Distance range matrix

Figure 3.34. Distance matrix (a) in which unique interatomic distances for a particular conformation of a molecule are stored. Distance range matrix (b) in which ranges of interatomic distances representing conformational flexibilty of molecule are stored. U = upper bound, L = lower bound.

Figure 6. Distance range matrix for sterically allowed conformations of muscimol, a muscarinic agonist. Distances nonvarient under rotation are single entries. Paired entries represent maximum and minimum distances that are sterically...

In relation with these avoided crossings, the radial coupling matrix elements present sharp peaks at respectively 5.4, 6.6, 7.55 and 9.5 a.u. (Fig. 5). We may notice that these radial couplings are almost insensitive to the choice of the origin of electronic coordinates. The most sensitive one is the g23 function at short internuclear distance range, but we may expect weak translational effects for such electron capture processes dominated by collisions at large distance of closest approach. 

A very interesting series has been prepared and studied by Balzani, Belser, De Cola and co-workers [82], in which Ru(bpy)3 and Os(bpy)3 end groups are connected by three, five or seven phenylene units, the metal-metal distance ranging from 24 to 42 A. Energy transfer is deduced from the observed quenching of the Ru(II) phosphorescence, with a parallel sensitization of the Os(II) phosphorescence. Energy transfer rate constants vary from 6.7 x 10 s for n = 3 to 1.3 x 10 s for = 7 at 293 K in acetonitrile, and a decay rate of —0.32 A was established for the rate constants, corresponding to -0.16 A for the matrix elements. 

Distance geometry - is a general method for converting a set of distance ranges or bounds into a set of Cartesian coordinates consistent with these bounds. A molecular structure is described by the set of all pairwise interatomic distances in a distance matrix. Cartesian and internal coordinates have been used historically primarily for mathematical and computational convenience for many modeling applications a distance matrix representation is simpler because chemical struaure information is often described by distances. 

The first approach represents an individual molecule by the frequency distribution of the interatomic distances in its distance matrix the similarity between a pair of molecules can then be calculated by the goodness-of-fit between the two frequency distributions. Given a distance matrix, DA, the method involves sorting the elements DA(I,J) (l N(A)-l I J N(A)) into increasing order of distance and representing them as a frequency distribution FA such that the TT-th element of FA, FA(K)y contains the number of elements of DA that occur in the K-th distance range that has been defined. The reader is referred to the paper elsewhere in these proceedings by Artymiuk et for a detailed description of the way in which this is carried out. 

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