AX system

First-order spectra (mulliplels) are observed when the eoupling constant is small compared with the frequency difference of chemical shifts between the coupling nuclei This is referred to as an A n spin system, where nucleus A has the smaller and nucleus X has the considerably larger chemical shift. An AX system (Fig. 1.4) consists of an T doublet and an X doublet with the common coupling constant J x The chemical shifts are measured from the centres of eaeh doublet to the reference resonance. 

Figure 2.12. Two-dimensional (2D-)INADEQUATE diagram of 1-butanol (12) [ CDajzCO, 95% v/v, 25°C, 50 MHz, 128 scans, 128 experiments], (a) Contour plot with the AB systems of bonded C atoms on the horizontal axis (b) plots of the three AB systems of the molecule obtained from (a) (c) contour plot of the symmetrised INADEQUATE experiment showing the AB or AX systems of bonded C atoms in the HH COSY format (cross signals on the axes perpendicular to the diagonal)...

INADEQUATE Incredible natural abundance double quantum transfer experiment, segregates AB or AX systems due to homonuclear one-bond couplings of less abundant nuclei, e.g. 

Figure 7.3 One-dimensional COSYspectram for an AX system, (a) A common ID sjjectrum. (b) Selective excitation of spin A leads to a ID COSY spectrum with antiphase X lines and maximum transfer of magnetization from A to X. (Reprinted from Mag. Reson. Chem. 29, H. Kessler et at, 527, copyright (1991), with permission from John Wiley and Sons Limited, Baffins Lane, Chichester, Sussex P019 lUD, England.)...

A theoretical COSY spectrum for two coupled methine protons (AX system) is shown in Figure 9.44, the chemical shifts of the two protons being 8A and 8X ppm. The theoretical 1 -D proton spectrum is shown alongside each frequency axis, Ft and F2, the two scales being equal. Two types of... 

Fig. 12.3 Regular NMR (upper) and high-field PHIP-NMR spectrum (lower) of a two-spin AX system.

Figure 1.34 Energy level diagram for a two spin AX system, where A and X are inequivalent. Their corresponding NMR patterns are shown, (a) regular distribution (b) parahydrogen-derived distributions.

The sodium chloride structure, AX systems. Cubic Fm3m (Space Group 225) The sodium chloride or rock salt, NaCl, structure has a simple face-centered cubic unit cell (Figure 8) with alternating cations-anions along the three cubic axes. 

Ring inversion of the azepine ring between the two stable boat forms has been studied extensively by H NMR spectra Early work on 2-anilino-3//-azepine demonstrated that at 25 °C the methylene group appears as an AX system (7(HAHB-HX) 7 Hz), whereas at -75 °C in acetone- 6 an ABX system (7ab H Hz, 7ax 6 Hz, JBX 8 Hz) is evident... 

Let us now look at what happens when the chemical shift difference between the coupled nuclei is small and the simple patterns become distorted, i.e. non-first-order spectra. The simplest example of this is an AB spin system. Remembering that an AX system will give a pair of doublets, we will now look at a system in which the chemical shift difference is relatively small, so that the spin system is now described as... 

AB. The two doublets of the AX system now become distorted (with the amount of distortion from the AX spectrum increasing as the chemical... 

In the case of a heteronuclear AX system, e.g. a CH bond with A = 1H and X = 13C, the transverse magnetization dephases to the doublet components with v0 + J(H and v0 — 7CI, because of CH coupling (Fig. 2.38(a)). A 13C- H pair thus responds to the echo sequence shown in (Fig. 2.37 (a-c), provided the 180" pulse covers the range of carbon-13 shifts At time 2z after the initial pulse, a spin-echo builds up along the negative y axis. Subsequent Fourier transformation computes a negative signal (Fig. 2.38(a)). 

The INADEQUATE spectrum of a molecule collects all AB or AX systems due to carbon-carbon coupling. Identical 13C — 13C couplings localize carbon-carbon bonds, so that the carbon skeleton of the sample molecule can be derived. Complete analysis of an... 

The AB and AX systems of all 13C —13C bonds appear in one spectrum when the INADEQUATE pulse sequence (Fig. 2.48) is applied. Complete interpretation usually becomes difficult in practice due to signal overlapping, isotope shifts and AB effects (Section 2.9.4). A separation of the individual 13C— 13C two-spin systems by means of a second dimension would be desirable. It is the frequency of the double quantum transfer (d e) in Fig. 2.48 which introduces a second dimension to the INADEQUATE experiment. This double quantum frequency vDQ characterizes each 13CA — I3CX bond, as it depends on the sum of the individual carbon shieldings vA and vx in addition to the frequency v0 of the transmitter pulse located in the center of the spectrum if quadrature detection is applied [69c, 71] ... 

The net effect and the multiplet effect may occur together. Figure A 1.10 shows how excess population in the lowest level of our AX system, and a smaller excess in the highest level, will yield a superposition of a net and a multiplet effect, A + EjA. 

Figure 11.23 The change from a weakly coupled AX system to a strongly coupled AB system.

If we prefer to describe the bonding of a polyatomic molecule using localized two-center, two-electron (2c-2e) bonds, we can turn to the hybridization theory, which is an integral part of the valence bond method. In this model, for AX systems, we linearly combine the atomic orbitals on atom A in such a way that the resultant combinations (called hybrid orbitals) point toward the X atoms. For our BeH2 molecule in hand, two equivalent, colinear hybrid orbitals are constructed from the 2s and 2pz orbitals on Be, which can overlap with the two Is hydrogen orbitals to form two Be-H single bonds. (The 2p and 2py... 

As introduced in Chapter 3, for AX systems, the hybrid orbitals are the linear combinations of atomic orbitals on central atom A that point toward the X atoms. In addition, the construction of the sp" hybrids was demonstrated. In this section, we will consider hybrids that have d-orbital contributions, as well as the relationship between the hybrid orbital coefficient matrix and that of the molecular orbitals, all from the viewpoint of group theory. 

Before we conclude our discussion, we note that the INADEQUATE spectrum of caryophyllene oxide contains an uncommon phenomenon worth exploring. Carbons 6 and 7 of caryophyllene oxide nearly overlap in the 13C spectrum with each other and with the C-15 methyl we list their chemical shifts from Table 5.1 as 29.5 and 29.2 ppm. Because they are bonded to one another in caryophyllene oxide, they should show correlation in the INADEQUATE spectrum, but, instead of an AX system, we have an AB system with ZW/ being much less than ten. For this special case, we no longer expect two doublets whose midpoint lies on the diagonal instead, we predict that an AB multiple (see Chapter 3) should fall on the diagonal line itself. This prediction is borne out in Figure 5.19 where we find a cross peak directly below C-6 and C-7, and this cross peak intersects the diagonal line. 

---