Short Theory of Nuclear Magnetic Resonance Spectroscopy

Nuclear magnetic resonance spectroscopy (NMR) is one of the three foundational techniques in structural biology, alongside X-ray crystallography and cryo-electron microscopy (cryo-EM). It is an exceptionally versatile method capable of determining new molecular structures and measuring the dynamics of biological macromolecules and their complexes across various time scales. However, a key limitation of NMR spectroscopy is its restriction on the size of the molecules it can effectively analyze. It works by detecting the nuclei of certain atoms and providing information about their environment within the molecule. Only nuclei with odd atomic and mass numbers, such as the 1H isotope of hydrogen, the 13C isotope of carbon, the 15N isotope of nitrogen, the 19F, and the 31P, can be observed using NMR because they have a property called spin.

The spinning of a proton creates a magnetic field called a magnetic moment. When a proton is placed in an external magnetic field, either the proton’s magnetic moment aligns with it or against the field. Protons aligned with the field are in a lower-energy state (alpha-spin state), while those aligned against it are in a higher-energy state (beta-spin state). When radiation of a specific frequency is applied, it can change the orientation of these protons' magnetic moments, causing them to "flip" between states, a process known as "resonance." The energy released during this flip is detected and used to provide information about the molecule.

However, protons might not absorb the radiation at the same frequency as their environment affects it. If a proton is not surrounded by more electronegative atoms, such as oxygen, the electrons shield it from the external magnetic field, and we say the nucleus is shielded. Contrary to this, when a proton is surrounded by more electronegative atoms, the electrons will be pulled from the more electronegative atom, and the proton will become deshielded. Consequently, if a nucleus is shielded from the external magnetic field, it will require a lower frequency (lower energy) to flip its spin; if not, then higher energy will be required to flip the spin. The reason for this is that the felt magnetic field by a naked nucleus is greater than the nucleus surrounded by electrons, thereby making the gap between the α and β spins larger (high energy). The chemical environment of the hydrogen nuclei is revealed by this property [1], [2].

In the NMR spectrum, the value of the magnetic field gets lower to the left, which is called downfield, and gets higher to the right, which is called upfield. Shielded protons appear upfield, while deshielded protons appear downfield. TMS (tetramethylsilane) is one of the most shielded molecules, and all protons of it are equivalent; thus, TMS is used as a reference compound to set the scale of the spectrum, thereby neglecting the power of different magnets, which affect the resonance frequency. Therefore, peaks are located in the spectrum relative to the reference TMS, and the location of this peak is called its chemical shift, which is given in units of parts per million (ppm). Electron density around a nucleus and diamagnetic anisotropy are factors that affect the chemical shift the most. Electron-shielded nuclei have a smaller chemical shift than deshielded nuclei. Diamagnetic anisotropy is caused by pi electrons. Pi electrons in aromatic rings circulate and thereby create a local magnetic field under an external magnetic field. Hydrogens near the center of an aromatic ring will be shielded and have a lower chemical shift as the magnetic field induced by the inside of the ring opposes and weakens the external magnetic field. This means that the magnetic field induced by the outside of the ring makes the external magnetic field stronger; thereby, hydrogens near the outside of the ring will be deshielded and will have a higher chemical shift [1].

The NMR Experiment
NMR spectroscopy equipment includes a radio-frequency generator, a stable magnet, a sample holder, a sweep generator, an amplifier, a detector, and a recorder. The sample is put into a long thin glass tube. The NMR tube is positioned in a spinner in a way that the sample would sit within the probe's detection coil. When the spinner is lowered into the magnet, protons align with the generated radio frequency. The generated radio frequency is perpendicular to the receiver coil. The sample is lowered carefully into the center of the magnet using an air lift at a certain temperature. The resonance frequency of deuterium is locked by making slight adjustments to the magnetic field to ensure the resonance frequencies do not drift. Because the frequency of resonance is affected by the varying strength of the magnetic field, even a small change lowers the quality of the data. After locking the magnet, a homogeneous magnetic field across the sample is ensured by the process called shimming to get a good quality NMR spectrum. Shimming is achieved by applying different electrical currents to the shim coils located in the bore of the magnet. In the next step, the NMR probe is tuned so that the coils would transmit the RF pulses to the relevant nucleus and collect the NMR signals efficiently. Also, maximum RF energy transfer between the coil and the sample can be enabled by matching the impedance of the coil/sample combination. The resonance signal is amplified and recorded, producing a graph with absorption on the y-axis and magnetic field on the x-axis.

Imino Noesy NMR
In 1D NMR, the basic idea is to give a pulse and observe free induction decay. The pulse is 90°, and we get an amplitude. The time domain (time dimension) of this amplitude is then transferred to the frequency dimension in the units of ppm by Fourier transformation. Therefore, we just have one time dimension in 1D NMR.

In 2D NMR, we have two-time dimensions with the addition of varying the length of time after the first pulse. The system evolves the first pulse, and the ongoing signal gives a 2D spectrum with dimensions of F1 and F2. Nuclear Overhauser Effect Spectroscopy is a 2D NMR method to identify nuclear spins that are in close proximity to each other and to measure their cross-relaxation rates. In this method, the sequence consists of the first 90° pulse, evolution, second pulse, mixing time, third pulse, and detection of signal. The first pulse converts the magnetization to the z-plane from the transverse plane. After a short delay of time, the second pulse generates the initial condition for the mixing period in which there is a cross-relaxation between nuclei in close proximity, and the last third pulse creates transverse magnetization which can be detected. In the obtained NOESY spectrum, cross peaks give rise to information about which protons are close to each other. Therefore, NOESY is the determination of the relative orientation of atoms in a molecule [3].

Sources
1. Jonathan Clayden, Nick Greeves, Stuart Warren, Peter Wothers, Organic Chemistry, Oxford University Press USA, 2000, 56-60.

2. Arthur Winter, Organic Chemistry I For Dummies, For Dummies Wiley, 2014, 267-289.

3. 2D NMR Introduction, LibreTexts (https://chem.libretexts.org/ Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps /Supplemental_Modules_(Physical_and_Theoretical_Chemistry) /Spectroscopy/Magnetic_Resonance_Spectroscopies /Nuclear_Magnetic_Resonance/NMR:_Experimental /2D_NMR/2D_NMR_Introduction)

4. Glenn Facey, https://u-of-o-nmr-facility.blogspot.com/2008/03/2d-nmr.html