## 2 General Principles of NMR  
NMR spectrometers are composed of three primary components: a superconducting magnet, a probe, and a sophisticated electronic system (console) managed through a workstation (Figure 1). The superconducting magnet generates a highly uniform and stable magnetic field to house the sample. Key sections such as the probe section and magnet bore should be labeled. The NMR console, a rectangular control unit, is typically linked to the magnet. The workstation, which is a computer or display for observing the NMR spectrum, connects to the console.  
Accordingly, Figure 2 depicts the internal components of a superconducting magnet for an NMR spectrometer, focusing on the cryogenic cooling system and the probe setup used in NMR experiments. The key parts of the NMR magnet shown are the vacuum chamber, liquid nitrogen (N\({}_{2}\)) tank, liquid helium (He) tank, and bore. The vacuum chamber is used to insulate the cryogenic system, helping maintain the very low temperatures necessary for the superconducting magnets to function. The liquid nitrogen (N\({}_{2}\)) tank holds liquid nitrogen, which is used as part of the cooling system to reduce the temperature inside the spectrometer and typically serves as the first stage of cooling. The liquid helium (He) tank provides a much lower temperature than liquid nitrogen, cooling the superconducting magnet to around 4 K. Ensuring the superconductivity of the magnet is vital for generating the powerful magnetic fields required for NMR. The central bore is where the sample is placed for analysis, allowing it to pass through the magnetic field produced by the superconducting magnet. The field coil, an integral part of the superconducting magnet, creates the magnetic field that interacts with the sample's nuclear spins. Inside the magnet's bore, the sample is encased by the probe system, which subjects it to both the magnetic field and radiofrequency pulses during the measurement process. The radiofrequency probe delivers pulses to excite the nuclei in the sample. It forms the core of the detection system in NMR. After the nuclei in the sample are excited by the radiofrequency probe, they emit signals. The recording coil detects these signals, which are then processed to produce the NMR spectra.  
The fundamental concept of nuclear magnetic resonance spectroscopy is illustrated in Figure 3. In this figure, atomic nuclei possess spins (depicted by arrows) that can align either parallel or antiparallel to the applied magnetic field. These alignments correspond to two distinct energy states: a lower energy state (spins aligned with the magnetic field) and a higher energy state (spins aligned against it). The energy difference between these states is represented as \(\Delta\)E. A radiofrequency (RF) pulse is applied to the system at the Larmor frequency, which corresponds to the energy gap between the two spin states of spin-1/2 nuclei only. When the RF pulse resonates with this frequency, nuclei in the lower energy state absorb the energy and transition to the higher energy state-a phenomenon known as resonance. After the RF pulse is turned off, the spins relax to their thermal  
Figure 1: A schematic diagram illustrating the overall layout of an NMR spectrometer and its principal components. Copyright (2021) Technology networks.  
Figure 2: Internal components of a superconducting magnet for an NMR spectrometer, including a detailed view of the probe. Copyright (2021) Technology networks.  
equilibrium corresponding to a Boltzmann distribution, which is here close to an equal distribution over all levels.