Abstract
An algorithm to generate the molecular orbital graphs of a N-vertex molecular graph without solving the secular matrix equation is proposed. A total of 2^(N-1) configurations of vertex-signed graphs (VSG) can be divided into several groups according to its net sign. Summation of degenerate VSGs is found to generate the conventional, canonical molecular orbitals. The distribution of the number of VSGs with respect to the net sign is found to be binomial which can be connected to bond percolation in statistical physics. Combining this procedure with net sign analysis, a complete version of chemical signed-graph theory is established.
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