Correlation of free-electron molecular orbital energies with π ionization energies of aromatic hydrocarbons

With the introduction of an effective mass m^* into the simple free-electron model, the π-orbital energies of aromatic hydrocarbons containing up to 10 condensed benzene rings correlate closely with the π-band positions of the corresponding photoelectron spectra. For a sample of 70 π-orbitals the linear regression yields a standard error SE = 0.129 eV. Compared to HMO results, the number of accidental degeneracies is drastically reduced and the correlation is significantly improved. The free-electron results also compare favorably to those obtained by the PPP, EH and MINDO/2 methods which were scaled by two additional parameters.