Equivalence magnetic

In Chapter 3, Section 3.8, we discussed the idea of chemical equivalence. K two or more nuclei are equivalent by symmetry, they are said to be chemically equivalent. A plane of symmetry or an axis of symmetry renders nuclei chemically equivalent. 

Magnetically equivalent nuclei must be isochronous that is, they must have identical chemical shifts. 

Magnetically equivalent nuclei must have equal coupling (same J values) to all other nuclei in the molecule. 

A corollary that follows from magnetic equivalence is  

Magnetically equivalent nuclei, even if they are close enough to be coupled, do not split one another, and they give only one signal (for both nuclei) in the NMR spectrum. 

The molecule is rigid and the two nuclei are part of a W geometrical relationship. 

Electron pairs involved in the n component of multiple (i.e double or triple) bonds behave somewhat differently from those in single (a) bonds (Section 7.4.1). Not only are there differences in geometry, hybridization, and s character (Section 9.3), but 7i-bond electrons interact with (delocalize into) neighboring a molecular orbitals in the molecule (hyperconjugation). Because of this delocalization, 71-bond electrons can communicate nuclear spin information over distances further than three bonds. Several examples of this type of long-range coupling are listed in Table 9.5. 

The other situation where long-range coupling can be expected is when the orbitals connecting the two coupling nuclei (X and Y) are forced by a rigid molecular architecture to adopt a W relationship  

The bottom line is that observable long-range coupling (over more than three bonds) is possible, but only under limited circumstances. And even then, it usually involves relatively small coupling constants. 

In Chapter 4 we encountered the concept of equivalence. If two (or more) nuclei are related by virtue of an axis, center, or plane of symmetry, they are said to be symmetry (or chemically) equivalent. Furthermore, chemically equivalent nuclei precess at exactly the same frequency and hence give rise to one NMR signal (coupling notwithstanding). 

A more dramatic example occurs for an ortho-disubstituted benzene with two identical substituents X-0-C6H4-X (Fig. 2.28). In this case we can label the four adjacent protons on the benzene ring as Ha, Hb, H and Ha/ in that order. The two systems are very tightly connected because Hb and H have a large coupling (ortho or 3/hh = 8-10 Hz), similar to /ab and. This pattern is very distorted, and in many instances there is no recognizable underlying AB pattern. 

If a group or atom has a 60° dihedral angle with respect to a group or atom three bonds distant (e.g., from Hpj to Cp to C, to H, ) then Hpi and are said to be gauche to each other. If the dihedral is 180°, then the two are said to be trans. 

Two atoms are said to be chemically equivalent if they are in the same chemical environment, meaning that they are related by symmetry. Homotopic atoms are thus chemically equivalent. 

Two atoms are said to be magnetically equivalent if they have the exact same geometrical relationship to every other NMR-active atom 

Dihedral angle (O). The angle between two planes defined by four atoms connected by three bonds, the middle two of which share a common bond. 

Chemically equivalent. Atoms or functional groups in the same chemical environment. 

FIGURE 7.16 Examples of V W coupling in rigid bicyclic compounds. 

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FIGURE 5.17 A steroid ring skeleton showing several possible W couplings (V). 

248 Nuclear Magnetic Resonance Spectroscopy Part Three Spin-Spin Coupling 

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Canet D 1989 Construction, evolution and detection of magnetization modes designed for treating longitudinal relaxation of weakly coupled spin 1/2 systems with magnetic equivalence Prog. NMR Spectrosc. 21 237-91... 

Magnetorheological materials (fluids) are the magnetic equivalent of electrorheological fluids. In this case, the particles are either ferromagnetic or ferrimagnetic sohds that are either dispersed or suspended within a Hquid and the apphed field is magnetic (14). 

Magnetic equivalence ehemieally equivalent nuelei are magnetieally equivalent if they display the same eoupling eonstants with all other nuelear spins of the moleeule For example, the 2,2 -... 

The [12]annulene (96) has been prepared. In solution this molecule exhibits rapid conformational mobility (as do many other annulenes), so that above a certain temperature, in this case — 150°C, all protons are magnetically equivalent. However, at — 170°C the mobility is greatly slowed and the three inner protons are found at 85 while the nine outer protons are at 68. Annulene 96 suffers from hydrogen interference and is certainly not planar. It is very unstable and above —50°C rearranges to 97. Several bridged and dehydro[12]annulenes are known. 

The results for [16] annulene are similar. The compound was synthesized in two different ways, both of which gave 103, which in solution is in equilibrium with 104. Above -50°C there is conformational mobility, resulting in the magnetic equivalence of all protons, but at — 130°C the compound is clearly paratropic there are 4 protons at 10.565 and 12 at 5.35 5. In the solid state, where the compound exists entirely as 103, X-ray crystallography shows that the molecules are nonplanar with almost complete bond alternation The single bonds are 1.44-1.47 A and the double bonds are 1.31-1.35 A. A number of dehydro and bridged... 

