F2 frequency domain

During the detection period denoted t2 (not the relaxation time T2 ) the NMR signal is captured electronically and stored in a computer for subsequent workup. Although detection occurs after evolution, the first Fourier transformation is applied to the time domain data detected during the t2 detection period to generate the f2 frequency axis. That is, the t2 time domain is converted using the Fourier transformation into the f2 frequency domain before the tj time domain is converted to the fj frequency domain. This ordering may seem counterintuitive, but recall that q and t2 get their names from the order in which they occur in the pulse sequence, and not from the order in which the data set is processed. 

F2 axis, f2 axis. Syn. (2 frequency axis. The reference scale applied to the f2 frequency domain. The f2 axis may be labeled with either ppm or Hz. 

An alternative to absolute value presentation has been proposed by Bax and Marion (1988). We have found mixed-mode processing, in which the data is absorptive in the (Fi) frequency domain and absolute-value-calculated in the proton (F2) frequency domain to provide a superior presentation of HMBC spectral data. Williamson et al. (1989) carried the idea of absorptive HMBC experiments a step further, demonstrating in the specific case of the antibiotic distamycin-A that fully phase-sensitive HMBC spectra may be recorded. 

In 2D NMR experiments, the FIDs are relatively short and with fewer data points, so dc correction is more difficult to carry out accurately. Phase cycling procedures are recommended whenever required to remove dc offsets before dc correction, which is carried out before the first (F2) Fourier transform. Since the data points in the transform arise from frequency-domain spectra, no dc correction is normally required (we expect to see unchanging dc components at Fi = 0). 

The first correlation is observed at 40 ppm ( 48 ppm relative to the transmitter position) in the Fi frequency domain at the F2 shifts of the anisochronous Hll methylene protons in Figure 13. Rather than an m/cH transfer across three bonds, instead a 2/ch transfer is observed, probably an effect of the oxygen of the oxepin ring being attached to Cl 2 as shown by 43. The Jcc long-range correlation in this case is to the C7 resonance. 

Strongly overlapping multiplets may be resolved by two-dimensional J,<5-spectros-copy2" 11G 118, where the first frequency domain (F,) contains coupling and the second frequency domain (F2) chemical shift information. The spectrum in Figure 2 (homonuclear [JH H, 6 ( H)]) demonstrates the use of this technique by showing unperturbed multiplets for ll signals. Second-order effects are principally not eliminated. Heteronuclear experiments [7uc,<5(13C)] are also common. 

In an ordinary Fourier transform NMR experiment the time-domain signal (the FID) is converted into a frequency-domain representation (the spectrum) thus a function of time, S(t2), is converted into a function of frequency, S(f2). The very simple basic idea of 2D NMR is to treat the period preceding the recording of the FID (known as the evolution period ) as the second time variable. During this period, tu the nuclear spins are manipulated in various ways. In the 2D experiment a series of S(t2) FID s are recorded, each for a different t u and the result is considered a function of both time variables, S(tu t2). A twofold application of the Fourier transformation (see Fig. 82) then yields a 2D spectrum, S(fi,f2), which has two frequency... 

FIGURE 5.6 Fourier transformation of a series of FIDs like the ones in Figure 5.5 (C) to give the frequency-domain spectrum as both a peak and as contours. The contour plot also shows a projection parallel to F2. 

The l3C— H COSY (HETCOR) experiment correlates l3C nuclei with directly attached (i.e., coupled) protons these are one-bond ( /CH) couplings. The frequency domains of FI (v,) and F2 (v2) are of different nuclei, and so there is no apparent diagonal or symmetry. 

We have a different spectrum of B for each t value, differing only in the value of the first term. For each column in the data matrix, we have a function of t for a fixed value of F2 (Fig. 9.14, right). Now the first term is the variable (function of t ) and the last term is a constant. Fourier transformation of the column converts the t FID into a spectrum of A in the indirect frequency domain F ... 

