Quantum Mechanical Spin Magnetic Resonance Can Determine the Structure of Self-Assembled Molecules

The self-assembly of matter generates structures. The physical basis for living systems is informed by elucidating the structures and transformations of biomolecules. Quantum mechanics shows how structures are formed, but it also gives us the ability to measure the properties of such structures by using discrete quantum states, one of which is spin, a nonclassical, internal state having the SU(2) properties of angular momentum. Charged particles with nonzero spin possess magnetic moments that are degenerate in the absence of external magnetic fields. The degeneracy of spin states is lifted in the presence of external magnetic fields and the individual spin states can be monitored. We review the quark model origin of the magnetic moments of the proton and neutron. Through Curie’s law we investigate the magnetic moments of macroscopic samples of spins. The spin Hamiltonian is introduced in order to describe spin magnetic resonance in general and nuclear magnetic resonance (NMR) in particular. The chemical shift is defined in terms of the probability of locating an electron in the nucleus. We provide a Mathematica notebook simulating the Fourier transform NMR experiment. The motivation for the filtration of NMR signals is accomplished by deriving the convolution theorem. The weak magnetic coupling of nuclei to their environment and its attendant role in nuclear spin relaxation can be exploited to measure the structures and dynamics of native-state biomolecules. An example is given of its usage for the structural elucidation of antiviral peptides by means of multidimensional Fourier transform NMR.