ABSTRACTThe values of a free-electron eigenfunotion at the carbon nuclei of a conjugated hydrocarbon are found to satisfy a system of algebraic equations. These equations are similar in form to those obtained in the method known as the linear combination of atomic orbitale but only coincide with them for linear polyenes and benzene. The symmetry, degeneracy and energy of the eigenvectors of these free-electron equations correspond exactly to those of the free-electron wave functions found by the usual methods. From this correspondence, a theorem is deduced about the free-electron charge density in alternant hydrocarbons.
The model of the free electron theory is presented. The density of states and the Fermi–Dirac distribution function are discussed, leading to the specific heat of the electrons, the work function, thermionic emission, and the Schottky effects. As examples of applications the field-emission microscope and quartz–halogen lamps are discussed. The photoelectric effect and the energy diagrams relating to the junction between two metals are also discussed.
