Bond-path length

Bond length re Bond path length rb rb is larger than the geometrical distance rc for bent bonds... 

The first line lists the experimental result the second line- the atomic procrystal p is the electron density V2p is the Laplacian, g, v and he are the kinetic, potential and total electronic energies at the critical point R is the bond path length. 

Bond path length Interpath angle p Distance d Bond order n (local property)... 

Molecule indices describe structural features of entire molecules. The molecular connectivity index (also called %-index) encodes total size, branching, unsaturation, heteroatom content and cyclicity in only one descriptor for a given bond path length [56, 57]. 

The first topological index to be published is the Wiener index W, which is half the sum of the bond-by-bond path lengths between each atom [41]. It is easily calculated from each offdiagonal element Dtj of the distance matrix of a structure ... 

B-N bond length [A] Bond path length [A] p(rBcp) [eA- ] VV(fBCp) [eA- ] fi(rBCp)... 

At the low end of the hierarchy are the TS descriptors. This is the simplest of the four classes molecular structure is viewed only in terms of atom connectivity, not as a chemical entity, and thus no chemical information is encoded. Examples include path length descriptors [13], path or cluster connectivity indices [13,14], and number of circuits. The TC descriptors are more complex in that they encode chemical information, such as atom and bond type, in addition to encoding information about how the atoms are connected within the molecule. Examples of TC descriptors include neighborhood complexity indices [23], valence path connectivity indices [13], and electrotopological state indices [17]. The TS and TC are two-dimensional descriptors which are collectively referred to as TIs (Section 31.2.1). They are straightforward in their derivation, uncomplicated by conformational assumptions, and can be calculated very quickly and inexpensively. The 3-D descriptors encode 3-D aspects of molecular structure. At the upper end of the hierarchy are the QC descriptors, which encode electronic aspects of chemical structure. As was mentioned previously, QC descriptors may be obtained using either semiempirical or ab initio calculation methods. The latter can be prohibitive in terms of the time required for calculation, especially for large molecules. 

We see, therefore, that the pth moment of the eigenspectrum is given by the sum over all bonding paths of length, p, that start and finish on the same atom within the molecule. 

Figure B3.5.13 A convincing artifact. In an attempt to study the conformational consequences of adding an acceptor, D-glutamine, to a DD-peptidase, far-UV CD spectra were recorded for the enzyme in the presence of increasing concentrations of glutamine a = 0 mM, b = 3 mM, c = 7 mM, d = 10 mM, e = 20 mM, f = 30 mM, g = 50 mM, and h = 95 mM. The enzyme concentration was 0.1 mg/ml, equivalent to 10 3 M peptide bond, in 10 mM sodium phosphate pH 7.2. A 2-mm cell path length was used.

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