Electronic molecular cloud

A measure of the ability of an atom within a molecule to attract bonding electrons toward itselP . For a bond between two atoms of different electronegativities, the electron molecular orbital cloud is not symmetric, and the atom with the higher electronegativity attracts the larger proportion of the cloud. The most popular quantitative description was presented by Pauling, who based his scale on bond dissociation energies (measured in kcal per mol). 

Mezey, P. G. (1998) The proof of the metric properties of a fuzzy chirality measure of molecular electron density clouds. J. Molec. Struct. (Theochem.) 455, 183-190. 

Third harmonic generation is used to study the purely electronic molecular second hyperpolarizability of centrosymmetric materials no other mechanism but the nonresonant electron cloud distortion can respond rapidly... 

In the general scheme described in subsequent sections, a functional group is regarded as a fuzzy body of electronic charge cloud, a fuzzy subset of the electronic charge density cloud of the complete molecule. In this context, a functional group is a special case of a fuzzy fragment of a molecular body, obtained by some subdivision... 

The density domain approach was first proposed [4] as a tool for the description of chemical bonding where the complete shape information of the molecular electron density was taken into account. Density domains are formal bodies of electron density clouds enclosed by MIDCOs defined by eq. (1) [or by eq. (2) if there is no need to specify the nuclear configuration K],... 

These fuzzy electron density membership functions properly describe the mutual interpenetration of fuzzy electron density clouds within the molecular family L, and it provides a description of how molecules share some common regions of space. 

In quantitative modeling of PESs the description of the molecular shape as a superposition of atomic components remains an attractive approach, but it is clear from the earlier discussion that it must be extended to accommodate two important factors. The atomic shape is not a rigid, but rather a soft, exponentially decaying electronic charge cloud. In addition, it should be anisotropic with the anisotropy depending not only on the atom itself, but also on its partner in the chemical bond. 

Most of these reactions have been measured and their rates are thus reasonably well known (Fehsenfeld et al. 1967). In comparing the two reaction schemes, it is interesting to note that HjO does recombine dissociatively with an electron to form H2O and OH, but that the analoguous reaction sequence with seems to take place. The branching ratio of the H30 dissociative recombination is not accurately known. In this connection, it is also important to note that reactions of H with atomic carbon seem to be endothermic (Burt et al. 1970 and references therein), and thus the carbon chemistry in dense molecular clouds can not start this way. 

Fig. 1. Interstellar formation scheme illustrating the CH, CH, C H and higher hydrocarbon cycle. The left side of the reaction cycle pertains to tenous clouds (Uj, 100 cm ), whereas the right hand side is more appropriate to areas where is present, i.e. dense molecular clouds (n 10 -10 cm" ). The thick arrows indicate assumed preferential reaction paths leading to the higher order hydrocarbons. The following processes are involved (v, e) photoionization (v, H) photodissociation (e, v) radiative recombination (H) (Hj, v) radiative association (e, H), (e, Hj) dissociative electron recombination. (Hj, H) hydrogen abstraction reaction (C, H) charge exchange (M, M ) metal charge exchange metal = Mg, Fe, Ca, Na,...

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. ... 

For the description of shape differences between fuzzy objects, such as molecular electron density clouds, it is useful to generalize the Hausdorff metric for fuzzy sets. The ordinary Hausdorff distance, a formal dis-... 

This contrast is in part due to the difficulty of invoking fuzzy three-dimensional electron density clouds in a mechanistic interpretation of reactions, which is also hindered by the perceived classical nature of the concept of localization. Classical objects, often used in analogies when modeling molecular structures, usually exhibit localized features, yet the very concept of localization apparently conflicts with the delocalized nature of molecular electron distribution and the Heisenberg uncertainty relation. 

Within the quantum chemical description of molecular electron density clouds, a natural criterion, the Density Domain criterion, provides a quantum chemical definition for functional groups [14-18]. Furthermore, techniques that generate fuzzy electron density contributions for local molecular moieties that are analogous to the fuzzy electron density clouds of complete molecules, determined by the analytic Additive Fuzzy Density Fragmentation (AFDF) method [19-21], or the earlier numerical-grid MEDLA method [22,23], are also... 

The observation of molecular hydrogen by means of its electronic transitions in a sense follows classical optical interstellar spectroscopy. It is, however, considerably more complex, requiring essentially controlled satellite observatories. Thus, it serves to determine molecular-hydrogen column densities in translucent clouds, but cannot provide images of the dense molecular clouds. For these, carbon monoxide is the generally accepted tool. The reported results are in terms of H2 column densities under the assumption that the H2 CO ratio is the accepted value of 10. CO is observable by means of its many isotopomers. This is extremely useful, as the common isotopomer is frequently optically opaque, making... 

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