Topological connectivity

For dynamical studies of diffusion, conformational and transport behavior under shear stress, or kinetics of relaxation, one resorts to dynamic models [54,58,65] in which the topological connectivity of the chains is maintained during the simulation. 

The most important approximations of the HMO method are, the consideration of only the it-electrons, the neglect of the interaction between them and the neglect of all atom-atom-interactions, if the atoms are not neighbouring. Contrary to the other methods, the molecular geometry does not play a role in the HMO method because only the topologic connection of the atoms in the molecule is considered. In spite of these drastic approximations, the HMO method proved its worth as the first semiempirical procedure with a wide field of applications as well as in the theoretical interpretation of many chemical phenomenons. The method was broadly used in the field of cationic polymerizations in the 60-70 years too (see 2)). 

Dl) A molecular unit is an aggregate of atoms that is linked by a topologically connected network of covalent bonds equivalently, an electronic distribution that links a collection of nuclei by a contiguous network of covalent bonds. 

The rigorous and systematic nomenclature addressed by 1UPAC (14), in which all atoms and their topological connections are defined unambiguously, is too complicated here. Thus we use traditional names. But the semi-systematic nomenclature accepted by IUPAC (75) is mentioned briefly. 

Fold a common fold between proteins is indicated by the same major secondary structures in the same spatial arrangement and the same topological connection. 

Each species is also denoted by a three-letter structure code that describes the framework topology (connectivity, channel dimensionality etc). Examples are given in Table 9.1 common structures of some representative zeolites are shown in Figure 9.6. 

In the era of systems biology, great attention is paid to the structures of networks of reactions and interacting molecules (i.e., the topological connectivities). In some ways network structures have replaced molecular structures as the central object of biological attention. 

Description Reference Calculation of topological connectivity indices. Last release 2.3 [Basak et al, 1988a]... 

Fig. 11 Representation of lowest adiabatic potential of singlet (S = 0) and triplet (S = 1) Fe(CO)4 around T Jahn-Teller conical intersection at tetrahedral (7 ) geometry. There are three equivalent two-dimensional troughs in the space spanned by each pair-wise selection of equal L-M-L angles (boxed vs unboxed). The topological connectivity where the troughs intersect is indicated. There are two non-equivalent epikemel distortion directions E[ 2(Td,h) leading to 6 equivalent C2v minima ( ), and 12 equivalent Cs(x) saddle-points respectively. The non-Berry pseudo-rotation barrier is very small ( 5kcal mol ). CASSCF optimised geometrical parameters for singlet and triplet states are shown at the top left...

Fredrickson and Helfand incorporated coupling terms in the transport equation and showed that "these terms provide mobility to molecules that are absorbed into microvoids, even if the molecules have an intrinsic diffusion coefficient in the hole phase that vanishes." These investigators proposed experiments that could provide information on the size and topological connectivity of microcavities (51). Related studies have also been made by Chern, Koros, et al. (52) and by Barrer (53). However, Petropoulos (54) has expressed the opinion that the treatment of Fredrickson and Helfand (51 ) as well as that of Barrer (53) "introduces more diffusion parameters than can reasonably be expected to be measurable on the basis of past experience". Petropoulos also showed that these treatments impose certain limitations on the physical meaning of the diffusion parameters. In the same study, Petropoulos has examined the modification of his dual-mode sorption model ( 5) which are necessary if the Langmuir domains are sufficiently extensive to constitute a macroscopically recognizable phase rather than scattered individual sites (or microcavities) (54). ... 

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