Nuclear distribution

Fig. 3. Z-scaled electron-nuclear distribution functions for H, He, Li, and Ne (a) radial probability distribution D(r ) Z (b) radial density /o(ri)/Z. The curves can be identified from the fact that higher maxima correspond to higher Z.

One of the desirable features of compact wavefunctions is the ability to use them to examine additional features of the electron distribution without the necessity of repeating extensive computations to recreate complicated wavefunctions. We illustrate this point, and also exhibit the similarity of our wavefunctions with those of the 66-configuration study of Thakkar and Smith [15] by looking at the pair distribution functions. It is most instructive to present these as Z-scaled quantities Figure 3 contains the electron-nuclear distributions D r ) and p(ri) for clarity we only plot data for H, He, Li, and Ne. Even after Z scaling, a small but systematic narrowing of the distributions with increasing Z is still in process at Z-10. 

Bravo, R and MacDonald-Bravo, H. (1987) Changes in the nuclear distribution of cyclin (PCNA) but not its synthesis depend on DNA replication EMBO J 4, 655-661... 

The natural appearance of nuclear magic numbers, and the golden-ratio limitation on nuclear distribution, indicate the development of an excess surface layer of protons, which correlates well with periodic variation of nuclear spin, and which may be an important parameter in the understanding of superconductivity. 

A molecule contains a nuclear distribution and an electronic distribution there is nothing else in a molecule. The nuclear arrangement is fully reflected in the electronic density distribution, consequently, the electronic density and its changes are sufficient to derive all information on all molecular properties. Molecular bodies are the fuzzy bodies of electronic charge density distributions consequently, the shape and shape changes of these fuzzy bodies potentially describe all molecular properties. Modern computational methods of quantum chemistry provide practical means to describe molecular electron distributions, and sufficiently accurate quantum chemical representations of the fuzzy molecular bodies are of importance for many reasons. A detailed analysis and understanding of "static" molecular properties such as "equilibrium" structure, and the more important dynamic properties such as vibrations, conformational changes and chemical reactions are hardly possible without a description of the molecule itself that implies a description of molecular bodies. 

It is clear that the entire electronic density in a molecule has the role of determining the nuclear distribution hence bonding, consequently, chemical bonding cannot be confined to lines in space. It is well understood that bond diagrams represent only an oversimplified, "short-hand" notation for the actual molecular structure, nevertheless, as most successful notations do, chemical bonds as formal lines have acquired an almost unquestioned reputation of their own as if they were truly responsible for holding molecules together. 

K7. Kitiyakara, A., Cytologic study of dystrophia muscularis mouse muscles. Observations on nucleic acid metabolism and nuclear distribution. Arch. Pathol. 71, 579 (1961). 

All aspects of molecular shape and size are fully reflected by the molecular electron density distribution. A molecule is an arrangement of atomic nuclei surrounded by a fuzzy electron density cloud. Within the Born-Oppenheimer approximation, the location of the maxima of the density function, the actual local maximum values, and the shape of the electronic density distribution near these maxima are fully sufficient to deduce the type and relative arrangement of the nuclei within the molecule. Consequently, the electronic density itself contains all information about the molecule. As follows from the fundamental relationships of quantum mechanics, the electronic density and, in a less spectacular way, the nuclear distribution are both subject to the Heisenberg uncertainty relationship. The profound influence of quantum-mechanical uncertainty at the molecular level raises important questions concerning the legitimacy of using macroscopic analogies and concepts for the description of molecular properties. ... 

Electron Distributions and Nuclear Distributions the Heisenberg Uncertainty Relation and Molecular Shape... 

Hence, a simple, essentially classical model provides a useful approximation to the relations between the electronic and nuclear distributions one may think of the electron distribution as a formal charge cloud, and the nuclear distribution as an... 

Hareven, D. Koltin, Y. Nuclear Distribution in the Mycelium of Claviceps and the Problem of Strain Selection Applied Microbiology (1970) 19 (6) 1005-1006... 

S-100 protein, the immunostaining pattern for calretinin was cytoplasmic and nuclear (Tig. 12.48). Reactive multipotential subserosal spindle cells typically express calretinin in a cytoplasmic and nuclear distribution. 

The approximation of the nucleus as an infinitely heavy point charge makes possible analytical solution of the Dirac equation for the hydrogen-like problem. The resulting orbitals are, however, too tightly bound and clearly unphysical within the nucleus. A homogeneously charged nucleus is a significant improvement and is sufficient for many applications. For more detailed studies of nuclear properties, it is, however, desirable to use a more physical nuclear distribution, such as the Fermi and the Fourier-Bessel distributions described below. 

The two-parameter Fermi model gives a realistic description of the nuclear distribution [38,39], and at the same time provides considerable flexibility in the analysis ... 

The shape of an arbitrary nuclear distribution can often be adequately described by the moments (r ") of the distribution. For the Fermi distribution above, these moments are given, to a good approximation [40], by the relations... 

D. Binding energies, nuclear distributions and isotope shifts... 

Molecular shape has a fundamental influence on both the static and dynamic properties of molecules for example, the shapes of the nuclear and electronic distributions determine the molecular dipole moments as well as the likely sites of approach by a nucleophilic reagent. The evolution of concepts and models used by cbemists and physicists for the description of molecular shape closely mirrors the advances made in our understanding of molecular behavior. Whereas most of the early models focused on the nuclear arrangements, the more advanced recent approaches have placed increasingly more emphasis on the electronic distribution. Molecules consist of interacting nuclear and electronic distributions, where the nuclear distribution is fully reflected in the electronic density. This fact allows one to obtain a complete description of molecular shapes in terms of the electronic density. ... 

The intimate relation between the nuclear distribution and the electronic density distribution is a natural bridge that connects the more conventional, essentially classical, ball-and-stick models, and the more accurate, quantum-chemical electronic density descriptors of molecular shape. It is somewhat surprising that relatively little effort has been devoted to the natural relation between the purely nuclear interactions and the electronic density. In this contribution this connection will be discussed from a specific viewpoint, leading to a 3D representation of molecular shape and to an interpretation of chemical bonding. 

Concerning the nuclear location of the DNA belonging to bands endowed with ditTerent compositional features, the results are in agreement with the nuclear distribution of the GC-richest and the GC-poo rest isochores (Fig. 7.24). In fact, we observed a more peripheral iocali/iition of the GC-poor bands compared lo a more internal position of the GC-... 

Manuelidis, L. and Ward, D. C. (1984) Chromosomal and nuclear distribution of the Hindin 1.9 kb human DNA repeat segment. Chromosoma 91,23-38. 

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