Figure 3.17

7.25 real samples, well over the minimum of two samples per cycle. The spectral width (SW) is 1/(2 x 180 jxs) or 2777.8 Hz. The high-frequency signal (from CHCl3) has a frequency of 375 Hz (one cycle = 1/375 s = 2.67 ms), and the low-frequency signal (from CH2Cl2) has a frequency of -11.5 Hz. The sign of the frequency can be determined only by examining the relative phases of the real and imaginary parts of the FID (quadrature detection). When you set the spectral reference using a standard such as TMS, you establish a third frequency scale (in addition to the absolute RF scale and the audio frequency scale relative to the reference frequency), which is the chemical shift scale in parts per million. Because the data were acquired on a 200 MHz spectrometer, an audio frequency of 200 Hz is 1 ppm away from the center of the spectral window. In this case the center of the spectral window is 5.37 ppm, so that the CHCl3 chemical shift is 5.37 + (375/200) = 7.24 ppm and the CH2Q2 chemical shift is 5.37 - (11.5/200) = 5.31 ppm.

The 99 data points shown in Figure 3.17 are part of a total FID of 8000 complex pairs (total number of data points NP = 16,000). Since a single data point takes 180 ^s (the dwell time) to acquire on average, 16,000 points require 16,000 x 180 ^s = 2,880,000 ^s or 2.88 s to acquire. This is called the acquisition time (Bruker: AQ; Varian: AT), and it represents the time required to record the entire FID once. This is not the time required for the entire spectrum to be acquired, since it does not include the relaxation delay and the pulse width, and it does not take into account the number of times the whole sequence is repeated (i.e., the number of scans or transients). In general,

Acquisition time

= number of points (real and imaginary) x time required per data point AT = NP x DW

But the dwell time (DW) is determined by the spectral width: DW = 1/(2 x SW). Substitution of 1/(2 x SW) for DW gives

Multiplying by (2 x SW) on both sides:

NP = 2 x SW x AT (Varian) TD = 2 x SW x AQ (Bruker) Number of data points = 2 x spectral width x acquisition time

This is the fundamental equation of NMR data acquisition (the mnemonic "swat" is useful). It tells us that the three parameters NP, SW, and AT (or TD, SW, and AQ in Bruker) are wedded by this equation such that changing any one of the three will require changing another to maintain the equality. For example, if we double the spectral width, either the number of points will double or the acquisition time will be cut by half. This is because the larger spectral width requires a faster sampling rate (half the dwell time) to assure that all of the frequencies in the spectral window are sampled at least twice in each cycle. With twice the sampling rate, you will either complete sampling the fixed number of points in half the time or keep the acquisition time constant and sample twice as many points. Bruker keeps the number of points constant and changes the acquisition time; Varian leaves the acquisition time unchanged and calculates a new value for the number of points. This can be frustrating because parameters you thought you had not changed are changing before your eyes!

The spectrum resulting from Fourier transformation of this FID is diagramed in Figure 3.18. The three frequency scales shown illustrate the progression in recording the FID from RF (actual frequency observed) to audio frequency (after subtracting out the reference RF signal, vr = 200.010 MHz in this example) to a referenced chemical shift scale (after setting the spectral reference of TMS). The Sum to Memory The sequence: (relaxation delay-pulse-acquisition of FID) is repeated a number of times (Fig. 3.19) with the acquired and digitized FID added each time to a "sum" FID stored in memory. The figure shows Bruker parameter names with Varian names in parentheses. The "recycle time" is the total time required to acquire one scan: relaxation delay + pulse width + acquisition time. The total experiment time is the

Figure 3.19

product of the recycle time, RD + PW + AQ (Varian: D1 + PW + AT), and the number of scans, NS (Varian: NT). Each individual FID contains the same signal (sum of decaying sine waves for all the sample nuclei), but the noise is different in each FID because it is random. The signal intensity increases directly with the number of repeats ("scans" or "transients"), but the noise increases with the square root of the number of repeats (Chapter 1, Fig. 1.6). This is like two people walking from the same starting point: one is sober and walks continuously in a straight line and the other is drunk and changes direction regularly in a random fashion. The distance from the start is directly proportional to the time for the sober one, but the drunk walk is less efficient, gradually drifting farther and farther from the start. The signal-to-noise ratio (S/N) is thus proportional to the number of scans divided by the square root of the number of scans:

This means that if you want to improve the S/N by a factor of 2, you will need to acquire four times as many scans. Since the total experiment time is proportional to the number of scans

Time required = NS (RD + PW + AQ) (Bruker) = NT (D1 + PW + AT)(Varian)

you will need four times as much time on the spectrometer to get a factor of 2 improvement in S/N.

