Distance matrix separation

Here HaB is a quantum mechanical matrix whose strength decreases exponentially with the distance of separation R as e where P is a coefficient of the order of 9-14 nm-1. At the closest contact (R = 0) the rate fcET, by extrapolation from experimental data on small synthetic compounds, is close to the molecular vibration frequency of 1013 s 1.151152 At distances greater than 2 nm the rate would be negligible were it not for other factors. 

Pyka and Sliwiok separated six esters of nicotinic acids methyl nicotinate, ethyl nicotinate, isopropyl nicotinate, butyl nicotinate, hexyl nicotinate, and benzyl nicotinate by adsorption HPLC on a LiChrospher Si 60 column. The mixtures containing benzene and methanol in volume proportions (O-i-lO, 1h-9, 2h-8, 3h-7, 4-1-6, and 5-1-5) were used as the mobile phases. The (min) values of esters investigated have been correlated with the dipole moments (/imph) of the mobile phases apphed, with numerical values of one topological index from among those based on the distance matrix (A, W, °7J, B) or the... 

Djakovic-Sekulic et al. " separated eight anilides of 2,2-dimethylpropanoic acid, nine anilides of benzoic acid, and nine anilides of ot-phenyl acetic acid by RP-18 HPLC using mixtures containing methanol and water in volume proportions 6h-4, 6.5h-3.5, and 7-1-3 as the mobile phases. The log k values of investigated anilides have been correlated with the dipole moments ( raph) or permittivities (Emph) of the mobile phases applied, with numerical values of one topological index from among those based on the distance matrix R, W, A, B, B) or on the adjacency matrix (M, M, x with... 

Pyka and Sliwiok separated a-tocopherols, p-tocopherols, y-tocopherols, and 8-tocopherols by normal-phase high-performance liquid chromatography (NP-HPLC) and RP-Cig-HPLC. The selected topological indices based on connectivity (M, x ")> distance matrix W, MTI), and information theory (Zac, Tag) were... 

The atom pairs button enables a special mode for the display of a list of atom pairs if the mouse is clicked on a certain descriptor point. The corresponding distance is calculated, and a list of atom pairs together with their original values from the distance matrix is displayed. The statistics button calculates some statistical parameters for the actual descriptor and for a superimposed descriptor if available. The peak areas button separates the individual peaks and calculates the peak areas. The transform buttons enable the display of an additional transformed descriptor. 

Sometimes it is overlooked that characterization of molecules as 3D objects is deficient,] x% as is the characterization of molecules based on the molecular adjacency or the graph-distance matrix. In the former there is no information on connectivity, in the latter there is no information on spatial geometry. In a way the two approaches complement each other, one having the information that is absent in the other. Therefore, it should not be surprising that combining such matrices will yield a matrix that has information on adjacency as well as on interatomic separations. 

Luhua et al. separated by normal-phase thin-layer chromatography (NP-TLC) (-)-ephedrine and (- -)-pseudoephedrine. The topological indices based on connectivity and distance matrix A, W, and were calculated. The structures in particular of (-)-ephedrine and (+)-pseudoephedrine were described by topological indices that were applied to interpret the chromatographic separations. 

Example Suppose there are four atoms in space each separated from the other atoms by 1.4142 A (V5). What is a set of coordinates that satisfies this relationship The distance matrix is as follows ... 

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