NMR spectrometers consist of a strong magnet, a radiofrequency transmitter, and a detector attached to a computer console for recording spectra of samples containing NMR-active nuclei. In first-generation NMR instruments called continuous-wave spectrometers, the resonance frequencies of the nuclei are determined by frequency-sweep or field-sweep methods. The magnetic field strength is fixed and the rf signal is swept in the former, while the radiofrequency signal is fixed and the magnetic field...

A pulse is a short burst of radio waves distributed over a range of frequencies that simultaneously excites all the nuclei in the sample. Upon passing a radio frequency pulse along the x-axis, the nuclei absorb energy corresponding to their Larmor frequencies and achieve resonance. This shifts the net magnetization vector from the z-axis toward the transverse plane. This angle of rotation of the magnetization vector, or the flip angle, is proportional to the duration and intensity of the pulse.

In an NMR sample, precise measurement of the absolute absorption frequencies of nuclei is difficult. A standard internal reference compound is added, and the frequency difference between the reference signal and sample signals is measured.
The internal reference compound generally used in NMR spectroscopy is tetramethylsilane (TMS). TMS is preferred because it is chemically inert, soluble in NMR solvents, and easily removable. Also, the highly shielded methyl protons in TMS yield an intense...

The position of the absorption signal of a sample is reported relative to the position of the signal of tetramethylsilane (TMS), which is added as an internal reference while recording spectra. The difference between the absorption frequencies of the sample and TMS (in Hz) is divided by the spectrometer operating frequency (in MHz) to obtain a dimensionless quantity called the chemical shift. It is reported on the δ (delta) scale and expressed in parts per million.
For instance, the proton...

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...