Because in each repeated acquisition the observed data is simply added into the accumulated sum in memory, the size of the data file is not changed by increasing the number of scans. The individual FIDs are lost as their data values are added to memory. Consider a simplified example in which four FIDs are summed in memory. Although these calculations are always done in the computer with binary numbers, we will use decimal numbers in this example for clarity. Assume that the digitizer has only one decimal digit (typically there are 16 binary digits) available and that the memory allotment for each data point is two decimal digits (typically there are 16, 24, or 32 binary digits). Thus, the FID data coming out of the digitizer can range from a value of —9 to a value of +9, and the sum-to-memory value at each time point can range from —99 to +99. Although this list may be very long (16384

or 32768 data points in all for a 1D spectrum), we will consider only the first six real data points (DW = 40 jxs).

In this case the receiver would overflow ("clip") with any FID value greater than +9 or less than —9. Notice that the FID values for different scans at any given time point are roughly the same, since only the noise is different. At each time point the FID value is added to the running total in memory; for example, the 160 ^s time point of FID3 has a value of 3, which is added to the previous sum value of 5 to give the new sum value of 8. As more and more FIDs are acquired, the sum increases steadily and will overflow the number of digits allotted to it in memory after a certain number of scans (sum greater than 99 or less than —99). On Varian instruments this will stop acquisition, resulting in the error message "maximum number of transients accumulated." This will only occur on long (e.g., overnight) acquisitions and can be avoided by setting the variable DP (double precision) to Y (Yes). This doubles the number of digits used in memory (from 16 to 32 binary digits) and also doubles the size of the data file. On the Bruker a memory overflow (beyond the 24 or 32 binary digits reserved) results in the whole FID sum in memory being divided by 2; acquisition continues with the new FIDs being divided by 2 before being added in. In this way Bruker never has a problem with memory overflow, but accuracy is lost in the division process because 1 bit is discarded with each overflow.

The number of scans needed is primarily determined by the concentration of the sample and the desired signal-to-noise ratio. Another factor to consider is the phase cycle. Artifacts that are inherent in the electronics of the spectrometer can be canceled out by changing the phase of the RF pulse in a fixed pattern (e.g., 0°, 90°, 180°, and 270° in scans 1, 2, 3, and 4) and changing the phase of the receiver (by subtracting the signal instead of adding, or switching the real and imaginary parts) to follow this progression. The number of scans should be an integer multiple of the phase cycle length (a multiple of four for simple 1D acquisition) to assure optimal cancelation of artifacts. Some experiments, which subtract undesired signals from desired ones, will not work if the number of scans is set wrong. The phase cycle cancelation can also be screwed up if the first scan or two are acquired with the nuclei not in the "steady state" in terms of relaxation. Often the relaxation delay is not long enough for complete return of all spins to the equilibrium state, so the spins reach a steady state after a few scans where the degree of relaxation is always the same at the start of each scan. This steady state can be established by using dummy (or steady-state) scans. These are scans that include a relaxation delay, pulse, and acquisition just like a normal scan, but the data are not added into memory. The number of dummy (steady-state) scans is DS (Bruker) or SS (Varian). The Computer On newer (Bruker AMX, Varian Unity and newer) NMR spectrometers there is an acquisition computer that runs the NMR console and a data processing computer (usually a UNIX system purchased off the shelf from Sun Microsystems or Silicon Graphics) that communicates with the NMR console through an Ethernet (Internet-like) or SCSI (device interface) communication cable. When the data acquisition is complete, the FID data in the sum to memory is transferred to the acquisition computer in the console, and this data is then sent to the "master" (or "host") computer that the user is running. All the data processing—display on the screen, weighting functions, Fourier transform, phase correction, baseline correction, peak and integral analysis, and plotting—is done on this computer using the vendor's own software package.

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