Spectral window center

The number of bands present in a spectral window and their centers of symmetry are pre-requisites to other signal processing procedures i. e. curve fitting. For in situ spectroscopic reaction studies, a set of tracks can be assigned which specify the centers of symmetry for all the bands. Since the bands move as a function of composition, the tracks in a matrix or AF %xv drift. 

The Pearson VII model contains four adjustable parameters and is particularly well suited for the curve fitting of large spectral windows containing numerous spectral features. The adjustable parameters a, p, q and v° correspond to the amplitude, line width, shape factor and band center respectively. As q —the band reduces to a Lorenzian distribution and as q approaches ca. 50, a more-or-less Gaussian distribution is obtained. If there are b bands in a data set and... 

Why would you need to move the spectral window upfield or downfield The lock system changes the magnetic field strength of the spectrometer (B0) slightly to center the 2H frequency of the solvent at the null point of the lock feedback circuit. Changing the field changes all of the resonant frequencies of the spectrum by the same amount, effectively moving the whole spectrum upfield or downfield by as much as 5 ppm when you... 

Note that we use A v to refer to the rotating-frame frequency (sometimes called the resonance offset). This is the difference between the Larmor frequency and the reference frequency v0 - vr. The above equation shows that the same physical law expressed in the equation on the left-hand side (precession rate is proportional to y and to B0) is operating in the equation on the right-hand side (resonance offset is proportional to y and to fires) in the rotating frame of reference, as long as we introduce the pseudofield. In the NMR spectrum, A v is the distance from the center of the spectral window to the NMR peak (Fig. 6.2), also represented as 2 in units of radians per second. If the peak is in the downfield half (left half) of the spectrum, the Larmor frequency is greater than the reference frequency ( v0 > vr) and we have a positive resonance offset (A v > 0). This corresponds to the motion of the net magnetization... 

The angle between the two vectors is 45° and the center position (chemical shift position of the doublet) has rotated 67.5° (360° x 225 Hz x 0.0008333 s) to find itself exactly between the two vectors. We will represent this position with a dotted line (Fig. 6.13, r = 1/(87)). Note that the H = a vector moves faster than the H = f vector because the NMR line that corresponds to it is farther from the center of the spectral window. 

There is, however, one very important assumption we have made that is not practical The carbon resonance was assumed to be on-resonance. Obviously, we cannot guarantee this for all carbon resonances in a spectrum because different13 C peaks have different resonant frequencies. What happens if the carbon chemical shift is not at the center of the spectral window The magnetization, which starts on the / axis, will precess in the x-y plane at an angular frequency An, where Av is the position of the 13C resonance relative to the center of the spectral window on a hertz scale. Components of the multiplet will rotate a little faster or a little slower relative to the central component for example, the three components of a triplet will rotate at angular frequencies Av +./, Av, and Av — J. This additional rotation due to the chemical shift (Av) will affect the phase of the magnetization when acquisition... 

These simple product operators precess in the x -y plane of the rotating frame at a frequency corresponding to the chemical shift in hertz relative to the center of the spectral window (the resonance offset Av = v0 — vr). The chemical shift frequency Av can also be represented as the angular velocity 2 in units of rad/s ( 2 = 2ttAv). Using 2 allows us to skip all the 2tt terms. 

In the acquisition of a simple ID spectrum, our goal is to excite all of the spins of a certain type (e.g., H) in the sample, regardless of chemical shift, at the same time. This requires a radio frequency pulse of very high power and short duration. The frequency of the pulse is adjusted to correspond to the resonance frequency at the center of the spectral window, so that it will be close to the resonance frequency of all of the spins in the sample. 

For a spin whose chemical shift is exactly at the center of the spectral window, we call the pulse an on-resonance pulse because the pulse (or carrier ) frequency is exactly equal to the resonant frequency (precession frequency or Larmor frequency vG) of the spin. During the pulse, we can use the vector model to show the B field (the pulse) as stationary in the rotating frame of reference, because the x and y axes are rotating about the z axis at exactly the frequency of the pulse. The position of the B field in the x -y plane depends on the phase of the pulse, which is just the place in the sine function (0-360°) where the radio frequency oscillation starts at the beginning of the pulse. This can be controlled by the spectrometer and is written into the pulse sequence by the user ... 

During the pulse, the spins do not experience the fix field alone, but rather an effective field fieff, which is the vector sum of the small residual field along the +z axis (fires) and the fii field in the x -y plane (Fig. 8.2, left). If the resonance is not far from the center of the spectral window, the fieff vector will tilt slightly out of the x -y plane and get slightly longer than B. ... 

Thus, we can avoid off-resonance effects by making B as strong as possible (highest power pulse possible, shortest duration) and by making v0 — vr as small as possible (avoid having resonances peaks very far from the center of the spectral window). 

There are many tricks to get around the problem, such as sandwich 180° pulses (e.g., 90 -180 -90 ) and broadband shaped pulses. Figure 8.4 (top) shows the inversion profile for a simple 180° pulse at the highest available power (fp = 28.4 p,s, yB l2it — 17.6 kHz). The profile is obtained using an inversion-recovery sequence (180°x — r — 90° ) with recovery time r = 0. The final 90° pulse frequency and the 13C peak (13CH3l) are both at the center of the spectral window, but the frequency of the 180° pulse is moved in 10 ppm (1500 Hz)... 

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