Cross-relaxation The mutual intermolecular or intramolecular relaxation of magnetically equivalent nuclei, e.g., through dipolar relaxation. This forms the basis of nOe experiments. 

The pairs of fluorines in all of these molecules, except those in 1,1-difluoroethene, would also be magnetically equivalent. In order to... 

Any spin system that contains fluorine substituents that are chemically equivalent, but not magnetically equivalent is, by definition, second order. Such spectra can appear deceptively simple, or more commonly they can be amazingly complex. The fluorine and proton spectra of the simple, symmetrical compound, 1,1-difluoroethene exemplify the latter situation (Figures 2.5 and 2.6). 

The symmetry of this molecule makes the fluorines chemically equivalent, but not magnetically equivalent. Examination of the three staggered conformations of AA XX spin system (Fig. 2.8) helps one understand this situation. 

In spite of bearing nonequivalent fluorine substituents, both PF5 and all compounds of the type R-PF4 exhibit only a single signal in their fluorine NMR spectra. The observed magnetic equivalence of the fluorines in such compounds is believed to derive from a rapid intramolecular, pseudorotational exchange process that is too rapid, even at -80 °C, to allow distinction of the axial and equatorial fluorine atoms (Scheme 7.7). 

Moving on to multisubstituted aromatic systems, the real value of Table 5.4 soon becomes apparent. In dealing with such systems, it will not be long before you encounter a 1,4 di-substituted benzene ring. This substitution pattern (along with the 1,2 symmetrically di-substituted systems) gives rise to an NMR phenomenon that merits some explanation - that of chemical and magnetic equivalence and the difference between them. Consider the 1,4 di-substituted aromatic compound shown in Structure 5.1. 

In terms of chemical equivalence, (or more accurately, chemical shift equivalence) clearly, Ha is equivalent to Ha. But it is not magnetically equivalent to Ha because if it was, then the coupling between Ha and Hb would be the same as the coupling between Ha and Hb. Clearly, this cannot be the case since Ha is ortho to Hb but Ha is para to it. Such spin systems are referred to as AA BB systems (pronounced A-A dashed B-B dashed). The dashes are used to denote magnetic non-equivalence of the otherwise chemically equivalent protons. What this means in practise is that molecules of this type display a highly characteristic splitting pattern which would be described as a pair of doublets with a number of minor extra lines and some broadening at the base of the peaks (Spectrum 5.6). 

When several magnetically equivalent nuclei are present in a radical, some of the multiplet lines appear at exactly the same field position, i.e., are degenerate , resulting in variations in component intensity. Equivalent spin-1/2 nuclei such as 1H, 19F, or 31P result in multiplets with intensities given by binomial coefficients (1 1 for one nucleus, 1 2 1 for two, 1 3 3 1 for three, 1 4 6 4 1 for four, etc.). One of the first aromatic organic radical anions studied by ESR spectroscopy was the naphthalene anion radical,1 the spectrum of which is shown in Figure 2.2. The spectrum consists of 25 lines, a quintet of quintets as expected for hyperfine coupling to two sets of four equivalent protons. 

Equation (2.3) describes line positions correctly for spectra with small hyperfine coupling to two or more nuclei provided that the nuclei are not magnetically equivalent. When two or more nuclei are completely equivalent, i.e., both instantaneously equivalent and equivalent over a time average, then the nuclear spins should be described in terms of the total nuclear spin quantum numbers I and mT rather than the individual /, and mn. In this coupled representation , the degeneracies of some multiplet lines are lifted when second-order shifts are included. This can lead to extra lines and/or asymmetric line shapes. The effect was first observed in the spectrum of the methyl radical, CH3, produced by... 

Rapid rotation of the end groups and/or bridging hydrides is required to account for apparent magnetic equivalencies. The molecule does, however, have built in pseudo-cylindrical symmetry, i.e., one set of metal TT-type orbitals binds the bridging hydrides and the other set forms the TT-component of the metal-metal double bond. 

In the first row of (3.1) the terms denote the electron Zeeman (2 EZ), the hf (2 hft), the nuclear Zeeman (XNZ) and the nuclear quadrupole interaction (CXQ) of the central (metal) ion. The second row represents the hf, the nuclear Zeeman and the nuclear quadrupole interactions for sets of magnetically equivalent ligand nuclei. Each particular set is denoted by the index k, the individual nuclei of set k by kx. 

First order ENDOR frequencies of nonequivalent nuclei or of pairs of magnetically equivalent nuclei are given by Eq. (3.3) which is derived from the direct product spin base. To obtain correct second order shifts and splittings, however, adequate base functions have to be used. We start the discussion of second order contributions with the most simple case of a single nucleus and will then proceed to more complex nuclear spin systems. 

A typical nitrogen ENDOR spectrum of a copper complex (Cu(sal)2) with two magnetically equivalent 14N nuclei and with the EPR observer at mF = 0 (two sets of six ENDOR lines) is shown in Fig. 9. The pronounced splitting of the lines into a doublet structure is described by the term 4/Jai. The splitting of the more intense lines by 4/ a3 is not resolved (see B5). 

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