The term 2D NMR, which stands for two-dimensional NMR, is something of a misnomer. All the NMR spectra we have discussed so far in this book are two dimensional in the sense that they are plots of signal intensity versus frequency (or its Fourier equivalent, signal intensity versus time). By contrast, 2D NMR refers to spectroscopic data that are collected as a function of two time scales, tx (evolution and mixing) and t2 (detection). The resulting data set is then subjected to separate Fourier transformations of each time domain to give a frequency-domain 2D NMR spectrum of signal intensity versus two frequencies, Fx (the Fourier transform of the t time domain) and F2 (the Fourier transform of the t2 time domain). Thus, a 2D NMR spectrum is actually a three-dimensional data set ... 

The 13C spectrum of 2-chlorobutane, first encountered in Figure 7.1, consists of signals at 8 60.4 (CH), 33.3 (CH2), 24.8 (CHj), and 11.0 (CH3). In our experiment, we will first collect the i3C DEPT spectrum (using the pulse sequence in Figure 12.15), with the variable y pulse width set to zero degrees. The process is then repeated 18 more times, with ,. incremented by 10° each time. Finally, the data are subjected to Fourier transformation to give a frequency-domain data set with the F2 axis corresponding to 13C chemical shift and the F axis to y. 

The term two-dimensional (2D) NMR spectrum refers to a data set where signal intensity is a function of two frequency domains (Fj and F2). The corresponding FID data are collected as a function of two time domains (detection and evolution/mixing) and then Fourier transformed in each dimension. The resulting data are most commonly displayed in a contour format. 

FIGURE 2 The COSY spectrum has two frequency domains, FI and F2. Both of them represent one-dimensional H NMR spectra. The cross-peaks have coordinates in the form The coordinate indicates that the two protons /, and coupled. This coupling... 

The individual overlaps, <0i 10i(f)> and <02102(0) peak at different times and the product <010(t)) peaks at some intermediate time Therefore the observed progression has the spacing cu = in the frequency domain. Two or more displaced modes can conspire to give such a partial recurrence which is not expected of any mode alone. The compromise recurrence time is not just the average of fi and f2. The MIME frequency may be smaller than any of the individual frequencies, but it is usually between the highest and lowest frequencies. It cannot be larger than the highest frequency [91-93]. 

In 2D WIN-NMR the 2D time domain data matrix can only be split into rows corresponding to the acquired FID as shown in Fig. 3.13. In a 2D frequency domain data matrix both rows (f2) and columns (fl) can be extracted with the proviso that the column data is only available after the 2D Fourier transformation. Zero filling may cause the results obtained from the extraction of rows in the frequency domain to be different from the results obtained from the time domain. This is particular true for the fl dimension where the zero filling will effect the modulation in fl as well as altering the overall row numbering. 

Figure 5.15 Diagrammatic representation of HNCA FT 3D NMR correlation experiment involving multiple 90° and 180° pulses with signal observation and acquisition in time domain prior to fourier series transformation of time domain signal information SFiD(ti, t2, ts) into frequency domain (spectral intensity) information, Jnmr (fi, F2, fa).

Figure 5.17 Cartoon diagram to represent general structure of 4D correlation experiments. This is the same as for 3D correlation experiments (Fig. 5.14) except that an extra resonant population of heteroatom nuclei are involved in generation of transverse magnetisation (in time ts) and magnetisation transfer (during M3). Final pulse sequence generates transverse magnetisation in the Destination Nuclei S that is observed, acquired and digitised in time t/,. Fourier series transformation is used to transform time domain signal information Sfid (ti, ta, ts, 4) into frequency domain (spectral intensity) information, /NMR(fi, F2,...

Figure 5.18 Diagrammahc representahon of presentahon of data from FT 4D NMR correlahon experiments. In this representation, frequency domain (spectral) information, /nmr(Fi, F2, F3, Ft,) is plotted as a stack or cube of 2D NMR Jnmr(Fi, F4) contour plots, each plot resolved at a different value of f2 and also fs. Double frequency resolution is carried out when single frequency resolution fails to achieve proper signal resolution and/or unique and unambiguous assignment of resonance signals to resonating nuclei.

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