EPR, NMR and Condensed Matter

It is interesting that now we've looked at more of the electron interactions, there is actually quite a bit of overlap between PHYS4030 and my Honours project (a nice change!).

The first thing that comes to mind is the description of pulsed-experiment magnetisation using the Bloch equations: since one detects magnetisation in a resonance measurement, these are quite crucial equations to describe the problem! Of course, this is possible because an ensemble of electrons/nuclei in a sample can be looked at as an crystal and always acts as if it's in some kind of 'lattice' anyway with the nearby electrons/nuclei.

And, of course, the equations describing the energy of a system of electrons in a magnetic field is very similar to the Hartree-Fock method of generating solutions. For my project we are looking at biradicals, with each radical electron near a nitrogen atom. The Hamiltonian is a bit hard to write here but essentially looks like this:

H = 2*hbar.gamma.(S.B) + 2*hbar.gamma2.(I.B) + dipolar coupling terms between the nitrogens and the electrons + scalar coupling terms between the nitrogens and the electrons + an exchange term between the two electrons + an exchange term between the two nitrogens.

As you can see, even with words this equation gets pretty complex! The hbar.gamma.(S.B) and hbar.gamma2.(I.B) terms are the Zeeman interaction of the respective particle and the magnetic field B (S.B is a dot product) and you get two of them because there are two electrons and two nitrogens in my case; this bit is already simplified because we assume the electrons and nitrogens are completely symmetrical on either side of the molecule, which is not necessarily the case because the molecule changes shape in solution. The dipolar and scalar coupling terms between the electrons and the nuclei also have 4 terms each for the possible pairs (although some of these terms will be small compared with the other terms), and are known as hyperfine couplings in spectro-speak. For my project, we are essentially investigating how the changes in the exchange couplings of the electrons affect the energy.

After all of this, you get your experimental spectrum as a squiggly line showing the resonance frequency of all of these features! So you do see the energies directly, but they're all jumbled together with noise—this is why I spend so much time in the lab! It takes about 3'10" to do a 1 scan and you need about 100 for reasonable signal-to-noise ratio!

So, the reach of Felix Bloch was far beyond simple condensed matter! It's also pretty amazing that Albert Overhauser (I think his first name was Albert) and a few other guys you can look at on Wikipedia essentially derived all of this stuff in the 60s, and now almost every chemistry lab uses NMR or EPR every week (even every day if they're fast at synthesising stuff)!