Evolution period

The evolution period tl is systematically incremented in a 2D-experiment and the signals are recorded in the form of a time domain data matrix S(tl,t2). Typically, this matrix in our experiments has the dimensions of 512 points in tl and 1024 in t2. The frequency domain spectrum F(o l, o 2) is derived from this data by successive Fourier transformation with respect to t2 and tl. 

Before the application of a pulse, only equilibrium magnetization exists, directed toward the z-axis corresponding to the zero coherence level for all coherence pathways. When the pulse is applied, two coherence levels, + 1 and —1, are created during the evolution period that evolve into M and respectively, where [Pg.74]

In the one-dimensional NMR experiments discussed earlier, the FID was recorded immediately after the pulse, and the only time domain involved (ij) was the one in which the FID was obtained. If, however, the signal is not recorded immediately after the pulse but a certain time interval (time interval (the evolution period) the nuclei can be made to interact with each other in various ways, depending on the pulse sequences applied. Introduction of this second dimension in NMR spectroscopy, triggered byjeener s original experiment, has resulted in tremendous advances in NMR spectroscopy and in the development of a multitude of powerful NMR techniques for structure elucidation of complex organic molecules. 

Figure 3.1 The various time periods in a two-dimensional NMR experiment. Nuclei are allowed to approach a state of thermal equilibrium during the preparation period before the first pulse is applied. This pulse disturbs the equilibrium ptolariza-tion state established during the preparation period, and during the subsequent evolution period the nuclei may be subjected to the influence of other, neighboring spins. If the amplitudes of the nuclei are modulated by the chemical shifts of the nuclei to which they are coupled, 2D-shift-correlated spectra are obtained. On the other hand, if their amplitudes are modulated by the coupling frequencies, then 2D /-resolved spectra result. The evolution period may be followed by a mixing period A, as in Nuclear Overhauser Enhancement Spectroscopy (NOESY) or 2D exchange spectra. The mixing period is followed by the second evolution (detection) period) ij.

The spectral width SWj relates to the frequency domain. With the variation of the evolution period tj, the intensity and phase of the signals... 

The next step after apodization of the t time-domain data is Fourier transformation and phase correction. As a result of the Fourier transformations of the t2 time domain, a number of different spectra are generated. Each spectrum corresponds to the behavior of the nuclear spins during the corresponding evolution period, with one spectrum resulting from each t value. A set of spectra is thus obtained, with the rows of the matrix now containing Areal and A imaginary data points. These real and imagi-... 

The matrix obtained after the F Fourier transformation and rearrangement of the data set contains a number of spectra. If we look down the columns of these spectra parallel to h, we can see the variation of signal intensities with different evolution periods. Subdivision of the data matrix parallel to gives columns of data containing both the real and the imaginary parts of each spectrum. An equal number of zeros is now added and the data sets subjected to Fourier transformation along I,. This Fourier transformation may be either a Redfield transform, if the h data are acquired alternately (as on the Bruker instruments), or a complex Fourier transform, if the <2 data are collected as simultaneous A and B quadrature pairs (as on the Varian instruments). Window multiplication for may be with the same function as that employed for (e.g., in COSY), or it may be with a different function (e.g., in 2D /-resolved or heteronuclear-shift-correlation experiments). 

Let us consider the magnetization vectors of a C nucleus of a CH group, for purposes of illustration. A 90 C pulse will bend the magnetization by 90° to the y -axis. During the subsequent evolution period, the magnedza-tion vector will be split into two component vectors under the influence of the coupling with the attached protons, and these vectors will oscillate in the x y -plane. 

Figure 5.3 (A) Many FIDs are recorded at incremented evolution periods, <, as...

