Graph Theory and Molecular Orbitals . XX . * Local and Long Range Contributions to Bond Order
where w is the length of the path W, P(G, x) is the characteristic polynomial of the graph G and G-W is the graph obtained by deletion of the path W from G. For non-alternant systems the formulas for T(W) are much more complicated and are given elsewhere1. There is a straighforward interpretation of eq 1, namely T(W) can be understood as the (additive) contribution of the path W to the bond order Prs· The case of adjacent r and s is certainly the most interesting one, because of the well known relations between Prs and bond length, -bond strength, vibrational frequency, reactivity, etc.2 In the present study we shall consider exclusively the bond orders between the adjacent centers. Then since there is always a path of length one between the adjacent centers r and s, i.e., the bond connecting the atoms r and s, eq 1 is rewritten as