Uses of the term homonuclear

M. Deschamps, F. Fayon, S. Cadars, A.-L. RoUet, D. Massiot, H and F ultra-fast MAS double-quantum single-quantum NMR correlation experiments using three-spin terms of the dipolar homonuclear Hamiltonian, Phys. Chem. Chem. Phys. 13 (2011) 8024-8030. 

For two spins, we start with equilibrium I magnetization and follow the evolution of things as pulses and time delays are applied. Spins I and S are, in this case, homonuclear in opposition to the general literature convention of using them as heteronuclear spin symbols. One could perhaps use 11 and 12 but I find that with all of the terms generated it makes things clearer to... 

The values for the dipoles, polarizabilities, and hyperpolarizabilities of the H2 series were obtained using (a) a 16-term basis with a fourfold symmetry projection for the homonuclear species and (b) a 32-term basis with a twofold symmetry projection for the heteronuclear species. These different expansion lengths were used so that when combined with the symmetry projections the resulting wave functions were of about the same quality, and the properties calculated would be comparable. A crude analysis shows that basis set size for an n particle system must scale as k", where k is a constant. In our previous work [64, 65] we used a 244-term wave function for the five-internal-particle system LiH to obtain experimental quality results. This gives a value of... 

As R —> oo, the CSF energies (i H T>j) are more difficult to "intuit" because the O and o orbitals become degenerate (in the homonuclear case) or nearly so. To pursue this point and arrive at an energy ordering for the CSFs that is appropriate to the R — °° region, it is useful to express each of the above CSFs in terms of the atomic orbitals sx and sy that comprise o and o. To do so, the LCAO-MO expressions for o and o, ... 

The term metal-metal bonding is used when homoelement bonding involves the more electropositive element of a binary pair, e.g. HgCl contains homonuclear Hg2Cl2 units with Hg Hg bonds. In GaS also... 

Recently,30-31 it has been shown that the lowest Riemann sheet of the twovalued potential-energy surface for a homonuclear triatomic system can be represented by a function which shows the correct analytical structure when expanded in terms of the Dih coordinates (17), (18) near the conical intersection. Such a procedure has been suggested for the analytical continuation of the potential energy from the lower to the upper Riemann sheet.30 By carrying out a similar expansion for the LSTH potential, it is easy to show that it contains improper terms in the sense of ref. 30, thus invalidating its use for the analytical continuation of the energy to the upper Riemann sheet of the H3 surface. 

The most important examples of 2S states to be described in this book are CO+, where there is no nuclear hyperfine coupling in the main isotopomer, CN, which has 14N hyperfine interaction, and the Hj ion. A number of different 3E states are described, with and without hyperfine coupling. A particularly important and interesting example is N2 in its A 3ZU excited state, studied by De Santis, Lurio, Miller and Freund [19] using molecular beam magnetic resonance. The details are described in chapter 8 the only aspect to be mentioned here is that in a homonuclear molecule like N2, the individual nuclear spins (1 = 1 for 14N) are coupled to form a total spin, It, which in this case takes the values 2, 1 and 0. The hyperfine Hamiltonian terms are then written in terms of the appropriate value of h As we have already mentioned, the presence of one or more quadrupolar nuclei will give rise to electric quadrupole hyperfine interaction the theory is essentially the same as that already presented for1 + states. 

The simplest technique that enables phosphorus-phosphorus correlations for complex multi-component system and elucidation of structural constraints is the PDSD sequence.48 This experiment is relatively easy to set up however, the distances between spins cannot be established with satisfactory precision. One common way of determining distance type information using spin-7i NMR is based on the acquisition of the DQ filtered spectra as a function of the DQ mixing time.49 The recently introduced DQ homonuclear recoupling sequences based on C and/or R symmetry developed by Levitt and co-workers allows very precise analysis of intemuclear distances.50 The accuracy of distances obtained from these DQ experiments depends on the effective suppression of contributions to the spin Hamiltonian other than the required homonuclear dipolar coupling terms. 

For the heteronuclear two-spin system we found that we could create an average of the two X spin states by decoupling. Clearly such heteronuclear decoupling is inapplicable to the homonuclear two-spin system, but examination of the Hamiltonian of Eq. 7.6 suggests another approach—manipulate the spin system to make the two spin terms equal on the average so that pulse sequences. Prior to our discussion of pulse sequences in Chapters 9—11, we are not prepared to treat this rather complex process in detail, but a simple pictorial presentation gives the essential features. 

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