Figure 5.5 shows the heteronuclear 2Dy-resolved spectrum of camphor. The broad-band decoupled C-NMR spectrum is plotted alongside it. This allows the multiplicity of each carbon to be read without difficulty, the F dimension containing only the coupling information and the dimension only the chemical shift information. If, however, proton broad-band decoupling is applied in the evolution period tx, then the 2D spectrum obtained again contains only the coupling information in the F domain, but the F domain now contains both the chemical shift and the coupling information (Fig. 5.6). Projection of the peaks onto the Fx axis therefore gives the Id-decoupled C spectrum projection onto the F axis produces the fully proton-coupled C spectrum.

Figure 5.6 If proton broad-band decoupling is applied in the evolution period, t, then the resulting 2D spectrum contains only chemical shift information in the F, domain, while both chemical shift and coupling information is present in the F domain. Projection onto the /-j-axis therefore gives the H-decoupled C spectrum, whereas projection along F. gives the fully coupled C spectrum.

Figure 5.7 (A) Pulse sequence for gated decoupled /-resolved spectroscopy. It involves decoupling only during the first half of the evolution period

Many variations of this experiment are known. Some of the pulse sequences used for recording heteronuclear 2D/resolved spectra are shown in Fig. 5.8. In a modified gated decoupler sequence (Fig. 5.8b), the decoupler is off during the first half of the evolution period and is svdtched on during the second half. Any C resonances that are folded over in the F, domain may be removed by employing the fold-over corrected gated decoupler sequence (FOCSY) (Fig. 5.8c) or the refocused fold-over corrected decoupler sequence (RE-FOCSY) (Fig. 5.8d). 

In the spin-flip method, 180° pulses are applied simultaneously to both H and C nuclei at the midpoint of the evolution period so that the C... 

Figure 5.10 (A) Selective spin-flip pulse sequence for recording heteronuclear 2D / resolved spectra. (B) Its effect on magnetization vectors. The selective 180° pulse in the middle of the evolution period eliminates the large one-bond coupling constants, /< ...

Figure 5.14 Pulse sequence for selective indirecty-spectroscopy. The three proton pulses at the center of the evolution period flip attached protons selectively, resulting in decoupling between distant and attached protons. (Reprinted from J. Magn. Reson. 60, V. Rutar, et ai, 333, copyright (1984), with permission from Academic Press, Inc.)...

The pulse sequence used in homonuclear 2D y-resolved spectroscopy is shown in Fig. 5.18. Let us consider a proton, A, coupled to another proton, X. The 90° pulse bends the magnetization of proton A to the y -axis. During the first half of the evolution period, the two vectors (faster... 

Fiffire 5.38 Pulse sequence for delayed COSY—a modification of the COSY experiment. The fixed delays at the end of the evolution period t and before the acquisition period <2 allow the detection of long-range couplings between protons. 

The basic pulse sequence employed in the heteronuclear 2D shift-correlation (or HETCOR) experiment is shown in Fig. 5.40. The first 90° H pulse bends the H magnetization to the y -axis. During the subsequent evolution period this magnetization processes in the x y -plane. It may be considered to be made up of two vectors corresponding to the lower (a) and higher (/3) spin states of carbon to which H is coupled. These two... 

The delay is generally kept at Vi x> The coupling constant Jcc for direcdy attached carbons is usually between 30 and 70 Hz. The first two pulses and delays (90J -t-180 2-t) create a spin echo, which is subjected to a second 90J pulse (i.e., the second pulse in the pulse sequence), which then creates a double-quantum coherence for all directly attached C nuclei. Following this is an incremented evolution period tu during which the double quantum-coherence evolves. The double-quantum coherence is then converted to detectable magnetization by a third pulse 0,, 2, and the resulting FID is collected. The most efficient conversion of double-quantum coherence can... 

Precession A characteristic rotation of the nuclear magnetic moments about the axis of the applied magnetic field Bo at the Larmor frequencies. Preparation period The first segment of the pulse sequence, consisting of an equilibration delay. It is followed by one or more pulses applied at the beginning of the subsequent evolution period. 

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