Edge bond orders, calculated

The average edge bond order for a particular closo species can be calculated by dividing the total number of skeletal bond pairs ( 4- 1) by the number of edges, which, for exclusively triangular-faced poly-hedra with n vertices, is (3 — 6). This leads directly to the formal boron-boron bond order for those borane anions (ITU) and... 

Calculated Charge Distributions and Edge Bond Orders... 

Therefore, the ith edge degree calculated on the weighted edge adjacency matrix is the sum of the bond orders associated with all e, bonds adjacent to the / th edge ... 

Bond multiplicity is taken into account by augmenting the edge distance matrix with a supplementary column and row where the elements are conventional bond orders, therefore obtaining an edge distance matrix for multigraphs [Bonchev, 1983]. All the local vertex invariants and molecular descriptors defined above can also be calculated on this matrix. 

The weight tvy, is calculated by multiplying the conventional bond order Ji of all m edges (bonds) of the path ""p/y ... 

The J index for multigraphs is calculated by the distance sums of the multigraph distance matrix D where the distances are obtained by weighting each edge with the reciprocal of its conventional bond order (—> relative topological distance) ... 

The bond order-weighted edge adjacency matrix "E is obtained for weighted graphs whose edges are weighted by the foond order tt calculated by computational chemistry methods on... 

As shown in Fig. 3, the calculation for the large-U case allo ws a satisfactory fit of both the conductivity and the reflectance spectra. Note that the plasma edge in reflectance, the conductivity levels in the infrared, and the e-mv structure are simultaneously fitted to a reasonable level of accuracy, although further refinement of the parameter values is still possible. The parameters used are collected in Table 1. The corresponding picture of the electronic structure exhibits a total bandwidth of 1 eV, with a small gap of amplitude 2 A, = 66 meV, associated with a bond-order wave. The gap opens at the Fermi surface, which is shifted... 

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