Notes on the molecular orbital treatment of linearly coupled systems

Abstract

It is well known (1) that for an unsaturated hydrocarbon of the type CnHn+2 (where n is the number of carbon atoms in the linear chain), the theory of molecular orbitals applied to calculate the binding energy of the mobile π-electrons leads to the secular determinant, of continuant type,where β is the resonance integral between adjacent carbon centres and x stands for the quantity generally written E0 − E, E being the energy of a mobile electron, which we seek to calculate. The equation for the allowed energies E is, of course, simply Pn = 0.