Bond topology determination

In this chapter the symmetry properties of atomie, hybrid, and moleeular orbitals are treated. It is important to keep in mind that both symmetry and eharaeteristies of orbital energetics and bonding "topology", as embodied in the orbital energies themselyes and the interaetions (i.e., hj yalues) among the orbitals, are inyolyed in determining the pattern of moleeular orbitals that arise in a partieular moleeule. 

A common feature of the various methods that we have developed for the calculation of electronic effects in organic molecules is that they start from fundamental atomic data such as atomic ionization potentials and electron affinities, or atomic polarizability parameters. These atomic data are combined according to specific physical models, to calculate molecular descriptors which take account of the network of bonds. In other words, the constitution of a molecule (the topology) determines the way the procedures (algorithms) walk through the molecule. Again, as previously mentioned, the calculations are performed on the entire molecule. 

Peptide bonds are cleaved in a nonselective, but not in a completely random manner. Based on anchimeric side-chain assistance, steric factors, and bond strains, acid-labile peptide bonds are predicted to include sites containing Asp, Glu, Ser, Thr, Asn, Gin, Gly, and ProJ22l The disulfide topologies of circulin B and cyclopsychotride, backbone-cyclized peptides with three disulfide bonds, were determined by partial hydrolysis for 5 hours.[22 Occasionally, the bond between adjacent half-cystine residues is cleaved due to the nonselective nature of the mechanism of partial acid hydrolysis.[21] By this procedure, in all cases, a complex mixture of peptide fragments is produced which requires careful chromatographic separation by RP-HPLC for subsequent analysis by mass spectrometry (see Section 6.1.6.2.7). 

The values of Cy, of course, depend on which equipotential surface is used to represent the ion. Since these surfaces can be arbitrarily chosen, it might be supposed that all the values of Cy can also be arbitrarily chosen. However, the number of ions is always less than the number of bonds. If there are ions in the array, it is only possible to assign arbitrary values of Cy to - 1 bonds, those in the spanning tree described in Section 2.5 below. For the remaining bonds, those that close the loops in the network, a knowledge of the bond topology alone is insufficient to determine Cy. To find these values of Cy, the geometry of the array, i.e. the positions of the ions, must also be known. 

A structural feature is defined by nine numbers. The first four numbers (nl-n4) serve to identify the specific atom type, atom pair, or atom environment by means of a predefined set of properties, while the remaining five numbers (n5-n9) determine which bits of the whole key are set by the feature. Specifically, in the case of single atom descriptors, nl is 0 and n2 and n3 encode one or two properties of the atom for atom pair descriptors, nl encodes the number of bonds (topological distance) between the atoms, while nl and n3 encode the property values of the two atoms finally, for custom atom environment descriptors, nl is equal to 7, while n2 encodes the specific atom environment and n3 encodes the property of the atom in the center of that environment. The number n4 encodes the number of occurrences in the molecule of the considered feature. The number n5 is used to specify the number of bits that are set, while n6 is a flag indicating whether or not hashing is allowed the final three numbers, n7, n8, and n9 identify the bits in the structural key. 

Further analysis of the computed energy parameters either requires some special symmetry such as that found in octahedral BeHe or icosahedral Bi2Hi2 or some further assumptions concerning the chemical bonding topology for less symmetrical systems in order to minimize the number of independent unknowns to be determined. In the cases of BeHe ... 

The property of chirality is determined by overall molecular topology, and there are many molecules that are chiral even though they do not possess an asymmetrically substituted atom. The examples in Scheme 2.2 include allenes (entries 1 and 2) and spiranes (entries 7 and 8). Entries 3 and 4 are examples of separable chiral atropisomers in which the barrier to rotation results from steric restriction of rotation of the bond between the aiyl rings. The chirality of -cyclooctene and Z, -cyclooctadiene is also dependent on restricted rotation. Manipulation of a molecular model will illustrate that each of these molecules can be converted into its enantiomer by a rotational process by which the ring is turned inside-out. ... 

The chemical bonding and the possible existence of non-nuclear maxima (NNM) in the EDDs of simple metals has recently been much debated [13,27-31]. The question of NNM in simple metals is a diverse topic, and the research on the topic has basically addressed three issues. First, what are the topological features of simple metals This question is interesting from a purely mathematical point of view because the number and types of critical points in the EDD have to satisfy the constraints of the crystal symmetry [32], In the case of the hexagonal-close-packed (hep) structure, a critical point network has not yet been theoretically established [28]. The second topic of interest is that if NNM exist in metals what do they mean, and are they important for the physical properties of the material The third and most heavily debated issue is about numerical methods used in the experimental determination of EDDs from Bragg X-ray diffraction data. It is in this respect that the presence of NNM in metals has been intimately tied to the reliability of MEM densities. 

Tsirelson, V.G., Zou, P.F. and Bader, R.F.W. (1995) Topological definition of crystal structure determination of the bonded interactions in solid molecular chlorine, Ada Cryst., A51, 143-153. 

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