Self-Consistent Molecular-Orbital Methods. II. Projection of Diatomic Differential Overlap (PDDO)

A method is developed for approximating 1- and 2-electron integrals over Slater-type orbitals (STO's) involving 2-center charge distributions. The latter are projected by least-squares, with overlap and dipole constraints, onto STO's with appropriate exponents, located only on the relevant atomic centers. The approach is applicable to any AO basis set, and is illustrated for first-row atom minimal STO basis sets. Error analysis is given for the projection per se, and for the 1- and 2-electron integrals obtained from the projected distributions. For integrals with magnitude 10−2 a.u., the rms relative error is ∼1%. Integral errors are sytematic, and balance of errors in nuclear attraction and hybrid 2-electron integrals is examined. Comparison is made with earlier results of Boys and Shavitt for 1s orbitals.