Spin-coupling

Karplus M 1959 Contact electron spin coupling of nuclear magnetic moments J. Chem. Phys. 30 11-15... 

Bax A and Freeman R 1981 Investigation of complex networks of spin-spin coupling by two-dimensional NMR J. Magn. Reson. 44 542-61... 

Figure Bl.13.8. Schematic illustration of (a) an antiphase doublet, (b) an in-phase doublet and (c) a differentially broadened doublet. The splitting between the two lines is in each case equal to J, the indirect spin-spin coupling constant.

The third alternative is a more robust, sensitive and specialized fonn of the first, in that only hydrogen nuclei indirectly spin-spin coupled to in a specific molecular configuration are imaged. In achieving selectivity, the technique exploits the much wider chemical shift dispersion of compared to H. The metliod involves cyclic transfer from selected H nuclei to indirectly spin-spin coupled C nuclei and back according to the sequence... 

Figure Bl.15.8. (A) Left side energy levels for an electron spin coupled to one nuclear spin in a magnetic field, S= I =, gj >0, a<0, and a l 2h)<(a. Right side schematic representation of the four energy levels with )= Mg= , Mj= ). +-)=1, ++)=2, -)=3 and -+)=4. The possible relaxation paths are characterized by the respective relaxation rates W. The energy levels are separated horizontally to distinguish between the two electron spin transitions. Bottom ENDOR spectra shown when a /(21j)< ca (B) and when co < a /(2fj) (C).

The most stable nuclear configuration of this system is a pair of H2 molecules. There are three possible spin coupling combinations for H4 corresponding to three distinct stable product H2 pairs H1 H2 with H3 H4, H1 H3 with H2 H4, and H1 H4 with H2 H3. Each H atom contributes one electron, the dot diagrams indicate spin pairing. The three combinations are designated as Hfl), HOT), and H(III), respectively. They may be interconverted via square transition states, Figure 2. 

Study the making or breaking of bonds, and change of spin couplings (e.g. dissociation of II2)... 

Another approach is spin-coupled valence bond theory, which divides the electrons into two sets core electrons, which are described by doubly occupied orthogonal orbitals, and active electrons, which occupy singly occupied non-orthogonal orbitals. Both types of orbital are expressed in the usual way as a linear combination of basis functions. The overall wavefunction is completed by two spin fimctions one that describes the coupling of the spins of the core electrons and one that deals with the active electrons. The choice of spin function for these active electrons is a key component of the theory [Gerratt ef al. 1997]. One of the distinctive features of this theory is that a considerable amount of chemically significant electronic correlation is incorporated into the wavefunction, giving an accuracy comparable to CASSCF. An additional benefit is that the orbitals tend to be... 

T orbital for benzene obtained from spin-coupled valence bond theory. (Figure redrawn from Gerratt ], D L oer, P B Karadakov and M Raimondi 1997. Modem valence bond theory. Chemical Society Reviews 87 100.) figure also shows the two Kekule and three Dewar benzene forms which contribute to the overall wavefunction Kekuleform contributes approximately 40.5% and each Dewar form approximately 6.4%. 

Unlike semiempirical methods that are formulated to completely neglect the core electrons, ah initio methods must represent all the electrons in some manner. However, for heavy atoms it is desirable to reduce the amount of computation necessary. This is done by replacing the core electrons and their basis functions in the wave function by a potential term in the Hamiltonian. These are called core potentials, elfective core potentials (ECP), or relativistic effective core potentials (RECP). Core potentials must be used along with a valence basis set that was created to accompany them. As well as reducing the computation time, core potentials can include the effects of the relativistic mass defect and spin coupling terms that are significant near the nuclei of heavy atoms. This is often the method of choice for heavy atoms, Rb and up. 

The methods listed thus far can be used for the reliable prediction of NMR chemical shifts for small organic compounds in the gas phase, which are often reasonably close to the liquid-phase results. Heavy elements, such as transition metals and lanthanides, present a much more dilficult problem. Mass defect and spin-coupling terms have been found to be significant for the description of the NMR shielding tensors for these elements. Since NMR is a nuclear effect, core potentials should not be used. 

The most common description of relativistic quantum mechanics for Fermion systems, such as molecules, is the Dirac equation. The Dirac equation is a one-electron equation. In formulating this equation, the terms that arise are intrinsic electron spin, mass defect, spin couplings, and the Darwin term. The Darwin term can be viewed as the effect of an electron making a high-frequency oscillation around its mean position. 

The proton-proton spin couplings (Thh) have been measured for a large number of thiazole derivatives. The results are shown in Tables 1-35 and 1-36. 

The C-H spin couplings (Jen) have been dealt with in numerous studies, either by determinations on samples with natural abundance (122, 168, 224, 231, 257, 262, 263) or on samples specifically enriched in the 2-, 4-, or 5-positions (113) (Table 1-39). This last work confirmed some earlier measurements and permitted the determination for the first time of JcH 3nd coupling constants. The coupling, between a proton and the carbon atom to which it is bonded, can be calculated (264) with summation rule of Malinovsky (265,266), which does not distinguish between the 4- and 5-positions, and by use of CNDO/2 molecular wave functions the numerical values thus - obtained are much too low, but their order agrees with experiment. The same is true for Jch nd couplings. 

One kind of 2D NMR is called COSY, which stands for correlated spectroscopy With a COSY spectrum you can determine by inspection which signals correspond to spin coupled protons Identifying coupling relationships is a valuable aid to establishing a molecule s connectivity... 

Section 13 19 2D NMR techniques are enhancements that are sometimes useful m gam mg additional structural information A H H COSY spectrum reveals which protons are spin coupled to other protons which helps m deter mining connectivity A HETCOR spectrum shows the C—H connections by correlating C and H chemical shifts... 

COSY (Section 13 19) A 2D NMR technique that correlates the chemical shifts of spin coupled nuclei COSY stands for... 

Froude number Fr Indirect spin-spin coupling J AS,... 

Separation factor a Spin-spin coupling constant AB... 

Table 7.56 One-Bond Carbon-Hydrogen Spin Coupling Constants 7.107...

Table 7.58 Carbon-Carbon Spin Coupling Constants 7.108...

Table 7.59 Carbon-Fluorine Spin Coupling Constants 7.109...

Table 7.66 Nitrogen-15 to Hydrogen-1 Spin Coupling Constants 7.115...

Table 7.67 Nitrogen-15 to Carbon-13 Spin Coupling Constants 7.116...

Table 7.71 Fluorine-19 to Fluorine-19 Spin Coupling Constants 7.118...

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