Molecular compactness

The Harary index increases with both molecular size and - molecular branching, it is therefore a measure of molecular compactness like the - Wiener index. However, the Harary index seems to be a more discriminating index than the Wiener index. 

The radius of gyration is a measure of molecular compactness for long-chain molecules such as polymers, i.e. small values are obtained when most of the atoms are close to the centre of mass. It is also related to the - characteristic ratio. 

Tlie Wiener index increases with the number of atoms (i.e. with the molecular size) and, for a constant number of atoms, reaches a maximum for linear structure and a minimum for the most branched and cyclic structures. For this reason it was suggested as a measure of - molecular branching. It is insensitive to atom type. Moreover, the Wiener index seems to be related to the molecular surface area, thus reflecting molecular compactness and, in some way, the intermolecular forces [Gutman and Kortev-lyesi, 1995]. 

From structural data, Rq can be determined without knowing the nuclear connectivity. In this sense, Rq measures size, not molecular shape. However, Rq contains more information than R. The radius of gyration also provides an absolute measure of molecular compactness. Note that Rq will have small values if most nuclei are close to the center of mass. In this case, the contribution of a few far nuclei to Rq may be negligible. 

While he was practicing for his oral qualifying exam, Ranil Wickramasinghe was asked by a classmate about interfacial resistances to mass transfer. Such resistances are rare, usually due to a molecularly compact interfacial film. Transfer across such an interface is like a reversible heterogeneous first-order reaction. For example, for gas absorption, it is... 

The systematic lUPAC nomenclature of compounds tries to characterize compounds by a unique name. The names are quite often not as compact as the trivial names, which are short and simple to memorize. In fact, the lUPAC name can be quite long and cumbersome. This is one reason why trivial names are still heavily used today. The basic aim of the lUPAC nomenclature is to describe particular parts of the structure (fi agments) in a systematic manner, with special expressions from a vocabulary of terms. Therefore, the systematic nomenclature can be, and is, used in database systems such as the Chemical Abstracts Service (see Section 5.4) as index for chemical structures. However, this notation does not directly allow the extraction of additional information about the molecule, such as bond orders or molecular weight. 

An alternative way to represent molecules is to use a linear notation. A linear notation uses alphanumeric characters to code the molecular structure. These have the advantage of being much more compact than the connection table and so can be particularly useful for transmif-ting information about large numbers of molecules. The most famous of the early line notations is the Wiswesser line notation [Wiswesser 1954] the-SMILES notation is a more recent example that is increasingly popular [Weininger 1988]. To construct the Wiswesser... 

Molecular orbitals are useful tools for identifying reactive sites m a molecule For exam pie the positive charge m allyl cation is delocalized over the two terminal carbon atoms and both atoms can act as electron acceptors This is normally shown using two reso nance structures but a more compact way to see this is to look at the shape of the ion s LUMO (the LUMO is a molecule s electron acceptor orbital) Allyl cation s LUMO appears as four surfaces Two surfaces are positioned near each of the terminal carbon atoms and they identify allyl cation s electron acceptor sites... 

Branching occurs to some extent and can be controlled. Minimum branching results in a high-density polyethylene because of its closely packed molecular chains. More branching gives a less compact solid known as low-density polyethylene. 

GaAs, GaAlAs, and GaP based laser diodes are manufactured using the LPE, MOCVD, and molecular beam epitaxy (MBE) technologies (51). The short wavelength devices are used for compact disc (CD) players, whereas the long wavelength devices, mostly processed by MBE, are used in the communication field and in quantum well stmctures. 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

Other apphcatioas for 4-/ f2 -octylpheaol iaclude chaia termination of polycarboaates (54). The properties of low molecular weight polycarboaates used ia injection-molding apphcatioas to form compact disks are enhanced when the polymer is termiaated usiag 4-/ f2 -octylphenoL... 

When the catalyst is expensive, the inaccessible internal surface is a liabihty, and in every case it makes for a larger reactor size. A more or less uniform pore diameter is desirable, but this is practically reahz-able only with molecular sieves. Those pellets that are extrudates of compacted masses of smaller particles have bimodal pore size distributions, between the particles and inside them. Micropores have diameters of 10 to 100 A, macropores of 1,000 to 10,000 A. The macropores provide rapid mass transfer into the interstices that lead to the micropores where the reaction takes place. 

The asymmetric unit contains one copy each of the subunits VPl, VP2, VP3, and VP4. VP4 is buried inside the shell and does not reach the surface. The arrangement of VPl, VP2, and VP3 on the surface of the capsid is shown in Figure 16.12a. These three different polypeptide chains build up the virus shell in a way that is analogous to that of the three different conformations A, C, and B of the same polypeptide chain in tomato bushy stunt virus. The viral coat assembles from 12 compact aggregates, or pen tamers, which contain five of each of the coat proteins. The contours of the outward-facing surfaces of the subunits give to each pentamer the shape of a molecular mountain the VPl subunits, which correspond to the A subunits in T = 3 plant viruses, cluster at the peak of the mountain VP2 and VP3 alternate around the foot and VP4 provides the foundation. The amino termini of the five VP3 subunits of the pentamer intertwine around the fivefold axis in the interior of the virion to form a p stmcture that stabilizes the pentamer and in addition interacts with VP4. 

The way in which molecular chaperones interact with polypeptides during the folding process is not completely understood. What is clear is that chaperones bind effectively to the exposed hydrophobic regions of partially folded structures. These folding intermediates are less compact than the native folded proteins. They contain large amounts of secondary and even some tertiary... 

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