Molecular branching

M Randic. On characterization of molecular branching. J Am Chem Soc 97 6609-6615, 1975. LB Kier, LH Hall. Molecular Connectivity in Structure-Activity Analysis. Chichester, England Research Studies Press, 1986. 

Fig. 11 The scattering properties of a five branches - four electrodes molecular bridge, (a) Detailed atomic structure of the molecule. A central perylene branch was included to mimic an internal measurement branch, (b) EHMO-ESQC calculated T12(E) transmission coefficient (plain) and predicted T12(E) transmission coefficient (dashed), applying the intramolecular circuit rules discussed for the four molecular fragments given in Fig. 12. The dashed (dotted) line is the Ti2(E) variation for the single molecular branch, as presented in the inset, to show the origin of the destructive interference...

A very good example is the conductance of a dianthra[a,c]naphtacene starphenelike molecule presented in Fig. 20, interacting with three metallic nano-pads. The EHMO-NESQC T(E) transmission spectrum per tunnel junction looks like a standard conjugated molecule T(E) with well-identified molecular orbitals and their resonances. For the Fig. 20 case all the T(E) are the same. One can note a small deviation after the LUMO resonance, due to a little asymmetry in the adsorption site between the three branches on the nano-pads [127]. A lot of asymmetric star-like three-molecular-branches system can be constructed, in particular in reference to chemical composition of the central node. This had been analyzed in detail [60]. But in this case, each molecule becomes a peculiar case. The next section presents one application of this central-node case to construct molecule OR and molecule XOR logic gates. 

Fig. 14 The three-branches dianthra[a,c]naphtacene molecule circuit of symmetry formed by three anthracene fragments equivalently bonded to a central phenyl group. The molecule is adsorbed by the three branch ending phenyls onto the Au nano-pads. A semilogarithmic plot of the Tij(E) EHMO-NESQC electron transmission spectra (in valence energy range) per pair of branches. The presented frontier MOs show how the valence n electrons are delocalized on the molecule. At resonance, this provides a good electronic conductance through each pair of molecular branches, almost one quantum of conductance...

Note Excess can lead to undesirable molecular branching and cross-linking. Chain branching can severely hamper the crystallization capability of PET and this may lead to a loss in performance properties. 

A connectivity index, Xr> similar to the M2 index was introduced by Randic5) for characterization of molecular branching ... 

Bonchev, D., and N. Trinajstic, Information Theory, Distance Matrix, and Molecular Branching. J. Chem. Phys., 1977 67, 4517-4533. 

Fig. 8.4 Encapsulation of anionic dye mole- printboard (schematic only 23 of the 64 ter-cules (green) by the dendrimer bound supra- minal adamantyl groups are shown and the molecularly to the surface of the molecular branches are symbolised)...

Degree of molecular branching in general, the more branching, the greater the rejection, for example, isopropanol is rejected better than normal propanol. 

The quantitative measures of molecular branching derived by Bonchev and Trinajstic are very important since they correlate with many physical and chemical properties of compounds. ... 

The pruning partition is related to - molecular branching, and the reversed order of ng numbers is due to the fact that the number of branches cannot decrease when starting from the centre of the tree. Moreover, the first entry is always equal to one (centre) or two (bicentre) and the pruning partition is a partition of A, i.e. the number of molecule atoms. 

This index provides a measure of molecular branching the higher the value of B, the more branched the tree. It is called centric index because it reflects the topology of the tree as viewed from the centre. 

Note that the total structure connectivity index is the square root of the - simple topological index proposed by Narumi for measuring molecular branching. 

Both the MSD and Di indices decrease with increasing molecular branching in an isomeric series. 

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