Circuit Resonance Energy. On the Roots of Circuit Characteristic Polynomial

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Abstract The circuit characteristic polynomial plays an important role in the theory of circuit resonance energy of polycyclic conjugated molecules. Although in the use of circuit resonance energy it is essential that the circuit characteristic polynomial has real roots, the definition of circuit characteristic polynomial does not ensure that the roots of this polynomial are real numbers. It is proved that the circuit characteristic polynomial for any circuit in a polycyclic conjugated molecule has no imaginary roots if this molecule is a nonfused polycyclic conjugated molecule or a fused bicyclic system.