Polynomial matrix method for the calculation of charge densities and bond orders in linear conjugated π-electron systems

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Abstract
The polynomial matrix method (PMM) described earlier for evaluating the π-electron energies of linear conjugated polymers has been extended to calculate the charge densities and bond orders. The formulae used are those given by Heilbronner, and it is shown that the PMM enables the various terms in his equations to be calculated conveniently. The method has been applied to p-quaterphenyl. The values of charge densities and bond orders obtained by this method are in very good agreement with those obtained by solving the secular determinant directly by computer.