Knowledge Bank

By considering the fact that the Hamiltonian in the energy integrals, $\alpha r=(\psi r\ast H\psi r)$ and $\beta rs=-(\psi r\ast H\psi s)$, of the simple L.C.A.O. methods, is the complete molecular Hamiltonian, it is suggested that the Coulomb integral is given by $\alpha r=-(Ir+NmaxEs)$, where $Ir$ is the valence state ionization potential of $rsEs$ is the valence state electron-affinity of s, and $Nmax$ is the maximum value of the x-bond order of atom r. By a rationalization based on the united atom model it is assumed that a parabolic relation holds between $\beta$ and the overlap integral $Srs$. The parameters of the parabola are determined empirically. All $\beta rs$ and $Srs$ are included. Alternant and non-alternant hydrocarbons and N-heterocyclic compounds are studied. Bond orders, $\pi$-electron densities and free valences are calculated and compared with the values obtained by other simple L.C.A.O. methods and by advanced MO calculations. The results suggest that the proposed values for the parameters introduce some electron-electron interaction in $H\backslash ""u$ckel type treatments.