Empirical penetration functions and two-center electron repulsion integrals for semiempirical calculations of electronic structure

Explicit functional forms for both the two-electron Coulomb integral, (aa∣bb), and the one-center core–orbital integrals, Z (aa∣Z_A), are derived which permit the penetration integrals to be fully derived and calculated. With these forms the ³Σ of the H₂ molecule is unstable. These forms are generalized so that they are suitable for optimizing semiempirical predictions of experimental one-electron properties.