Principal axis values

The first reports showing 31P NMR study of nucleic acids were published in the 1970s.82 Terao et al. determined the size of the principal axis values of the 31P CSA tensor for RNA molecules (polyU, polyG, polyC, polyA and tRNA). Very recently, Rinnenthal et al.83 have reported the 31P NMR data for RNA cUUCGg tetraloop model hairpin prepared under various salt and hydration conditions. The experimental results were found to be consistent with theoretical DFT calculations published by Sklenar and co-workers.84... 

The functions I accordingly correspond to an oblate antiprism and II to a prolate antiprism. There is a simple explanation for the difference in orientation of the principal axes. The theorem that the sum of the squares of the values of the functions for a complete set (a subshell) is constant requires that the shape parameters vary in a satisfactory way with change in orientation of the principal axes. For the prolate set (II) the maximum value in the plane orthogonal to the principal axis of the function lies in the basal plane of rhe antiprism, and thus serves to increase the electron... 

Figure 9.4. The orientation of structural entities (rods) in space with respect to the (vertical) principal axis and the values of for, the uniaxial orientation parameter (Hermans orientation function) for (a) fiber orientation, (b) isotropy, (c) film orientation...

The form of the g tensor depends upon the choice of orthogonal axes. If the axis system is chosen along the molecular symmetry axes, the tensor contains only diagonal terms with the off-diagonal terms being zero. Conveniently, the principal g values derived from the polycrystalline spectrum are just those of a diagonalized matrix, i.e.,... 

One should realize, however, that for polycrystalline samples it is not possible to assign one of the principal g values to a particular molecular axis on the basis of experimental data alone. Such assignments usually are rationalized from theoretical considerations. 

The principal axis of the cone represents the component of the dipole under the influence of the thermal agitation. The component of the dipole in the cone results from the field that oscillates in its polarization plane. In this way, in the absence of Brownian motion the dipole follows a conical orbit. In fact the direction of the cone changes continuously (because of the Brownian movement) faster than the oscillation of the electric field this leads to chaotic motion. Hence the structuring effect of electric field is always negligible, because of the value of the electric field strength, and even more so for lossy media. 

It is observed that when the field is applied toward the central atom (say from the line joining the two H atoms to the O atom along the principal axis, in case of H20) of all the species, and if the central atom is more electronegative, the chemical potential and hardness decrease with increasing field values [41], For example, when the electric field is applied toward the O atom in H20, the chemical potential and hardness decrease. On the other hand, when the field is applied along the principal axis toward the central atom, the nucleophilicity decreases for that atom, provided the central atom is more electronegative. The nucleophilicity of O in H20 decreases when the electric field is applied toward that atom. Moreover, the electrophilicity of H atoms in H20 decreases. This trend is the same as observed in case of linear molecules. Here, the results of only one molecule (H20) are presented. For details, the reader may refer to our recent paper [41],... 

The blue copper protein stellacyanin, with a molecular weight of about 20,000, is obtained from the Japanese lacquer tree Rhus vemicifera. The EPR spectrum is described by roughly axial g and ACu hfs tensors and an unusually small a j value. As shown in Fig. 39 a, only the largest copper hf value A u can be directly determined from the EPR spectrum202. This coupling does not lie along the largest g-principal axis, in contrast to the usual behaviour of square planar copper complexes. 

Then the (w -f 1) x (m -f 1) eigenvalue matrix can be constructed from (9) and can be solved exactly by direct diagonalization or with the aid of perturbation methods for the eigenvalues with the external magnetic field along any principal axis, (m -f 1) Energy values and therefore m Am, = 1... 

The second term in (6) is due to dipolar interaction the energy levels are therefore dependent on 3 cos tp — 1, where tp is the angle between the external magnetic field and any principal axis. The experimental data of such an angular dependence will be of use in determining the zfs values. 

The spin-dynamics method was applied to the intramolecular PRE in the case of aqueous and methyl protons in the Ni(II)(acac)2(H20)2 complex (acac = 2,4-pentanedione) (131,132). The two kinds of protons are characterized by a different angle between the principal axis of the static ZFS and the dipole-dipole axis. The ratio, p, of the proton relaxation rates in the axial (the DD principal axis coinciding with the ZFS principal axis) and the equatorial (the DD principal axis perpendicular to the ZFS principal axis) positions takes on the value of unity in the Zeeman limit and up to four in the ZFS limit. A similar spin-dynamics analysis of the NMRD data for a Mn(II) complex has also been reported (133). 

When the gradient of the electric field does not have axial symmetry another parameter must be introduced to describe the magnitude of the electric field gradients in the solid. This is the asymmetry parameter j , which is a measure of the deviation from axial symmetry (5, 94). In addition, the direction of the principal axis of the electric field gradient tensor must be specified. From single crystal rotation patterns, the values of these parameters may be deduced (94). 

For the nitrogen hyperfine tensors, there is no satisfactory empirical scheme for estimating the various contributions, so that Table II compares the total observed tensor to the DSW result. The tensors are given in their principal axis system, with perpendicular to the plane of the heme and along the Cu-N bond. The small values (0.1 - 0.2 MHz) found for A O in the nonrelativistic limit are not a consequence of orbital motion (which must vanish in this limit) but are the result of inaccuracies in the decomposition of the total tensor into its components, as described above. 

Figure 4. The eight-pulse line shape and the peak locations of the Th4Hi5 (LP) powder sample as a function of temperature using a Ca(OH)2 single crystal as reference. The reference is oriented such that the major principal axis of the proton chemical shift tensor is parallel to the external magnetic field. A shift to the left signifies an increase in the value of

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