrum reveal more than just different elements. Electrons near precessing nuclei alter their precession frequencies and cause a "chemical shift", moving the signal or splitting it into separate lines in the NMR spectrum. This is the principal goal of conventional NMR, because chemical shifts point to particular chemical species; for example, even when two hydrocarbons contain the same number of hydrogen, carbon, or other atoms, their signatures differ markedly according to how the atoms are arranged. But without a strong magnetic field, chemical shifts are insignificant.

The down-side is that NMR relies on huge, very low-temperature, superconducting magnets so it is an expensive and non-portable tool. Scientists at Berkeley Lab and UC Berkeley have shown that chemical analysis with NMR is practical without using any magnets at all.

Firstly the scientists have increased the net spin orientation via hyperpolarization which increases the proportion of parahydrogen (in which the proton in each hydrogen nucleus spins in the opposite direction resulting in spin 0) in relation to orthohydrogen (in which the proton in each hydrogen nucleus spins in the same direction resulting in spin 1).

Second, the scientists use optical-atomic magnetometers instead of the huge superconducting magnets used in conventional NMR. Optical-atomic magnetometers measure whole atoms, not just nuclei. An external magnetic field is measured by measuring the spin of the atoms inside the magnetometer's own vapor cell, typically a thin gas of an alkali metal such as potassium or rubidium. Their spin is influenced by polarizing the atoms with laser light; if there's even a weak external field, they begin to precess. A second laser beam probes how much they're precessing and thus just how strong the external field is.

Third, the scientists use J-coupling, instead of chemical shift, for the chemical analysis because you cannot detect chemical shift in a zero field. Discovered in 1950 by the NMR pioneer Erwin Hahn and his graduate student, Donald Maxwell, J-coupling provides an interaction pathway between two protons (or other nuclei with spin), which is mediated by their associated electrons. The signature frequencies of these interactions, appearing in the NMR spectrum, can be used to determine the angle between chemical bonds and distances between the nuclei. You can even tell how many bonds separate the two spins.

Experiments to date have been performed on molecules that are easily hydrogenated and therefore easily hyperpolarized. Beginning with styrene, a simple hydrocarbon, J-coupling has been measured for a series of hydrocarbon derivatives including hexane and hexene, phenylpropene, and dimethyl maleate, important constituents of plastics, petroleum products, even perfumes.

Reference
T. Theis, P. Ganssle, G. Kervern, S. Knappe, J. Kitching, M. P. Ledbetter, D. Budker, A. Pines. Parahydrogen-enhanced zero-field nuclear magnetic resonance. Nature Physics, 2011; DOI: 10.1038/nphys1986

Further Reading
¹H NMR Spectroscopy
Quantum Numbers
Isotopes

Study Questions

1. For conventional ¹H NMR, define the following terms:
   • chemical shift
   • magnetic coupling or spin-spin coupling
   • J-coupling
   • internal standard
2. In conventional ¹H NMR, what is the purpose of an internal standard such as TMS?
   
   
3. In conventional ¹H NMR, what does the number of signals tell you about a sample molecule?
4. In conventional ¹H NMR, what does the relative area of each signal tell you about the sample molecule?
5. In conventional ¹H NMR, what does the relative position of the signals tell you about the sample molecule?
6. For an atom of hydrogen-1, given the possible value(s) for the spin quantum number, m_s.
7. Consider a diatomic molecule of hydrogen, H₂. For each possible spin quantum number for each hydrogen atom, draw a representative diagram using ↑ to represent up-spin and ↓ to represent down-spin.
   
8. For each diagram above, add the values of the spin quantum number for each nucleus in the molecule to find the net spin on the molecule.
9. How many parahydrogen and orthohydrogen molecules did you draw?