Nucleus deformation

The incorporation of metals into metal-free porphyrins has been reported to proceed by a dissociative mechanism.278 The porphyrin and metal form an outer-sphere complex, the porphyrin nucleus deforms to provide a suitable configuration to complex with the metal ion, and then dissociative exchange occurs as shown ... 

Knight MM, van de Breevarrt Bravenboer J, Lee DA, van Osch GJ, Weinans H, Bader DL. Cell and nucleus deformation in compressed chondrocyte-alginate constructs Temporal changes and calculation of cell modulus. Biochim Biophys Acta. 2002 1570 1-8. 

If the nucleus deforms axially, the spherical states will split into (2j+ l)/2 levels, each still with twofold degeneracy. It is instmctive to trace the breaking of the degeneracy back to first principles, namely that the nuclear interaction is short range and attractive. In a deformed nucleus it can therefore be expected that the overlap of the nuclear wavefunction with the bulk of the nucleus determines the energy gain. 

The authors (85) have also mentioned the deformational vibrations (7) of the out-of-plane group -CH= of a pentatomic heterocyclic nucleus, showing that there exists a relationship between the absorption frequencies of this group and the electronegativity of the heteroatom (86). 

The effects of a rather distinct deformed shell at = 152 were clearly seen as early as 1954 in the alpha-decay energies of isotopes of californium, einsteinium, and fermium. In fact, a number of authors have suggested that the entire transuranium region is stabilized by shell effects with an influence that increases markedly with atomic number. Thus the effects of shell substmcture lead to an increase in spontaneous fission half-Hves of up to about 15 orders of magnitude for the heavy transuranium elements, the heaviest of which would otherwise have half-Hves of the order of those for a compound nucleus (lO " s or less) and not of milliseconds or longer, as found experimentally. This gives hope for the synthesis and identification of several elements beyond the present heaviest (element 109) and suggest that the peninsula of nuclei with measurable half-Hves may extend up to the island of stabiHty at Z = 114 andA = 184. 

The natural orbitals %2v and %3p are, in contrast to the hydrogenlike functions, localized within approximately the same region around the nucleus as the Is orbital. This means that the polarization caused by the long-range interaction is associated mainly with an angular deformation of the electronic cloud on each atom. If %2p and %3p are expanded in the standard hydrogen-like functions, an appreciable contribution will again come from the continuum. 

The first-order perturbation theory in this case does not give good results, since the mutual interaction of two electrons on one nucleus is so large as to greatly deform the eigenfunctions it leads... 

An ellipsoidal nucleus with two spherons in the inner core has major radius greater than the minor radii by the radius of a spheron. about 1.5 f, which is about 25 percent of the mean radius. The amount of deformation given by this model is accordingly in rough agreement with that observed (18). In a detailed treatment it would be necessary to take into account the effect of electrostatic repulsion in causing the helions to tend to occupy the poles of the prolate mantle, with tritons tending to the equator. 

In this assignment the assumption is made that the 22 helions of the mantle occupy the end regions of the highly deformed nucleus, as a result of their strong Coulomb repulsion. 

The entry into the first mitotic M phase at the end of the first embryonic cell cycle requires activation of MPF. In the mouse one-cell embryo this activation is fully autonomous from the nucleus (Ciemerych 1995, Ciemerych et al 1998). It proceeds within the cytoplasts obtained either by enucleation or by bisection of the embryo. Other autonomous phenomena are the cortical activity, or the deformation of the one-cell embryo, directly preceding the entry into first mitosis (Waksmundzka et al 1984) and the cyclic activity of K+ ion channels (Day et al 1998). The role of the cortical activity remains unknown however, the fact that it directly precedes the entry into the first mitotic M phase suggests that it could be linked to the activation... 

Pyridine (62), like benzene, has six n electrons (one being supplied by nitrogen) in delocalised n orbitals but, unlike benzene, the orbitals will be deformed by being attracted towards the nitrogen atom because of the latter s being more electronegative than carbon. This is reflected in the dipole of pyridine, which has the negative end on N and the positive end on the nucleus ... 

Figure 6.1 shows the stockholder decomposition of the theoretical deformation density of the cyanoacetylene molecule, H—Cs=C—C=N (Hirshfeld 1977b). The overlap density in the bonds is distributed between the bonded atoms. The assignment of part of the density near the hydrogen nucleus to the adjacent carbon atom manifests the difference between fuzzy and discrete boundary partitioning methods. 

Stewart s conclusion underscores the need for short-wavelength, low-temperature studies, if very high accuracy electrostatic properties are to be evaluated by Fourier summation. But, as pointed out by Hansen (1993), the convergence can be improved if the spherical atoms subtracted out are modified by the k values obtained with the multipole model. Failure to do this causes pronounced oscillations in the deformation density near the nuclei. For the binuclear manganese complex ( -dioxo)Mn(III)Mn(IV)(2,2 -bipyridyl)4, convergence of the electrostatic potential at the Mn nucleus is reached at 0.7 A" as checked by the inclusion of higher-order data (Frost-Jensen et al. 1995). 

The most toxic quinolizidine alkaloids are tetracyclic with a pyridone nucleus. One of these is anagyrine. One case mentions in anagyrine being passed to the human body via milk from goats foraging on Lupinus latifolius. The anagyrine caused severe bilateral deformities of the distal thoracic limbs in a baby boy. 

Fig. 3.2. Derivation of the derivative rule general case. In the shaded region, the tip wavefunction does not satisfy the Schrodinger equation in the vacuum. However, the expansion in Eq. (3.30) satisfies the Schrodinger equation in the vacuum except at the nucleus of the apex atom. Thus the surface on which the Bardeen integral is evaluated can be deformed to be any surface that encloses the nucleus of the apex atom.

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