Components: Number of Points [np] and Spectral Width [sw]

Performing a mathematical operation called the Fourier transformation (ft) on the FID (time-domain data) generates a spectrum which gives intensity of signals as a function of frequency (frequency-domain data), as shown in Figure II-3. This familiar NMR spectrum is characterized by

two important parameters, the spectrometer frequency (sf), and the spectral width (sw). As

shown in Figure II-4, at a spectrometer frequency of 299.957 Hz on the Unity+300, a spectral width (sw) of approximately 3000 Hz is required to observe 10 ppm (10 ppm x 300 Hz/ppm). At a spectrometer frequency of 399.964 MHz on the VXR-S 400, a spectral width (sw) of

approximately 4000 Hz is required to observe the same 10 ppm (10ppm x 400 Hz/ppm)

The spectral width sw in Hz, acquisition time at in seconds and the number of points np are related to each other by the following equation:

at = np/2sw equation 1

The digital resolution is related to acquisition time at as follows.

resolution = 1/at = 2sw/np equation 2

From equation 2, it follows that resolution or digital resolution is in the units of Hz/point. To obtain properly digitized NMR spectra, the digital resolution must be less than one-half the peak width at half-height of the narrowest peak in the NMR spectrum. Using this optimum digitization condition guarantees that each peak is represented by at least 3 points. For example, if the narrowest peak width is 0.7 Hz at half-height, the required digital resolution is less than 0.35 Hz. It follows that for a spectrometer frequency of 399.964 MHz, a spectral width of 4000Hz (10 ppm) and a digital resolution of 0.35 Hz/point, the number of points can be calculated from equation 2 as follows:

np = 2sw/resolution ; np = 2*4000/0.35 = 22857 points

Normally, the spectral width is fixed for a given NMR experiment and either the number of points or the acquisition time is modified to achieve the desired digital resolution. On both the Unity+300 and VXR-S 400 NMR spectrometers, it is best to modify acquisition time by setting at to the proper value to achieve the resolution (see equation 2). The spectrometer will automatically set the correct number of points np. The standard parameters for ¹H observation are as follows.

Unity+300 VXR-S 400

Spectral Width (sw) = 4000 Hz (13 ppm) Spectral Width (sw) = 5199.5 Hz (13 ppm)

Acquisition Time (at) = 4.096 sec Acquisition Time (at) = 4.099 sec

Number of points (np) = 32768 Number of Points = 42624

Digital Resolution = 0.24 Hz/point Digital Resolution = 0.24 Hz/point